,,! ,,my/]y ,,( ,,space ,! doma9 ( ! s5ses1 9 nature1 is almo/ inf9itely small 9 comp>ison ) ! va/ region accessible to ?\ght :i* lies beyond !m4--,,tyndall1 ,on ,radiant ,heat4 ,,! ,,my/]y ,,( ,,space ,a ,/udy ( ! ,hyp]space ,movem5t 9 ! ,light ( ! ,evolution ( ,new ,psy*ic ,faculties & ,an ,inquiry into ! ,g5esis & ,ess5tial ,nature ( ,space ,,by ,,rob]t ,t4 ,,br[ne ,,new ,,york ,e4 ,p4 ,,dutton ,,company #fha ,,fif? ,,av5ue ,,copyright #aiai1 ,,by ,e4 ,p4 ,,dutton ,,company ,all ,rights ,res]v$ ,pr9t$ 9 ! ,unit$ ,/ates ( ,am]ica ,,to ,,! ,,*]i%$ ,,memory ,,( ,mylie ,de ,pr ,,^: ,,wifely ,,devotion1 ,,sympa!tic ,,assi/ance ,,& ,,enc\ragem5t ,,dur+ ,,! ,,e>ly ,,labors ,,on ,,! ,,text ,,7 ,a ,,con/ant ,,s\rce ,,( ,,inspiration ,,& ,,=titude ,,to ,,! ,,au?or1 ,,?is ,,book ,,is ,,d$icat$ ,,affectionately ,,preface ,ma!matics is ! biomet] ( intellectual evolution4 ,h5ce1 ! det]m9ation ( ! /atus quo ( ! intellect at any "t c be accompli%$ mo/ satisfactorily by apply+ to x ! rigor\s measure ( ! ma!matical me?od4 ,! intellect has b "o true div9+ rod & t is ma!matics4 ,by day & by night x po9ts ! way un]r+ly1 s long z x leads ?r\gh mat]iality2 b1 falt]+ly1 bl9dly1 fatally1 :5 t way ve]s into ! t]ritory ( vitality & spirituality4 ,:]e=e1 :5 we h wi%$ to asc]ta9 ! real /atus ( ! intellect1 z well z its limitations1 t5d5cies1 possibilities1 we h turn$ to its conduct 9 ! field ( ma!sis :]e x is lea/ trammel$ 9 its +ressive & egressive motivations because ( ! natural & easy accommodation :i* is (f]$ = intellectual movem5t4 ,:e!r !re are signs ( moribundity or symptomatic evid5ces ( m>k$ gr[? or ( a t]m9ation ( intellectual regnancy1 or :atev] may be ! occasion = ! exam9ation1 no sur] index ?an ! ma!matical may be f\nd = ! purpose4 ,full logical ju/ification is1 !re=e1 claim$ = ! *oice ( ma!matical evid5ces to te/ ! assumption t a new era ( consci\s m5tal conque/ is op5+ = ! vangu>d ( humanity & sequ5tly = ! human family4 ,! treatm5t ( ^! evid5ces has fall5 logically into two divisions1 namely1 ! fir/1 a brief & elem5t>y review ( ! pr9ciples ( ! non-,euclidean geometry & _! be>+s ^u ! "q ( space z ! subject ( ma!matical /udy2 & second1 ! consid]ation ( space z a psy*ological1 vital & dynamic or creative ph5om5on4 ,9 ,"p ,i an ef=t has be5 made to trace ! gr[? ( ! notion ( hyp]space & to %[ t x is a symbol ( a new epo* ( intellectual expansion1 an actual seizure ( a new doma9 ( aw>5ess by ! m9d4 ,& = ?is purpose a critical exam9ation ( ! fundam5tal "q ( dim5sionality is ent]$ ^u f :i* x develops t ! /atus ( ?is prim>y norm ( ma!matical ?\ght exhibits a relatively in*oate "* because ( its insuffici5cy z a def9itive quantity1 & fur!r1 because ( its r sup]foetat$ aspect :5 utiliz$ z a panacea = ma!tic symptoms4 ,also1 x has be5 f\nd necess>y to survey ! field ( ! f\r-space :i* has be5 accord$ su* a prom95t place 9 ! ma!matical ?\ght ( ! day4 ,! read] %\ld f9d 9 ! *apt] devot$ to x adequate mat]ial = ?\ght & suffici5t compreh5sion ( its mean+s z a ma!matical contrivance4 ,9 ,"p ,,ii an endeavor is made to int]pret ! evid5ces (f]$ by high ma!matic consid]ations 9 ! light ( ! l>g] psy*og5etic movem5t4 ,= ?is und]tak+ ! quality ( aw>5ess has be5 /udi$ ) ! view to e/abli%+ its priority z a det]m9+ ag5cy 9 ! consid]ation ( space 9 aspects broad] & less re/rict$ ?an ^? embrac$ 9 ! ma!matical premises4 ,:]e=e1 x appe>s t !re are massive implications aris+ out ( ! hyp]space propag&a :i* h hi!rto be5 neglect$ 9 ! prelim9>ies incid5t to ! fabrication ( its /ructure4 ,a v brief1 & m or less symbolic1 sket* ( ! g5esis ( space has s]v$ to demon/rate its ess5tial nature z a consub/antive ( mat]iality1 vitality & intellectuality1 ! ?ree major objective processes4 ,consequ5tly x becomes imp]atively necess>y t any view ( space :i* neglects its kosmic int5t & purpose %\ld be reg>d$ z gravely fragm5t>y & insuffici5t4 ,x is only by l9k+ up ! two aspects ( space1 ! ma!matical & ! psy*ological1 9 su* a mann] t ! "o %all supplem5t ! o!r1 t we %all be able to arrive at a truly satisfactory und]/&+ ( its nature4 ,9 ,*apt] ,,ix att5tion is invit$ to "s ( ! extremities ( ma!matical laws :]e9 x is %[n t1 because ma!matical goods are /rictly ( intellectual texture & fabric1 va9 is ! hope ( rea*+ any reliable c]ta9ty ) respect to _m vital que/ions1 ev5 reg>d+ space itself1 by means ( ! ma!matical me?od4 ,! intellect1 &1 !re=e1 ma!matics enc\nt] ! mo/ =midable /ricture :5 ef=t is made to maneuv] 9 ! field ( vitality or realism4 ,9 addition1 x is %[n t1 :5 pu%$ to ! utmo/ logical limits1 metageometry proves n only futile1 b emphasizes ! ne$ = a %>p turn+ ( ! pa? ( se>* f ! intellectual or mat]ial to ! spiritual or intuitional4 ,inde$1 x becomes pa9fully c]ta9 t ! ,gold5 ,fleece ( pr(\nd] k w be discov]$ nev] by an exp$ition ^: b>k has its sails set = ! w9ds ( ma!matical seas4 ,b1 contr>ily1 a new b>k1 moor$ at ! fur!rmo/ %ore ( ! sea ( intellectuality ) sails set = ! w9ds :i* come f ! realm ( intuitional p]ception1 mu/ be seiz$4 ,:]eupon1 by ! /raighte/ l9e1 we %all1 at ! la/1 l& ^u ! %ore ( realism1 ( tru? all inclusive4 ,ma!matical evid5ces h be5 us$ 9 ^! discussions because !y1 ( all l9es ( k1 af=d a m j exemplification ( intellectual evolution4 ,! sci5ce ( ma!matics is ! measure ( ! quality ( intellectual gr[? &1 !re=e1 its data1 its po/ulates1 hypo!ses & advances cle>ly m>k ! /ages ( ! intellectual movem5t4 ,*apt] ,x is ! natural & logical sequ5ce ( ! inquiry into ! "q ( spatiality4 ,! conclusions rea*$ !re9 & ! obvi\s inf]5ces :i* %\ld be drawn f ! argum5ts pres5t$ fl[ inevitably n only f ! evid5ces ( ma!matical data b ( ! common obs]vations ( life4 ,& :ile we disclaim any int5tion ( dem&+ acceptance ( !m z f9al1 au?oritative decl>ations1 we %all be satisfi$ if ! read]s ( ?is volume be incit$ to solve = !mselves ! problems :i* ^! qu]ies naturally sugge/4 ,happy inde$ %all be ! outcome if !re be any :o1 foll[+ ! pa? sket*$ h]e91 %all f9d ! solution ( ! ,my/]y ( ,space & apply its mean+s to ! enhancem5t ( ! values ( ! intuitive life4 ,9 conclusion1 ! au?or e/eems x a special obligation ( gratitude t he %\ld "h ackn[l$ge ! debt :i* he owes to all ( 8 fri5ds :o h 9 any way assi/$ or enc\rag$ him 9 ! completion ( ?is "w4 ,among ^? :om he is p]mitt$ to ?ank 9 ?is way is ,mr4 ,,james ,,r9dfleis* :o1 hav+ v k9dly prep>$ ! illu/rations = ! photo-engrav]s1 is des]v+ ( special m5tion4 ,,rob]t ,t4 ,,br[ne4 ,new ,york ,city1 #aiai4 ,,cont5ts ,,page ,,preface vii ,,introduction3 ,explanatory ,notes x ,,"p ,,"o ,,*apt] ,i ,,! ,,prologue ,on ! ,v>iability ( ,psy*ic ,p[]s--,! ,discov]y ( ! ,f\r? ,dim5sion ,m>ks a ,di/9ct ,/age 9 ,psy*og5esis--,! non-,me?odical ,"* ( ,discov]ies--,! ,?ree ,p]iods ( ,psy*og5etic ,developm5t--,! ,scope & ,p]missibility ( ,ma!tic ,lic5se--,kosmic ,unit>9ess ,und]ly+ ,div]sity #bc ,,*apt] ,,ii ,,hi/orical ,,sket* ,,( ,,! ,,hyp]space ,,movem5t ,egypt ! ,bir?place ( ,geometry--,precursors3 ,nasir-,edd91 ,*ri/oph ,clavius1 ,sac*]i1 ,lamb]t1 ,la ,grange1 ,kant--,influ5ce ( ! ,mecanique ,analytique--,! ,p>allel ,po/ulate ! ,root & ,sub/ance ( ! ,non-,euclidean ,geometry--,! ,?ree ,great ,p]iods3 ,! ,=mative1 ,det]m9ative & ,elaborative--,riemann & ! ,prop]ties ( ,analytic ,spaces #dd ,,*apt] ,,iii ,,ess5tials ,,( ,,! ,,non-,,euclidean ,,geometry ,! ,non-,euclidean ,geometry ,conc]n$ ) ,conceptual ,space ,entirely--,outcome ( ,failures at ,solv+ ! ,p>allel-,po/ulate--,! ,basis ( ! ,non-,euclidean ,geometry--,space ,curvature & ,manifoldness--,"s ,elem5ts ( ! ,non-,euclidean ,geometry--,c]ta9ty1 ,necessity & ,univ]sality z ,bulw>ks ( ,geometry--,"s ,consequ5ces ( ,ef=ts at ,solv+ ! ,p>allel-,po/ulate--,! ,f9al ,issue ( ! ,non-,euclidean ,geometry--,ext5d$ ,consci\sness #fi ,,*apt] ,,iv ,,dim5sionality ,arbitr>y ,"* ( ,dim5sionality--,v>i\s ,def9itions ( ,dim5sion--,real ,space & ,geometric ,space ,diff]5tiat$--,! ,f9ity ( ,space--,diff]5ce ,betwe5 ! ,purely ,=mal & ! ,actual--,space z ,dynamic ,appe>ance--,! ,a ,priori & ! ,a ,po/]iori z ,def9$ by ,paul ,c>us #ib ,,*apt] ,v ,,! ,,f\r? ,,dim5sion ,! ,ideal & ! ,repres5tative ,nature ( ,objects 9 ! ,s5sible ,_w--,! ,fluxional1 ! ,basis ( ,m5tal ,diff]5ces--,natural ,symbols & ,artificial ,symbols--,use ( ,analogies to ,prove ! ,exi/5ce ( a ,f\r? ,dim5sion--,! ,g5]ation ( a ,hyp]cube or ,tess]act--,possibilities 9 ! ,_w ( ! ,f\r? ,dim5sion--,"s ,logical ,difficulties ,inh]+ 9 ! ,f\r-,space ,conception--,! ,fallacy ( ! ,plane-,rotation ,hypo!sis--,c4 ,h4 ,h9ton & ,major ,ellis on ! ,f\r? ,dim5sion #aah ,,"p ,,two ,,spatiality3 ,,an ,,inquiry ,,into ,,! ,,ess5tial ,,nature ,,( ,,space ,,z ,,di/+ui%$ ,,f ,,! ,,ma!matical ,,int]pretation ,,*apt] ,,vi ,,consci\sness ,,! ,,norm ,,( ,,space ,,det]m9ations ,realism ,is ,det]m9$ by ,aw>5ess--,succession ( ,degrees ( ,realism--,suffici5cy ( ,tridim5sionality--,! ,insuffici5cy ( ,self-consi/5cy z a ,norm ( ,tru?--,g5]al ,=w>d ,movem5t 9 ! ,evolution ( ,consci\sness ,impli$ 9 ! ,hyp]space ,concept--,! ,hypo!tical ,nature ( ,our ,k--,hyp]space ! ,symbol ( a ,m ,ext5sive ,realm ( ,aw>5ess--,v>iations 9 ! ,me?ods ( ,int]pret+ ,intellectual ,notions--,! ,tuitional & ! ,intuitional ,faculties--,! ,illusion>y ,"* ( ! ,ph5om5al--,consci\sness & ! ,degrees ( ,realism #afa ,,*apt] ,,vii ,,! ,,g5esis ,,& ,,nature ,,( ,,space ,symbology ( ,ma!matical ,k--,manife/ation & ,non-manife/ation ,def9$--,! ,pyknon & ,pyknosis--,! ,kosmic ,eng5d]m5t ( ,space--,on ! ,consub/antiality ( ,spatiality1 ,intellectuality1 ,mat]iality1 ,vitality & ,kosmic ,geometrism--,*aos-,!os-,kosmos--,*aog5y & ,*aomorphog5y--,n4 ,malebran*e on ,god & ! ,_w--,! ,space-,m9d--,space & ,m9d ,are ,"o--,! ,kosmic ,p5toglyph #bjc ,,*apt] ,,viii ,,! ,,my/]y ,,( ,,space ,! ,?9k] & ! ,ego--,incresc5t ,automatism ( ! ,intellect--,! ,egopsy*e & ! ,omnipsy*e--,kosmic ,ord] or ,geometrism--,life z ,eng5d]+ ,elem5t--,! ,my/]y ( ,space ,/at$--,ka!kos & ,ka!kotic ,consci\sness--,function ( ! ,ideal--,! ,pa? ( ,se>* = an ,und]/&+ ( ! ,nature & ,ext5t ( ,space ,mu/ ,proce$ 9 an ,inv]se ,direction #bdb ,,*apt] ,,ix ,,metageometrical ,,ne>-,,tru?s ,realism ,is ,psy*ological & ,vital--,! ,imp]man5ce ( ,facts--,on ! ,t5d5cy ( ! ,intellect to ,fragm5tate--,! ,intellect & ,logic--,! ,passage ( ,space--,kosmomet] & ,zoomet]1 ,in/rum5ts = ! ,measurem5t ( ! ,passage ( ,space & ! ,fl[ ( ,life--,! ,disposal ( ,life & ! ,p[] to ,create--,space1 a ,dynamic1 ,creative ,process--,numb]s & ,kosmogony--,kosmic ,significance ( ! ,circle & ! ,pi-proportion--,me*anical ,t5d5ce ( ! ,intellect & ,its ,inaptitude = ! ,und]/&+ ( ,life--,! ,crit]ion ( ,tru? #bhd ,,*apt] ,x ,,m$ia ,,( ,,new ,,p]ceptive ,,faculties ,! ,spiritualization ( ,matt] ,is ! ,end ( ,evolution--,sequ5ce & ,design 9 ! ,evolution ( ,human ,faculties--,! ,upspr++ ,intuition--,evid5ces ( ,sup]normal ,p[]s ( ,p]ception & ! ,possibility ( ,atta9m5t--,! ,influ5ce & ,place ( ! ,pituit>y ,body & ! ,p9eal ,gl& 9 ! ,evolution ( ,additional ,faculties--,! ,skeptical ,attitude ( ,empirical ,sci5ce & ! ,ne$ = a ,m ,lib]al ,po/ure--,! ,g5]al ,results ( ,pituit>ial ,awak5+ ,^u ,man & ! ,!ory ( ,k #cbg ,,bibliography #cei ,,index #cfg ,,! ,,my/]y ,,( ,,space ,,introduction ,,explanatory ,,notes ,! foll[+ int]pretation ( words1 phrases & notions occurr+ 9 ! text1 & also biographical sket*es :i* ! scope & purpose ( ! book itself make x impracticable to elaborate1 are app5d$ ) ! view to facilitat+ its p]usal4 ,,at-,,"o-,,m5t 7/ate ( unity1 unit>9ess72 d5otes ! ultimate /ate ( on5ess t[>ds :i* all evolution>y movem5t t5ds2 appli$ to consci\sness1 indicates ! f9al expansion ( consci\sness :]e9 x co9cides ) ! univ]sal consci\sness 9 ext5t & quality ( compreh5sion4 ,z appli$ to ?+s1 d5otes ! unification ( all movem5ts1 t5d5cies1 & evolutions z a s+ul>ity2 ! end ( all evolution>y activity 7vide p4 #bgj74 ,,beltrami1 ,,eug5io1 0 born at ,cremona1 ,novemb] #af1 #ahce2 !re he att5d$ ! elem5t>y s*ools1 ! gymnasium & ! lyceum1 except+ ! s*ola/ic ye> #ahdh-di :5 he 0 at ! ,gymnasium ( ,v5ice1 n[ kn[n z ,m>co ,polo4 ,he f9i%$ 8 lyceal /udies 9 ! summ] ( #ahec1 & 9 ! foll[+ autumn 7,novemb]7 became a /ud5t 9 ! ,ma!matical ,faculty ( ! ,univ]sity ( ,pavia1 aft] hav+ obta9$ a s*ol>%ip !re on ! ,ca/iglioni ,f\ndation 9 ! ,collegio ,ghisl]i4 ,9 #ahed1 ! succe$+ ye>1 he 0 expell$ f ?is college 9 company ) five ( 8 colleagues :o 7 accus$ ( promot+ disord]s aga9/ ! ,abbot ,,leon>di1 rector ( ! college4 ,! expulsion br\ght him _m h>d%ips & disappo9tm5ts1 & = two ye>s he drift$ along m]ely exi/+ z 8 family 0 too poor to h him matriculat$ at ano!r univ]sity4 ,b 9 #ahef1 he w5t to ,v]ona :]e he succe$$ 9 secur+ employm5t z secret>y to ! eng9e]1 ,,diday1 9 ! ,gov]nm5t s]vice ( ,lomb>dy-,v5ice4 ,on ,janu>y #aj1 #aheg1 he 0 dismiss$ f ?is position = political reasons2 b z ! annexation ( ,lomb>dy to ,pi$mont occurr$ soon !reaft]1 he became aga9 atta*$ to ! (fice ( ,,diday1 8 =m] employ]1 :5 x 0 transf]r$ to ,milan z a consequ5ce ( political *anges4 ,at ,milan ,,beltrami took up 8 ma!matical education 9 real e>ne/ z he n[ _h access to ,pr(essor ,,brios*i1 8 =m] tutor1 & also ,,luigi ,,cremona4 ,?r\gh ! influ5ce ( ^! two m5 he 0 designat$ 7,octob] #ah1 #ahfb7 ,pr(essore /raord9>io 9 ! ,univ]sity ( ,bologna4 ,8 "w on ,surfaces ( ,con/ant ,negative ,curvature1 z ! pseudosph]e1 & 8 application ( ! expression giv5 by ,,loba*evski 7q4v47 = ! angle ( p>allelism1 v def9itely secure = him a place among ! =emo/ work]s 9 ! field ( ! non-,euclidean geometry4 ,he po/ulat$ a !orem1 kn[n z ,beltrami's ,!orem1 :i* he /at$ z foll[s3 ,! c5t] ( a circle circumscrib+ a triangle is ! c5t] ( gravity ( ! c5t]s ( its inscrib$ & escrib$ circles4 ,he di$ 9 ! ye> #aijj4 7,vide ,am]4 ,ma?4 ,mo41 ,vol4 ,,ix1 p4 #ei47 ,,bolyai1 ,,janos 7#ahjb-ahfj71 0 born at ,kleans5burg1 ,hung>y4 ,he is said to h inh]it$ 8 ma!matical g5ius f 8 fa!r1 ,,bolyai ,,f>kas 7#agge-ahef71 :o 0 born at ,bolya1 ,hung>y4 ,be+ a v spirit$ y\?1 8 progress 9 8 /udies 0 mo/ rem>kable4 ,he complet$ ! curriculum at ! ,lat9 s*ool :5 only twelve ye>s ( age4 ,0 graduat$ f ! ,philosophical ,curriculum z a result ( two ye>s ( /udy & !n ent]$ ! ,vi5nese ,academy ( ,eng9e]s4 ,0 appo9t$ lieut5ant at ,temesvrl91 #ahbc1 :5ce on ,novemb] #c1 #ahbc1 he wrote 8 fa!r3 ,i h discov]$ su* magnific5t ?+s t ,i am myself a/oni%$ at !m4 ,x w\ld be damage et]nal if !y 7 lo/4 ,:5 y see !m1 my fa!r1 y y\rself w ackn[l$ge x4 ,n[1 ,i _c say m1 only s mu*3 t f no?+ ,i h creat$ ano!r :olly new _w4 ,?is lett] 0 writt5 9 ! ,magy> language & has be5 pres]v$ at ! ,m>cos ,vsrhely1 ,hung>y4 ,! ma!matical conceptions =mulat$ by him became ! app5dix ( ! ,t5tam51 a book :i* 8 fa!r _h writt5 on ! ,!ory ( ,p>allels4 ,8 ,sci5ce ,absolute ( ,space 0 translat$ into ! ,fr5* 9 #ahfh by ! ,fr5* ma!matician1 ,j4 ,,ho,,el1 to :om belongs ! cr$it ( popul>iz+ ! works bo? ( ,,bolyai & ,,loba*evski4 7,vide ,sci5ce1 n4 s41 ,vol4 #ce1 ,no4 #ijf1 #aiab47 ,,cayley1 ,,ar?ur1 born at ,ri*mond1 ,surrey1 ,engl&1 ,augu/ #af1 #ahba2 /udi$ at ,k+'s ,college s*ool2 ent]$ ,tr9ity ,college1 ,cambridge1 already a well equipp$ ma!matician at ! age ( sev5te54 ,:5 b tw5ty-"o ye>s ( age he took two ( ! highe/ honors 9 ! ,univ]sity ( ,cambridge4 ,he 0 ,s5ior ,wrangl] & ,fir/ ,smi?'s ,prizeman4 ,he publi%$ 8 fir/ pap] 9 #ahda & ?is 0 foll[$ by eight hundr$ memoirs4 ,= f\rte5 ye>s he practic$ z ,conveyanc]4 ,9 #ahfc ,lady ,,sadl]',s v>i\s tru/s 7 consolidat$1 & a new ,sadl]ian pr(essor%ip ( ,pure ,ma!matics 0 creat$ = ! express purpose ( af=d+ a place = ,cayley4 ,mean:ile1 z e>ly z #aheb he 0 a fell[ ( ! ,royal ,society2 9 #aheh he jo9$ ,,sylve/] & ,,/okes 9 publi%+ ! ,qu>t]ly ,j\rnal ( ,pure & ,appli$ ,ma!matics4 ,he 0 = a consid]able "t pr9cipal advis] z to ! m]its ( all ma!matical pap]s :i* 7 pres5t$ = publication to ! ,royal ,society1 ! ,a/ronomical ,society1 ! ,ma!matical ,society & ! ,cambridge ,philosophical ,society4 ,he is said to h be5 ! mo/ le>n$ & erudite ( ma!maticians1 & mu* ( ! mat]ial1 !re=e1 :i* n[ con/itutes ! basis ( ! non-,euclidean geometry is due to 8 labori\s ef=ts & compreh5sive k ( ma!matics4 7,vide ,review ( ,reviews1 ,vol4 ,,ii1 #ahie1 ,sket*1 repr9t$ f ,moni/47 ,,*aog5y 7,gr4 ,*aos1 disord]1 g5y--g5]at+1 evolution72 ! evolution ( *aos into ord]4 ,a kosmic process involv+ ! elaboration ( ! orig9al1 =mless _w-plasm into ! fir/ fa9t signs ( ord]l9ess2 ! beg9n+s ( ! movem5t ( life or ! ,creative ,logos 9 prep>ation ( ! field ( evolution4 ,,*aomorphog5y 7,gr4 ,*aos1 disord]--,morphe1 =m--g5y1 becom+1 g5]at+72 evolution ( ! space-=m1 ! univ]se2 ! e/abli%m5t ( ! metes & b\nds ( ! univ]se2 also1 ! orig9ation & *>act]ization ( all =ms z to t5d5ce1 purpose & limitations4 ,,conceptualization--,! act ( conceptualiz+1 ! =mulation ( concepts2 ! process by :i* ! ,?9k] arrives at concepts2 ! logical proc$ure by :i* ! consi/5cy ( a s*eme ( ?\ght is e/abli%$4 ,,con/ruction1 ,,ideal--,a purely =mal conception2 a !ory1 hypo!sis2 a logical det]m9ation n necess>ily bas$ ^u facts1 b possess+ virtue because ( consi/5cy2 a self-consi/5t s*eme ( ?\ght4 ,,cosmos--,:5ev] ! t]m cosmos appe>s 9 ! text spell$ z "h %[n1 x ref]s to ph5om5a p]ta9+ to ! e>? or ! sol> sy/em2 :5 spell$ kosmos ref]5ce is made to ! univ]se z a :ole4 ,,crit]ion ,,( ,,tru?--,def9$ 9 ! text z a f\r-fold /&>d ( ref]5ce1 embrac+ ! foll[+ elem5ts1 namely1 ! causal1 ! su/5tative1 relational & developm5tal4 ,lack+ any "o ( ^!1 no view ( tru? is m ?an fragm5t>y4 ,appli$ to space1 x contemplates an inquiry into ! g5esis or causal aspect1 an acc\nt+ = ! duration aspect1 a recognition ( its relation to ! totality ( objects1 & la/ly1 a prophecy ( its tele/ic or p]fective culm9ation4 ,?is te/ has be5 appli$ to ! /udy ( space z sket*$ 9 ! text & ! conclusions rea*$ are an outcome ( ! inquiry direct$ along ^! l9es4 ,,curvature ,,( ,,space--,a doctr9e =mulat$ by ,,riemann & :i* ma9ta9s t space is curv$1 & consequ5tly1 all l9es drawn !re9 are curv$ l9es4 ,pr(essor ,,pick]+ aptly describes ! results ( movem5ts 9 a curv$ space by po9t+ out t if we g f> en\gh ea/ we arrive at ! we/2 nor?1 we arrive at ! s\?2 t[>ds ! z5i?1 we arrive at ! nadir1 & vice v]sa4 ,,dei=m--,! basic idea indicat$ is t ! univ]se is ! =m or body ( ! supreme deity1 s9ce ,he is n only imman5t 9 ! kosmos1 b su/a9s x by ,8 life2 t 9 ord] to create a manife/$ univ]se1 x 0 necess>y to limit1 or sacrifice1 9 a measure1 ,8 own illimitability4 ,view$ 9 ?is light1 ! kosmos assumes an add$ significance4 ,,dim5sion--7,l4 ,dim5sio1 to measure71 measurem5t2 a sy/em ( space measurem5t4 ,! ,euclidean geometry recognizes ?ree dim5sions or cord9ates z be+ necess>y to e/abli% a po9t position2 witness1 ! corn]s ( a cube to =m :i* ?ree ( ! edges come toge!r at a po9t4 ,^! edges repres5t cord9ates4 ,= ! purposes ( metageometry1 ! t]m dim5sion has be5 v>i\sly def9$1 z1 direction1 ext5t1 a sy/em ( space measurem5t1 or a sy/em ( cord9ates4 ,reg>d$ z a s]ies ( cord9ates1 x became possible to po/ulate a sy/em :i* requir$ f\r cord9ates to e/abli% ! position ( a po9t1 z 9 ! hyp]cube4 ,!re may be five1 six1 sev51 eight1 or any numb] ( su* cord9ate sy/ems accord+ to ! k9d ( space involv$ 9 ! calculations4 ,det]m9ations bas$ ^u ! logical necessities ( ! v>i\s cord9ate sy/ems h be5 f\nd to be self-consi/5t ?r\gh\t &1 !re=e1 valid = metageometrical purposes4 ,mu* dep5ds ^u ! def9ition2 =1 aft] ! def9ition has be5 once det]m9$ x rema9s !n m]ely to make inf]5ces & conclusions con=m to ! int5t ( ! def9ition4 ,,div]sity--,philosophically1 ! idea indicat$ has ref]5ce to all dissimil>ities1 diff]5ces1 inequalities1 div]g5t t5d5cies1 movem5ts & *>act]i/ics to be not$ 9 ! univ]sum ( life2 ! anti!sis ( kosmic unity2 ! natural outcome ( life 9 seek+ expression2 ! result ( ! fragm5tative t5d5cy ( life4 ,,duodim 7duo1 two2 dim1 abbreviation ( dim5sion7--,a hypo!tical be+ suppos$ to be possess$ ) a consci\sness adapt$ only to two dim5sions2 a dwell] 9 ,flatl& or two-space ^: scope ( motility is limit$ to two directions1 z on ! face ( a plane2 a t]m inv5t$ by hyp]space advocates = ! purpose ( e/abli%+ by analogy "s ( ! *>act]i/ics ( ! f\r space & also its rationality4 ,,duopyknon 7duo1 two--pyknon1 prim>y unit 9 ! process ( kosmic involution1 a cond5sation7--,second>y phase 9 ! elaboration ( *aos into kosmic ord]4 ,,duopyknosis 7duo1 two1 second>y--pyknosis1 process ( cond5sation & orig9ation7--,! second p]iod ( ! involution>y movem5t ( life dur+ :i* ! duadic plane ( ! kosmos is be+ e/abli%$2 ! second1 9 ! s]ies ( sev5 di/9ct phases1 ( space-g5esis2 dual diff]5tiation ( kosmic plasm4 ,duopyknosis contemplates t1 9 ! passage ( ! kosmos-to-be f ! plane ( non-manife/ation to ! plane ( manife/ation1 !re are sev5 di/9ct1 ?\gh int]dep5d5t & int]relational1 /ages ?r\gh :i* life passes1 & t1 ( ^!1 x is ! second4 ,x relates to ! plane ( non-manife/ation & is1 !re=e1 beyond ! k5 ( ! intellectuality1 be+ a symbol4 ,,egopsy*e 7,ego1 ! self-consci\s ,i--psy*e1 s\l7--,! m5tal1 emotional & physical me*anisms ( man1 ! ,?9k]4 ,^! include ! purely m5tal sy/em1 ! emotional or affective me*anism1 ! n]ve-sy/ems 7c]ebro-sp9al & sympa!tic7 & ! bra92 ! objective or s5se-d]iv$ consci\sness ( ! ,?9k] :i* is elaborat$ f ! total mass ( p]ceptions transmitt$ ?r\gh ! s5ses2 ! m$ium ( self-consci\sness2 ! intellectual consci\sness z di/+ui%$ f ! intuitional or omnipsy*ic consci\sness 7q4v474 ,! notion ( ! egopsy*ic consci\sness is bas$ ^u data already empirically det]m9$ f ! mass ( evid5ces ev]y:]e obs]vable4 ,x seems to be app>5t t !re is a consci\sness1 a seat ( k1 9 man ! cont5t ( :i* is unkn[n to ! s5se-consci\sness4 ,dreams1 premonitions1 intuitions1 impressions & ! totality ( all su* ph5om5a sub/antiate ?is view4 ,fur!rmore1 x is agre$ t ! s\rce ( ! intuition is n id5tical ) t ( ! intellect4 ,! egopsy*ic consci\sness1 accord+ly1 is purely intellectual4 ,,fluxion1 ,,psy*ic--,! diff]5ce betwe5 a m5tal image & an object2 an image is ! repres5tation ( c]ta9 sali5t or c>d9al *>act]i/ics ( an object1 suffici5t = id5tification2 b an image is n congru5t1 9 e respect1 ) ! object4 ,?us :5 we p]ceive an object1 al?\gh z ,,b]gson cont5ds we p]ceive x 9 ! place :]e x is & n 9 ! bra91 x is ! image ( ! object :i* takes its place 9 memory & n ! object itself4 ,!re is1 ( c\rse1 a m>k$ disp>ity betwe5 ?is memory-image & ! object4 ,ev5 if ! image possess$ "o ( ! prop]ties ( ! object1 z1 size1 x c\ld n take its place 9 memory1 & nei!r c\ld x d s if x possess$ any ( ! prop]ties ( ! real object4 ,consci\sness is su* t all due all[ances are made = ^! conditions & ! m9d is able to reta9 m or less exact k ( ^! prop]ties 9 ! image2 b !re is a diff]5ce1 small ?\gh x may be4 ,?is diff]5ce is ! psy*ic fluxional4 ,,fohat 7,skt7--,a t]m appli$ to ! ,creative ,logos :o is said to be ! g5]at+ elem5t 9 ! diff]5tiation ( *aos into kosmic ord]l9ess2 ! supreme deity 9 ! rle ( ,creator4 ,,=m1 ,,pure--,an ab/raction arriv$ at by subtract+ ! la/ ve/ige ( mat]iality or sub/antiality f an idea & view+ ! rema9s z a pure unsub/antial =m or idealization2 ! %ell or frame-"w ( a mat]ial object or condition2 exi/+ 9 idea or ?\ght only2 a m5tal conception reg>d$ z a type or norm2 a purely hypo!tical con/ruction4 ,,f\r ,,space--,(t5 ref]r$ to z ! f\r? dim5sion 7vide ,*apt] ,v72 a space 9 :i* f\r cord9ates 7f\r l9es drawn p]p5dicul> to ea* o!r7 are necess>y & suffici5t to e/abli% ! position ( a po9t1 z1 a hyp]cube4 ,,gauss1 ,,*>les ,,fr$]ick1 born at ,brunswick1 ,april #cj1 #aggg4 ,8 fa!r1 be+ a bricklay]1 _h int5d$ t he %\ld foll[ ! same occupation4 ,s1 9 #aghd1 ,*>les 0 s5t to ! ,btn] ,public ,s*ool 9 ,brunswick1 9 ord] t he might be taught ! ord9>y elem5ts ( education4 ,b dur+ 8 att5dance at ?is s*ool1 8 unusual intellig5ce & aptitude attract$ ! att5tion & fri5d%ip ( ,pr(essor ,,b>tels :o lat] became ! ,pr(essor ( ,ma!matics at ,dorpat4 ,9 #agib1 ?r\gh ! k9dly repres5tations ( ,pr(essor ,,b>tels to ! ,duke ( ,brunswick1 "y ,gauss 0 s5t to ! ,collegium ,c>ol9um4 ,?is greatly displeas$ 8 fa!r z he saw 9 ?is move ! fru/ration ( 8 plans = ,*>les4 ,9 #agid1 h[ev]1 ,,gauss ent]$ ! ,univ]sity ( ,gtt+5 /ill undecid$ :e!r he %\ld make ma!matics or philology 8 life "w4 ,:ile resid+ at ,gtt+51 he made 8 celebrat$ discov]ies 9 analysis & ^! turn$ 8 att5tion def9itely to ! field ( ma!matics4 ,he complet$ 8 /udies at ,gtt+5 & return$ to ,brunswick 9 #agih1 resid+ at ,helm/adt :]e he _h access to ! ,libr>y 9 ! prep>ation ( 8 ,disquisitiones ,ari?meticae :i* 0 publi%$ 9 #ahja4 ,he receiv$ 8 doctorate degree 7,ph4,d47 on ,july #af1 #agii4 ,8 next notable "w 0 ! inv5tion ( a me?od by :i* he calculat$ ! elem5ts ( ! orbit ( ! planet ,c]es :i* _h be5 discov]$ by ,,piazzi1 ,janu>y #a1 #ahjj1 & :o _h left no record ( 8 calculations by :i* o!r a/ronom]s c\ld locate ! planet4 ,,gauss also calculat$ an ephem]is ( ,c]es' motion by means ( :i* ,,de ,,za* r$iscov]$ ! planet ,decemb] #ca1 #ahjj4 ,8 ,!oria ,motus ,corporum ,coele/ium 9 ,conicis ,sectionibus ,solem ,ambi5tium1 9 :i* ! au?or gives a complete sy/em ( =mul & processes = comput+ ! movem5ts ( a heav5ly body revolv+ 9 a conic section is an outgr[? ( 8 e>ly rese>*es & br\ght him la/+ fame4 ,?r\gh ! influ5ce ( 8 fri5d ,,olb]s1 he 0 appo9t$1 ,july #i1 #ahjg1 fir/ director ( ! new ,gtt+5 ,obs]vatory1 & ,pr(essor ( ,a/ronomy 9 ! ,univ]sity1 a position :i* he held until ! end ( 8 life4 ,he di$ ,febru>y #bc1 #ahee4 7,vide ,a/ronomical ,society ,notices1 ,vol4 #af1 p4 #hj1 #ahef2 also ,nature1 ,vol4 ,,xv1 pp4 #ecc-ecg1 #ahgg47 ,,geometrism--,( geometrical quality2 a notion d]iv$ f ,,plato',s decl>ation3 ,god geometrizes4 ,x 0 8 belief t ! creative acts ( ! deity are execut$ 9 accordance ) geometric design & laws2 t 9 ! totality ( su* acts !re necess>ily inh]es a lat5t geometric quality4 ,,kant closely adh]$ to ?is notion 9 8 discussions ( space z an aspect ( div9e intellig5ce4 ,he believ$ t ! intellect m]ely r$iscov]s ?is lat5t geometrism :5 x turns to ! /udy ( mat]iality1 & ?is belief is %>$ by ,,b]gson1 ! =emo/ metaphysician ( ! pres5t "t4 ,,hyp]space 7hyp]1 above1 beyond1 transc5d+--space7--,t species ( space con/ruct$ by ! intellect = conv5i5ce ( measurem5t2 an idealiz$ con/ruction2 a purely arbitr>y1 conv5tional ma!matical det]m9ation2 ! f\r? dim5sion2 any space t requires m ?an ?ree cord9ates to fix a po9t position 9 x1 z1 a five space1 an n-space4 ,,intuitograph--,! means by :i* ! omnipsy*ic consci\sness transmits intuitional impressions to ! egopsy*ic or intellectual consci\sness4 ,an intuitogram is a direct cognition1 an intuition2 a prim>y tru? project$ into ! egopsy*ic consci\sness by ! ,?9k]4 ,x is recogniz$ t1 "u ! necessities ( ! pres5t s*ematism ( ?+s1 x is exce$+ly difficult to propagate an intuition1 especially ) ! same degree ( ease z concepts are propagable2 yet1 ?is is believ$ to be a condition :i* w be ov]come z ! evolution ( ! high] faculties proce$s4 ,,involution--,process ( enfold+1 involv+2 anti!sis ( evolution2 philosophically1 ! doctr9e ( involution ma9ta9s t1 dur+ ! process ( kosmic pyknosis 7space-g5esis71 all t is to be express$1 develop$ & p]fect$ z a result ( ! evolution>y movem5t 0 fir/ involv$1 enfold$ or deposit$ z lat5t ar*etypal t5d5cies & radicles 9 ! orig9al _w-plasm2 t1 z ! involution>y movem5t proce$$ ?r\gh ! v>i\s phases ( space-g5esis1 ^! became m & m ph5om5al until at la/ !y t]m9at$ 9 ! elaboration ( a manife/ univ]se3 ea* /age1 accord+ly1 ( ! involution>y proc$ure became ! basic sub/ructure ( a plane ( specializ$ sub/ance or mat]iality & consci\sness4 ,?us x appe>s t evolution really beg9s :]e involution ends 7vide ,fig4 #ah71 & ! two oppos+ processes con/itute ! dualism ( life z g5]at+ elem5t4 ,?is notion has be5 symboliz$ 9 ! ,l+am yoni ( ,hell5i/ic philosophies1 also 9 ,yang & ,y9 ( ,*9ese philosophy1 :i* repres5t ! orig9al pair ( opposites4 ,,ka!kos--,a purely arbitr>y t]m devis$ = ! express purpose ( provid+ a conv5i5t symbol to convey ! idea embodi$ 9 ! triglyph1 ,*aos-,!os-,kosmos1 & is compos$ ( ! fir/ ?ree lett]s 9 ea* "o ( ! t]ms ( ! triglyph2 h5ce1 symbolizes ! triunity & int]action involv$ 9 ! resolution ( *aos into an ord]ly kosmos by ! w ( ! ,creative ,logos4 ,?us1 ka!kos embodies a quadruplicate notion1 namely1 *aos1 ,creative ,logos1 manife/$ kosmos1 & ! creational activity ( ! ,logos 9 ! transmutation ( disord] into ord]4 ,! ju/ification = ?is t]m1 !re=e1 resides 9 its conv5i5ce1 brevity & compreh5siv5ess4 ,by ref]r+ to figure #ag1 x w be se5 t ,ka!kos divides into two k9ds--involution>y1 or t :i* p]ta9s to involution1 & evolution>y1 or t t p]ta9s to evolution4 ,x ?us comprises ! beg9n+ & ! end ( ! _w age or cycle & p]ta9s to non-manife/ation4 ,! raison d'tre ( ?is diff]5tiation is embodi$ 9 ! notion t1 on ! involution>y arc ( ! cycle1 ! *aog5ic p]iod repres5ts a phase ( ! _w age :5 space-g5esis is 9 an ar*etypal /ate :]e9 are involv$ all possibilities t are to become manife/ 9 ! kosmos1 & on ! evolution>y arc1 ! ka!kotic p]iod :i* is p>allel to ! *aog5ic & repres5ts a phase ( ! _w age :5 ! kosmos has rea*$ ultimate p]fection1 embody+ ! p]fect$ results ( ! possibilities :i* inh]$ 9 ! *aog5ic p]iod or 9 involution>y ka!kos4 ,?us1 ka!kos is dual 9 nature1 on ! "o h& repres5t+ kosmic pot5cy1 & on ! o!r1 kosmic p]fection ( ^! pot5cies4 ,x is ,alpha1 z relat$ to involution1 & ,omega1 z relat$ to evolution4 ,,ka!kosity--,a d]ivative1 signify+ creative activity & all t x implies2 ! /ate ( consci\sness or cognition correspond+ !reto4 ,,kle91 ,,felix 7#ahdi--71 born at ,dusseldorf2 /udi$ at ,bonn1 & :5 only sev5te5 ye>s ( age 0 made assi/ant to ! not$ ,,pl,,ck] 9 ! ,physical ,in/itute4 ,he took 8 doctorate degree 9 #ahfh1 !n w5t to ,b]l91 & lat] to ,gtt+5 :]e he assi/$ 9 edit+ ,,pl,,ck]',s works4 ,he ent]$ ! ,gtt+5 faculty 9 #ahga2 became ,pr(essor ( ,ma!matics at ,erlang5 9 #ahgb2 & subsequ5tly held pr(essor%ips at ,muni*1 #ahge2 ,leipzig1 #ahhj1 & ,gtt+51 #ahhf4 ,no "o else 9 ,g]many has ex]t$ s great influ5ce ^u ,am]ican ma!matics z he4 ,,kosmos--,see ,cosmos4 ,,la ,,grange1 ,,joseph ,,l\is1 born at ,tur91 ,janu>y #be1 #agcf2 di$ at ,p>is1 ,april #aj1 #ahac2 reg>d$ z ! greate/ ma!matician s9ce ! "t ( ,newton4 ,x may be int]e/+ to note t ,,la ,,grange rem>k$ t me*anics is really a bran* ( pure ma!matics analog\s to a geometry ( f\r dim5sions1 namely1 "t1 & ! ?ree cord9ates ( ! po9t 9 space4 7,vide ,ball's ,acc\nt ( ! ,hi/ory ( ,ma!matics47 ,,lie1 ,,sophus1 a not$ ma!matician1 ref]r$ to z ! great comp>ative anatomi/ ( geometric !ories1 creator ( ! doctr9es ( ,contact ,trans=mations & ,inf9ite ,cont9u\s ,gr\ps1 & revolutioniz] ( ! ,!ory ( ,diff]5tial ,equations4 ,,logos--,! supreme deity ( ! ph5om5al univ]se2 ,creator2 ,fohat2 a planet>y god2 ! deity ( a sol> sy/em4 ,,manvant>a 7,skt47--,a _w age2 ! p]iods ( involution & evolution comb9$2 ! /age dur+ :i* ! univ]se is 9 manife/ation2 a ,day ( ,brahma4 ,,ma!sis 7,gr4 ma!91 to le>n7--,erudition2 pr(\nd le>n+2 ! realm ( metaphysical conceptions2 ! field ( high] ma!matics2 ! sph]e ( conceivability2 ! !oretical4 ,,m5tograph--,a cognitive factor consi/+ ( a complete p]ception fus$ or 9 coalesc5ce ) a memory-image4 ,pure memory1 ( itself1 is )\t utility z an aid to cognition2 b1 :5 n\ri%$ or supplem5t$ by ! sub/ance ( p]ception x becomes ! basis ( intellectual consci\sness4 ,,metageometry 7,gr4 ,meta1 beyond1 transc5d+--geometry7--,commonly1 any k9d ( geometry t diff]s f ! ,euclidean1 z ! non-,euclidean2 a geometry bas$ ^u ! assumption t ! angul> sum ( a triangle is great] or less ?an two "r angles2 ! highe/ =m ( geometry2 a sy/em ( idealiz$ ma!matical con/ructions4 ,sometimes call$ pangeometry2 designat$ by ,,gauss z ,a/ral ,geometry2 ! geometry ( hyp]space4 ,x consi/s ( results arriv$ at by geomet]s 9 seek+ a pro( ( ! p>allel-po/ulate4 ,,meta-,,self--,! high] self 9 man2 ! univ]sal self2 ! "o self ( :i* all individual selves are b fragm5ts or p>ts4 ,9 man1 x is cord9ate ) ! omnipsy*e 7q4v47 & z su* is ! m$ium ( kosmic consci\sness4 ,,morphog5y 7,gr4 ,morphe1 =m1 vehicle1 body--g5y1 evolution7--,! evolution ( =ms1 ! production ( individual bodies or vehicles = life1 includ+ organs & faculties4 ,morphog5ic--a d]ivative2 p]ta9+ to morphog5y2 a kosmic process 7vide figs4 #ag & #ah74 ,n-,,dim5sionality--,quality ( conceptual space by virtue ( :i* x may be reg>d$ z possess+ an indef9ite numb] ( dim5sions4 ,,ne>-,,tru?--,any /atem5t or view :i* is bas$ ^u p>tial k2 pr$icates conc]n+ a class or g5us d]iv$ f limit$ acqua9tance ) p>ticul>s ( ! class or g5us2 /atem5ts bas$ ^u logical det]m9ations inh]+ 9 idealiz$ con/ructions & appli$ to concrete or objective conditions2 an ab/raction view$ z a reality2 ! application ( ! qualities ( ab/ractions to realities4 ,,neurogram--,psy*ologically1 a movem5t receiv$ by ! aff]5t n]ves 9 ! =m ( a /imulation & transmitt$ ?r\gh ! bra9 & eff]5t n]ves z ei!r a reflex or volunt>y action2 a n]ve impulse2 a p]ception2 a prim>y unit ( intellectual consci\sness2 cf4 ,intuitogram4 ,,newcomb1 ,,simon 7#ahce-aiji71 born at ,wallace1 ,nova ,scotia2 educat$ 9 8 fa!r's s*ool & came to ! ,unit$ ,/ates 9 #ahec4 ,began1 9 #ahed1 tea*+ 9 ,m>yl&2 0 appo9t$ comput] on ,nautical ,almanac at ,cambridge 9 #aheg2 0 graduat$ at ,lawr5ce ,sci5tific ,s*ool 9 #aheh2 appo9t$ ,pr(essor ( ,ma!matics 9 ! ,u4 ,s4 ,navy 9 #ahfa4 ,he sup]vis$ ! con/ruction ( ! #bf-;in* equatorial telescope at ! ,naval ,obs]vatory1 & 0 secret>y ( ! ,transit ( ,v5us ,commission2 0 a memb] ( ne>ly all ( ! ,imp]ial & ,royal societies ( ,europe & ( ! v>i\s societies 9 ! ,unit$ ,/ates1 receiv+ ! ,copley ,m$al 9 #ahgd2 ! ,huyg5s1 #ahgh2 ! ,royal ,society1 #ahij1 & ! ,bruce ,m$al 9 #ahih2 held ! presid5cy ( ! foll[+ le>n$ societies1 viz3 ,am]ican ,association = ! ,advancem5t ( ,sci5ce1 #ahgg2 ,society = ,psy*ical ,rese>*1 #ahhe-ahhf2 ,am]ican ,ma!matical ,society1 #ahig-ahih2 ! ,a/ronomical & ,a/rophysical ,society ( ,am]ica f its f\ndation 9 #ahii4 ,he r5d]$ notable s]vice 9 popul>iz+ ! doctr9e ( hyp]space4 ,,norm--,an au?oritative /&>d2 model or type2 /&>d ( ref]5ce4 ,! *oice ( a norm = spatial det]m9ations _c abide 9 any premise except t :i* naturally1 & n artificially & conv5tionally1 con=ms to :at is actually p]ceiv$2 if s1 !re %\ld be ju/ification = *all5g+ ! wisdom & utility ( ! pres5t s*ematism ( ?+s4 ,!re is an inh]5t con=mity ( space ) intellect & intellect ) space1 & because ( ?is natural complem5t>ity ( "p ) "p & :ole ) :ole1 space _c be o!rwise ?an ! intellectuality normally conceives x to be1 provid$1 ( c\rse1 t ! cognitive movem5t is free & untrammel$ by arbitr>y h9drances4 ,consci\sness1 !re=e1 is ! norm or /&>d ( ref]5ce = all que/ions aris+ out ( a consid]ation ( spatiality4 ,,omnipsy*e--,a t]m us$ to d5ote ! ,?9k]'s cognitive app>atus2 ! univ]sal s\l manife/+ 9 individuals2 ! consci\sness ( ! ,?9k] 9 virtue ( :i* he is at-"o ) ! univ]sal consci\sness2 ! m$ium ( kosmic consci\sness2 ! s\rce ( ! intuition1 cf4 ,egopsy*e4 ,! div9ity 9 man 7:i* is tak5 = grant$71 or 8 highe/ self c 9 no way be said ju/ly to take its rise f s5se-exp]i5ce or f any bodily process4 ,if div9e1 !n et]nal1 & !re=e1 p]si/5t4 ,broadly1 ! doctr9e ( evolution recognizes ! passage ( life f =m to =m1 add+ a little to ea* successive =m & inevitably pu%+ ea* to a high] degree ( p]fection4 ,n[1 :at is x t passes f =m to =m8 ,is x undiff]5tiat$ life or is x a specializ$ =m ( life8 ,f e evid5ce1 x w\ld be judg$ t ! life t ens\ls an individual =m is a specializ$ pr9ciple1 i4e41 limit$ to ! execution ( a giv5 purpose4 ,if life z a specializ$ pr9ciple1 limit$ to ! execution ( a giv5 purpose 9 ea* =m1 passes on1 x mu/ pres]ve1 at lea/1 ! sublimat$ results obta9$ dur+ its resid5ce 9 ea* individual =m4 ,x w\ld ?us become a sort ( res]voir conta9+ all ^! transmut$ results4 ,! omnipsy*e1 )9 ! mean+ ( ! text1 is precisely ?is specializ$ life pr9ciple4 ,,p>allel-,,po/ulate--,v>i\sly ref]r$ to z ! ,x,ith1 ,x,i,ith & ,x,i,i,ith axiom ( ! ,elem5ts ( ,euclid2 /at$ by ,,mann+1 9 ,non-,euclidean ,geometry1 p4 #ia1 9 ! foll[+ =m3 ,if two l9es are cut by a ?ird1 & ! sum ( ! int]ior angles on ! same side ( ! cutt+ l9e is less ?an two "r angles1 ! l9es w meet on t side :5 suffici5tly produc$4 ,?is celebrat$ po/ulate has prov5 to be ! mo/ fruitful ev] devis$2 = x embodies 9 itself ! possibility ( ?ree geometries bas$ respectively ^u ! foll[+ assumptions1 namely3 ,i4 ,t !re exi/s a triangle1 ! sum ( ^: angles is congru5t to a /raight angle1 ! ,euclidean2 ,,ii4 ,t !re exi/s a triangle ! sum ( ^: angles is less ?an a /raight angle1 ! ,,loba*evskian2 ,,iii4 ,t !re exi/s a triangle ! sum ( ^: angles is great] ?an a /raight angle1 ! ,,cayley-,,kle94 ,speak+ ( ! cont5t ( ! la/ two nam$1 ,,edw>d ,,m(fat ,,wey]#a says3 ,hypo!tical realms1 :]e9 ! dim5sions ( space are assum$ to be great] 9 numb] ?an ?ree1 yield /range geometries1 :i* are only c>d ca/les1 products ( a sort ( intellectual play 9 ! con/ruction ( :i* ! laws ( logic supply ! rules ( ! game4 ,! "* ( ea* is det]m9$ by :atsoev] assumption its build] lays d[n at ! />t4 #a ,vide ,popul> ,sci5ce ,mon?ly1 vol4 #gh1 p4 #eed1 #aiaa4 ,,passage ,,( ,,space--,a phrase connot+ ! movem5t ( space f *aos to p]fect ord]1 a process believ$ to be inf9ite4 ,! g5esis ( space necess>ily implies an elaboration1 a proc$ure1 by :i* ! metamorphosis f disord] to kosmic ord] is made1 & ?is movem5t is ref]r$ to z ! passage ( space1 a ph5om5on ?\ght to be measurable by means ( a suitable in/rum5tality4 ,,p]isophism--,see ,ne>-,tru?4 ,,pseudosph]e--,a surface ( con/ant negative curvature2 basis ( ,,beltrami',s metageometrical calculations2 surface resembl+ a *ampagne glass or common spool4 ,! assumption t space is pseudosph]ical has giv5 rise to ! notion ( space-curvature & v>i\s o!r conceptions4 ,,psy*og5y 7,gr4 ,psy*e1 ,s\l--g5y7--,hi/ory ( ! evolution ( ! s\l or ! developm5t ( ! s5so-me*anism 9 organisms4 ,,ern/ ,,haeckel has trac$ ! psy*og5y ( man ?r\gh tw5ty-two diff]5t /ages f ! mon]on to ! an?ropoid apes1 & man4 ,,pralaya 7,skt47--,kosmic quietude2 ! p]iod dur+ :i* ! univ]se is n 9 manife/ation2 ge/atory p]iod2 kosmic inactivity2 oppos$ to manvant>a 7q4v472 figuratively1 ! kosmic womb2 _w egg4 ,,pyknon 7,gr4 pyknon1 h>d7--,! pr9ciple ( kosmic cond5sation2 ! prim>y basis ( space-g5esis2 ! initiation ( ! process by virtue ( :i* *aos is elaborat$ into kosmic ord]4 ,,pyknosis--,! process ( spatial eng5d]m5t4 ,!re are sev5 ( ^! processes1 ea* indicat+ a phase ( duration1 namely3 ,,monopyknosis1 ! prim>y phase2 ,,duopyknosis1 second>y2 ,,tripyknosis1 t]ti>y4 ,^! ?ree p]ta9 to ! plane ( non-manife/ation1 ! pralayic or ge/atory duration-phase4 ,! results arriv$ at dur+ ^! duration-phases are conc5trat$ 9 ! ,qu>topyknotic :i* corresponds to ! causal plane ( manife/ation or pure kosmic spirituality4 ,,qu9topyknosis1 a process conc]n$ 9 ! g5esis ( m5tality2 ,,sextopyknosis1 kosmic s5sibility2 ,,septopyknosis1 kosmic mat]iality4 ,^! sev5 phases ( duration con/itute ! scope ( space g5esis or kosmog5esis1 & incid5tally depose ! sub/ructure ( kosmic mat]iality1 s5sibility1 intellectuality & spirituality1 z well z ! high] tr9ity ( kosmic modes4 ,! ramifications ( ^! pr9ciples are innum]able & omnipres5t4 7,see ,*apt] ,,vii47 ,,qu>todim--,a hypo!tical be+ assum$ to h a consci\sness adapt$ to hyp]space or ! f\r? dim5sion1 & ^: scope ( action is encompass$ )9 a space :i* requires f\r cord9ates1 z ! f\r-space4 ,,reality 7,realism7--,life2 ! h>mony exi/+ among ! p>ts to ma9ta9 _! equilibrium 9 ! :ole2 ! pr9ciple ( integrity subsi/+ among p>ts2 kosmic vitality4 ,,riemann1 ,,george ,,fr$]i* ,,b]nh>d1 0 born ,septemb] #ag1 #ahbf1 9 ! village ( ,bresel5z1 ne> ,dann5burg1 9 ,hanov]4 ,until he 0 eight ye>s ( age 8 fa!r 0 8 sole tutor1 b ev5 at ?is age he exhibit$ great p[]s ( ari?metical calculation4 ,9 ! ,spr+ ( #ahdj "y ,,riemann 0 s5t to ! ,hanov] ,lyceum :]e he rema9$ = two ye>s1 leav+ 9 #ahdb = ! ,gymnasium at ,luneburg4 ,"h1 "u ! direction ( ,pr(essor ,,s*malfuss1 he le>n$ v rapidly1 & is said to h requir$ only "o week ?or\ghly to famili>ize himself ) ,,leg5dre',s ,!ory ( ,numb]s4 ,on ,april #ab1 #ahdf 7,ea/]71 he ent]$ ! ,univ]sity ( ,gtt+5 z a /ud5t ( ,!ology 9 accordance ) 8 fa!r's wi%es4 ,8 passion = ma!matics1 h[ev]1 0 s ar\s$ by ! lectures ( ,,gauss t ,he begg$ 8 fa!r to be all[$ to devote himself entirely to ! /udies ( 8 *oice4 ,= two ye>s he /udi$ "u ,,jacobi at ,b]l94 ,he !n return$ to ,gtt+51 & 0 graduat$1 8 !sis be+ a diss]tation on ! f\ndations ( a g5]al !ory ( functions ( a v>iable complex magnitude4 ,9 #ahed he qualifi$ z a tea*] by giv+ a lecture on ! ,hypo!sis on :i* ,geometry is ,f\nd$4 ,9 #aheg he became ,pr(essor ,extraord9>ius1 & 9 #ahei 0 elect$ ,correspond+ ,memb] ( ! ,academy ( ,sci5ces ( ,b]l9 & 9 #ahfj a memb] ( ! ,academy ( ,sci5ces ( ,gtt+54 ,aft] f\r ye>s ( fail+ heal?1 dur+ :i* he visit$ ,mess9a1 ,pal]mo1 ,naples1 ,rome1 ,flor5ce1 ,pisa & ,milan1 he di$ at ,lago ,maggiore1 ,july #bj1 #ahff1 9 full possession ( 8 faculties & consci\s ( 8 approa*+ end4 ,,s*weik>t1 ,,f]d9& ,,k>l 7#aghj-aheg71 /udi$ f #agif to #agih 9 ,m>burg1 att5d+ ! ma!matical lectures ( ,j4 ,k4 ,f4 ,,hauff4 ,9 #ahab he became pr(essor 9 ,*>kov1 a position :i* he held = f\r ye>s4 ,9 #ahaf he became a tutor 9 ! ,city ( ,m>burg :]e he rema9$ until #ahbj :5 he transf]r$ 8 labors to ,knigsb]g4 ,x 0 dur+ 8 tutor%ip at ,*>kov1 ,m>burg & ,knigsb]g t he1 entirely alone & )\t ! slighte/ sugge/ion f any man1 develop$ & taught a non-,euclidean geometry to ! /ud5ts "u 8 c>e4 ,= copy ( 8 treatise on non-,euclidean geometry1 see ,hi/orical ,sket* ( ! ,hyp]space ,movem5t1 ,*apt] ,,ii4 ,,scopographic ,,impressions--,sight p]ceptions fus$ ) an associat$ memory-image1 & =m+ ! basis ( action on ext]nal ph5om5a4 ,,s5sographic ,,impressions--,p]ceptions or impulses transmitt$ ?r\gh ! n]ves ( a s5se-organ2 any impression act+ ?r\gh ! m$ia ( ! s5ses4 ,,s5sible ,,_w--,! _w ( ! s5ses2 t :i* responds to ! s5ses2 ! doma9 ( p]ception2 ! ph5om5al _w2 _w ( p]ceptual space4 ,,space-,,curvature 7see ,curvature ( ,space74 ,,space-,,g5esis--,! process ( spatial eng5d]m5t2 ! movem5t ( life z eng5d]+ ag5t 9 br++ into manife/ation ! kosmos2 ! /ory ( ! appe>ance ( ! organiz$ kosmos4 ,! g5esis ( space c only be symboliz$1 z has be5 done 9 ! text1 = ! limitations ( human consci\sness d n o!rwise admit ( ! empirical e/abli%m5t ( ! notion ( its detail$ proc$ure4 ,,spatiality--,space z a dynamic1 creative movem5t2 kosmic ord]1 z oppos$ to disord]2 ! pa? ( ! eng5d]+ movem5t ( life2 ! place ( life4 ,spatiality1 mat]iality1 intellectuality & geometricity or ! lat5t geometrism ( ! kosmos are ?\ght ( z be+ consub/antial & int]dep5d5t2 b1 ( ^!1 spatiality is reg>d$ z ! sub/ance out ( :i* ! latt] ?ree are elaborat$4 ,,sup]conceptual--,! purely intuitional2 an act ( cognition p]=m$ )\t ! detail$ "w ( conception d]iv$ f s5se-data2 conception ( intuitions & _! int]-relations2 ! ,?9k]'s consci\sness fre$ f intellectual *>act]ization4 ,,sup]p]ception--,p]ception ( conceptual relations2 a /ate ( cognition :]e91 in/ead ( receiv+ p]cepts or images f ! ext]nal _w1 !n elaborat+ !m into concepts1 ! ,?9k] appreh5ds composite images or concepts at fir/ h&4 ,x is a p[] :i* ! lib]at$ m9d ( ! future w possess ow+ to ! gr[+ automatism ( ! intellect & ! m facile expression ( ! intuitional consci\sness4 ,,tess]act 7,gr4 ,tess]a1 f\r1 cube1 tessella7--,a hyp]cube 7see ,*apt] ,v47 ,,?9k] 7,skt4 ,manu1 ?9k]7--,! real1 spiritual man1 z diff]5tiat$ f 8 p]ceptive vehicles--m9d1 emotions & physical body2 ! omnipsy*ic intellig5ce :o receives1 classifies1 int]prets & pres]ves p]cepts2 ! manipulator ( concepts2 9 f9e1 ! high]1 spiritual man4 ,! ,?9k] uses ! v>i\s p]ceptive in/rum5talities z s _m t5tacles or ant5nae by :i* he contacts ! s5sible _w & makes ! necess>y adaptations to environm5t4 ,he is ! pure intellig5ce :i* is ! s\rce ( all cognitive motivation2 oppos$ to ego1 because ! egopsy*ic in/rum5tality is ess5tially an individualiz+1 sep>ative ag5cy2 :ile ! ,?9k]'s omnipsy*ic intellig5ce is ! basis ( 8 unity ) ! univ]sal intellig5ce4 ,?is conception ( ! ,?9k] implies t1 z a spiritual intellig5ce1 he is )9 & )\t ! body1 fill+ x z ! ocean fills ! sponge1 encompass+1 envelop+ x &1 at ! same "t1 orig9at+ ! totality ( activities :i* manife/ 9 & ?r\gh ! body4 ,he is limit$1 !re=e1 9 8 manife/ations 9 ! s5sible _w only by ! pliability ( 8 vehicles4 ,,transf9ity--,a /ate or condition t is incompreh5sible to f9ite intellig5ce2 t :i* transc5ds ! f9ite1 yet is n inf9ite2 less ?an inf9ity & great] ?an f9ity4 ,space is ref]r$ to z be+ transf9ite r ?an inf9ite 9 ext5t4 ,b space transf9ite %\ld be di/+ui%$ f space f9ite ?\gh unb\nd$4 ,=1 !re w\ld seem to be little wor?y ( *oice betwe5 a f9ite1 unb\nd$ space & an inf9ite "o4 ,! abs5ce ( b\nd>y w\ld naturally sugge/ an inf9ite ext5t4 ,& al?\gh ,,riemann :o is ! au?or ( ! unb\nd$ space arbitr>ily det]m9$ t su* a space %\ld be a manifold possess+ a measure ( curvature :i* c\ld be det]m9$ ei!r by c\nt+ or actual measurem5t1 he und\bt$ly knew1 nev]!less1 t :ile ea* manifold might be an unb\nd$ space ! totality ( su* manifolds1 inf9ite 9 numb]1 mu/ also be inf9ite 9 ext5t4 ,x w\ld seem to d viol5ce to common s5se1 if n to logical necessity1 to view space bo? z unb\nd$ & f9ite 9 ext5t1 yet !re w\ld be no su* difficulty 9 ! recognition ( space z be+ bo? transf9ite & f9ite2 because x is conceivable t ! ext5t & "* ( space f9ite %\ld transc5d a f9ite intellectuality1 & yet n be inf9ite4 ,,tridim--,a be+ ^: scope ( consci\sness is limit$ to a space ( ?ree dim5sions1 z ord9>y human be+s4 ,,tridim5sionality--,t quality possess$ by p]ceptual space by virtue ( :i* x is necess>y & suffici5t to h ?ree cord9ates1 & only ?ree1 to e/abli% ! position ( a po9t4 ,,unodim--,a hypo!tical be+ assum$ to h a consci\sness limit$ to l9e> or "o-space4 ,,zones ,,( ,,aff9ity--,regions 9 ! doma9 ( intellectuality :]e9 m9ds1 possess+ a common diff]5tial1 rate ( vibration or quality1 adh]e to c]ta9 t5ets f *oice4 ,s*ools ( philosophy1 religions1 & all ^? major divisions ( intellectual ef=t :i* divide & subdivide intellectual allegiance are believ$ to take _! rise 9 ?is prop]ty ( intellectuality 9 virtue ( :i* all m9ds hav+ a simil> coeffici5t gravitate t[>ds a common agreem5t1 especially :]e ! movem5t is volunt>y & untrammel$4 ,,"p ,,"o ,,! ,,ess5tials ,,( ,,! ,,geometry ,,( ,,hyp]space ,,& ,,_! ,,significations ,,*apt] ,i ,,! ,,prologue ,on ! ,v>iability ( ,psy*ic ,p[]s--,! ,discov]y ( ! ,f\r? ,dim5sion ,m>ks a ,di/9ct ,/age 9 ,psy*og5esis--,! ,non-,me?odical ,"* ( ,discov]ies--,! ,?ree ,p]iods ( ,psy*og5etic ,developm5t--,! ,scope & ,p]missibility ( ,ma!tic ,lic5se--,kosmic ,unit>9ess ,und]ly+ ,div]sity4 ,9 pres5t+ ?is volume to ! public pr(\nd apologies are made to ! pr(essional ma!matician = ! tem]ity :i* is %[n !reby4 ,all te*nical discussion ( ! problems p]t95t to ! geometry ( hyp]space1 h[ev]1 has be5 c>efully avoid$4 ,! read] is1 !re=e1 ref]r$ to ! bibliography publi%$ at ! end ( ?is volume = matt] relat+ to ?is aspect ( ! subject4 ,! aim r has be5 to outl9e briefly ! progress ( ma!matical ?\ght :i* has l$ up to ! idea ( ! multiple dim5sionality ( space2 to /ate ! c>d9al pr9ciples ( ! ,non-,euclidean geometry & to (f] an int]pretation ( ! metageometrical concept 9 ! light ( ! evolution>y nature ( human faculties & mat]ial *>act]i/ics & prop]ties4 ,! onus ( ?is treatise is1 !re=e1 to di/+ui% betwe5 :at is commonly kn[n z s5sible space & t o!r species ( space kn[n z geometric spaces4 ,also to %[ t ! notion :i* has be5 /yl$ hyp]space is no?+ m nor less ?an an evid5ce ( ! fa9t1 e>ly outcropp+s 9 ! human m9d ( a faculty :i*1 9 ! c\rse ( "t1 w become ! normal possession ( ! entire human race4 ,?us ! weight ( all pres5tations w be to give curr5cy to ! belief1 v /rongly held1 t humanity1 n[ 9 its infancy1 is yet to evolve faculties & capabilities1 bo? m5tal & spiritual1 to a degree hi!rto view$ z inconceivable4 ,on ?is view x mu/ appe> t ! faculty ( ?\ght includ+ ! p[]s ( imag9ation & conceptualization are n psy*ological inv>iants1 b1 on ! o!r h&1 are true v>iants4 ,!y are1 consequ5tly1 answ]able to ! pr9ciple ( evolution j z all vital ph5om5a are4 ,"s h ?\ght t no matt] :at idea may come into ! m9d ( ! human race or at :at "t ! idea may be born ! m9d always has be5 able to conceive x4 ,t is1 _m believe t ! nature ( m9d is su* t no matt] h[ complex an idea may be !re has always be5 9 ! m9d ! p[] ( conceiv+ x4 ,b ?is view _c be said to h ! support ( any tru/wor?y te/imony4 ,if s1 !n ! m9d mu/ at once be recogniz$ z fully matur$ & capable dur+ e epo* ( human evolution1 no less 9 ! fir/ ?an 9 ! late/1 :i*1 ( c\rse1 is absurd4 ,x is und\bt$ly m reasonable & correct to believe t ! p[]s ( conceptualization are matt]s ( evolution>y conc]n4 ,= in/ance1 ! ass]tion t ! m9d 0 incapable ( conceiv+1 9 ! realm ( !ology1 a non-an?ropomorphic god1 or1 9 ! field ( biology1 ! doctr9e ( evolution1 or1 9 ! doma9 ( inv5tion1 ! wireless telegraph1 or1 9 ma!matics1 ! concept ( hyp]space be=e ! actual "t ( ^! conceptions1 _c be successfully controv]t$4 ,9 fact1 x may be laid d[n z "o ( ! fir/ pr9ciples ( psy*og5esis t ! m9d r>ely1 if ev]1 conceives an idea until x has previ\sly develop$ ! p[] ( conceptualiz+ x & giv+ x expression 9 ! t]ms ( prior exp]i5ce4 ,z 9 ! gr[? ( ! body !re are c]ta9 processes :i* require ! full developm5t ( ! organ ( expression be=e !y c be safely execut$ s 9 ! phyletic developm5t ( faculties !re are c]ta9 ideas1 conceptions & scopes ( m5tal vision :i* _c be visualiz$ or conceptualiz$ until ! basis = su* m5tation has be5 laid by ! appe>ance ( previ\sly develop$ faculties ( expression4 ,& especially is ?is true ( ! intellect4 ,inasmu* z ! entire cont5t ( ! intellect is con/itut$ ( s5se-d]iv$ k1 ) ! exception ( intuitions :i* are n ( intellectual orig9 ?\gh dep5d5t ^u ! intellect = int]pretation1 !re c be no d\bt z to ! necessity ( !re be+ fir/ depos$ 9 ! intellect a s5se-d]iv$ basis = intellection be=e x c become manife/4 ,! ,s5sationali/s1 l$ by ,,leibnitz1 prop\nd$ z _! fundam5tal premise ?is dictum3 ,!re is no?+ 9 ! intellect :i* has n fir/ be5 9 ! s5ses except ! intellect itself1 & ?is has nev] be5 ga9said by any s*ool t c\ld disprove x4 ,! intuitionali/ does n d5y x3 he m]ely claims t we are ! recipi5ts ( ano!r =m ( k1 ! intuitional1 :i*1 in/ead ( be+ d]iv$ f s5se-exp]i5ce1 is project$ into ! intellectual consci\sness f ano!r s\rce :i* we designate ! ,?9k]4 ,?us1 f ! two =ms ( consci\sness1 come into ! area ( aw>5ess tru?s t spr+ f entirely diff]5t s\rces4 ,f ! "o s\rce a /eady /ream ( impressions fl[ con/itut+ ! sub/ance ( intellectual consci\sness2 f ! o!r only a drop1 e n[ & !n1 falls into ! great inru%+ mass s z to add a dim phosphoresc5ce to an o!rwise unillum9at$ pool4 ,obvi\sly1 :5 !re is a lack ( s5su\s data f :i* a c]ta9 concept may be elaborat$ !re c be no conception bas$ ^u !m1 & z ! v>iety & quality ( concepts are 9 exact proportion to ! v>iety & quality ( s5se-exp]i5ce !re c be no dem& = a p>ticul> species ( notions su* z might be elaborat$ out ( ! abs5t or non-exi/5t p]ception4 ,h5ce1 ! p[] ( conceiv+ spr+s =? f s5se-exp]i5ce4 ,s5se-exp]i5ce is ess5tially a mass ( p]ceptions3 ^!1 creat+ a dem& = additional adaptations1 conspire1 z if1 to evoke ! p[] or faculty to meet ! dem&1 & consequ5tly1 an add$ conceptualization is made4 ,progress 9 human ?\ght is made 9 a mann] simil> to t :i* prevails 9 ! developm5t ( o!r natural processes1 su* z1 ! p[] ( spee* 9 ! *ild4 ,9 ! developm5t ( ?is faculty !re are c]ta9 def9ite /ages :i* appe> 9 due sequ5ce4 ,! *ild is n gift$ ) ! p[] ( spee* at once4 ,x comes1 by gradual & sometimes pa9ful gr[?1 into a full use ( ?is faculty4 ,n[1 mu* ! same pr9ciple holds true 9 ! evolution ( ! m9d 9 ! human species4 ,x is an e/abli%$ biologic pr9ciple t ! ontog5etic processes manife/$ 9 ! individual are b a recapitulation ( ! phylog5etic processes :i* are obs]vable 9 ! progress ( ! entire species4 ,! view becomes ev5 m cog5t :5 note is tak5 ( ! fact t ! foetus1 dur+ embryog5esis1 passes successively ?r\gh /ages ( gr[? :i* h be5 %[n to be analog\s1 if n id5tical1 ) ^? /ages ?r\gh :i* ! human species has develop$1 namely1 ! m9]al1 vegetal & animal4 ,:]e=e x may be said t ! f\r? dim5sional concept m>ks a di/9ct /age 9 psy*og5esis or evolution ( m9d4 ,x requir$1 z w be %[n 9 ,*apt] ,,ii1 ne>ly two ?\s& ye>s = x to g]m9ate1 take root & come to full fruition4 ,= x 0 n until ! e>ly ye>s ( ! n9ete5? c5tury t ma!maticians1 tak+ inspiration f ,,riemann 7#ahbf-ahff7 fully recogniz$ ! concept z a metaphysical possibility1 or ev5 ! idea 0 conceiv$ at all4 ,s]i\s d\bt is ent]ta9$ z to ! possibility ( its conception by any human m9d be=e ?is date1 t is1 ! "t :5 x 0 actually born4 ,prior to t "t1 ma!matical ?\ght 0 tak+ ^u itself t %ape & t5d5ce :i* w\ld ev5tually lead to ! discov]y ( hyp]space2 b x c\ld n h rea*$ ! z5i? ( its upw>d /riv+s at "o b\nd4 ,t w\ld h be5 unnatural4 ,su* is ! con/itution ( ! m9d t al?\gh x is ! quantity :i* bridges ! *asm betwe5 ! two /ages ( man's evolution :5 he m]ely ?9ks & :5 he really kn[s x is entirely "u ! doma9 ( law & mu/ obs]ve ! times & seasons1 z x 71 9 ! p]=mance ( its functions4 ,! scope ( psy*og5esis is v broad1 p]haps unlimit$2 b its v>i\s /ages are v cle>ly def9$ not)/&+ ! bread? ( its scope ( motility4 ,& :ile ! di/ance f mon]on to man1 or f feel+ to ?9k+ is va/1 ! gulf :i* sep>ates man1 ! ,?9k]1 f man1 ! kn[]1 is va/] /ill4 ,:o1 !re=e1 c say :at are ! delights yet 9 /ore = ! m9d z x approa*es1 by sl[ paces1 ! goal :]eat x w n ne$ to /ruggle ?r\gh ! devi\s pa?s ( p]ceiv+1 conceiv+1 analyz+1 comp>+1 g5]aliz+1 inf]r+ & judg+2 b w be able to "k def9itely1 absolutely & in/antane\sly8 ,t "s su* consummation z ?is %all cr[n ! labors ( m5tal evolution seems only natural & logical4 ,x may be ?\ght by "s t ! "* & cont5t ( revelational impressions con/itute a v>iation f ! requirem5ts ( ! law above ref]r$ to1 b a little ?\ght w expose ! fallacy ( ?is view4 ,! nature ( a reveal$ message is su* z to make x ?or\ghly am5able to ! re/rictions impos$ by ! evolution>y aspects ( m9d 9 g5]al4 ,t ?is is true becomes app>5t ^u an exam9ation ( ! f\r c>d9al *>act]i/ics ( su* impressions4 ,fir/1 we h to consid] ! indef9ite "* ( an apocalyptic ideograph :i* is due to its symbolic nature4 ,?is is a feature :i* relieves ! impression ( any pragmatic value :atsoev]1 especially = ! p]iod embrac+ its promulgation4 ,!n1 su* cryptic messages may or may n be und]/ood by ! recipi5t 9 :i* latt] case x is nonpropagable4 ,second1 ! necessity ( previ\s exp]i5ce 9 ! m9d ( ! recipi5t 9 ord] t he may be able to int]pret to 8 own m9d ! psy*ic imp+em5t4 ,! basis :i* su* exp]i5ce af=ds mu/ necess>ily be pres5t 9 ord] t !re may be an adequate m$ium ( m5tal qualities & p[]s 9 :i* ! ideogram may be pres]v$4 ,a ?ird *>act]i/ic is t revelations q inv>iably presuppose a contemplative attitude ( m9d :i*1 9 ! v nature ( ! case1 sup]9duces a /ate ( prep>$ness 9 ! m9d = ! prop] ent]ta9m5t ( ! concept involv$4 ,?is fact proves q conclusively t revelational impressions are n exceptions to ! g5]al rule4 ,la/ly1 a dissatisfaction ) ! conditions ) :i* ! symbolism deals or to :i* x p]ta9s is also a pr]equisite4 ,?is condition is really t :i* calls =? ! cryptic annunciation1 & yet1 prec$+ x is a long s]ies ( causes :i* h produc$ bo? ! conditions & ! revolt :i* ! revelator feels at _! pres5ce4 ,9 view ( ! =ego+1 x w\ld appe> t objections bas$ ^u ! alleg$ noncon=mity ( ! reveal$ or inspir$ _c be ent]ta9$ z x mu/ be manife/ t x1 too1 falls )9 ! scope ( ! laws ( m5tal gr[?4 ,discov]ies1 :e!r ( philosophical or me*anical nature1 or :e!r ( e?ical or purely ma!matical t5d5ce1 are nev] ! results ( a delib]ate1 me?odical or purposive reflection4 ,= in/ance1 let u take ,,lie',s trans=mation gr\ps1 ma!matic contrivances us$ 9 ! solution ( c]ta9 !orems4 ,n[1 x ought to be obvi\s t ^! ma!tic ma*9ations 7 n discov]$ by ,,sophus ,,lie z a consequ5ce ( any me?odic or purposeful int5tion on 8 "p4 ,t is1 he did n set out delib]ately to discov] trans=mation gr\ps4 ,= back ( ! gr\ps lay ! entire range ( analytic inve/igations2 ! ma!matical ?\ght ( m ?an a ?\s& ye>s furni%$ ! sub/ructure ^u :i* ,lie built ! conception ( 8 gr\ps4 ,simil>ly1 x may be said ) equal assurance t no matt] h[ great ! int5sity ( ?\ght1 nor h[ purposeful1 nor ( h[ long duration ! s]ies ( conc5trat$ ab/ractions :i* l$ up to ! inv5tion ( ! pr9t+ press1 ! l9otype or multiplex pr9t+ press ( our day c\ld n h be5 produc$ abruptly1 nor by use ( ! m5tal dynamics ( ! human m9d ( remot] days4 ,its production _h to foll[ ! pa? outlaid by ! laws ( psy*og5esis & await ! developm5t ( ^? p[]s :i* alone c\ld give x bir?4 ,! :ole "q resolves itself1 !re=e1 into ! idea ( ! complete subs]vi5cy ( ! m9d1 9 all matt]s ( special mom5t1 to ! laws a=em5tion$4 ,! sup]session ( ! law ( its own life by ! m9d is well-nigh un?9kable1 if n q s4 ,if we n[ view ! hi/ory ( ! m9d z manife/$ 9 ! human species1 ?ree great epo*s :i* divide ! scope ( m5tal evolution into m or less well-def9$ /ages pres5t !mselves4 ,^! are3 fir/1 ! =mative /age2 second1 ! det]m9ative /age2 ?ird1 ! /age ( fre$om1 or ! elaborative /age4 ,9 all ( ! e>ly races ( m51 ?r\gh e /ep :i* ev5 prec$$ ! g5us homo1 ! g5]ic m9d 0 be+ =mulat$4 ,x 0 be+ giv5 %ape1 outl9e & direction4 ,all ( ! fir/ /age1 ! =mative1 0 devot$ to organization & direction4 ,^? elem5t>y s5sations :i* con/itut$ ! basis ( m9d 9 ! primitive man 7 accord+ly /rongly det]m9ative ( :at ! m9d %\ld be 9 ^! latt] days4 ,to ?is g5]al result 7 contribut$ ! effects ( ! activity ( cells1 n]ves1 bones1 fib]s1 muscles & ! blood4 ,! =mative p]iod naturally cov]$ a v ext5sive area 9 ! hi/ory ( m9d or psy*og5etic developm5t4 ,x 0 foll[$ closely1 b almo/ ins5sibly1 by ! det]m9ative p]iod dur+ :i* all ! lat5t p[]s1 capacities & faculties :i* 7 ! direct products ( ! =mative p]iod 7 be+ utiliz$ 9 meet+ ! dem&s ( ! law ( necessity4 ,! mak+ ( provisions aga9/ dome/ic want1 aga9/ ! attacks ( ext]nal foes2 ! combat+ ( diseases1 physical ineffici5cy1 ! wea!r1 wild bea/s1 ! asp]ities ( tribal enmities2 z well z fur!r+ ! production ( art1 music1 sculpture1 ! v>i\s bran*es ( h&iwork1 lit]ature1 philosophies1 religions & ! effectuation ( all ^? ?+s :i* n[ appe> z ! result ( ! m5tal activity ( ! pres5t-day man make up ! ess5ce & purpose ( ! det]m9ative p]iod4 ,signs ( ! dawn ( ! elaborative /age1 also call$ ! /age ( fre$om1 h be5 manife/ n[ = upw>ds ( ?ree c5turies & x is1 !re=e1 9 its beg9n+s4 ,x is n fully ^u u4 ,n yet c we fully realize :at x may mean1 nor c we un]r+ly =eca/ its ultimate outcome2 b we feel t x is ev5 n[ "h 9 all ! glories ( its matut9al fre%ness4 ,& ! m9d is beg9n+ to be free f ! gr9d+ necessities ( ! con/ructive p]iod hav+ already fre$ itself f ! re/rictive h&icaps ( ! primeval =mulation p]iod4 ,already ! upgr[+ rejuv5esc5ces s common at ! beg9n+ ( a new p]iod are comm5c+ to %[ !mselves 9 e dep>tm5t ( human activity 9 ! almo/ univ]sal desire = great] fre$om4 ,& ?is is p>ticul>ly noticeable 9 ! _m political upheavals :i*1 f "t to "t1 are com+ to ! surface z well z 9 ! c\ntless o!r aspects ( ! wide-spread r5aissance4 ,p]haps ! "t may come1 nev] q fully1 :5 !re w be no long] any necessity to provide aga9/ ! ext]nal exig5cies ( life2 p]haps1 ! "t w nev] be :5 ! m9d %all no m be b\nd by ! law ( self-pres]vation1 n ev5 :5 x has atta9$ unto ! immortality ( absolute k2 yet1 x is intuitively felt t x mu/ come to pass t ! m9d %all be va/ly fre] ?an x is to-day4 ,& ) ?is new fre$om mu/ come lib]ation f ! necessities ( ! elem5t>y problems ( m]e physical exi/5ce4 ,! inf]5ce is1 !re=e1 drawn t ! f\r? dim5sional concept1 & all t x connotes ( hyp]space or spaces ( n-dim5sionality are "s ( ! evid5ces t ?is /age ( fre$om is dawn+4 ,& ! m9d1 joy\s at ! prospect ( unb\nd$ lib]ty :i* ^! concepts (f]1 _c re/ra9 itself b has already begun to revel 9 ! sunlit glories ( a new] day4 ,:at ! end %all be2 :at effect ?is new lib]ty w h on man's spiritual & economic life2 & :at x may mean 9 ! upw>d /riv+s ( ! ,?9k] = t sublime p]petuity :i* is always ! prop]ty ( imm$iate k no "o c hope1 at ! pres5t "t1 to fa?om4 ,x is1 h[ev]1 believ$ ) ,,keys] t x is by ! creation ( hyp]spaces t ! rational _s secures release f limitation2 =1 z he says1 9 !m x lives ev] joy\sly1 su/a9$ by an unfail+ s5se ( inf9ite fre$om4 ,! elevat+ influ5ce ( ab/ract ?9k+1 su* z excogitation ^u problems deal+ ) entities inhabit+ ! doma9 ( ma!sis is1 )\t d\bt1 incalculable 9 view ( ! fact t x is only ?r\gh ?is k9d ( ?\ght t ! _s is enabl$ to rea* its highe/ possibilities4 ,?is is und\bt$ly ! philosophy ( ^? religi\s & occult ex]cises kn[n z m$itations1 & ?is p]haps 0 ! ma9 idea 9 ! m9d ( ! ,hebrew poet :5 he exclaim$3 ,let ! words ( my m\? & ! m$itation ( my he>t be acceptable 9 ?y sight1 ,o ,"l1 my /r5g? & my ,r$eem]4 ,! pr9cipal1 if n ! only1 value possess$ by ! summitless hi]>*ies ( hyp]spaces :i* ! ma!matician con/ructs 9 ! _w ( pure ?\ght is ! enri*5+ & ennobl+ influ5ce :i* !y ex]t ^u ! m9d4 ,b admitt$ly ?is unb\nd$ doma9 ( ma!tic t]ritory :i* he explores & :i* he f9ds peopl$ ) ideas1 ensembles1 propositions1 relations & implications 9 endless v>iety & multiplicity is q real to him & subsi/s "u a reign ( law ! p5alties ( :i*1 :ile n z au/]e & unreasonable z "s :i* we f9d 9 our tridim5sional _w1 are nev]!less q z palpable & z mu* to be fe>$4 ,= ! or?odoxy ( ma!matics is z cold & intol]ant z ev] ! religi\s fanatic c be4 ,b ! reality & ev5 ! actuality :i* may be imput$ to ! doma9 ( ma!sis is ( an entirely diff]5t quality f t :i* we exp]i5ce 9 our _w ( triune dim5sionality & x is a regrettable error ( judgm5t to id5tify !m4 ,x ought1 !re=e1 nev] be expect$1 nor is x logically reasonable to assume t ! entities :i* inhabit ! ma!tic realm ( ! analy/ %\ld be submissive to ! laws ( s5sible space2 nor t ! conditions :i* may be f\nd !re9 c ev] be made con=mable to ! conditions :i* exi/ 9 p]ceptual space4 ,x 0 ,,plato',s belief t ideas alone possess$ reality & :at we reg>d z actual & real is on acc\nt ( its ephem]ality & evanesc5ce n real b illusion>y4 ,?is view has be5 %>$ by a numb] ( em95t ?9k]s :o foll[$1 ) "s o/5tation1 ! lead e/abli%$ by ,,plato4 ,= a consid]able p]iod ( "t ?is s*ool ( ?9k]s _h _m adh]5ts2 b ! pr9ciples at l5g? fell into disrepute ow+ to ! absurdities indulg$ 9 by "s ( ! less c>eful foll[]s4 ,! realism1 or = t matt]1 ! actuality ( ideas _c be d5i$2 yet x is a realism :i* is nei!r to be comp>$ ) ! physical reality ( s5se-impressions nor its ph5om5a4 ,! "* & peculi>ity ( ideas are 9 a class ap>t f simil> notions ( p]ceptual space cont5t4 ,x is z if we 7 consid]+ ! pot5tialities ( ! _s _w & ! entities !re9 9 connection ) inc>nate entities :i* 9 ! v nature ( ! case is n all[able4 ,fur!rmore1 x is unreasonable to suppose t ! conditions on a high] plane ?an ! physical c be made responsible to a simil> set ( conditions on ! physical plane4 ,!re are c]ta9 a/ronom]s :o base _! speculations z to ! habitability ( o!r planets ^u ! absurd hypo!sis t ! conditions ( life ^u all planets mu/ be ! same z ^? on ! e>?1 =gett+ t ! ext5t ( ! univ]se & ! scope ( motility ( life itself are ( su* a nature z to admit ( endless v>iations & adaptations4 ,!re is a realism ( ideas & a realism ( p]ceptual space4 ,yet ?is is no reason :y ! two %\ld be id5tifi$4 ,on ! o!r h&1 ow+ to ! div]sity 9 ! univ]se1 e consid]ation w\ld naturally lead to ! assumption t !y are dissimil>4 ,to inve/ ideas1 notions1 implications & inf]5ces ) a reality ne$ n logically or o!rwise affect ! reality ( a /one1 a fig1 or ev5 ( a s5se-impression4 ,to a be+ on ! _s levels our grosse/ realities mu/ appe> z non-exi/5t4 ,!y are nei!r palpable nor contactable 9 any mann] )9 ! ord9>y range ( physical possibilities4 ,= u 8 grave/ exp]i5ces c h no reality :atsoev]2 = no matt] h[ real an exp]i5ce may be to him x is altoge!r beyond our p[]s ( p]ception1 & !re=e1 to u non-exi/5t also4 ,x %\ld1 h[ev]1 be /at$ t ! /ate ( our k ab\t a giv5 condition c 9 no way affect its exi/5ce4 ,x m]ely e/abli%es ! fact t two or m realities may exi/ indep5d5t ( "o ano!r & fur!r t ! gamut ( realism 9 ! univ]se is inf9ite & approa*es a f9al /ate :5 its occlusion into absolute be+ foll[s z a logical sequ5ce4 ,recurr+ to ! consid]ation ( ! reality ( _s-realms z comp>$ ) t ( s5sible space1 x comes to view t our idealism1 t is1 ! idealism :i* is a quality ( conceptualization1 may be reg>d$ z id5tical ) _! realism1 at lea/ z be+ on ! same plane z x4 ,/at$ diff]5tly1 ! ?+s t are ideal to u & :i* con/itute ! data ( our consci\sness may be z real to !m z ! commone/ object ( s5se-k is to u4 ,:at1 !re=e1 appe>s to u z ! mo/ e!real & ideali/ic may h q a reali/ic "* = !m4 ,ultimately1 h[ev]1 & 9 ! f9al deeps ( analysis x w be f\nd und\bt$ly t bo? our realism & our idealism z well z simil> qualities ( ! _s _w are 9 all ess5tial consid]ations q illusion>y4 ,all k ga9$ 9 a condition %ort ( div9ity itself is sadly relative4 ,ev5 ma!matical k falls f> %ort ( ! absolute1 ! fonde/ claims ( ! or?odox ma!matician to ! contr>y not)/&+4 ,x has be5 said frequ5tly t a ma!matical fact is an absolute fact & t its v]ity1 necessity & c]ta9ty _c be que/ion$ any:]e 9 ! univ]se :e!r on ,jupit]1 ,neptune1 ,fomalhaut1 ,canopus or ,spica4 ,b hav+ s decl>$1 ! fact ( ! %e] relativity ( our k is n di/urb$ !reby nor controv]t$4 ,happily1 nei!r di/ance nor a lack ( di/ance c 9 any way affect ! quality ( human k1 ma!matical k n except$4 ,t c only be affect$ by conditions :i* cause x to approa* p]fection & no?+ b evolution c d t4 ,9 ! light ( results obta9$ 9 analytic inve/igations ! "q ( ! flexibility ( ma!matical applications becomes evid5t & "o in/ead ( be+ conv9c$ ( ! vaunt$ inv>iability ( ! laws obta9+ 9 ! _w ( ma!sis is1 on ! o!r h&1 made aw>e ( ! rem>kable & seem+ly unre/ra9$ facility ) :i* ^! laws may be made to apply to any conditions or set ( assumptions )9 ! range ( ! m9d's p[]s ( conception4 ,ma!maticians h deifi$ ! def9ition & end[$ x ) omnific p[]s imput+ unto x all ! attributes ( div9ity--immutability1 inv>iance1 & sempit]nity4 ,9 ?is !y h err$ griev\sly al?\gh1 p]haps1 necess>ily4 ,ma!tic conclusions are entirely conditional & dep5d = _! c]ta9ty ^u ! imput$ c]titude ( o!r propositions :i* 9 turn are dep5d5t1 9 ev] increas+ & endlessly complex relations1 ^u previ\sly assum$ po/ulates4 ,^! facts make x exce$+ly difficult to und]/& ! attitude ( m9d :i* has obscur$ ! utt] mutability & consequ5t ultimate unreliability ( ! f9e-spun !ories ( analytic ma*9ations4 ,! apriority ( all ma!matical k is op5 to s]i\s que/ion+4 ,& al?\gh !re is no hesitancy 9 admitt+ ! basic agreem5t ( ! mo/ prim>y facts ( ma!matical k ) ! ess5tial "* ( ! intellect ! exi/5ce ( well-def9$ limits = su* congru5ce _c be ga9said4 ,! subjunctive quality ( geometric & analytical propositions is made app>5t by an exam9ation ( ! possibilities fall+ )9 ! scope ( p]missibility (f]$ by ma!tic lic5se4 ,= in/ance1 privileg$ to proce$ accord+ to ! analytic me?od x is all[able to recon/ruct ! sequ5ce ( values 9 our ord9>y sy/em ( enum]ation s z to admit ( ! specification ( a new value = say1 ! entire s]ies ( odd numb]s4 ,?is value might be assum$ to be a plus-or-m9us "o1 dep5d5t ^u its po/ure 9 ! s]ies4 ,t is1 all odd numb]s 9 ! s]ies beg9n+ ) ! digit #c1 & cont9u+1 #e1 #g1 #i1 #aa1 #ac1 #ae1 #ag1 #ai1 444 n1 c\ld be assum$ to h only a place value :i* might be reg>d$ z a con/ant-v>iable4 ,! s]ies ( ev5 numb]s1 #b1 #d1 #f1 #h1 #aj1 #ab1 #ad1 #af1 444 n1 may be assum$ to reta9 _! pres5t sequ5ce values4 ,"u ?is sy/em ! digit #a w\ld h an absolute value2 all o!r odd numb]s w\ld h a con/ant-v>iable value2 con/ant1 because always no m nor less ?an #a dep5d5t ^u _! place 9 ! op]ations & :e!r _! values 7 to be appli$ by addition or subtraction to or f "o ( ! values 9 ! ev5 numb] s]ies2 v>iable1 because _! values w\ld be det]m9able by _! application & algebraic use4 ,!re w\ld1 ( c\rse1 be utilit>ian objection to a sy/em ( ?is k9d2 b "u ! conditions ( a supposition>y hypo!sis1 x w\ld be self-consi/5t ?r\gh\t1 & if giv5 univ]sal ass5t w\ld suit our purposes equally z well z our pres5t sy/em4 ,b ! fact t ?is c be done "u ! ma!matic me?od v]ily proves ! violability ( ma!matical laws & completely negatives ! assumption t ! sum ( any two digits1 z say #b plus #b equals #d1 is necess>ily & unavoidably immutable4 ,= x c be se5 t ! sum-value ( all numb]s may be made dep5d5t ^u ! assum$ value :i* may be assign$ to !m or to any collection !re(4 ,fur!rmore1 x is a matt] ( hi/orical k t x 0 ! cu/om ( anci5t races ( m5 to acc\nt = values by an entirely diff]5t me?od f :at we use to-day4 ,! latt] is a result ( evolution & :ile exp]i5ce tea*es t x is by f> ! mo/ conv5i5t1 x is nev]!less true t e>li] m5 manag$ at lea/ fairly well on a diff]5t basis4 ,!n1 too1 ! fact ( ! utility & univ]sal applicability ( our pres5t sy/em1 bas$ ^u univ]sal ass5t1 does n obviate ! conclusion t any o!r sy/em1 consi/5t 9 itself1 might be made to s]ve our purposes z well4 ,x ought to be said1 h[ev]1 9 ju/ice to ! r utilit>ian results obta9$ by ,,la ,,grange1 ,,helmholtz1 ,,fe*n]1 & o!rs :o /rove to make use ( _! discov]ies 9 analysis 9 solv+ me*anical1 physiological & o!r problems ( m or less pragmatic import t1 9 s f> z ?is is true1 ma!matical k mu/ be recogniz$ z be+ consi/5t ) ! necessities ( a priori requirem5ts4 ,b ev5 ^! results may n be reg>d$ z transc5d+ ! scope ( ! mo/ fundam5tal pr9ciples ( s5se-exp]i5ce4 ,x w be discov]$ f9ally1 p]haps1 t ! en]gy sp5t 9 elaborat+ complicate s]ies ( analytic curiosities has be5 misappropriat$4 ,x w !n be necess>y to turn ! att5tion def9itely to ! /udy ( t :i* lies n at ! t]m9us ( ! intellect's modus viv5di1 b :i* is bo? ! orig9 ( ! intellect & its et]nal su/a9]--! intuition1 or life itself4 ,?is c result 9 no?+ less ?an ! complete spiritualization ( man's m5tal outlook & ! consequ5t inevitable recognition ( ! und]ly+ & ev]-su/a9+ "o-ness ( all vital manife/ations4 ,"o ( ! curiosities ( ! t5d5cy 9 man's m9d to specialize 9 analytics1 :e!r 9 ! field ( pure ma!matics or metaphysics1 is ! fact t x almo/ inv>iably leads to an attempt to acc\nt = cosmic orig9s on ! basis ( p>alogic !ories4 ,?is 9 times pa/ has giv5 rise to ! !ory ( ! purely me*anical orig9 ( ! univ]se z well z _m o!r fanta/ic fallacies ! *ief error ( :i* lay 9 ! failure to di/+ui% betwe5 ! realism ( m5tal concepts & t ( ! s5sible _w4 ,9 spite ( ?is1 h[ev]1 "o is b\nd to appreciate ! b5eficial effects ( analytic op]ations because !y s]ve z invigorants to m5tal gr[?4 ,x c\ld n1 !re=e1 be wi%$ t !re 7 no su* ?+ z analytics2 = ! equilibria-re/or+ prop]ty ( ! m9d may at all times be reli$ ^u to m9imize ! dang] ( excesses 9 ei!r direction4 ,j z ! tide fl[+ 9 fl[s out aga91 !reby re/or+ ! ocean's equilibrium1 s ! m9d asc5d+ 9 "o g5]ation beyond ! safety m>k has its equilibrium re/or$ 9 ! next by a rel9qui%m5t ( ! follies ( ! =m]4 ,! f\r-space is "o ( ! curiosities ( analytics2 yet x ne$ n be a m5ace to ! sane contemplation ( ! v>iegat$ products ( analysis4 ,safety "h abides 9 ! re/ra9t :i* %\ld *>act]ize all discussion & application ( ! concept4 ,if en?usia/s w\ld be cont5t n to transport ! s-call$ f\r? dim5sional space out ( ! sph]e ( hyp]space & cease try+ to speculate ^u ! results ( its int]posal into ?ree space conditions1 :i* is 9 e way a con/ructual impossibility1 !re c\ld n be any possible objection to its due consid]ation4 ,?is w\ld obviate ! dang] ( call+ into "q ei!r ! s9c]ity or p]spicacity ( ^? ^: en?usiasm tempts !m to transgress ! limits ( propriety 9 _! behavior t[>ds ! inquiry4 ,!re is b "o life1 "o m9d1 "o ext5sion1 "o quantity1 "o quality1 "o be+1 "o /ate1 "o condition1 "o mood1 "o affection1 "o desire1 "o feel+1 "o consci\sness4 ,!re is also b "o numb] & t is unity4 ,all s-call$ integ]s are b fractional p>ts ( ?is kosmic unity4 ,! idea repres5t$ by ! ^w two really connotates two p>ts ( unity & ! same is true ( a decillion1 or any numb] ( p>ts4 ,^! are m]ely ! inf9itesimals ( unity & !y gr[ less 9 size & consequ5ce z ! divisions increase 9 numb]4 ,! analysis ( unity into an inf9ity ( p>ts is purely an a po/]iori proc$ure4 ,t x is an inh]5t m9d-process is a fallacy4 ,all our common quantities1 z ! mile1 kilomet]1 y>d1 foot1 in*1 gallon1 qu>t1 are conv5tional & arbitr>y & susceptible ( wide v>iations4 ,z ! basis ( all physical ph5om5a is unity2 x is only 9 ! ephem]al manife/ations ( s5su\s objects t !y appe> z sep>ate & di/9ct quantities4 ,we see on a tree _m leaves1 _m apples or *]ries2 on a cob _m gra9s ( corn4 ,we h le>n$ to assign to ea* ( ^! quantities 9 _! summation a sequ5ce value4 ,b ?is is an empirical notion & _c be said to inh]e 9 ! m9d itself4 ,let u take1 = in/ance1 ! mu/>d se$4 ,if x 7 true t 9 "o ( ^! se$s !re exi/$ all ! subsequ5t se$s :i* appe> 9 ! mu/>d plant z sep>ate & id5tifiable quantities1 & n 9 ess5ce1 !n !re w\ld p]haps be w>rant = ! notion t div]sity1 z ! calculable elem5t1 is an a priori conception4 ,b1 z ?is is n ! case & s9ce div]sity is purely empirical & p]ta9s only to ! effloresc5ce ( ! "o life x is manife/ly absurd to take t view4 ,"u ! mo/ *>itable all[ances1 !re=e1 !re c be b two quantities--unity & div]sity2 yet n two1 = ^! are "o4 ,unity is ! "o quantity & div]sity is ! division ( unity into a transf9ity ( p>ts4 ,unity is inf9ite1 absolute & all-inclusive4 ,div]sity is f9ite al?\gh x may be admitt$ to be transf9ite1 or great] ?an any assignable value4 ,unity alone is incompreh5sible4 ,9 ord] to und]/& some?+ ( its nature we divide x into a div]sity ( p>ts2 & because we fail to und]/& ! transf9ity ( ! multitude ( p>ts we mi/ak5ly call !m inf9ite4 ,:5 analysis %all h proce$$ f> en\gh into ! abysmal my/]ies ( div]sity2 :5 ! ma!matical m9d %all h be5 ov]come by ! ov]:elm+ p]plexity ( ! maze ( div]se p>ts1 x %all !n fall asleep & ^u awak+ %all f9d t wond]fully simple ?+--unity4 ,x is ! "o quantity t is end[$ ) a magnitude :i* is bo? inconceivable & irresolvable4 ,! "o ineluctable fact 9 ! univ]se is ! incompreh5sibility & all-inclusivity ( "o-ness4 ,x is incompreh5sible1 inconceivable & inf9ite at ! pres5t /age ( m9d developm5t4 ,b ! goal ( m9d is to und]/& ! ess5tial "* ( unity1 ( life4 ,its evolution w !n /op1 = x w h rea*$ ! prize ( div9ity itself :]eupon ! intellect exalt$ by & unit$ ) ! intuition %all also become "o ) ! div9e consci\sness4 ,,*apt] ,,ii ,,hi/orical ,,sket* ,,( ,,! ,,hyp]space ,,movem5t ,egypt ! ,bir?place ( ,geometry--,precursors3 ,,nasir-,,edd91 ,,*ri/oph ,,clavius1 ,,sac*]i1 ,,lamb]t1 ,,la ,,grange1 ,,kant--,influ5ce ( ! ,mecanique ,analytique--,! ,p>allel-,po/ulate ! ,root & ,sub/ance ( ! ,non-,euclidean ,geometry--,! ,?ree ,great ,p]iods3 ,! ,=mative1 ,det]m9ative & ,elaborative--,,riemann & ! ,prop]ties ( ,analytic ,spaces4 ,! evolution ( ! idea ( a f\r? dim5sion ( space cov]s a long p]iod ( ye>s4 ,! e>lie/ kn[n record ( ! beg9n+s ( ! /udy ( space is f\nd 9 a hi]atic papyrus :i* =ms a "p ( ! ,rh9d ,collection 9 ! ,briti% ,museum & :i* has be5 deciph]$ by ,,eis5lohr4 ,x is believ$ to be a copy ( an old] manuscript ( date #cdjj ,b4 ,c41 & is entitl$ ,directions = ,kn[+ ,all ,d>k ,?+s ,! copy is said to h be5 made by ,,ahmes1 an ,egyptian prie/ betwe5 #agjj & #aajj ,b4 ,c4 ,x beg9s by giv+ ! dim5sions ( b>ns2 !n foll[s ! consid]ation ( v>i\s rectil9eal figures1 circles1 pyramids1 & ! value ( pi 7,greek3 p74 ,al?\gh _m ( ! solutions giv5 9 ! manuscript h be5 f\nd to be incorrect 9 m9or p>ticul>s1 ! fact rema9s t ,egypt is really ! bir?-place ( geometry4 ,& ?is fact is buttress$ by ! k t ,,?ales1 long be=e he f\nd$ ! ,ionian ,s*ool :i* 0 ! beg9n+ ( ,greek influ5ce 9 ! /udy ( ma!matics1 is f\nd /udy+ geometry & a/ronomy 9 ,egypt4 ,! concept ( hyp]space began to g]m9ate 9 ! latt] "p ( ! fir/ c5tury1 ,b4 ,c4 ,= x 0 at ?is date t ,,gem9os ( ,,rhodes 7,b4 ,c4 #gj7 began to ?9k s]i\sly ( ! ma!matical labyr9? into :i* ,,euclid',s p>allel-po/ulate mo/ c]ta9ly w\ld lead if an attempt at demon/rat+ its c]titude 7 made4 ,he recogniz$ ! difficulties :i* w\ld engage ! att5tion ( ^? :o might v5ture to delve into ! my/]i\s possibilities ( ! problem4 ,!re is no d\bt1 too1 b t ,,euclid himself 0 aw>e1 9 "s measure at lea/1 ( ^! difficulties2 = 8 own attitude t[>ds ?is po/ulate seems to h be5 "o ( noncommittance4 ,x is1 !re=e1 n /range t ! a/ronom]1 ,,ptolemy 7,a4 ,d4 #hg-afe71 %\ld be f\nd seek+ to prove ! po/ulate by a consid]ation ( ! possibilities ( int]/ell> triangles4 ,8 rese>*es1 h[ev]1 br\ght him no relief f ! g5]al dissatisfaction :i* he felt ) respect to ! validity ( ! problem itself4 ,= ne>ly "o ?\s& ye>s aft] ! attempts at solv+ ! po/ulate by ,,gem9os & ,,ptolemy1 ! field ( ma!matics lay undi/urb$4 ,= x 0 at ?is "t t !re arose a /range ph5om5on1 m commonly kn[n z ! ,d>k ,ages1 :i* put an effectual *eck to fur!r rese>* or indep5d5t inve/igations4 ,ma!maticians ?r\gh\t ?is long lapse ( "t 7 cont5t to accept ,,euclid z ! "o incontrov]tible1 unimpea*able au?ority1 & ev5 su* inve/igations z 7 made did n h a rebelli\s t5d5ce1 b 7 ma9ly endeavors to sub/antiate 8 claims4 ,accord+ly1 x 0 n until ab\t ! fir/ half ( ! ?irte5? c5tury t any real advance 0 made4 ,at ?is "t !re appe>$ an ,arab1 ,,nasir-,,edd9 7#abja-abgd7 :o attempt$ to make an improvem5t on ! problem ( p>allelism4 ,8 "w on ,,euclid 0 pr9t$ 9 ,rome 9 #aeid ,a4 ,d41 ab\t ?ree hundr$ & tw5ty ye>s aft] 8 demise & 0 communicat$ 9 #afea by ,,john ,,wallis 7#afaf-agjc7 to ! ma!maticians ( ,ox=d ,univ]sity4 ,al?\gh 8 calculations & conclusions 7 respectfully receiv$ by ! ,ox=d au?orities no def9ite results 7 reg>d$ z accompli%$ by :at he _h done4 ,x is believ$1 h[ev]1 t 8 "w reop5$ speculation ^u ! problem & s]v$ z a basis1 h[ev] slight1 = ! great] "w t 0 to be done by ^? :o foll[$ him dur+ ! next succe$+ eight hundr$ ye>s4 ,ab\t tw5ty ye>s be=e ! pr9t+ ( ! "w ( ,,nasir-,,edd91 ,,*ri/oph ,,clavius 7#aegd7 d$uc$ ! axiom ( p>allels f ! assumption t a l9e ^: po9ts are all equidi/ant f a /raight l9e is itself /raight4 ,9 8 consid]ation ( ! p>allel-po/ulate he is said to h reg>d$ x z ,,euclid',s ,x,i,i,ith axiom4 ,lat] ,,bolyai spoke ( x z ! ,x,ith & lat] /ill1 ,,todhunt] treat$ x z ! ,x,i,ith4 ,h5ce1 !re does n seem to h be5 any g5]al unanimity ( op9ion z to ! exact /atus ( ! p>allel-po/ulate1 & especially is ?is true 9 view ( ! unc]ta9ty n[ kn[n to h exi/$ 9 ,,euclid',s m9d conc]n+ x4 ,,girolamo ,,sac*]i 7#affg-agcc71 a le>n$ ,jesuit1 born at ,san ,remo1 came next ^u ! /age4 ,& s important 0 8 "w t x w p]petuate ! memory ( 8 "n 9 ! hi/ory ( ma!matics4 ,he 0 a tea*] ( gramm> 9 ! ,jesuit ,collegio di ,br]a :]e ,,tommaso ,,ceva1 a bro!r ( ,,giovanni1 ! well-kn[n ma!matician1 0 tea*] ( ma!matics4 ,8 association ) ! ,,ceva bro!rs 0 especially b5eficial to him4 ,he made use ( ,,ceva',s v +5i\s me?ods 9 8 fir/ publi%$ book1 #afic1 entitl$ ,solutions ( ,six ,geometrical ,problems ,propos$ by ,c\nt ,rog] ,v5timiglia4 ,a -------------------------------- ,b ,c -------------------------------- ,d ,,fig4 #a4 ,,sac*]i attack$ ! problem ( p>allels 9 q a new way4 ,exam9+ a quadrilat]al1 ,,abcd1 9 :i* ! angles ,a & ,b are "r angles & ! sides ,,ac & ,,bd are equal1 he det]m9$ to %[ t ! angles ,c & ,d are equal4 ,he also s\ght to prove t !y are ei!r "r angles1 obtus acute4 ,he und]took to prove ! falsity ( ! latt] two propositions 7t !y are ei!r obtuse or acute71 leav+ z ! only possibility t !y mu/ be "r angles4 ,9 do+ s1 he f\nd t 8 assumptions l$ him into contradictions :i* he exp]i5c$ difficulty 9 expla9+4 ,8 labors 9 connection ) ! solution ( ! problems propos$ by ,,c\nt ,,v5timiglia1 includ+ 8 "w on ! "q ( p>allels1 l$ directly into ! field ( metageometrical rese>*es1 & p]haps to him z to no o!r :o _h prec$$ him1 or at lea/ to him 9 a l>g] degree1 belongs ! cr$it = a cont9u$ r5ewal ( int]e/ 9 t s]ies ( inve/igations :i* result$ 9 ! =mulation ( ! non-,euclidean geometry4 ,! la/ publi%$ "w ( ,,sac*]i 0 a recital ( 8 endeavors at demon/rat+ ! p>allel-po/ulate4 ,?is receiv$ ! ,imprimatur ( ! ,inquisition1 ,july #ac1 #agcc2 ! ,prov9cial ,company ( ,jesus took possession ( ! book = p]usal on ,augu/ #af1 #agcc2 b un=tunately )9 two mon?s aft] x _h be5 review$ by ^! au?orities1 ,,sac*]i pass$ away4 ,all ef=ts :i* _h be5 made prior to ! "w ( ,,sac*]i 7 bas$ ^u ! assumption t !re mu/ be an equival5t po/ulate :i*1 if x c\ld be demon/rat$1 w\ld lead to a direct1 positive pro( ( ,,euclid',s proposition4 ,al?\gh ^! & all o!r attempts at rea*+ su* a pro( h signally fail$ & al?\gh x may correctly be said t ! entire hi/ory ( demon/rations aim+ at ! solution ( ! fam\s po/ulate has be5 "o long s]ies ( utt] failures1 x c be ass]t$ ) equal c]titude t x has prov5 to be "o ( ! mo/ fruitful problems 9 ! hi/ory ( ma!matical ?\ght4 ,= out ( ^! failures has be5 built a sup]/ructure ( analytical inve/igations :i* surpasses ! mo/ sangu9e expectations ( ^? :o _h labor$ & fail$4 ,9 #agff ,,john ,,lamb]t 7#agbh-aggg7 wrote a pap] ^u ! ,!ory ( ,p>allels dat$ ,sept4 #e1 #agff1 fir/ publi%$ 9 #aghf1 f ! pap]s left by ,f4 ,,b]n\lli1 :i* conta9$ ! foll[+ ass]tions3#b #a4 ,! p>allel-axiom ne$s pro(1 s9ce x does n hold = geometry on ! surface ( ! sph]e4 #b4 ,9 ord] to make intuitive a geometry 9 :i* ! triangle's sum is less ?an two "r angles1 we ne$ an imag9>y sph]e 7! pseudosph]e74 #c4 ,9 a space 9 :i* ! triangle's sum is diff]5t f two "r angles !re is an absolute measure 7a natural unit = l5g?74 ,at ?is "t ,,immanuel ,,kant 7#agbd-ahjd71 ! not$ ,g]man metaphysician1 0 9 ! mid/ ( 8 philosophical labors4 ,& x is believ$ t x 0 he :o fir/ sugge/$ ! idea ( diff]5t spaces4 ,bel[ is giv5 a /atem5t tak5 f 8 ,prolegom5a#c :i* corroborates ?is view4 ,t complete space 7:i* is itself no long] ! b\nd>y ( ano!r space7 has ?ree dim5sions1 & t space 9 g5]al _c h m1 is bas$ on ! proposition t n m ?an ?ree l9es c int]sect at "r angles 9 "o po9t4444 ,t we c require a l9e to be drawn to inf9ity1 a s]ies ( *anges to be cont9u$ 7= example1 spaces pass$ ?r\gh by motion7 9 indef9itum1 presupposes a repres5tation ( space & "t :i* c only atta* to intuition4 #b ,vide ,new ,york ,ma!matical ,society ,bullet91 ,vol4 ,,iii1 #ahic-d1 p4 #gi1 ,g4 ,b4 ,,hal/ead on ,lamb]t's ,non-,euclidean ,geometry4 #c ,prolegom5a1 ,,kant1 p4 #cg1 ,trans4 by ,j4 ,p4 ,,mahaffy & ,j4 ,h4 ,,b]n>d4 ,8 diff]5tiation betwe5 space 9 g5]al & space :i* may be consid]$ z ! b\nd>y ( ano!r space %[s1 9 ! light ( ! subsequ5t developm5ts ( ! ma!matical idea ( space t he v fully appreciat$ ! m>vel\s scope ( analytic spaces4 ,8 conception ( space1 !re=e1 mu/ h _h a pr(\nd influ5ce ^u ! ma!matic ?\ght ( ! day caus+ x to und]go a rapid recon/ruction at ! h&s ( geomet]s :o came aft] him4 ,"u ! ma/]ly influ5ce ( ,,la ,,grange 7#agcf-ahac7 ! idea ( diff]5t spaces began to take def9ite %ape & direction2 ! geometry ( hyp]space began to cry/allize2 & ! field ( ma!sis prep>$ = ! gr[? ( a conception ! compreh5sion ( :i* 0 de/9$ to be ! pr(\nde/ und]tak+ ev] attempt$ by ! human m9d4 ,unlike mo/ great m5 :om ! _w le>ns t>dily to admire1 ,,la ,,grange liv$ to see 8 tal5ts & g5ius fully recogniz$ by 8 compe]s2 = he 0 ! recipi5t ( _m honors bo? f 8 c\ntrym5 & 8 admir]s 9 =eign l&s4 ,he sp5t tw5ty ye>s 9 ,prussia :]e he w5t ^u ! invitation ( ,,fr$]ick ! ,great :o 9 ! ,royal summons ref]r$ to himself z ! greate/ k+ 9 ,europe & to ,,la ,,grange z ! greate/ ma!matician 9 ,europe4 ,9 ,prussia ! ,mecanique ,analytique & a long s]ies ( memoirs :i* 7 publi%$ 9 ! ,b]l9 & ,tur9 ,transactions 7 produc$4 ,,la ,,grange did n exhibit any m>k$ ta/e = ma!matics until he 0 #ag ye>s ( age4 ,soon !reaft] he came into possession ( a memoir by ,,halley q by accid5t & ?is s ar\s$ 8 lat5t g5ius t )9 "o ye> aft] he _h review$ ,,halley',s memoir he became an accompli%$ ma!matician4 ,he creat$ ! calculus ( v>iations1 solv$ mo/ ( ! problems propos$ by ,f]mat1 add+ a numb] ( !orems ( 8 own contrivance2 rais$ ! !ory ( diff]5tial equations to ! position ( a sci5ce r ?an a s]ies ( +5i\s me?ods = ! solution ( special problems & furni%$ a solution = ! fam\s isop]imetrical problem :i* _h baffl$ ! skill ( ! =emo/ ma!maticians = ne>ly half a c5tury4 ,all ^! /up5d\s tasks he p]=m$ by ! "t he rea*$ ! age ( n9ete54 ,! ,mecanique ,analytique is 8 greate/ & mo/ compreh5sive "w4 ,9 ?is he e/abli%$ ! law ( virtual "w f :i*1 by ! aid ( 8 calculus ( v>iations1 he d$uc$ ! :ole ( me*anics1 includ+ bo? solids & liquids4 ,x 0 8 object 9 ! ,analytique to %[ t ! :ole subject ( me*anics is implicitly embrac$ 9 a s+le pr9ciple1 & to lay d[n c]ta9 =mulae f :i* any p>ticul> result c be obta9$4 ,he frequ5tly made ! ass]tion t he _h1 9 ! ,mecanique ,analytique1 trans=m$ me*anics :i* he p]si/5tly def9$ z a geometry ( f\r dim5sions#d into a bran* ( analytics & _h %[n ! s-call$ me*anical pr9ciples to be ! simple results ( ! calculus4 ,h5ce1 !re c be no d\bt b t ,,la ,,grange n only complet$ ! f\ndation1 b provid$ mo/ ( ! mat]ial 9 8 analyses & o!r ab/ract results ( great g5]ality :i* he obta9$ 9 8 num]\s calculations1 = ! sup]/ructure subsequ5tly kn[n z ! geometry ( hyp]space1 & 9 :i* ! f\r? dim5sional concept occupies a v fundam5tal place4 #d ,9 #aged ,d',,alemb]t 7#agag-aghc7 publi%$ an article 9 ! fam\s old ,encyclop$ia edit$ by ,,did]ot & himself on ,dim5sion4 ,9 ?is article ! idea ( ! f\r? dim5sion is dwelt ^u at l5g?4 ,! view :i* he express$ 9 ?is article1 ( c\rse1 s]v$ greatly to popul>ize ! conception among ! le>n$ m5 ( ! day1 & ow+ to ! close relation%ip exi/+ betwe5 ,d',,alemb]t & ,,la ,,grange1 x is n surpris+ t ! latt] %\ld h be5 v mu* enamor$ ( ! idea4 ,x is z if = ne>ly sev5te5 hundr$ ye>s workm51 su* z ,,gem9os1 ( ,,rhodes1 ,,ptolemy1 ,,sac*]i1 ,,nasir-,,edd91 ,,lamb]t1 ,,clavius1 & hundr$ ( o!rs :o /ruggl$ ) ! problem ( p>allels1 _h made m or less sporadic attempts at ! excavation ( ! l& :]eon a m>vel\sly intricate build+ 0 to be con/ruct$4 ,!re is no hi/orical evid5ce to %[ t any ( !m ev] dream$ t ! results ( _! labors w\ld be utiliz$ 9 ! mann] 9 :i* !y h be5 us$4 ,!n came ,,kant ) ! wond]fully p5etrat+ se>*light ( 8 ma/]ful intellect :o f ! elevation :i* he occupi$ saw t ! site _h great possibilities1 b he _h n ! ma!matical tal5t to und]take ! "w ( actual1 me?odical con/ruction4 ,inde$ 8 task 0 ( a diff]5t sort4 ,h[ev]1 he succe$$ 9 op5+ ! way = ,,la ,,grange & o!rs :o foll[$ him4 ,,la ,,grange imm$iately seiz$ ^u ! idea :i* = m ?an a ?\s& ye>s _h be5 imp++ ^u ! m9ds ( ma!maticians va9ly seek+ lodgm5t & began ! elaboration ( a plan 9 accordance ) :i* m9ds bett] skill$ 9 ! pragmatic application ( ab/ract pr9ciples ?an 8 c\ld complete ! "w begun4 ,un=tunately1 on acc\nt ( 8 int5se devotion & loyalty to ! /udy ( pure ma!matics1 & :5 he _h rea*$ ! summit ( 8 greatness :]e he /ood )\t a rival z ! =emo/ liv+ ma!matician1 8 heal? became s]i\sly affect$1 caus+ him to suff] con/ant attacks ( pr(\nd melan*olia f :i* he di$ on ,april #aj1 #ahac4 ,we come n[ to "o ( ! mo/ rem>kable p]iods 9 ! hi/ory ( m5tal developm5t4 ,dur+ ! six hundr$ ye>s betwe5 ! bir? ( ,,nasir-,,edd9 & ! dea? ( ,,la ,,grange ! entire _w ( ma!sis 0 be+ recon/itut$4 ,s9ce !re _h be5 gradually go+ on an int]nal process :i*1 :5 complet$1 =ev] w\ld lib]ate ! m9d f ! n>r[ conf9es ( consci\sness limit$ to ! ?ree-space1 x is n surpris+ t we %\ld f9d1 9 ! ma!matical ?\ght ( ! "t1 an absolutely epo*-mak+ dep>ture4 ,! innum]able attempts at ! solution ( ! p>allel-po/ulate1 all failures 9 ! s5se t !y did n prove1 h int5sifi$ greatly ! e/eem 9 :i* ! nev]-dy+ elem5ts ( ,,euclid are held to-day4 ,& despite ! fact t !re may come a "t :5 8 axioms & conclusions may be f\nd to be incongru5t ) ! facts ( s5su\s reality2 & ?\gh all ( 8 fundam5tal conceptions ( space 9 g5]al1 8 !orems1 propositions & po/ulates may h to give way be=e ! se>*+ gl>e ( a deep] k because ( "s reveal$ fault1 ! p]fection ( 8 "w 9 ! realm ( pure ma!matics w rema9 =ev] a ma/] piece dem&+ ! undim9i%$ admiration ( mank9d4 ,! p>allel-po/ulate1 z /at$ by ,,euclid 9 8 ,elem5ts ( ,geometry1 reads z foll[s3 ,if a /raight l9e meet two /raight l9es s z to make ! two int]ior angles on ! same side ( x tak5 toge!r less ?an two "r angles1 ^! /raight l9es be+ cont9ually produc$1 %all at l5g? meet ^u t side on :i* are ! angles :i* are less ?an two "r angles4 ,on ?is po/ulate hang all ! law & ! prophets ( ! non-,euclidean ,geometry4 ,9 x are ! virtual elem5ts ( ?ree possible geometries4 ,fur!rmore1 x is bo? ! w>p & ! wo( ( ! loom ( pres5t-day metageometrical rese>*es4 ,x is ! gold5 egg laid by ! god ,,seb at ! beg9n+ ( a new life cycle 9 psy*og5esis4 ,its prog5y are num]\s--hyp]spaces1 sects1 /raights1 digons1 equidi/antials1 pol>s1 plan>s1 coplan>s1 inv>iants1 quat]nions1 complex v>iables1 gr\ps & _m o!rs4 ,a wond]fully int]e/+ bre$1 full ( mean+ & pregnant ) ! p[] ( f9al emancipations = ! human intellect6 ,:5 ! conclusions :i* 7 sy/ematically =mulat$ z a result ( ! inve/igations along ! l9es ( hypo!ses :i* controv]t$ ! p>allel-po/ulate 7 exam9$ x 0 f\nd t !y fell into ?ree ma9 divisions1 namely3 ! syn!tic or hyp]bolic2 ! analytic or ,,riemannian & ! elliptic or ,,cayley-,,kle94 ,^! divisions or gr\ps are bas$ ^u ! ?ree possibilities :i* inh]e 9 ! conception tak5 ( ! sum ( ! angles ref]r$ to 9 ! above po/ulate z to :e!r x is equal to1 great] or less ?an two "r angles4 ,! assumption t ! angul> sum is congru5t to a /raight angle is call$ ! ,euclidean or p>abolic hypo!sis & is to be di/+ui%$ f ! syn!tic or hyp]bolic hypo!sis e/abli%$ by ,,gauss1 ,,loba*evski & ,,bolyai & :i* assumes t ! angul> sum is less ?an a /raight angle4 ,! elliptic or ,,cayley-,,kle9 hypo!sis assumes t ! angul> sum is great] ?an a /raight angle4 ,,loba*evski1 h[ev]1 n satisfi$ ) ! /atem5t ( ! p>allel-po/ulate z giv5 by ,,euclid & :i* _h caus$ ! age-long controv]sy1 sub/itut$ = x ! foll[+3 ,all /raight l9es :i*1 9 a plane1 radiate f a giv5 po9t1 c1 ) respect to any o!r /raight l9e1 9 ! same plane1 be divid$ into two classes--! int]sect+ & ! non-int]sect+4 ,! b\nd>y l9e ( ! "o & ! o!r class is call$ p>allel to ! giv5 l9e4 ,?is is b ano!r way ( say+ ab\t ! same ?+ t ,,euclid _h decl>$ be=e1 & yet1 curi\sly en\gh x af=d$ j ! lib]ty t ,,loba*evski ne$$ to enable him to elaborate 8 !ory4 ,= ! purposes ( ?is sket* ! field ( ! developm5t ( non-,euclidean geometry is divid$ into ?ree p]iods to be kn[n z3 7#a7 ! =mative p]iod 9 :i* ma!matical ?\ght 0 be+ =mulat$ = ! new dep>ture2 7#b7 ! det]m9ative p]iod dur+ :i* ! ma!matical ideas 7 giv5 direction1 purpose & a g5]al t5d5ce2 7#c7 ! elaborative p]iod dur+ :i* ! results ( ! =m] p]iods 7 elaborat$ into def9ite k9ds ( geometries & attempts made at popul>iz+ ! hypo!ses4 ,! ,=mative ,p]iod ,,*>les ,,fr$]i* ,,gauss 7#aggg-ahee7 by "s has be5 reg>d$ z ! mo/ influ5tial ma!matician t figur$ 9 ! =mulation ( ! non-,euclidean geometry2 b clos] exam9ation into 8 ef=ts at inve/igat+ ! prop]ties ( a triangle %[s t :ile 8 rese>*es l$ to ! e/abli%m5t ( ! !orem t a regul> polygon ( sev5te5 sides 7or ( any numb] :i* is prime1 & also "o m ?an a p[] ( two7 c be inscrib$1 "u ! ,euclidean re/rictions z to means1 9 a circle1 & also t ! common sph]ical angle on ! surface ( a sph]e is closely connect$ ) ! con/itution ( ! area inclos$ !reby1 he _c ju/ly be designat$ z ! lead] ( ^? :o =mulat$ ! syn!tic s*ool4 ,& ?is1 too1 = ! simple reason t1 z he himself admits 9 "o ( 8 lett]s to ,,taur9us1 he _h n publi%$ any?+ on ! subject4 ,9 ?is same lett] he in=ms ,,taur9us t he _h pond]$ ! subject = m ?an ?irty ye>s & express$ ! belief t !re c\ld n be any "o :o _h conc]n$ himself m exhau/ively ) ?is second "p 7t ! sum ( ! angles ( a triangle _c be m ?an #ahj degrees7 ?an he _h4 ,writ+ f ,gtt+5 to ,,taur9us1 ,novemb] #h1 #ahbd1 & comm5t+ ^u ! geometric value ( ! sum ( ! angles ( a triangle1 he says3 ,y\r pres5tation ( ! demon/ration t ! sum ( ! angles ( a plane triangle _c be great] ?an #ahj degrees does1 inde$1 leave some?+ to be desir$ 9 po9t ( geometrical precision4 ,b ?is c\ld be suppli$1 & !re is no d\bt t ! impossibility 9 "q admits ( ! mo/ rigor\s demon/ration4 ,b ! case is q diff]5t ) ! second "p1 namely1 t ! sum ( ! angles _c be small] ?an #ahj degrees2 ?is is ! real difficulty1 ! rock ^u :i* all endeavors are wreck$4444 ,! assumption t ! sum ( ! ?ree angles is small] ?an #ahj degrees leads to a new geometry entirely diff]5t f our ,euclidean--a geometry :i* is ?r\gh\t consi/5t ) itself1 & :i* ,i h elaborat$ 9 a mann] entirely satisfactory to myself1 s t ,i c solve e problem 9 x ) ! exception ( ! det]m9+ ( a con/ant :i* is n a priori obta9able4 ,x appe>s f ?is correspond5ce t ,,gauss _h 9 ! privacy ( 8 own /udy elaborat$ a complete non-,euclidean geometry1 & _h s ?or\ghly famili>iz$ himself ) its *>act]i/ics & possibilities t ! solution ( e problem embrac$ )9 x 0 v cle> to him except t ( ! det]m9ation ( a con/ant4 ,he conclud$ ! above lett] by say+3 ,all my endeavors to discov] contradiction or inconsi/5cies 9 ?is non-,euclidean geometry h be5 9 va91 & ! only ?+ 9 x t conflicts ) our reason is ! fact t if x 7 true !re w\ld necess>ily exi/ 9 space a l9e> magnitude q det]m9ate 9 itself2 yet unkn[n to u4 ,judg+ f ! correspond5ce betwe5 ,,gauss & ,,g]l+ 7#aghh-aheg71 ,,bessel 7#aghd-ahdf71 ,,s*uma*] & ,,taur9us1 ! nephew ( ,,s*weik>t1 & t betwe5 ,,s*weik>t & ,,g]l+1 !re _h gr[n up a g5]al dissatisfaction 9 ! m9ds ( ma!maticians ( ?is p]iod ) ,euclidean geometry & especially ! p>allel-po/ulate & its connotations4 ,,bessel expresses ?is g5]al discont5t 9 "o ( 8 lett]s to ,,gauss1 dat$ ,febru>y #aj1 #ahbi1 9 :i* he says3 ,?r\gh t :i* ,,lamb]t said & :at ,,s*weik>t disclos$ orally1 x has become cle> to me t our geometry is incomplete1 & %\ld receive a correction1 :i* is hypo!tical1 & if ! sum ( ! angles ( ! plane triangle is equal to #ahj degrees1 vani%es4 ,! op9ion ( lead+ ma!maticians at ?is "t seems to h be5 cry/alliz+ v rapidly4 ,unconsci\sly ! m5 ( ?is =mative p]iod 7 adduc+ evid5ce :i* w\ld give =m & t5d5ce to ! developm5ts 9 ! field ( ma!sis at a lat] date4 ,!y appe> to h be5 rea*+ out = t :i*1 ignis fatuus-l1 0 always )9 easy rea*1 b n q appreh5sible4 ,a bold] /ud5t ?an ,,gauss 0 ,,f]d9& ,,c>l ,,s*weik>t 7#aghj-aheg7 :o also has be5 cr$it$ ) ! f\nd+ ( ! non-,euclidean geometry4 ,9 fact1 if judg$ by ! same /&>ds z ,,gauss1 he w\ld be call$ ! fa!r ( ! geometry ( hyp]space2 = he really publi%$ ! fir/ treatise on ! subject4 ,?is 0 9 ! nature ( an inclosure :i* he ins]t$ betwe5 ! leaves ( a book he loan$ to ,,g]l+4 ,he also ask$ t x be %[n to ,,gauss t he might give 8 judgm5t z to its m]its4 ,,s*weik>t',s treatise1 dat$ ,m>burg1 ,decemb]1 #ahah1 is "h quot$ 9 full3 ,!re is a two-fold geometry--a geometry 9 ! n>r[] s5se1 ! ,euclidean1 & an a/ral sci5ce ( magnitude4 ,! triangles ( ! latt] h ! peculi>ity t ! sum ( ! ?ree angles is n equal to two "r angles4 ,?is presum$1 x c be mo/ rigor\sly prov53 7a7 ,t ! sum ( ! ?ree angles 9 ! triangle is less ?an two "r angles4 7b7 ,t ?is sum becomes ev] small]1 ! m cont5t ! angle incloses4 7c7 ,t ! altitude ( an isosceles "r-angl$ triangle inde$ ev] increases1 ! m "o l5g!ns ! side2 t x1 h[ev]1 _c surpass a c]ta9 l9e :i* ,i call ! con/ant4 ,squ>es h consequ5tly ! foll[+ =m3 ,illu/ration3 ,,fig4 #b4 ,if ?is con/ant 7 = u ! radius ( ! e>? 7s t e l9e drawn 9 ! univ]se1 f "o fix$ /> to ano!r1 di/ant #ij f ! fir/1 w\ld be a tang5t to ! surface ( ! e>?7 x w\ld be inf9itely great 9 comp>ison ) ! spaces :i* occur 9 daily life4 ,! above1 be+ ! fir/ publi%$1 n pr9t$1 treatise on ! new geometry occupies a unique place 9 ! hi/ory ( high] ma!matics4 ,x gave additional /r5g? to ! =mative t5d5cies :i* *>act]iz$ ?is p]iod & m>k$ ,,s*weik>t z a con/ructive & orig9al ?9k]4 ,! nasc5t aspects ( ?is /age receiv$ a fruitful contribution :5 ,,nicolai ,,loba*evski 7#agic-ahdg7 creat$ 8 ,imag9>y ,geometry & ,,janos ,,bolyai 7#ahjb-ahfj7 publi%$ z an app5dix to 8 fa!r's ,t5tam51 8 ,sci5ce ,absolute ( ,space4 ,,loba*evski & ,,bolyai h be5 call$ ! ,creators ( ! ,non-,euclidean ,geometry4 ,& ?is appellation seems ri*ly to be des]v$ by ^! pione]s4 ,_! "w gave j ! impetus mo/ ne$$ to fix ! /atus ( ! new l9e ( rese>*es :i* l$ to su* rem>kable discov]ies 9 ! m rec5t ye>s4 ,! ,imag9>y ,geometry & ! ,sci5ce ,absolute ( ,space 7 translat$ by ! ,fr5* ma!matician1 ,j4 ,,ho,,el 9 #ahfh & by him elevat$ out ( _! =ty-five ye>s ( obscurity & non-effectiv5ess to a position :]e !y became available = ! ma!matical public4 ,to ,,bolyai & ,,loba*evski1 consequ5tly1 belong ! honor ( />t+ ! movem5t :i* result$ 9 ! developm5t ( metageometry & h5ce t :i* has prov$ to be ! gateway ( a new ma!matical fre$om4 ,,gauss1 ,,s*weik>t1 ,,loba*evski1 ,,wolfgang & ,,janos ,,bolyai 7 ! pr9cipal figures ( ! =mative p]iod & ! value ( _! "w ) respect to ! =mulation ( pr9ciples ^u :i* 0 con/ruct$ ! ,temple ( ,metageometry _c be ov]e/imat$4 ,! ,det]m9ative ,p]iod ,?is p]iod is *>act]iz$ *iefly by its close relation%ip to ! !ory ( surfaces4 ,,riemann',s ,habilitation ,lecture on ,! ,hypo!ses ,:i* ,con/itute ! ,bases ( ,geometry m>ks ! beg9n+ ( ?is epo*4 ,9 ?is diss]tation1 ,,riemann n only promulgat$ ! sy/em ^u :i* ,,gauss _h sp5t m ?an ?irty ye>s ( 8 life 9 elaborat+1 = he 0 a disciple ( ,,gauss2 b he disclos$ 8 own views ) respect to space :i* he reg>d$ z a p>ticul> case ( manifold4 ,8 "w conta9s two fundam5tal concepts1 namely1 ! manifold & ! measure ( curvature ( a cont9u\s manifold1 possess$ ( :at he call$ flatness 9 ! smalle/ p>ts4 ,! conception ( ! measure ( curvature is ext5d$ by ,,riemann f surfaces to spaces & a new k9d ( space1 f9ite1 b unb\nd$1 is %[n to be possible4 ,he %[$ t ! dim5sions ( any space are det]m9$ by ! numb] ( measurem5ts necess>y to e/abli% ! position ( a po9t 9 t space4 ,conceiv+1 !re=e1 t space is a manifold ( f9ite1 b unb\nd$1 ext5sion1 he e/abli%$ ! fact t ! passage f "o elem5t ( a manifold to ano!r may be ei!r discrete or cont9u\s & t ! manifold is discrete or cont9u\s accord+ to ! mann] ( passage4 ,:]e ! manifold is reg>d$ z discrete two portions ( x c be comp>$1 z to magnitude1 by c\nt+2 :]e cont9u\s1 by measurem5t4 ,if ! :ole manifold be caus$ to pass ov] into ano!r manifold ea* ( its elem5ts pass+ ?r\gh a "o-dim5sional manifold1 a two-dim5sional manifold is ?us g5]at$4 ,9 ?is way1 a manifold ( n-dim5sions c be g5]at$4 ,on ! o!r h&1 a manifold ( n-dim5sions c be analyz$ into "o ( "o dim5sion & "o ( 7n-#a7 dim5sions4 ,to ,,riemann1 !n1 is due ! cr$it = fir/ promulgat+ ! idea t space be+ a special case ( manifold is g5]able1 & !re=e1 f9ite4 ,he laid ! f\ndation = ! e/abli%m5t ( a special k9d ( geometry kn[n z ! elliptic4 ,space1 z view$ by him1 possess$ ! foll[+ prop]ties1 viz43 g5]ability1 divisibility1 measurability1 pond]ability1 f9ity & flexity4 ,^! are ! six pill>s ^u :i* re/s ! /ructure ( hyp]space analyses4#e #e ,vide ,nature1 ,vol4 ,,viii1 pp4 #ad-ag2 #cf1 #cg 7#ahgc72 also ,ma!matical ,pap]s1 pp4 #fe-ga4 ,g5]ability is t prop]ty ( geometric space by virtue ( :i* x may be g5]at$1 or con/ruct$1 by ! movem5t ( a l9e1 plane1 surface or solid 9 a direction )\t itself4 ,divisibility is t prop]ty ( geometric space by virtue ( :i* x may be segm5t$ or divid$ into sep>ate p>ts & sup]pos$1 or ins]t$1 ^u or betwe5 ea* o!r4 ,measurability is t prop]ty by virtue ( :i* geometric space is det]m9$ to be a manifold ( ei!r a positive or negative curvature1 also by :i* its ext5t may be measur$4 ,pond]ability is t prop]ty ( geometric space by virtue ( :i* x may be reg>d$ z a quantity :i* c be manipulat$1 assort$1 %elv$ or o!rwise dispos$ (4 ,f9ity is t prop]ty by virtue ( :i* geometric space is limit$ to ! scope ( ! individual consci\sness ( a unodim1 a duodim or a tridim & by virtue ( :i* x is f9ite 9 ext5t4 ,flexity is t prop]ty by virtue ( :i* geometric space is reg>d$ z possess+ curvature1 & 9 consequ5ce ( :i* progress ?r\gh x is made 9 a curv$1 r ?an a geodetic l9e1 also by virtue ( :i* x may be flex$ )\t disruption or dilatation4 ,,riemann :o ?us prep>$ ! way = entrance into a v]itable labyr9? ( hyp]spaces is1 !re=e1 correctly /yl$ ,! fa!r ( metageometry1 & ! f\r? dim5sion is 8 elde/ born4 ,he di$ :ile b =ty ye>s ( age & nev] liv$ long en\gh fully to elaborate 8 !ory ) respect to its application to ! measure ( curvature ( space4 ,?is 0 left = 8 v en]getic disciple1 ,,eug5io ,,beltrami 7#ahce-aijj7 :o 0 born n9e ye>s aft] ,,riemann & liv$ ?irty-f\r ye>s long] ?an he4 ,8 labors m>k ! *>act]i/ic /&po9t ( ! det]m9ative p]iod4 ,,beltrami',s ma!matical inve/igations 7 devot$ ma9ly to ! non-,euclidean geometry4 ,^! l$ him to ! r rem>kable conclusion t ! propositions embodi$ !re9 relate to figures ly+ ^u surfaces ( con/ant negative curvature4 ,,beltrami s\ght to %[ t su* surfaces p>take ( ! nature ( ! pseudosph]e1 & 9 do+ s1 made use ( ! foll[+ illu/ration3 ,illu/ration3 ,,fig4 #c4 ,illu/ration3 ,,fig4 #d4 ,if ! plane figure aabb is made to revolve ^u its axis ( symmetry ,,ab ! two arcs1 ab & ab w describe a pseudosph]ical concave-convex surface l t ( a solid an*or r+4 ,above & bel[1 t[>d aa & bb1 ! surface w turn outw>d ) ev]-increas+ flexure till x becomes p]p5dicul> to ! axis & ends at ! edge ) "o curvature inf9ite4 ,or1 ! half ( a pseudosph]ical surface may be roll$ up into ! %ape ( a *ampagne glass1 z 9 ,fig4 #d4 ,9 ?is way1 ! two /raighte/ l9es ( ! pseudosph]ical surface may be indef9itely produc$1 giv+ a k9d ( space 7pseudosph]ical7 9 :i* ! axiom ( p>allels does n hold true4 ,! det]m9ative p]iod m>ks ! mo/ important /age 9 ! developm5t ( non-,euclidean geometry & c]ta9ly ! mo/ significant 9 ! evolution ( ! idea ( hyp]spaces & multiple dim5sionality4 ,,riemann & ,,beltrami are *ief among ^? ^: labors *>act]ize ! scope ( ?is p]iod4 ,_! "w gave direction & g5]al outl9e = lat] developm5ts & all subsequ5t rese>*es along ^! l9es h be5 conduct$ 9 /rict con=mity ) ! pr9ciples laid d[n by ^! pione] con/ructioni/s4 ,!y laid out ! field & designat$ its conf9es beyond :i* no adv5tur] has s9ce d>$ to pass4 ,! great importance ( ! "w ( ,,riemann at ?is "t may be se5 fur!r 9 ! fact t x n only m>k$ ! beg9n+ ( a new epo* 9 geometry2 b 8 pron\ncem5t ( ! hypo!sis t space is unb\nd$1 ?\gh f9ite1 is really ! fir/ "t 9 ! hi/ory ( human ?\ght t expression 0 ev] giv5 to ! idea t space may yet be only ( limit$ ext5t4 ,be=e t "t ! m9ds ( all m5 seem$ to h be5 unanim\s 9 ! consid]ation ( space z an illimitable & inf9ite quantity4 ,! ,elaborative ,p]iod ,! elaborative /age includes ! "w ( all ^? :o1 work+ ^u ! bases laid d[n by ,,loba*evski1 ,,bolyai1 ,,s*weik>t & ,,riemann1 h s\ght to amplify ! conclusions rea*$ by !m4 ,among ^? ^: inve/igations h greatly multipli$ ! applications ( hyp]space conceptions are ,,ho,,el 7#ahff7 & ,,flye ,,/4 ,,m>ie 7#ahga7 ( ,france2 ,,helmholtz 7#ahfh71 ,,fris*auf 7#ahgb71 ,,kle9 7#ahdi71 & ,,baltz] 7#ahgg7 ( ,g]many2 ,,beltrami 7#ahgb7 ( ,italy2 ,,de ,,tilly 7#ahgi7 ( ,belgium2 ,,clif=d & ,,cayley 7#ahba7 ( ,engl&2 ,,newcomb 7#ahce7 & ,,hal/ead ( ,am]ica4 ,^! h be5 mo/ active 9 popul>iz+ ! subject ( non-,euclidean geometry & incid5tally ! idea ( ! f\r? dim5sion4 ,! great mass ( non-pr(essional ma!matical read]s1 !re=e1 owe ^! m5 an immeasurable debt ( gratitude = ! "w t !y h done 9 ! matt] ( r5d]+ ! conceptions :i* con/itute ! fabric ( metageometry und]/&able & ?9kable4 ,a glance at ! bibliography app5d$ at ! end ( ?is volume w give "s idea ( ! enorm\s am\nt ( labor t has be5 exp5d$ 9 an ef=t to translate ! mo/ ab/ract ma!matical pr9ciples into a language t c\ld easily be compreh5d$ by ! av]age intellig5t p]son4 ,! *>act]i/ic /&po9t ( ?is p]iod is ! popul> compreh5sion ( ! hyp]space concept & ! consequ5t m5tal lib]ation :i* foll[s4 ,= !re is no d\bt b t unhe>d ( possibilities ( ?\ght h be5 reveal$ by inve/igations into ! nature ( space4 ,an entirely new _w has be5 op5$ to view & only a beg9n+ has be5 made at ! exploration ( its ext5t & res\rces4 ,"o ( ! notable incid5ts ( ! e>ly ye>s ( ?is p]iod is ! position tak5 by ,,felix ,,kle9 :o /&s 9 ab\t ! same relation to ,,cayley z ,,beltrami does to ,,riemann1 9 t he assum$ ! task ( complet+ ! "w ( 8 pr$ecessor4 ,,kle9 held t !re are only two k9ds ( ,,riemannian space--! elliptical & ! sph]ical4 ,or 9 o!r words1 t !re are only two possible k9ds ( space 9 :i* ! propositions ann\nc$ by ,,riemann c\ld apply4 ,,sophus ,,lie1 call$ ! great comp>ative anatomi/ ( geometric !ories1 c>ri$ 8 classifications to a f9al conclusion 9 connection ) spaces ( all k9ds & decid$ t !re are possible only f\r k9ds ( ?ree dim5sional spaces4 ,b :e!r m5 ) pe]+1 microscopic1 hi/ological vision %all e/abli% ! exi/5ce ( "o or _m spaces1 & reg>dless ( ! ma!matic rigor ) :i* !y %all demon/rate ! self-consi/5cy ( ! doctr9es :i* !y hold1 ! fact rema9s t ! hypo!ses ?us ma9ta9$1 :ile !y may be reg>d$ z true descriptions ( ! spaces conc]n$1 are1 nev]!less1 incompatible4 ,all ( !m _c be valid4 ,x w p]haps be f\nd t none ( !m are valid1 especially objectively s4 ,! only true view1 !re=e1 ( ^! sy/ems ( hyp]spaces is t :i* assigns !m to _! rightful place 9 ! inf9itely va/ _w ( pure ma!sis :]e _! validity may g un*all5g$ & _! exi/5ce unque/ion$2 = 9 t doma9 ( unconf9$ m5tation1 9 t realm ( div9e intuitability1 ! m>vel\s wond]l& ( ideas & notions1 "o is n only dis9cl9$ to d\bt _! logical actuality1 b is q will+ to acc$e _! claims4 ,,*apt] ,,iii ,,ess5tials ,,( ,,! ,,non-,,euclidean ,,geometry ,! ,non-,euclidean ,geometry ,conc]n$ ) ,conceptual ,space ,entirely--,outcome ( ,failures at ,solv+ ! ,p>allel-,po/ulate--,! ,basis ( ! ,non-,euclidean ,geometry--,space ,curvature & ,manifoldness--,"s ,elem5ts ( ! ,non-,euclidean ,geometry--,c]ta9ty1 ,necessity & ,univ]sality z ,bulw>ks ( ,geometry--,"s ,consequ5ces ( ,ef=ts at ,solv+ ! ,p>allel-,po/ulate--,! ,f9al ,issue ( ! ,non-,euclidean ,geometry--,ext5d$ ,consci\sness4 ,! t]m non-,euclidean is us$ to designate any sy/em ( geometry :i* is n /rictly ,euclidean 9 cont5t4 ,x is int]e/+ to note h[ ! t]m came to be us$4 ,x appe>s to h be5 employ$ fir/ by ,,gauss4 ,he did n /rike ^u x sudd5ly1 h[ev]1 z 9 ! correspond5ce betwe5 him & ,,wa*t] 9 #ahaf he us$ ! designation anti-,euclidean & !n1 lat]1 foll[+ ,,s*weik>t1 he adopt$ ! latt]'s t]m9ology & call$ x ,a/ral ,geometry4 ,?is he f\nd 9 ,,s*weik>t',s fir/ publi%$ treatise kn[n by t "n & :i* made its appe>ance at ,m>burg 9 ,decemb]1 #ahah4 ,f9ally1 9 8 correspond5ce ) ,,taur9us 9 #ahbd1 ,,gauss fir/ us$ ! expression non-,euclidean to designate ! sy/em :i* he _h elaborat$ & cont9u$ to use x 9 8 correspond5ce ) ,,s*uma*] 9 #ahca4 ,non-,leg5drean1 semi-,euclidean & non-,ar*im$ean are titles us$ by ,m4 ,,dehn to d5ote all k9ds ( geometries :i* repres5t$ v>iations f ! hypo!ses laid d[n by ,,leg5dre1 ,,euclid & ,,ar*im$es4 ,! semi-,euclidean is a sy/em ( geometry 9 :i* ! sum ( ! angles ( a triangle is said to be equal to two "r angles1 b 9 :i* "o may draw an inf9ity ( p>allels to a /raight l9e ?r\gh a giv5 po9t4 ,! non-,euclidean geometry embraces all ! results obta9$ z a consequ5ce ( ef=ts made at f9d+ a satisfactory pro( ( ! p>allel-po/ulate & is1 !re=e1 bas$ ^u a conception ( space :i* is at v>iance ) t held by ,,euclid4 ,accord+ to ! ,ionian s*ool space is an inf9ite cont9uum possess+ uni=mity ?r\gh\t its entire ext5t4 ,! non-,euclideans ma9ta9 t space is n an inf9ite ext5sion2 b a f9ite ?\gh unb\nd$ manifold capable ( be+ g5]at$ by ! movem5t ( a po9t1 l9e or plane 9 a direction )\t itself4 ,x is also held t space is curv$ & exi/s 9 ! %ape ( a sph]e or pseudosph]e & is consequ5tly elliptical4 ,! inapplicability ( ,,euclid's p>allel-po/ulate to l9es drawn ^u ! surface ( a sph]e sugge/$ ! possibility ( a space 9 :i* ! po/ulate c\ld apply to all possible surfaces or t space itself may be sph]ical 9 :i* case ! po/ulate w\ld be invalidat$ altoge!r4 ,h5ce1 x is q natural t ma!maticians f9d+ !mselves unable to prove ! po/ulate ) due ma!tic precision %\ld turn _! att5tion to ! conceptually possible4 ,9 ?is virtual ab&onm5t ( ! p]ceptual = ! conceptual lies ! fundam5tal diff]5ce betwe5 ! ,euclidean & ! non-,euclidean geometries4 ,x may be said to ! cr$it ( ! ,euclideans t !y h s\ght to make _! geometric conceptions con=m z closely z possible to ! actual nature ( ?+s 9 ! s5su\s _w :ile at ! same "t !y mu/ h p]ceiv$ t at be/ _! spatial notions 7 only approximations to ! s5su\s actuality ( objects 9 space4 ,on ! o!r h&1 non-,euclideans make no pret5se at discov]+ any congru5cy betwe5 _! notions & ?+s z !y actually are4 ,! attitude ( ! metageometricians 9 ?is respect is v aptly describ$ by ,,cassius ,,jackson ,,keys] :o says3 ,he con/ructs 9 ?\ght a summitless hi]>*y ( hyp]spaces1 an endless s]ies ( ord]ly worlds1 worlds t are possible & logically actual1 & he is cont5t n to "k if any ( !m be o!rwise actual or actualiz$4#f #f ,ma!matics1 by ,c4 ,j4 ,,keys]1 ,adrian ,pr(essor ( ,ma!matics1 ,columbia ,univ]sity4 ,! non-,euclidean is1 !re=e1 n conc]n$ ab\t ! applicability ( ensembles1 notions & propositions to real1 p]ceptual space conditions4 ,x is suffici5t = him to "k t 8 creations are ?9kable4 ,z soon z he c resolve ! nebulosity ( 8 consci\sness into ! conceptual />-=ms ( def9ite ideas & notions1 he sits d[n to ! fea/ :i* he f9ds provid$ by sup]foetat$ hypo!ses fabricat$ 9 ! deeps ( m9d & logical actualities imp]turb$ & unm9dful ( ! weal ( p]ceptual space 9 its homog5eity ( =m & dim5sionality4 ,fundam5tally1 ! non-,euclidean geometry is con/ruct$ ^u ! basis ( conceptual space almo/ entirely4 ,k ( its cont5t is accord+ly d]iv$ f a sup]p]ceptual repres5tation ( relations & int]relations subsi/+ betwe5 & among notions1 ideas1 propositions & magnitudes aris+ out ( a conceptual consid]ation !re(4 ,9 o!r words1 repres5tations ( ! non-,euclidean magnitudes1 _c be said to be /rictly p]ceptual 9 ! same s5se t ?ree-space magnitudes are p]ceiv$2 = ?ree-space magnitudes are really s5se objects :ile hyp]space magnitudes are n s5se objects4 ,!y are f> remov$ f ! s5su\s _w & 9 ord] to conceive !m "o mu/ raise 8 consci\sness f ! s5su\s plane to ! conceptual plane & become aw>e ( a class ( p]ceptions :i* are n p]ceptions 9 ! /rict s5se ( ! ^w1 b sup]p]ceptions2 because !y are repres5tations ( concepts r ?an precepts4 ,notions ( p]ceptual space are con/itut$ ( ! triple pres5tations aris+ out ( ! visual1 tactual & motor s5sations :i* are fus$ toge!r 9 _! f9al deliv]y to ! consci\sness4 ,! syn!sis ( ^! ?ree s5se-deliv]ies is accompli%$ by equilibrat+ _! respective diff]5ces & by correct+ ! p]ceptions ( "o s5se by ^? ( ano!r 9 su* a way z to obta9 a completely reliable p]ception ( ! object4 ,?is is ! mann] 9 :i* ! *>act]i/ics ( ,euclidean space are e/abli%$4 ,! *>act]i/ics ( non-,euclidean space are n arriv$ at exactly 9 ?is way4 ,be+ beyond ! scope ( ! visual1 tactile & motor s5se appreh5sions1 x _c be said to repres5t judgm5ts d]iv$ f any consid]ation or elaboration ( ! deliv]ies pres5t$ ?r\gh ^! m$ia4 ,yet1 ! sub/ance ( metageometry1 or ! sci5ce ( ! measurem5t ( hyp]spaces1 may n be reg>d$ z an a priori sub/ructure ^u :i* ! sy/em is f\nd$4 ,t is1 ! conceptual space ( non-,euclidean geometry is n pres5t$ to ! consci\sness z an a priori notion4 ,on ! o!r h&1 ! a po/]iori/ic quality ( metageometric spaces m>ks ! entire scope ( motility ( ! notions app]ta9+ !reto4 ,! notions1 !re=e1 ( conceptual space are d]ivable only f ! p]ception ( concepts1 or1 o!rwise consi/ ( judgm5ts conc]n+ int]conceptual relations4 ,! process ( app]ception involv$ 9 ! recognition ( relations :i* may be me?odically det]m9$ is mu* remov$ f ! prim>y proc$ure ( p]ceiv+ s5se-impressions & fus+ !m into f9al deliv]ies to ! consci\sness = conceptualization or ! elaboration into concepts or g5]al notions4 ,x is a proc$ure :i* is 9 e way sup]conceptual & extra-s5su\s4 ,! metageometrician or analy/ 9 no way relies ^u s5se-deliv]ies = ! data ( 8 con/ructions2 =1 if he did1 he %\ld1 !n1 be r$uc$ to ! necessity ( conf9+ 8 conclusions to ! sph]e ( motility impos$ by ! s5sible _w ) ! result t we %\ld be able to v]ify empirically all 8 po/ulations4 ,b1 contr>ily1 he goes to ! extra-s5su\s1 & !re 9 ! realm ( pure conceptuality1 he f9ds ! requisite fre$om = 8 !ories2 ?us1 environ$ by a sort ( intellectual an>*ism1 he pursues analytical pleasures q unre/ra9$ly4 ,! diff]5ce betwe5 ! two m5tal processes--t :i* leads f ! s5sible _w to conception & t :i* ve]s into ! fields beyond--is s great t x is h>dly p]missible to view ! results arriv$ at 9 ! outcome ( ! sep>ate processes z be+ id5tical4 ,to illu/rate ?is diff]5ce1 let u draw an analogy4 ,! m9] digs ! iron ore out ( ! gr\nd4 ,! iron is sep>at$ f ! extrane\s mat]ial & deliv]$ to ! furnaces :]e ! metal is melt$ & turn$ out z pig iron4 ,x is fur!r treat$1 & /eel1 ( v>i\s grades1 ca/ iron & o!r k9ds ( iron are produc$4 ,! treatm5t ( ! iron ore up to ?is /age is simil> to ! treatm5t ( s5se-impressions by ! ,?9k]4 ,/eel1 ca/ iron1 et cet]a1 are simil> to m5tal concepts4 ,lat]1 ! /eel & o!r products are conv]t$ into in/rum5ts & num]\s articles4 ,?is repres5ts ! sup]p]ceptual process4 ,traffick+ 9 iron ore products1 su* z in/rum5ts ( precision1 wat* spr+s1 & ! l1 repres5ts a /age /ill f>!r remov$ f ! prim>y treatm5t ( ! ore & is simil> to t to :i* concepts are treat$ :5 ! metageometrician manipulates !m 9 ! con/ruction ( conceptual space-=ms4 ,p]ception is ! deal+ ) raw iron ore :ile conception is analog\s to ! production ( ! f9i%$ product4 ,sup]p]ception w\ld be analog\s to ! traffick+ 9 ! f9i%$ product z su* & )\t any ref]5ce to ! s\rce or ! prec$+ processes4 ,?us ! notions & judgm5ts ( ! non-,euclidean geometry are arriv$ at z a result ( a triple process ( p]ception1 conception & sup]p]ception ! latt] be+ m]ely sup]conceiv$ z =mal space-notions4 ,b x is obvi\s t ! m complex ! processes by :i* judgm5ts purport+ to relate to p]ceptual ?+s are d]iv$ ! m likely are ^? judgm5ts to be at v>iance ) ! nature ( ! ?+s !mselves4 ,9 view ( ! =ego+1 ! dang]s result+ f id5tify+ ! products ( ! two processes are v obvi\s inde$4 ,b ! diff]5ce betwe5 ! two proc$ures is ! diff]5ce betwe5 ,euclidean & non-,euclidean geometries or ! diff]5ce betwe5 p]ceptual space notions & conceptual space notions4 ,h5ce1 x is n und]/ood j h[ or :y x has occurr$ to anyone t ! two notions c\ld be made congru5t4 ,magnitudes 9 p]ceptual1 s5sible space are ?+s ap>t f ^? t may be said to exi/ 9 ma!matical space or t space ^: qualities & prop]ties h no exi/5ce outside ( ! m9d :i* has conceiv$ !m4 ,x is believ$ to be q impossible to approa* ! /udy ( metageometrical propositions ) a cle>1 op5 m9d )\t previ\sly und]/&+ ! fundam5tal di/9ctions :i* exi/ betwe5 !m4 ,x foll[s1 !re=e1 z a logical conclusion t geometric space ( :atsoev] nature is a purely =mal con/ruction ( ! intellect1 & = ?is reason is completely "u ! sov]eignty ( ! intellect h[ev] :imsical its dem&s may be4 ,be+ ?us ! creature ( ! intellect1 its possibilities are limit$ only by ! limitations ( ! intellect itself4 ,p]ceptual space1 be+ nei!r ! creature ( ! intellect nor necess>ily an a priori notion resid5t 9 ! m5tal sub/ructure1 b exi/+ entirely indep5d5t ( ! intellect or its appreh5sion !re(1 _c be expect$ to con=m to ! purely =mal re/rictions impos$ by ! m9d except 9 s f> z ^? re/rictions may be det]m9$ by ! nature ( p]ceptual space4 ,& = t matt]1 x %\ld n be =gott5 t1 z yet1 we h no means ( det]m9+ :e!r or n ! te/imony ( ! intellect is ?or\ghly cr$ible simply because !re is no o!r /&>d by :i* we may prove its te/imony4 ,x is possible to ju/ify ! deliv]ies ( ! eye by ! s5se ( t\*1 or vice v]sa4 ,x is also possible to prove all our s5se-deliv]ies by "o or ! o!r ( ! s5ses4 ,b we h no su* good =tune ) ! deliv]ies ( ! intellect4 ,we h simply to accept its te/imony z f9al2 because we _c d any bett]4 ,b if x 7 possible to correct ! te/imony ( ! intellect by "s o!r faculty or p[] :i* by nature might be m accurate ?an ! intellect x %\ld be f\nd t ! intellect itself is sadly limit$4 ,! possible curvature ( space is a notion :i* also *>act]izes ! cont5t ( ! non-,euclidean geometry4 ,x is ^u ?is notion t ! "q ( ! f9ity & unb\nd$ness ( space1 9 ! ma!matical s5se1 re/s4 ,9 ! curv$ space1 ! /raighte/ l9e is a curv$ l9e :i* returns ^u itself4 ,progression ea/w>d br+s "o to ! we/2 progression nor?w>d br+s "o to ! s\?1 et cet]a4 ,on ?is view space is f9ite1 b may n be reg>d$ z possess+ b\nd>ies4 ,space-curvature1 re9=c$ by ! idea t space is also a manifold is ! enabl+ clause ( metageometry & )\t !m ! analy/ d>es n proce$4 ,"h aga91 we are l$ to ! confession t h[ev] fanta/ic ^! two notions may seem & evid5tly are1 !re is nev]!less to be recogniz$ 9 !m a dim glimpse ( a v]itable reality--a slight =e%ad[+ ( ! revelation ( "s great kosmic my/]y4 ,! manifoldness ( space is ! fiat ( analysis4 ,x is ! inevitable outcome ( ! analy/'s me?od ( proc$ure4 ,8 education1 tra9+ & view ( ?+s 9 g5]al inhibit 8 arriv+ at any o!r result & he may be p>don$ ) good grace = 8 manufacture ( ! space-manifold4 ,= by x p]haps a bett] appreciation ( t wond]ful ext5sion ( consci\sness 9 ! nature ( :i* is involv$ ! explanation ( ! p]plex+ problems :i* ! manifold & o!r metageometrical exp$i5ts fa9tly adumbrate may be ga9$4 ,x is p]t95t1 9 ! light ( ! above1 to exam9e into "s ( ! relative m]its ( ! ?ree =mal bulw>ks ( geometrical k4 ,^! are c]ta9ty1 necessity & univ]sality4 ,geometric c]ta9ty is d]iv$ solely f ! nature ( ! premises ^u :i* x is bas$4 ,if ! premises be contradictory1 x is1 ( c\rse1 defective4 ,b if ! premises are non-contradictory or self-evid5t1 !n ! c]ta9ty ( geometric notions & conclusions is valid4 ,ano!r consid]ation ( prime importance 9 ?is connection is ! def9ition4 ,f x all premises proce$4 ,h5ce1 ! def9ition is ev5 m important ?an ! premise2 = x is ! p]si/+ det]m9ant ( all geometric conclusions :ile ! premise is dep5d5t ^u ! limitations ( ! def9ition4 ,! det]m9ative "* ( ! def9ition has l$ to its apo!osis2 b ?is1 admitt$ly1 has be5 necess>y 9 ord] to give /ability & p]man5cy to ! conclusions :i* foll[$4 ,b 9 spite ( ?is x w\ld appe> t ! c]ta9ty ( geometric conclusions is n a quality to be reckon$ z absolute or f9al4 ,) ! same c]ta9ty t x c be said ! sum ( ! angles ( ! triangle is equal to two "r angles x may be ass]t$ t t sum is also great] or less ?an two "r angles4 ,c]ta9ty :i* is bas$ ^u ! inh]5t congruity ( def9itions1 premises & propositions is an entirely diff]5t matt] f t c]ta9ty :i* arises out ( ! real1 abid+ validity ( a s*eme ( ?\ght4 ,b ?is diff]5ce is n less5$ by ! fact t ! latt] is dep5d5t1 9 a measure1 ^u ! correct sy/ematization ( our spatial exp]i5ces by means ( me?odical processes4 ,euclidean geometry1 accord+ly1 is n s c]ta9 9 its applications z x is utilit>ian2 b non-,euclidean geometry is ev5 less c]ta9 ?an ! =m] & consequ5tly m lack+ 9 its utilit>ian possibilities4 ,! necessity ( geometrical det]m9ations is m]ely ! necessity :i* inh]es 9 logical inf]5ces or d$uctions4 ,^! may or may n be valid4 ,inasmu* z ! necess>9ess ( d$uctions is prim>ily bas$ ^u ! conditional c]ta9ty ( premises & def9itions x appe>s t ?is quality is 9 no way peculi> to geometry :e!r ,euclidean or non-,euclidean4 ,9 l mann]1 ! univ]sality ( geometric judgm5ts may n prop]ly be reg>d$ z a peculi>ity ( geometry2 b is explicable ^u ! basis ( ! =mal "* ( ! assumptions :i* und]lie x4 ,! *ief value1 !n1 ( non-,euclidean geometry seems to abide 9 ! fact t x cl>ifies our und]/&+ z to ! complex processes by :i* x is possible to organize & sy/ematize our spatial exp]i5ces = assimilation & use 9 o!r bran*es ( k4 ,) ! above /atem5t ( ! case ( ! non-,euclidean geometry x is n[ ?\ght p]missible to /ate briefly "s ( ! elem5ts !re(4#g #g ,! sci5ce ( pure ma!matics is p]haps indebt$ to no "o 9 s great a degree z to ,,george ,,bruce ,,hal/ead1 =m]ly ( ! ,univ]sity ( ,texas1 ^: labors 9 connection ) ! popul> exposition ( ! non-,euclidean geometry h be5 mo/ untir+ & effectual4 ,vide ,popul> ,a/ronomy1 ,vol4 ,,vii & ,,viii1 #aijj1 ,dr4 ,g4 ,b4 ,,hal/ead4 ,bel[ w be f\nd "s ( ! elem5ts obta9$ z a consequ5ce ( ef=ts made bo? at prov+ & disprov+ ! p>allel-po/ulate ( ,euclid3 ,if two po9ts det]m9e a l9e x is call$ a /raight4 ,if two /raights make ) a transv]sal equal alt]nate angles !y h a common p]p5dicul>4 ,a piece ( a /raight is call$ a sect4 ,if two equal coplan> sects are erect$ p]p5dicul> to a /raight1 if !y d n meet1 !n ! sect jo9+ _! extremities makes equal angles ) !m & is bisect$ by a p]p5dicul> erect$ midway betwe5 _! feet4 ,! sum ( ! angles ( a rectil9eal triangle is a /raight angle1 9 ! hypo!sis ( ! "r 7angle72 is great] ?an a /raight angle 9 ! hypo!sis ( ! obtuse 7angle72 is less ?an a /raight angle 9 ! hypo!sis ( ! acute 7angle74 ,! hypo!sis ( "r is ,euclidean2 ! hypo!sis ( ! acute is ,,bolyai-,,loba*evskian2 ! hypo!sis ( obtuse is ,,riemannian4 ,if "o /raight is p>allel to a second ! second is p>allel to ! fir/4 ,p>allels cont9ually approa* ea* o!r4 ,! p]p5dicul>s erect$ at ! middle po9t ( ! sides ( a triangle are all p>allel1 if two are p>allel4 ,if ! foot ( a p]p5dicul> slides on a /raight its extremity describes a curve call$ an equidi/ant curve1 or an equidi/antial4 ,an equidi/antial w slide on its trace4 ,9 ! hypo!sis ( ! obtuse a /raight is ( f9ite size & returns into itself4 ,two /raights always int]sect4 ,two /raights p]p5dicul> to a ?ird /raight int]sect at a po9t half a /raight f ! ?ird ei!r way4 ,a pole is half a /raight f its pol>4 ,a pol> is ! locus ( coplan> po9ts half a /raight f its pole4 ,!re=e1 if ! pole ( "o /raight lies on ano!r /raight ! pole ( ?is second /raight is on ! fir/ /raight4 ,! cross ( two /raights is ! pole ( ! jo9 ( _! poles4 ,any two /raights inclose a plane figure1 a digon4 ,two digons are congru5t if _! angles are equal4 ,! equidi/antial is a circle ) c5t] at ! poles ( its basal /raight4 ,a typical po/ulate bas$ ^u ! ,,bolyai hypo!sis ( ! acute angle is ! foll[+3 ,f any po9t ,p drop ,,pc1 a p]p5dicul> to any giv5 /raight l9e ,,ab4 ,if ,d move (f indef9itely on ! ray ,,cb1 ! sect w approa* z limit ,,pf copunctal ) ,,ab at inf9ity4 ,illu/ration3 ,,fig4 #e4 ,,pd is said to be at ,p ! p>allel to ,,ab t[>d ,b4 ,,pf makes ) ,,pc an angle ,,cpf :i* is call$ ! angle ( p>allelism = ! p]p5dicul> ,,pc4 ,x is less ?an a "r angle by an am\nt :i* is ! limit ( ! defici5cy ( ! triangle ,,pcd4 ,on ! o!r side ( ,,pc1 an equal angle ( p>allelism gives ! p>allel ,p to ,,ba t[>ds ,,am4#h ,?us at any po9t !re are two p>allels to a /raight4 ,a /raight has1 !re=e1 two sep>ate po9ts at inf9ity4 ,/raights ?r\gh ,p :i* make ) ,,pc an angle great] ?an ! angle ( p>allelism & less ?an its supplem5t d n meet ! /raight ,,ab at all n ev5 at inf9ity4 #h ,,note4--,m may be any po9t on ! l9e ,,ba indef9itely produc$4 ,! p>allel-po/ulate is /at$ 9 ! non-,euclidean geometry z foll[s3 ,if a /raight l9e meet+ two /raight l9es make ^? angles :i* are inw>d & ^u ! same side ( x less ?an two "r angles ! two /raight l9es be+ produc$ indef9itely w meet ea* o!r on ?is side :]e ! angles are less ?an two "r angles4 ,x is /at$ by ,,mann+#i 9 ! foll[+ language3 ,if two l9es are cut by a ?ird & ! sum ( ! int]ior angles on ! same side ( ! cutt+ l9e is less ?an two "r angles ! l9e w meet on t side :5 suffici5tly produc$4 ,x is r significant t 9 ?is po/ulate :i* is really a def9ition ( space %\ld be f\nd gr\nds = su* div]se int]pretations z to its nature4 ,( c\rse1 ! mom5t ! m9d seeks to und]/& ! inf9ite by int]pret+ x 9 ! unmodifi$ t]ms ( ! app>5tly un*angeable f9ite x entangles itself into insurm\ntable difficulties4 ,z a dr[n+ man grasps aft] /raws s ! m9d1 imm]s$ 9 endless abysses ( inf9ity1 fails to conduct itself 9 a seemly mann]2 b gasps1 /ruggles & fl\nd]s & is happy if x c1 9 ! dep?s ( its p]plexity1 discov] a way ( logical escape4 ,! pure ma!matician has a hank]+ aft] ! logically consi/5t 9 all 8 pursuits2 to him x is ! ,holy ,grail ( 8 highe/ aspirations4 ,he seeks x z ! devotee seeks immortality4 ,x is to him a philosoph]'s /one1 ! elixir ( p]petual y\?1 ! et]nal crit]ion ( all k4 #i ,vide ,non-,euclidean ,geometry1 p4 #ia4 ,failures to demon/rate ! celebrat$ po/ulate ( ,,euclid l$1 z a matt] ( c\rse1 to ! sub/itution ( v>i\s o!r po/ulates m or less equival5t to x 9 t ea* ( !m may be d$uc$ f ! o!r )\t ! aid ( any new hypo!sis4 ,among ^? :o s\ght pro( by a re/atem5t ( ! problem are ! foll[+3 #a4 ,,ptolemy3 ,! int]nal angles :i* two p>allels make ) a transv]sal on ! same side are supplem5t>y4 #b4 ,,clavius3 ,two p>allel /raight l9es are equidi/ant4 #c4 ,,proclus3 ,if a /raight l9e int]sects "o ( two p>allels x also int]sects ! o!r4 #d4 ,,wallis3 ,a triangle be+ giv5 ano!r triangle c be con/ruct$ simil> to ! giv5 "o & ( any size :atev]4 #e4 ,,bolyai 7,w473 ,?r\gh ?ree po9ts n ly+ on a /raight l9e a sph]e c always be drawn4 #f4 ,,lor5z3 ,?r\gh a po9t betwe5 ! l9es b\nd+ an angle a /raight l9e c always be drawn :i* w int]sect ^! two l9es4 #g4 ,,sac*]i3 ,! sum ( ! angles ( a triangle is equal to two "r angles4 ,!re 71 ( c\rse1 _m o!r /atem5ts & sub/itutions us$ by ma!maticians 9 _! endeavors satisfactorily to e/abli% ! tru? ( ! p>allel-po/ulate4 ,t _! labors %\ld h t]m9at$1 fir/1 by d\bt+ x1 !n by d5y+1 & f9ally1 by build+ up a sy/em ( geometries :i* altoge!r ignores ! po/ulate is j :at might naturally be expect$ ( ^! m5 :o h giv5 to ! _w ! non-,euclidean geometry4 ,9 do+ :at !y did _m1 if n all ( !m1 7 n aw>e 9 any measure ( ! proportions ( ! impos+ sup]/ructure t w\ld be built ^u _! app>5t failures4 ,all ( !m und\bt$ly mu/ h s5s$ ! vague adumbrations =eca/ by ! unfold+ my/]ies :i* !y s\ght to lay b>e2 all ( !m mu/ h felt z !y execut$ ! e>ly tasks ( ^? crepuscul> days ( pure ma!matics t ! way :i* !y 7 travel+ w\ld lead to ! inn] %r9e ( a high] k & a wid] fre$om2 !y may h be5 l$ by div9e intuition to /rike out on ?is new pa? & yet !y c\ld n h kn[n h[ fully _! dreams w\ld be realiz$ by ! ma!maticians ( ! tw5tie? c5tury4 ,if s1 !y 7 truly gods & ma!sis is _! k+dom4 ,! analy/ proce$s ^u a basis entirely at v>iance ) t :i* guides ! ord9>y inve/igator 9 ! =mulation ( 8 conclusions4 ,! empirical sci5ti/ 9 arriv+ at 8 !ories or hypo!ses is gov]n$ at all times by ! degree ( con=mity :i* 8 po/ulates exhibit to ! actual ph5om5a ( nature4 ,he endeavors to asc]ta9 j h[ f> or 9 :at degree 8 hypo!sis is congru5t ) ?+s f\nd 9 nature4 ,if ! dissid5ce is f\nd to pr$om9ate he ab&ons 8 !ory & makes ano!r /atem5t & aga9 sets out to det]m9e ! degree ( con=mity4 ,if he !n f9ds t ! natural ph5om5a agree ) 8 !ory he accepts x z = ! "t be+ f9ally settl+ ! "q4 ,9 all ?+s he is limit$ by ! answ] :i* nature gives to 8 qu]ies4 ,n s ) ! expon5t ( pure ma!matics4 ,= him ! tru? ( hypo!ses & po/ulates is n dep5d5t ^u ! fact t physical nature conta9s ph5om5a :i* answ] to !m4 ,! sole det]m9+ factor = him is :e!r or n he is able to /ate ) rational consi/5cy ! assum$ fir/ pr9ciples & !n logically develop _! consequ5ces4 ,if he c d ?is1 t is1 if he c /ate 8 hypo!ses ) consi/5cy & develop _! consequ5ces into a logical sy/em ( ?\ght1 he is q satisfi$ & well pleas$ ) 8 p]=mances4 ,b ! fact t ?is is true is ( vital significance = all :o seek cle>ly to und]/& ! ess5tial "* ( hyp]spatiality4 ,x appe>s1 !re=e1 t ! sci5ce ( consequ5ces is ! radical ess5ce ( pure geometry4 ,! metageometrician enjoys unlimit$ fre$om 9 ! *oice ( 8 po/ulates & suff]s curtailm5t only :5 x comes to ! "q ( consi/5cy4 ,he is at lib]ty to =mulate z _m sy/ems ( geometry z ! b>ri]s ( consi/5cy w p]mit & ^! are practically innum]able4 ,s long !n z ! laws ( compatibility rema9 inviolate 8 multiplication ( po/ulate-sy/ems may proce$ indef9itely4 ,is x /range !n t "u conditions :]e an inve/igator has su* unbridl$ lib]ty he %\ld be f\nd indulg+ 9 ma!tic excesses8 ,,kant held t ! axioms ( geometry are syn!tic judgm5ts a priori2 b x appe>s t 9 ! /ricte/ s5se ?is is n ! case4 ,x dep5ds ^u ! type ( m9d :i* is tak5 z a /&>d ( ref]5ce4 ,if x be ! uncultivat$ m9d1 x is c]ta9 t to x ! relations express$ by an axiom w\ld nev] appe> spontane\sly4 ,if on ! o!r h&1 ! /&>d be t ( a cultivat$ m9d x is also equally c]ta9 t to x ^! relations w\ld be discov]$ only aft] me?odical op]ations4 ,all judgm5ts arriv$ at z a result ( logical processes %\ld1 x seems1 be reg>d$ z judgm5ts a po/]iori1 i4e41 ! results ( empirical op]ations4 ,confess$ly1 ! facts adduc$ 9 c\rse ( exp]im5tation s]ve z guides 9 *oos+ among all ( ! _m possible logical conv5tions2 b our *oice rema9s untrammel$ except by ! compulsion aris+ out ( a fe> ( inconsi/5cy4 ,! real crit]ion !n ( all geometries is nei!r tru?1 con=mability nor necessity1 b consi/5cy & conv5i5ce4 ,! difficulty ) ! non-,euclideans resolv$ itself into ! "q z to :e!r x is m consi/5t1 z well z conv5i5t1 to e/abli% a pro( ( ! po/ulate by tak+ advantage ( ! support to be f\nd 9 o!r po/ulates or :e!r1 by seek+ a demon/ration bas$ ^u ! deliv]ies ( s5se-exp]i5ce z to ! nature ( space & its prop]ties1 a /ill m consi/5t conclusion might be rea*$4 ,!y _h fur!r p]plexity1 h[ev]1 :5 x came to a decision z to :e!r ! organic _w is produc$ & ma9ta9$ 9 ,euclidean space or 9 a purely conceptual space :i* alone c be appreh5d$ by ! m9d's p[]s ( repres5tation4 ,unwill+ to admit ! exi/5ce ( ! _w 9 ,euclidean space1 !y turn$ _! att5tion to ! exam9ation ( ! prop]ties ( ano!r k9d ( space s-call$ :i* unlike ! space ( ! ,ionian s*ool c\ld be made to answ] n only all ! purposes ( plane & solid figures1 b ( sph]ics z well4 ,& s1 ! manifold space 0 inv5t$ by ,,riemann & lat] und]w5t "s rem>kable improvem5ts at ! h&s ( 8 disciple1 ,,beltrami4 ,b x may be said "h1 p>5!tically1 t ! tru? ( ! :ole matt] is t our _w is nei!r 9 ,euclidean nor non-,euclidean space1 bo? ( :i*1 9 ! la/ analysis1 are conceptual ab/ractions4 ,al?\gh x may n be d5i$ t ! ,euclidean space is ! m compatible4 ,! problem ( devis+ a space1 if only a v limit$ portion1 9 :i* c\ld be demon/rat$ ! assum$ alt]native hypo!sis & its consequ5ces logically develop$1 occasion$ no inconsid]able conc]n = ! non-,euclidean inve/igators2 b nei!r ,,loba*evski1 ,,bolyai nor ,,riemann 7 to be baffl$ by ! difficulties :i* !y met4 ,^! only cit$ !m to m labori\s toil4 ,hav+ succe$$ 9 m5tally con/ruct+ ! p>ticul> k9d ( space :i* 0 adaptable to _! rigor\s ma!tic requirem5ts x imm$iately occurr$ to !m t all ! qualities ( ! limit$ space ?us devis$ might logically be amplifi$ & ext5d$ to ! entire _w ( space & t :at is true ( figures con/ruct$ 9 ! segm5t$ portion ( space :i* !y us$ = exp]im5tal purposes is also true ( figures drawn any:]e 9 ! univ]se ( ?is space z all l9es drawn 9 ! f9ite1 b\nd$ portion c\ld be ext5d$ indef9itely & all magnitudes simil>ly treat$4 ,f ^! results1 x 0 b a s+le /ep to ! conclusion :i* foll[$--t ei!r an entirely new _w ( space _h be5 discov]$ or t our notion ( ! space 9 :i* ! organic _w 0 produc$ is :olly wrong & ne$s revision4 ,b not)/&+ ! insurm\ntable ob/acles :i* /ood 9 ! way ( ! inve/igators :o made ! attempt to discov] ! homology :i* might exi/ betwe5 ! *>act]i/ics ( ! newly fabricat$ space & ! ph5om5al _w1 inve/igations 7 c>ri$ =w>d ) almo/ amaz+ recklessness & loyalty to ! ma!tic _s until x 0 discov]$ t all ef=ts to trace out any def9ite l9es ( correspond5ce 7 futile4 ,!n ! policy ( ignor+ ! "q ( con=mability 0 adopt$ & has s9ce be5 pursu$ ) un*angeable regul>ity by ! analytical inve/igator4 ,among ! results obta9$ by ! non-,euclideans 9 _! pr(\nd rese>*es into ! nature ( hyp]space are ^!3 #a4 ,x 0 f\nd t ! angul> sum ( a triangle1 be+ ord9>ily assum$ to be a v>iable quantity1 is ei!r less or great] ?an two "r angles s t a /rictly ,euclidean rectangle c\ld n be con/ruct$4 #b4 ,! angle sums ( two triangles ( equal area are equal4 #c4 ,no two triangles n equal c h ! same angles s t simil> triangles are impossible unless !y are ( ! same size4 #d4 ,if two equal p]p5dicul>s are erect$ to ! same l9e1 _! di/ance ap>t increases ) _! l5g?4 #e4 ,a l9e e po9t ( :i* is equally di/ant f a giv5 /raight l9e is a curv$ l9e4 #f4 ,any two l9es :i* d n meet1 ev5 at inf9ity1 h "o common p]p5dicul> :i* measures _! m9imum di/ance4 #g4 ,l9es :i* meet at inf9ity are p>allel4 ,b x is app>5t t ^! results h n foll[$ ^u any ma!matical consequ5ce ( o!r support+ po/ulates or axioms su* z w\ld place !m on a cord9ate basis ) ^? us$ z a support = ! p>allel-po/ulate2 = !y are bas$ ^u ! envisagem5t ( an entirely new pr9ciple ( space-p]ception & belong to a :olly diff]5t set ( space qualities4 ,! f9al issue !n ( ! non-,euclidean geometry is nei!r 9 ! utility ( its processes & conclusions nor 9 ! incresc5t incl9ation t[>ds a new outlook ^u ! _w ( ma!sis2 b resides solely 9 ! possibilities yet to be develop$ 9 t va/ doma9 ( analytical ?\ght :i* x has discov]$ & op5$ to view4 ,to say t x %$s any light ^u ! nature ( ! univ]se is p]haps to take ! radical view2 yet x _c be d\bt$ t ! rese>*es incid5t to ! =mulation ( ! non-,euclidean geometry h greatly ext5d$ ! scope ( consci\sness4 ,:e!r ! ext5sion is valid & normal or simply a hyp]trophic excresc5ce ( m5tal fev]i%ness2 :e!r by virtue ( x we %all m closely approa* an und]/&+ ( ! true nature ( ! m9d ( ! ,inf9ite1 or %all all fall into insanity1 are c]ta9ly debatable que/ions4 ,x nev]!less appe>s evid5t t humanity has ga9$ some?+ ( real1 abid+ p]man5ce by ?is new dep>ture4 ,if t some?+ be m]ely an ext5d$ consci\sness or an awak5+ to ! fact t !re are /ages ( aw>5ess beyond ! /rictly s5su\s1 & e obs]vable evid5ce po9ts to ?is1 !n !re has only begun ! process by :i* ! faculty ( consci\s function+ 9 ?is new _w %all become ! normal possession ( ! human species4 ,b ?is new _w _c be said to be ( ma!matical import2 = x is d\btful if ma!matical laws su* z h be5 devis$ up to ! pres5t "t1 w\ld obta9 !re94 ,s t if any?+1 x mu/ be psy*ological & vital4 ,on ?is view ! worlds ( hyp]space inlaid ) analytic manifoldnesses & con/ant curvatures are b ! primal excitants :i* w f9ally awak5 9 ! m9d ! faculty ( aw>5ess 9 ! new doma9 ( psy*ological cont5t4 ,!n w come ! bloom+ ( ! diurnal fl[] ( ! m9d's immortality & ! outputt+ ( ! organ ( consci\sness :]e) ! inf9ite /ret*es ( hyp]spaces1 ! l[-ly+ valleys ( reals & imag9>ies & ! uplift+ hills ( f9ites & inf9ites %all be dive/$ ( _! my/]ies & /& out 9 _! unit>9ess no long] drap$ 9 ! veil ( ! inscrutable & ! incompreh5sible4 ,! f\r? dim5sion1 reg>d$ by "s z a new scope ( motion = objects 9 space1 by o!rs z a new & /range direction ( spatial ext5t & by o!rs /ill z ! doorway ( ! temple ( exegesis :]e9 an explanation may be f\nd = ! entire cong]ies ( my/]ies & sup]my/]ies :i* n[ p]plex ! human m9d1 may also be said to be ! key to ! non-,euclidean geometry4 ,b x really complicates ! situation2 = "o has to be capable ( prolong$ ab/ract ?\ght ev5 to envisage is z a conceptual possibility4 ,,po9c>#aj says3 ,any "o :o %\ld d$icate 8 life to x c\ld1 p]haps1 ev5tually imag9e ! f\r? dim5sion1 imply+ !reby t a lifetime ( prolong$ ab/ract ?\ght is necess>y to br+ ! m9d to t po9t ( ec/asy :]e x c\ld ev5 s mu* z imag9e ?is additional dim5sion4 ,nev]!less by x 7! f\r? dim5sion7 0 ! non-,euclidean geometry made & )\t x 0 n any ( ! hyp]spaces made t 7 made4 ,x is ! view :i* geomet]s h tak5 ( space 9 g5]al t has made ! f\r? dim5sion possible1 & n only ! f\r?1 b dim5sions ( all degrees4 ,! basis ( ! non-,euclidean geometry may be f\nd !n 9 ! notion ( space :i* has be5 pr$om9ant 9 ! m9ds ( ! inve/igators4 #aj ,vide ,nature1 ,vol4 ,,xlv1 #ahib4 ,f9ally1 x %\ld be po9t$ out t ! non-,euclidean geometry1 ?\gh a consi/5t sy/em ( po/ulates1 has be5 con/ruct$ ^u a misconception bas$ ^u ! id5tification ( real1 p]ceptual space ) sy/ems ( space-measurem5ts4 ,hyp]spaces :i* are n spaces at all %\ld n be conf\nd$ ) real space4 ,b !y con/itute ! sub/ance ( non-,euclidean geometry2 !y are its blood & s9ews4 ,_! /udy is int]e/+1 because ( ! possibilities ( speculation :i* x (f]s4 ,no m9d t has ?\ght deeply ^u ! intricacies ( ! f\r? dim5sion1 or hyp]space1 rema9s ! same aft] ! process4 ,x is b\nd to exp]i5ce a c]ta9 s5se ( humility1 & yet "s pride born ( a k t x has be5 9 ! pres5ce ( a great my/]y & has delv$ into ! fe>ful deeps ( kosmic m9d4 ,to ! m9d t has ?us be5 ano9t$ by ! sacr$ *rism ( ! inn] my/]ies ( creative m5tality !re always come t /illness & calm su* z *>act]ize ! aft]ma? ( reflection ^u ! incompreh5sible & ! transf9ite4 ,,*apt] ,,iv ,,dim5sionality ,arbitr>y ,"* ( ,dim5sionality--,v>i\s ,def9itions ( ,dim5sion--,real ,space & ,geometric ,space ,diff]5tiat$--,! ,f9ity ( ,space--,diff]5ce ,betwe5 ! ,purely ,=mal & ! ,actual--,space z ,dynamic ,appe>ance--,! ,a ,priori & ! ,a ,po/]iori z ,def9$ by ,,paul ,,c>us4 ,9 previ\s *apt]s we h trac$ ! gr[? & developm5t ( ! non-,euclidean geometry %[+ t ! s-call$ f\r? dim5sion is an aspect !re(4 ,x is n[ deem$ fitt+ t we %\ld ent] into a m detail$ /udy ( ! "q ( dim5sionality ) a view to exam9+ "s ( ! difficulties :i* encompass x4 ,! "q ( dim5sion is z old z geometry itself4 ,)\t x geometric conclusions are void & mean+less4 ,yet ! conception ( dim5sionality itself is purely conv5tional4 ,9 its application to space !re is involv$ a great deal ( confusion because ( ! inf]5tial "* ( its def9ition4 ,= in/ance1 commonly we measure a body 9 space & arbitr>ily assign ?ree elem5ts to det]m9e its position4 ,! simple/ /&>d = ?is purpose is ! cube hav+ ?ree ( its edges t]m9at+ at "o ( its corn]s4 ,d ,a ------------------------- ,b ,c ,,fig4 #f4 ,?us because x is f\nd t ! entire volume ( a cube is actually compreh5d$ )9 ! directions indicat$ by ! l9es ab1 bc & db x is det]m9$ t ! ?ree cord9ates ( ! po9t b are necess>y & suffici5t to e/abli% ! dim5sions ( ! cube & consequ5tly ( ! space 9 :i* x re/s4 ,! conception may be /at$ 9 ?is way3 ,if a collection ( elem5ts1 say po9ts or l9es1 be ( su* a nature or ord] t x is suffici5t to "k a c]ta9 def9ite numb] ( facts ab\t x 9 ord] to be able to di/+ui% e "o ( ! elem5ts f all ! o!rs1 !n ! assemblage or collection ( elem5ts is said to be ( ! same numb] ( dim5sions z !re are elem5ts necess>y to its det]m9ation4 ,9 ! above figure !re are ?ree elem5ts1 namely1 ! l9es ab1 bc1 & db1 :i* are necess>y & suffici5t = ! det]m9ation ( ! position ( ! po9t b4 ,9 ?is way geomet]s h det]m9$ t our space is tridim5sional2 b x is obvi\s t ?is conclusion is bas$ n ^u any exam9ation ( space itself b ^u ! measurem5t ( bodies 9 space4 ,^u ?is view x is se5 t conclusions bas$ ^u su* a proc$ure r5d] our notion ( ! ext5sion ( bodies 9 space id5tical ) ! notion ( spatial ext5sity4 ,9 o!r words1 we take bodies 9 space & by exam9+ _! *>act]i/ics & prop]ties arrive at an alleg$ apodeictic judgm5t ( space4 ,x is by means ( ?is conv5tional norm ( geometric k t v>i\s o!r spaces1 notably ! "o-1 two-1 f\r-& n-space1 h be5 devis$4 ,x w\ld appe> t if "s m absolute /&>d ( measurem5t or def9ition ( space 7 adopt$ ! confusion :i* n[ cl+s to ! conception ( dim5sion c\ld be obviat$4 ,= if x be true t ?ree & only ?ree elem5ts are necess>y to det]m9e a po9t-position 9 our space & t 9 ?is det]m9ation we also f9d ! numb] ( dim5sions ( space1 !n x may also be true t n-cord9ates w\ld j z truly det]m9e ! dim5sionality ( an n-space1 :i* is grant$4 ,b !n ! n-space w\ld be j z legitimate z ! ?ree-space2 = x is det]m9$ by exactly ! same /&>ds4 ,x is bo? quantitatively & qualitatively ! same4 ,if1 h[ev]1 on acc\nt ( ! exig5cies t might arise1 we are =c$ to seek solace 9 ! notion ( an n-space :i!r %all we turn = x8 ,x _c be f\nd2 = x is imp]ceptible1 un9habitable1 non-exi/5t1 & !re=e1 absolutely & purely an ab/raction4 ,consequ5tly1 !re mu/ be some?+ radically wrong ) ! def9ition ( space or ) its det]m9ants4 ,! purely arbitr>y "* ( dim5sionality is v aptly describ$ by ,,cassius ,,jackson ,,keys]1 :o says3 444 ,! dim5sionality ( a giv5 space is n unique1 b dep5ds ^u ! *oice ( ! geometric entity = prim>y or g5]at+ elem5t4 ,a space be+ giv51 its dim5sionality is n !re) det]m9$1 b dep5ds ^u ! w ( ! inve/igator :o by a prop] *oice ( g5]at+ elem5t end[s ! space ) any dim5sionality he pleases4 ,t fact is ( c>d9al significance = sci5ce & philosophy4#aa #aa ,vide ,moni/1 ,vol4 ,,xvi1 #ahif1 ,ma!matical ,emancipations4 ,x is a fact ( c>d9al significance = sci5ce2 because x emphasizes ! necessity = "s m rational proc$ure ?an t ( ! geometrician 9 arriv+ at an absolutely unique me?od ( det]m9+ ! dim5sion & ess5tial nature ( real space4 ,its significance = philosophy lies 9 ! ne$ ( a logical1 rigidly exclusive & absolutely peculi> /&>d ( space def9ition4 ,! def9ition ( p]ceptual space %\ld be su* z rigor\sly inhibits its inclusion z a p>ticul> 9 any g5]al class4 ,! necessity = ?is is w>rant$ by its univ]sality & uniqu5ess4 ,! l9es ( dem>kation betwe5 :at is recogniz$ z p]ceptual space & :at has be5 call$ geometric or conceptual space %\ld be v %>ply drawn4 ,s t :5 ref]5ce is made to ei!r !re w be no d\bt z to :i* is meant4 ,& !n1 too1 conceptual space is no space at all1 prop]ly speak+4 ,x is m]ely a sy/em ( space-measurem5t4 ,& z su* has no logical "r to be put 9 ! same category z p]ceptual space4 ,real space is unique4 ,geometric space belongs to a class ^: memb]s are capable ( indef9ite multiplication4 ,x is c]ta9ly mo/ illogical to id5tify !m4 ,p]ceptual space1 figuratively speak+1 is a quantity2 analytic space is ! foot-rule1 ! y>d-/ick1 ! kilomet]1 by :i* x is measur$ & apportion$4 ,x is logically impossible to pr$icate ! same conclusion = bo? ( !m4 ,t is1 to d s causes a pr(\nd fracture ( ! fundam5tal norms ( logic4 ,su* conclusions be+ ?us illegitimate x is r surpris+ t an error ( ?is nature %\ld h be5 made4 ,x is p]haps acc\ntable = on ! gr\nds ( ! geomet]'s complete ins\ciance z to h[ 8 po/ulates %all /& 9 _! relation to ?+s 9 ! ph5om5al _w4 ,x is agre$ t z conv5i5t z is ,euclid's sy/em ( space-measurem5t x is n by any means congru5t ) ! ext5sion ( real space objects4 ,x does1 h[ev]1 approximate congruity ) ^! objects z ne>ly z possible4 ,h[ !n c\ld x be expect$ t a sy/em ( space-measurem5t s f> remov$ f ?is prim>y congru5ce z ! non-,euclidean sy/em is %\ld exhibit m obvi\s signs ( correspond5ce8 ,b ! advocates ( ! n-dim5sionality ( space h illatively ass]t$ ! id5tity ( space & its dim5sions4 ,accord+ly1 !re is n recogniz$ any di/9ction betwe5 _! conception ( space itself & its qualitative peculi>ities4 ,!y use ! t]ms int]*angeably4 ,s t dim5sion means space & vice v]sa4 ,9 ?is lack ( discrim9ation may be f\nd ! s\rce ( mu* ( ! confusion :i* atta*es to ! conception ( space4 ,if x 7 arguable t ! relation betwe5 space & its dim5sions is ! same z t betwe5 matt] & its prop]ties !n ! re/riction ( ?is relation to ?ree & only ?ree directions ( ext5t w\ld be disall[$2 = ! reason t if1 z is commonly done1 dim5sion be made to mean direction ( ext5t1 !re w\ld be an unlimit$ numb] ( directions ( ext5t & !y w\ld all be p]ceptible4 ,b ?is is really ano!r fundam5tal fault4 ,non-,euclideans h /ret*$ ! mean+ ( ! t]m dim5sion s t x n only includes ! idea ( direction b an entirely new class ( qualities--! f\r? dim5sion4 ,& despite ?is re=mation ( ! orig9al conception1 !y dem& t x %all be call$ space4 ,we h j %[n t ! g5]ic concept ( dim5sionality is t ?ree & only ?ree cord9ates are necess>y & suffici5t = its det]m9ation4 ,grant+ t ?is is true1 are we n compell$ consequ5tly to see t we h1 by add+ a f\r? or n-dim5sions1 involv$ ourselves into a m complex situation ?an be=e8 ,= by po/ulat+ a f\r? dim5sion ei!r we h creat$ a new _w ^: dim5sions are f\r 9 numb] or we h explicitly admitt$ t ! ?ree dim5sions h a f\r?4 ,aside f ! logical difficulties :i* beset ^! conclusions !re is also set up a condition :i* is at v>iance ) ! mo/ elem5t>y requirem5ts ( common s5se4 ,?us f> ma!matical ?\ght has n s]v$ to cl>ify our notions ( space nor to %$ any new light ^u ! vital processes :i* are alleg$ to h _! explanation 9 ! new discov]y4 ,simply /at$1 metageometricians h br\ght u to ! place :]e we mu/ ei!r recognize t ! f\r? dim5sion is ano!r sph]e ly+ dang]\sly ne> ! e>? 9 :i* space ext5ds 9 f\r prim>y directions & 9 :i* f\r cord9ates are necess>y = its det]m9ation or we are driv5 to ! o!r horn ( ! dilemma :]e we are br\ght face to face ) ! conclusion t ! ?ree p]ceptual space dim5sions h 9 common a hi!rto unkn[n prop]ty or ext5sion 9 virtue ( :i* x may be view$ z hav+ an unlimit$ numb] ( dim5sions4 ,to accept ! latt] view is equival5t to say+ t1 9 ! above figure1 ! ?ree l9es ab1 bc & db h =m$ a triple ent5te by :i* !y h mutually & sev]ally acquir$ a new doma91 hyp]space1 & 9 :i*1 because ( ! va/ res\rces ( ! region1 !y are able to p]=m wondr\s ?+s4 ,let u exam9e briefly ! v>i\s curr5t def9itions ( dim5sion4 ,x is assum$ by n a few t dim5sion is ! same z direction4 ,b c we grant ?is :olly to be true8 ,if s1 !n a m]e *ild may see t !re are & mu/ necess>ily be z _m dim5sions z !re are directions4 ,prim>ily1 !re are six directions ( space & an unlimit$ numb] ( subsidi>y directions4 ,on ?is view x is n necess>y to inv5t a new doma9 ( space if ! object be m]ely to discov] & utilize a great] numb] ( dim5sions ?an has h]et(ore be5 all[$4 ,= ! id5tification ( ! t]m dim5sion ) direction already makes available an almo/ inf9ite numb] ( dim5sions4 ,b ?is view is object$ to by ! advocates1 = x is contr>y to ! hypo!sis ( n-dim5sionality4 ,dim5sion also means ext5t4 ,?is is p>tially true4 ,x _c be :olly true4 ,=1 if x 71 !n1 space w\ld h only "o dim5sion :i* is also n all[able "u ! hypo!sis4 ,!n ! def9ition leaves out ( acc\nt ! idea t space is at ! same "t a direction or collection ( directions4 ,! t]m ext5sion is g5]ic & :5 appli$ to space means ext5sion 9 all possible directions & n 9 any "o direction4 ,s t x is n p]missible to say t space ext5ds 9 ?is direction or t because x ext5ds 9 all directions simultane\sly & equally4 ,geomet]s claim t space is a sy/em ( cord9ates necess>y = ! e/abli%m5t ( a po9t-position 9 x4 ,?is view1 h[ev]1 id5tifies space ) a sy/em ( space-measurem5t & is !re=e faulty4 ,accord+ to ?is view !re may be z _m spaces z !re are sy/ems ( space-measurem5t & ! latt] may be limitless4 ,b if ! totality ( spaces are to be view$ z "o space !n we %all h "o space ) an indef9ite numb] ( dim5sions2 also an indef9ite numb] ( space measurem5ts :i* w\ld be confus+4 ,mu*1 if n all1 ( su* a sy/em's utility & conv5i5ce w\ld be unavailable or useless4 ,t1 too1 w\ld be 9 violation ( ! av[$ purpose ( ^! inve/igations :i* is to enhance ! utility & conv5i5ce ( ma!matic op]ations4 ,n[ x is evid5t t space is nei!r direction1 ext5sion1 a sy/em ( space-measurem5t nor a sy/em ( manifolds ^: dim5sions are g5]able4 ,& ?is is s = ! same reason t a piece ( clo? is n ! elem5ts ( measurem5t--in*es1 feet1 y>ds--by :i* x is apportion$4 ,& because we f9d t ! fabric ( space l5ds itself accommodat+ly to our conv5tional norms ( measurem5t is n suffici5t reason = id5tify+ x ) ^! norms4 ,"h we h ! s\rce ( all error 9 ma!matical conclusions ab\t ! nature ( space2 because all su* conclusions are bas$ n ^u ! intr9sic nature ( space1 b ^u artificial =ms :i* we *oose to impose ^u x = our own conv5i5ce4 ,b x %\ld be rememb]$ t ! irregul>ities :i* we note are n 9 space itself b inh]e 9 ! =ms :i* we use4 ,= ^! purposes space is extremely ela/ic & accommodates itself to ! %ape & scope ( any con/ruction we may decide to try ^u x4 ,9 ?is respect x is l wat] :i* has no reg>d = ! %ape1 size or k9d ( vessel into :i* x may be posit$4 ,!re is "o ?+ c]ta9 t judg+ f ! above consid]ations !re has be5 n yet any absolute1 all-satisfy+ def9ition devis$ = space by ma!maticians4 ,! be/ def9itions hi!rto con/ruct$ are purely artificial & arbitr>y det]m9ations4 ,x is r anomal\s t !re %\ld be s little unanimity ab\t :at is ! mo/ fundam5tal consid]ation ( ma!matical conclusions :i* are suppos$ to be s c]ta91 s necess>y & univ]sal z to be incontrov]tible4 ,confess$ly1 x is a condition :i* raises aga9 ! "q z to j :at are ! limits ( ma!matical c]ta9ty & necessity & j h[ f> we %all dep5d ^u ! validity ( ma!matics to det]m9e = u absolutely c]ta9 conclusions ab\t ! nature ( space4 ,9 view ( ! unc]ta9ty not$1 are we ju/ifi$ 9 foll[+ too closely ! ma!matic lead ev5 9 matt]s ( logic1 to say no?+ ( our conception ( space8 ,x seems t we %all h necess>ily1 on acc\nt ( ! recogniz$ limitations ( ma!matics 9 ?is matt]1 to turn to "s m t5able s\rce = ! norms ( our k conc]n+ space4 ,= 9 ! light ( ! r indef5sible position :i* metageometricians h involv$ !mselves !re appe>s to be no hope 9 ?is direction4 ,x is und\bt$ly saf] n to rely altoge!r ^u ! purely ab/ract1 ev5 9 ! _w ( ma!sis1 = any absolute crit]ion ( k4 ,x is p]haps well t we %\ld expunge ! ^w absolute f our vocabul>ies4 ,x is really a misnom] & has no mean+ 9 ! lexicon ( nature4 ,!re is 9 reality no absolute 9 ! s5se ( f9al absolution f all conditions or re/rictions4 ,9 ! ultimate analysis !re is unque/ionably no hue1 tone1 quality1 condition nor any imag9able po/ure ( life1 be+ or manife/ation t is absolv$ f e o!r "o ( its class or f ! totality4 ,all ^! are relational & int]dep5d5t4 ,!re is no room = ! absolute4 ,9 fact1 x is a quality :i* _c 9 any way be ascrib$ to any aspect ( kosmic manife/ation4 ,x has exi/5ce only 9 ! m9d & has be5 devis$ = ! purpose ( m>k+ ! limits ( its scope4 ,all be+ is relative2 all life is relative & is de/9$ to *ange its qualities z x evolves4 ,all k is also relative & :at is true ( "o /ate may n be true ( ano!r2 :at is true ( "o life may n be true ( ano!r life2 ! limitations ( "o degree ( k may n h any be>+s ^u ano!r degree4 ,! norms ( "o w n satisfy ! conditions ( ano!r /age ( manife/ation4 ,x is always )9 limits t ! crit]ion ( k w be f\nd to satisfy a giv5 set ( conditions4 ,h5ce )9 c]ta9 limits ma!matical conclusions w ma9ta9 _! validity4 ,error is committ$ by pu%+ ! validity ( ^! limits to a position )\t ! sph]e ( limitations4 ,?is seems to be ! crux ( ! :ole matt]4 ,ma!maticians1 notably non-,euclideans1 h s\ght to ext5d ! comp>atively small sph]e ( limits ( congru5ce betwe5 ma!matic & p]ceptual space to su* an ext5t z to cause x to encroa* ^u =bidd5 t]ritory4 ,9 do+ ?is !y h err$ griev\sly1 caus+ s]i\s (f5se to ! m s5sitive _s ( ! high-ca/e ma!maticians among :om are none m truly cons]vative ?an ,,paul ,,c>us1#ab :o says3 ,metageometricians are a hot-head$ race & display sometimes all ! *>act]i/ics ( sect>ian fanatics4 ,to !m x is q cle> !re may be two /raight l9es ?r\gh "o & ! same po9t :i* d n co9cide & yet are bo? p>allel to a ?ird l9e4 #ab ,vide ,moni/1 ,vol4 ,,xix1 p4 #djb 7#aiji74 ,to ! /ud5t :o has c>efully foll[$ ! developm5t ( ! non-,euclidean geometry & ! notion ( hyp]space ! above *>act]ization is none too sev]e nor ill-des]v$4 ,no?+ c\ld m vividly yet correctly portray ! impi\s tactics ( ! metageometrician & e/abli% 8 p]ceptual obliquity m surely ?an ! m]e fact1 m5tion$ by ,,c>us1 t he c ) evid5t lack ( m5tal p]turbation proclaim t two /raight l9es1 nonco9cid5t ) ea* o!r1 may pass ?r\gh a po9t & yet be p>allel to a ?ird l9e4 ,b ?is is a m]e trifle1 a bagatelle1 to ! _m o!r infractions ( :i* he is guilty4 ,! wond] is t he is able to secure su* obsequi\s acceptance ( 8 (f]+s z _m ( ! mo/ s]i\s m9d$ ma!maticians are incl9$ to give4 ,is x to be wond]$ at t1 despite ! pr(use prote/ations ( ! advocates1 _m :o take up ! /udy ( ! "q ( hyp]space %\ld exp]i5ce a deep revulsion f ! po/ure assum$ by metageometricians ) respect to ^! qu]ies8 ,l9k$ ) ! idea ( dim5sionality is ! notion t space is inf9ite4 ,?is is a conception :i* has its roots imb$d$ 9 ! dep?s ( antiquity4 ,primitive man1 look+ up into ! heav5s at :at appe>$ to him z a nev] end+ ext5sion1 0 aw$ by its va/ness2 b ! m9ds ( ! mo/ le>n$ ( ! pres5t-day m5 are n free f ?is innate dread ( inf9ity4 ,x p]meates ! ?\ght life ( all alike & none seems to be able to rise above x4 ,ma!maticians1 philosoph]s1 sci5ti/s all %>e 9 ! g5]al belief t space is )\t limit1 un5d+ 9 ext5t & et]nally exi/5t4 ,,riemann1 ^: ?\ght life f\nd its mo/ conv5i5t mode ( expression by means ( pure ma!matics1 0 ! fir/ 9 ! hi/ory ( human ?\ght to surmise t space is n inf9ite b limit$ ev5 ?\gh unb\nd$4 ,b 8 conception has be5 mu* vitiat$ on acc\nt ( its entanglem5t ) an idealiz$ con/ruction by :i* space is reg>d$ z a ?+ to be manipulat$ & g5]at$ by act ( ?\ght4 ,7 x n = ?is 8 conception w\ld inde$ m>k ! beg9n+ ( a new era 9 psy*og5esis4 ,z x is1 :5 all ! nons5sical effusions h be5 cle>$ away f our space conceptions & m5 come really to und]/& some?+ ( ! ess5tial nature ( space ?is new era w f9d its true beg9n+s 9 ! m9d ( ,,riemann4 ,al?\gh x mu/ be said1 z is ! case ) all progressive movem5ts1 ! lat] developm5t ( a rationale = ?is conclusion w v>y greatly f 8 orig9al conception4 ,= he _h 9 m9d a space t is g5]able & !re=e a logical con/ruction :ile ultimately ! m9d w sw+ back to a consid]ation ( real space4 ,already m5 are beg9n+ to see a new light4 ,already !y are beg9n+ to take a new view ( space 9 g5]al4 ,! dep>ture is especially noticeable 9 ! attitude assum$ by ,,hiram ,m4 ,,/anley4#ac ,he says3 ,if we seek ! mo/ satisfactory und]/&+ ( space we %all look nei!r to ma!matics nor ,psy*ology b to ,physics4 ,! tr5d ( ,physics1 say ) su* a repres5tative z ,,o/wald1 is to make ?+s ! expression ( =ce2 ! con/itution & appe>ance ( ?+s are det]m9$ by dynamism2 & we may be/ int]pret space z a mode ( ?is dynamic appe>ance4 ,space1 z a mode ( dynamic appe>ance is a slight improvem5t ^u ! old idea ( a pure vacuity2 = 9 ! light ( :at we n[ "k ab\t space cont5t mu* ( ! dignity ( t view has be5 lo/4 ,m5 n[ "k t space is n an empty void4 ,!y "k t ! atmosph]e fills a great deal ( space4 ,!y also h ext5d$ _! conception 9 ?is direction to include ! e!r & occultism goes fur!r & po/ulates f\r k9ds ( e!r--! *emical1 life1 light & psy*ographic e!rs4 ,b x does n /op "h4 ,x po/ulates a s]ies ( grades ( f9] matt] ?an ! physical :i* fills space & p]meates its entire ext5t ev5 to id5tification ) its ess5tial nature4 #ac ,philosophical ,review1 ,vol4 ,,vii 7#ahih74 ,,/anley cont9ues3 ,ev]y?+ does n1 z commonly conceiv$1 fall into "s pre-exi/5t space conv5i5t = x2 b ev]y?+ makes its own spaci\sness by its own def5sive & (f5sive =ce1 & ! totality ( all appe>ance is space 9 g5]al4 ,accord+ to ,,/anley1 n only d physical1 p]ceptual objects1 by _! (f5sive & def5sive =ce make _! own space b ! appe>ance ( t 9 :i* no physical object is makes room = itself by its own dynamic =ce4 ,9 o!r words1 t :i* we call pure ext5sity is by virtue ( its dynamism ! cause ( its own exi/5ce4 ,at fir/ h& !re appe>s to be little wor?y ( s]i\s consid]ation 9 ?is view ( ,,/anley2 yet1 if c>ri$ to its logical conclusion1 ! m]it ( ! hypo!sis becomes app>5t4 ,accord+ly1 int]/ell> di/ances :i* are commonly said to be ev5 )\t air or life ( any k9d are really an appe>ance possess$ ( a dynamism peculi> to itself4 ,& ?is v =ce-appe>ance1 con/itut+ space1 is t :i* makes x p]ceivable4 ,= in/ance1 let u say ! space t exi/s betwe5 ! e>? & ! moon1 is n really empty nor does x h an exi/5ce prior to itself1 b is a mode ( dynamic appe>ance :i* is ! cause ( its own exi/5ce4 ,its dynamic "* makes x to appe> p]ceptible to our s5ses4 ,logically1 if ! dynamism 7 remov$ !re w\ld rema9 nei!r space nor ! appe>ance ( space4 ,if ?is 7 true1 & x is wor?y ( s]i\s ?\ght1 !n space is c]ta9ly f9ite1 z 9 its totality1 accord+ to ,,/anley',s view1 x w\ld h to be reg>d$ z a ph5om5on ( ! inn] & f9ite life ( ! inf9ite4 ,x is believ$ t we may g a /ep fur!r & unqualifi$ly ass]t t space is f9ite1 ev5 d5y+ its inf9ity z a g5]al mode ( ! activity ( ! :ole4 ,yet x is transf9ite 9 ! s5se t x transc5ds ! compreh5sion ( f9ite m9ds or processes4 ,x is f9ite because x is 9 manife/ation4 ,ev]y?+ t is 9 manife/ation is f9ite4 ,! inf9ite is n 9 manife/ation4 ,inf9ity has to be limit$ always to become manife/4 ,! ,deity has limit$ ,8 be+ 9 ord] t !re may be a manife/$ univ]se4 ,all ?+s1 all appe>ances are f9ite2 because !y are ph5om5a connect$ ) manife/ation4 ,?is "q may be view$ f ano!r /&po9t4 ,all ?+s 9 manife/ation or exi/5ce are pol> 9 _! con/itution4 ,= in/ance3 !re _c be a "h )\t a !re4 ,!re _c be an upp] )\t a l[]4 ,"r is copol> ) wrong2 good is copol> ) evil2 night ) day2 manife/ation ) non-manife/ation2 tru? ) falsity2 inf9ity ) f9ity & s on1 ?r\gh\t ! :ole gamut ( ! pairs ( opposites4 ,:at is ! logical inf]5ce8 ,space is pair$ ) a lack ( space4 ,!re _c be :at we call space )\t !re be+ at ! same "t ! possibility1 at lea/1 ( ! lack ( space or spacelessness4 ,?is is a conclusion t is rigor\sly logical & incontrov]tible4 ,b x has be5 urg$ t x is impossible = ! m9d to imag9e a condition :]e !re is no space4 ,x ev5 has be5 ass]t$ t x is contr>y to ! con/itution ( ! m9d itself to imag9e no space4 ,b :e!r imag9able or n has no effect :atev] ^u ! validity ( ! conception4 ,nei!r1 x is said1 c we imag9e a f\r? dim5sion b ! m9d has come dang]\sly ne> to imag9+ x4 ,! di/ance f excogitat+ ^u1 discuss+ & describ+ ! prop]ties ( f\r-space to imag9+ x is n s great aft] all4 ,truly x is difficult inde$1 x seems1 to be able to describe a ?+ yet n be able to imag9e or make a m5tal image ( x4 ,!re is an evid5t fallacy "h4 ,ei!r ! description ( f\r-space is no description at all or x is a true del9eation ( an idealiz$ con/ruction :i* is well )9 ! m9d's p[]s ( imag9ation4 ,inde$ ! "q ( imag9ability is n det]m9ative 9 itself2 = :at ! m9d may n[ be unable to imag9e1 because ( its m or less nebul\s "*1 & ow+ to its infancy may 9 ! c\rse ( "t be easily accompli%$4 ,! univ]se is a compact$ pl5um4 ,x is *ock-full ( m9d1 ( life1 ( en]gy & matt]4 ,^! f\r are basically "o4 ,!y exi/1 ( c\rse1 9 v>y+ degrees ( t5uity & int5sity & answ] to a wide range ( vibrations4 ,toge!r1 9 _! manife/ation ( action & int]action1 9 _! dynamic appe>ance1 if y please1 !y con/itute space4 ,if ^! 7 remov$ ) all t _! exi/5ce implies !re w\ld result a condition ( spacelessness 9 :i* no "o ( ! appe>ances :i* we n[ p]ceive w\ld be possible4 ,ev5 %e] ext5sity w\ld be non-exi/5t4 ,all scope ( motility w\ld be lack+4 ,dim5sion1 cord9ates1 direction1 space-relations--all w\ld be impossible4 ,a /raight l9e is an ideal con/ruction ( ! m9d4 ,x does n exi/ 9 nature4 ,x c nev] be actualiz$ 9 ! ph5om5al univ]se4 ,betwe5 ! ideal & ! real1 or actual1 !re is a kosmic *asm4 ,x broad5s or n>r[s accord+ z ! ph5om5al appe>ance approa*es or rec$es f ! ideal4 ,:at1 !re=e1 c be po/ulat$ ( ! "o w n apply ) equal =ce to ! o!r4 ,!y are n congru5t & c nev] be 9 ! actualiz$ univ]se4 ,! mom5t ! actual becomes id5tifi$ ) ! ideal x ceases to be ! actual4 ,! univ]se does n exi/ z pure =m1 nei!r does space4 ,z purely =mal con/ructions ( ! intellect ^! c h no p]ceptible exi/5ce4 ,! ph5om5al or s5sible may n be judg$ by exactly ! same /&>d z ! =mal4 ,! ph5om5al or s5sible repres5ts ?+s z !y appe> to ! s5ses1 or1 s f> z ! actualiz$ univ]se is conc]n$1 z !y really are4 ,! =mal repres5ts ?+s z !y are made to appe> by ! m9d4 ,x _c be actualiz$4 ,x may be said t ! purely =mal is ! limit ( evolution4 ,! ph5om5al may approa* ! ideal z a limit1 b c nev] become fully congru5t ) x4 ,! diff]5ce betwe5 ! ideal & ! actual is a dynamic "o2 x is by virtue ( ?is diff]5ce t ! univ]se is held 9 manife/ation4 ,evolution is ! decrem5t ( ?is diff]5ce betwe5 ! purely =mal & ! actual4 ,s long !n z a kosmic diff]5tial is ma9ta9$ ! ph5om5al cont9ues to be manife/3 :5 x is f9ally r$uc$ to no?+ x goes out ( manife/ation4 ,! ph5om5al is f9ite2 ! ideal inf9ite4 ,:]e=e1 x is und\bt$ly improp] to ref] to space z be+ inf9ite4 ,! t]m really is inapplicable4 ,transf9ity is mu* bett] & m accurate4 ,space is transf9ite because its scope is great] ?an any f9ite scope ( motility c encompass1 because x exce$s f9ite compreh5sibility4 ,,riemann',s notion t space is limit$ ga9s weight 9 ! light ( ! =ego+ consid]ations4 ,b he c\ld n conceive ( ! limitability & unb\nd$ness ( space z su* 9 its pure ess5ce2 b 0 compell$1 by 8 own limitations1 to make an idealiz$ con/ruction 9 :i* he c\ld actualize 8 conception4 ,& = real1 dynamic space1 he sub/itut$ 8 ideal con/ruction & proce$$ ^u t basis4 ,& ( c\rse1 8 view :ile x _h no ref]5ce to p]ceptual space nev]!less possess$ an illative relation !reto & %\ld be recogniz$ z con/ruable 9 t light4 ,! process ( squ>+ ! circle recogniz$ z a geometric impossibility is significant ( ! fluxional nature ( ! univ]sal residuum p]petually ma9ta9$ betwe5 ! ar*etypal & ! manife/$ kosmos4 ,x seems t !re is a pr(\nd tru? embodi$ 9 ?is problem4 ,!re is a lesson t may be le>n$ by ma!maticians1 philosoph]s1 sci5ti/s & ?9k]s 9 g5]al4 ,!re is an elem5t ( et]nal necessity & univ]sality ab\t x :i* is truly symbolic ( ! f9ity ( ! univ]se & ! inf9ity ( ! ar*etypal4 ,j z a squ>e or a s]ies ( polygonal figures inscrib$ 9 a circle _c be made to co9cide exactly ) ! circle s _c ! actual be made to co9cide ) ! ideal4 ,! circumf]5ce ( ! circle is ! unapproa*able limit ( inscrib$ squ>es4 ,if x 7 possible s to multiply squ>es ?us inscrib$ t a figure co9cid5t ) ! circumf]5ce ( a circle might be con/ruct$1 su* a figure w\ld n be a squ>e b a circle4 ,! manife/$ univ]se is l t--! process ( inscrib+ squ>es )9 a circle4 ,x is ev] becom+1 evolv+1 develop+1 b nev] q atta9s4 ,inf9ity is a process4 ,b no s+le /age 9 t process is inf9ite4 ,ea* is f9ite & _! totality makes ! inf9ity ( ! process4 ,! univ]se manife/$ to ! s5ses or ! intellect is f9ite4 ,space1 says ,,paul ,,c>us1 is ! possibility ( motion 9 all directions4#ad ,to be sure1 x is admitt$ t space (f]s opportunity = motion 9 all directions4 ,b is space ?is opportunity ( motility8 ,or is possibility ( motion space8 ,! possibility ( motion mu/ re/ 9 ! ?+ t moves4 ,x implies a pot5cy 9 ! mov+ entity1 n 9 space4 ,if x is meant t space is ! pot5cy t resides 9 ! mov+ elem5t x is /ill m difficult to und]/& ! connotation4 ,b ev5 grant+ ?is view1 are we n compell$ to recognize ! dynamism ( space z a necess>y inf]5ce8 ,ano!r def9ition :i* ,,c>us gives is t space is a pure =m ( ext5sion4 ,if x be grant$ t space is a pure =m ( ext5sion we %\ld h to conclude t x has no actual exi/5ce2 = pure =m does n exi/ except z an idealiz$ con/ruction4 ,x _c be f\nd 9 nature4 ,pure =m is ideal4 ,impure or natural =m is actual4 ,!re=e ! space 9 :i* we live & 9 :i* ! univ]se exi/s _c be a pure =m because life _c exi/ 9 ! purely =mal4 ,x is useless to talk ab\t space z m]e =m s long z x ma9ta9s life4 ,! difficulty :i* ?is phase ( ! "q pres5ts is ano!r evid5ce ( ! inadequacy ( our def9itions4 #ad ,vide ,f\ndations ( ,ma!matics1 p4 #ajg4 ,x is also f\nd to be impossible to concur 9 ,,c>us' conception ( k a priori4 ,8 notion ( ! a priori v>ies some:at f ! ,kantian view4 ,he def9es x z an idealiz$ con/ruction1 ! m9d made1 ab/ract ?\ght1 & places x 9 ! same category z a concept4 ,?is is und\bt$ly born ( 8 desire to get rid ( ,,kant',s innate ideas :i* seem to be di/a/eful to him4 ,b 9 do+ s x appe>s t ! real a priori has be5 ov]look$4 ,let u exam9e = a mom5t ?is important "q4 ,! a po/]iori connotates all k ga9$ ?r\gh ! s5ses1 or s5se exp]i5ce4 ,all k !re=e ^: orig9 c be trac$ to ! s5ses is k a po/]iori4 ,n[1 k a priori %\ld be j ! opposite ( ?is4 ,x %\ld indicate su* k z t :i* does n h its orig9 9 ! s5ses1 or :i* is n dep5d5t ^u ! ord9>y av5ues ( s5se-exp]i5ce4 ,ab/ract ?\ght is z truly exp]i5ce z smell+1 see+ or he>+4 ,x is by trav]s+ its scope ( motility t ! m9d f9ds out :at ! norms ( logic are4 ,x c\ld n rema9 quiesc5t & discov] !m4 ,x has to be active1 exam9+1 comp>+ & judg+4 ,almo/ ! entire range ( ?\ght1 its entire scope1 is *>act]iz$ by ! a po/]iori/ic me?od4 ,9 fact1 all ?\ght is a po/]iori/ic4 ,despite ! fact t1 9 ?9k+ 9 ! ab/ract1 x is necess>y m5tally to remove all elem5ts ( concret5ess1 all mat]iality & all actuality1 ! conclusions rea*$ h to be ref]r$ to ! /&>ds ma9ta9$ by ! actual1 ! concrete & ! mat]ial4 ,!n we d n />t ) ! ab/ract 9 our ?9k+4 ,we beg9 ) ! concrete & by m5tally remov+ all physical qualities arrive at ! ab/ract4 ,! m9d has a con/itution4 ,x acts 9 a giv5 way because x is its nature s to act4 ,n because x has le>n$ to act 9 t mann]4 ,x p]=ms c]ta9 functions intuitively )\t previ\s in/ruction or exp]i5ce = ! same reason t wat] damp5s or heat w>ms4 ,x is natural = x to d s4 ,?is naturalness1 ?is p]=mance ( function )\t be+ taught or )\t exp]i5ce con/itute ! pr9ciple ( apriority 9 ! m9d4 ,aprior9ess is a pr9ciple ( m9d p>tak+ ( ! v nature & ess5ce ( m9d4 ,x is ! v ma9spr+ ( m5tality4 ,p]ception & conception are processes :i* ! m9d p]=ms intuitively4 ,! m9d p]ceives & conceives because x is impossible = ! normal m9d to d o!rwise4 ,we take a view ^u a giv5 "q2 we assume c]ta9 m5tal attitudes ( affirmation1 negation or indiff]5ce because we h le>n$ to d s by virtue ( ! tuitional capability ( m9d4 ,^! describe ! a po/]iori4 ,t is1 all k obta9$ z a result ( volunt>y m5tal processes con/itutes ! mass ( k a po/]iori4 ,! a priori is :at ! m9d is by nature3 ! a po/]iori is :at ! m9d becomes4 ,x is ! m9d-cont5t4 ,! a priori is n a m5tal con/ruction2 x is an ess5tial pr9ciple ( m9d4 ,x %\ld n be id5tifi$ ) ! purely =mal1 z is done by ,,paul ,,c>us3#ae #ae ,vide ,f\ndations ( ,ma!matics1 p4 #db4 ,he says3 ,! a priori is id5tical ) ! purely =mal :i* orig9ates 9 our m9d by ab/raction4 ,:5 we limit our att5tion to ! purely relational1 dropp+ all o!r features out ( sight1 we produce a field ( ab/raction 9 :i* we c con/ruct purely =mal comb9ation1 su* z numb]s1 or ! ideas ( types & species4 ,?us we create a _w ( pure ?\ght :i* has ! advantage ( be+ applicable to any purely =mal consid]ation & we "w out sy/ems ( numb]s :i*1 :5 c\nt+1 we c use z /&>ds ( ref]5ce = our exp]i5ce 9 practical life4 ,?us ,,c>us def9itely l9ks up ! a priori to a factor :i* is no?+ m nor less ?an a m5tal by-product4 ,= su* is ! category 9 :i* w\ld be plac$ bo? ! process ( ab/raction & its results4 ,x is !re=e exce$+ly difficult to und]/& :y s cursory a consid]ation %\ld h be5 giv5 to ! pr9ciple ( apriority ?an :i* no o!r elem5t ( m9d is m ess5tially a "p ( ! m9d itself4 ,! =mal is symbolic4 ,x signifies an in=m+ quantity4 ,pure =m itself is b a negation ( t :i* =m]ly fill$ x4 ,!n1 too1 ! =mal is purely artificial because x is a m5tal con/ruction4 ,ess5tially !re is z mu* diff]5ce betwe5 ! purely =mal & ! a priori z betwe5 creator & creature1 z betwe5 pott] & clay4 ,! "o is ! build]1 ! o!r is ! mat]ial2 ! "o ! kn[] & ! o!r ! kn[n4 ,?us1 ! only reason t ! =mal is f\nd to be answ]able to ! a priori at all is due to ! fact t x is con/ruable only ^u ! basis ( ! a priori4 ,b be+ s is n suffici5t w>rant = its id5tification ) ! a priori4 ,! =mal m]ely repres5ts ! totality ( possibilities 9 ! univ]se z view$ by ! m9d2 b z ! numb] ( possibilities op5 to ! m9d is1 on acc\nt ( its nature & purpose limit$1 x is n to be suppos$ t x 7! m9d7 %all measure up to all ! possibilities (f]$ by ! =mal4 ,moreov]1 x is c]ta9 t no sane m9d *]i%es ! hope t !re %all ev] be f\nd 9 ! univ]se ( life & =m a congru5ce = all ( ! possibilities held out by ! purely =mal4 ,z an et]nal pr9ciple ( m9d1 ! a priori is 9 agreem5t ) ! div9e m9d ( ! kosmos4 ,9 its apo/]iority ! m9d is ( div]se t5d5ces1 qualities & *>act]i/ics4 ,apriorily1 x acts 9 unison ) ! et]nal purpose ( life & ! univ]sal m9d4 ,9 its apo/]iority1 x (t5 goes awry4 ,9 its apriority x c nev] be insane2 insanity is a symptom ( ! morbid a po/]iori4 ,! m9d 9 man acts ! same z m9d 9 ! vegetal & l[] animal k+doms4 ,metabolism & katabolism1 inde$ all cell-activity1 are a priori p]=mances ( ! m9d4 ,gr[? & all its ph5om5a1 ! cyclicism ( natural processes1 & e activity connect$ !re) belong to ! category ( ! a priori4 ,cells multiply1 divide1 build up & te> d[n tissues & !y d x intuitively4 ,mo/ c]ta9ly ^! functions are p]=m$ )\t any assi/ance f ! intellect4 ,all ! myriad activities 9 nature ) :i* ! intellect 9 man has n ! slighte/ conc]n1 truly act+ 9 accord ) "s primordial impetus1 are activities a priori4 ,n[ :at is ! attitude ( ! intellect1 9 ! light ( ! a priori1 t[>ds space & ! "q ( dim5sionality8 ,x is evid5t t no matt] :at ?is attitude may be x is 9 agreem5t ) ! con/itution ( ?+s & ( ! univ]se4 ,& if s1 x is "r & )\t illusion4 ,x is also evid5t t :atev] notion a po/]iori ! intellect may ent]ta9 ) respect to ^! que/ions is unavoidably liable to ! illusion>y drawbacks common to conclusions bas$ ^u limit$ exp]i5ce4 ,! geometric view ( space belongs to ! category ( ! a po/]iori4 ,h5ce x is subject to ! usual imposition ( error4 ,t]sely /at$1 ,,kant's view ( space is t x is a =m ( intuition1 a =m a priori1 a transc5d5tal =m4 ,z su* he consid]$ x to be a native =m ( p]ception n belong+ to ! category ( s5se-deliv]ies4 ,accord+ly1 space is a =m ( intuition aris+ out ( & inh]+ 9 ! con/itution ( m9d4 ,x is a notion :i* con/itutes ! univ]sal & et]nal pr]equisite ( m9d & is1 !re=e1 intr9sically necess>y to all phases ( m5tation4 ,n[1 ?is be+ true j :at may be said to be ! relation ( dim5sionality to ?is a priori =m ( space :i* is f\nd to exi/ 9 ! m9d z an et]nal aspect ( its nature8 ,does ! m9d intuitively measure its cont5ts or its op]ations by ! empirical /&>d ( space-measurem5t kn[n z dim5sion8 ,is ! attitude ( ! m9d t[>ds ! objectively real "o ( discrim9ation a priori z to ! direction or dim5sion 9 :i* a p]cept may orig9ate8 ,9 o!r words1 does ! m9d habitually & intuitively ref] its data to a sy/em ( cord9ates = f9al det]m9ation8 ,!re is no o!r answ] b t ! m9d makes no su* ref]5ce & is dep5d5t ^u no k9d ( cord9ate sy/em 9 any ( its op]ations a priori4 ,z a =m ( intuition1 ! space notion is pres5t 9 ! m9d z a scope ( exi/5ce1 ( motility1 ( be+ & ( %e] room9ess4 ,! notion ( direction or dim5sion1 be+ an artificial con/ruction1 does n ent] into ?is =m ( intuition at all4 ,x is only :5 ! m9d comes to elaborate ^u its p]ceptive p]=mances & possibilities t ! que/ions ( relations1 positions & directions arise4 ,b ?is latt] is a matt] sep>ate & di/9ct f ! /ate ( aw>5ess :i* embodies ! notion ( space4 ,dim5sion is an arbitr>y norm con/ruct$ by ! m9d = ! det]m9ation ( v>i\s positions 9 space4 ,x is an accid5t or by-product ( ! process ( elaborative cognition1 a conv5i5t & appropriate means ( measurem5t = objects 9 space & _! space-relations4 ,b x is no m a priori ?an a foot rule or a squ>e4 ,b be+ purely an empirical product x may be said to be an aspect ( psy*og5esis because x relates to ! evolution>y aspect ( m9d4 ,! assumption may !re=e be all[$ t ! m9d may1 9 ! c\rse ( its evolution1 f9d x conv5i5t & appropriate to devise an additional ord9ate or dim5sion to satisfy ! necessities ( its m complex ramifications into ! nature ( ?+s & to det]m9e _! greatly increas$ space-relations4 ,x may be ev5 possible = ! m9d to function normally 9 a space ( f\r dim5sions4 ,b ?is w\ld simply be a new adju/m5t1 n a *ange 9 ! ess5tial nature ( m9d4 ,x w\ld be l ! s]ies ( adju/m5ts to environm5ts :i* man has made 9 ! onw>d movem5t ( civilization4 ,!re has be5 no s]i\s *ange 9 ! manhood p] se ( man4 ,t has rema9$ ! same2 !re has be5 m]ely a complication ( environm5tal influ5ces4 ,simil>ly1 9 ! acquisition ( f\r-dim5sional p[]s1 grant+ t su* an acquisition is possible1 !re is no?+ to be add$ to ! aprior9ess ( m9d itself4 ,is x n1 !re=e1 logical to assume t ! discov]y ( a f\r? cord9ate & ! consequ5t conceptualization ( ! same1 po9t to ! developm5t 9 ! m9d ( a greatly ext5d$ faculty1 m ke5ly p5etrative p[]s ( cognition & a fur!r div]sification ( its environm5ts ?an x has hi!rto enjoy$8 ,inde$1 x seems s4 ,,*apt] ,v ,,! ,,f\r? ,,dim5sion ,! ,ideal & ! ,repres5tative ,nature ( ,objects 9 ! ,s5sible ,_w--,! ,psy*ic ,fluxional ! ,basis ( ,m5tal ,diff]5ces--,natural & ,artificial ,symbols--,use ( ,analogies to ,prove ! ,exi/5ce ( a ,f\r? ,dim5sion--,! ,g5]ation ( a ,hyp]cube or ,tess]act--,possibilities 9 ! ,_w ( ! ,f\r? ,dim5sion--,"s ,logical ,difficulties ,inh]+ 9 ! ,f\r-,space ,conception--,! ,fallacy ( ! ,plane-,rotation ,hypo!sis--,c4 ,h4 ,,h9ton & ,major ,,ellis on ! ,f\r? ,dim5sion4 ,! _w ( ma!sis is truly a m>vel\s doma94 ,va/ are its possibilities & va/] /ill its sweep ( conceivability4 ,x is ! k+dom ( ! m9d :]e1 9 regal fre$om1 x may p]=m feats :i* x is impossible to actualize 9 ! ph5om5al univ]se4 ,9 fact1 !re is no necessity to consid] ! limitations impos$ by ! actualities ( ! s5su\s _w4 ,logic is ! ar*itect ( ?is region1 & = x !re is no limit to ! admissibility ( hypo!ses4 ,^! may be multipli$ at w1 & legitimately s4 ,! *ief error lies 9 ! attempt to make !m appe> z actual facts ( ! physical _w4 ,ma!maticians1 speculat+ ^u ! possibilities ( ma!tic con/ructions & =gett+ ! necess>y di/9ctions :i* %\ld be recogniz$ z diff]5tiat+ ! two worlds1 9 _! en?usiasm h be5 l$ into ! error ( po/ulat+ z qualities ( ! ph5om5al _w ! *>act]i/ics ( ! conceptual4 ,accord+ly1 a great deal ( confusion z to ! prop] limits & re/rictions ( ^! conceptions has aris5 & !re /ill may be f\nd ^? :o are en?usia/ically endeavor+ to pu% ! actualities ( ! physical ov] into ! conceptual4 ,b 9 assum+ any attitude t[>ds ma!tic propositions1 especially ) a view to demon/rat+ _! actuality1 v c>eful discrim9ation z to ! ess5tial qualities & _! connotations %\ld be made4 ,h5ce1 be=e tak+ up a brief /udy ( ! f\r? dim5sion prop]1 x is deem$ fitt+ to indicate "s ( ! fundam5tal di/9ctions :i* e /ud5t ( ^! que/ions %\ld be able to make ) ref]5ce to ! data :i* he meets4 ,all objects ( ! s5sible _w h bo? an ess5tial or ideal nature & a repres5tative or s5su\s nature4 ,t is1 !y may be /udi$ f ! /&po9t ( ! ideal z well z ! s5su\s4 ,! repres5tative nature is t :i* we recognize z ! mode ( appe>ance to our s5ses :i*1 z ,,kant held1 is n ! ess5tial or ideal "* ( ! ?+ itself4 ,= !re is q z mu* diff]5ce betwe5 ! s5su\s p]cept & ! real ?+ itself z betwe5 an object & its %ad[4 ,9 fact1 a concept view$ 9 ?is light1 may be se5 to h all ! *>act]i/ics ( an ord9>y %ad[2 = in/ance1 ! %ad[ ( a tree4 ,view x z ! sun is ris+2 x w !n be se5 to appe> v mu* elongat$1 becom+ less 9 l5g? & m di/9ct 9 outl9e z ! sun rises to a position directly ov]head4 ,! elongation may aga9 be se5 :5 ! sun is sett+4 ,?r\gh\t ! day z ! sun assumes diff]5t angles ) ref]5ce to ! tree ! proportions & def9it5ess ( ! %ad[ v>y accord+ly4 ,?us ! angul>ity ( ! sun1 ! int5sity & fullness ( ! light & ! %ape & size ( ! tree op]ate to det]m9e ! "* ( ! %ad[4 ,mu* ! same ?+ is true ( a s5su\s repres5tation4 ,if we exam9e c>efully our ideas ( geometric quantities & magnitudes1 x w be f\nd t ! concepts !mselves are n id5tical ) ! objects ( ! physical _w1 b m]e m5tal %ad[s ( !m4 ,! angul>ity ( consci\sness1 or ! di/9ctness ( "o's /ate ( aw>5ess1 be+ analog\s to simil> attitudes 9 ! sol> influ5ce are ! ma9 det]m9ants ( ! "* ( ! m5tal %ad[ or concept4 ,:]e=e ma!matical spaces or magnitudes are n s5su\s ?+s & h !re=e no m real exi/5ce ?an a %ad[1 & /rictly speak+ n z mu*2 = a %ad[ may be se51 :ile su* magnitudes c only be conceiv$4 ,x may be urg$ t s9ce we c conceive ( su* ?+s !y mu/ h exi/5ce ( "s k9d4 ,& s !y h1 b x is an exi/5ce ( a diff]5t k9d f t :i* we recognize z belong+ to ?+s 9 ! s5sible _w4 ,!y h a conceptual exi/5ce1 b n a s5su\s "o4 ,!re9 lies ! great diff]5ce4 ,to be sure1 a %ad[ is a m or less true repres5tation ( ! ?+ to :i* x p]ta9s4 ,t ?is is true c be e/abli%$ empirically4 ,simil>ly1 ! degree ( congruity betwe5 objects & concepts likewise may be det]m9$4 ,if ?is 7 n true we %\ld be v mu* disappo9t$ ) :at we f9d 9 ! ph5om5al _w & c\ld nev] be q sure t ! m5tograph exi/+ 9 our m9ds 0 a fai?ful repres5tation ( ! ?+ :i* we might be exam9+4 ,b really ! f\ndation = su* a disappo9tm5t is pres5t 9 e concept1 e p]cept ) :i* ! m9d deals4 ,?is disappo9tm5t1 al?\gh 9 actual exp]i5ce is r$uc$ to an almo/ negligible quantity1 is due to ! failure ( s5su\s objects to con=m :olly to ! specific details ( ! m5tal %ad[ or m5tograph4 ,?is lack ( congru5ce betwe5 ! m5tal picture & ! object itself is necess>y = obvi\s reasons4 ,x is m>k$ly obs]vable 9 ! e>ly ef=ts ( a *ild 9 le>n+ di/ances1 weights1 resi/ances1 temp]atures & ! l4 ,no inconsid]able "t is requir$ = ! *ild to be able correctly to h>monize 8 s5se-deliv]ies ) actual conditions4 ,o!rwise1 ! *ild w\ld nev] make any ( ! ludicr\s mi/akes ( judgm5t ( :i* x is guilty :5 try+ to get its be>+s 9 ! _w ( ! s5ses4 ,9 ! c\rse ( "t ! *ild gradually le>ns by exp]i5ce t c]ta9 ?+s are true ( objects1 di/ances1 temp]atures1 resi/ances1 etc41 & t c]ta9 ?+s are n true ( !m4 ,he le>ns ^! ?+s by actually contact+ v>i\s objects4 ,he is !n compet5t to r5d] correct judgm5ts1 )9 c]ta9 limits1 z to ! conditions :i* he f9ds 9 ! s5sible _w4 ,& ! all[ances1 equations & corrections :i* 8 motor1 s5sory & psy*ic me*anisms le>n to make 9 *ildhood s]ve = all subsequ5t "t4 ,& ?is is important to rememb]2 = ! mature m9d is apt to =get or ov]look ! adaptations :i* ! *ild-m9d has made 9 its gr[?4 ,if !re 7 no su* diff]5ces betwe5 ! concept & ! ?+ itself1 actual physical contact w\ld n be necess>y4 ,= "o c\ld rely :olly ^u ! s5se-deliv]ies & ea* s5se might op]ate entirely indep5d5tly ( all ! o!rs z !re w\ld be no necessity to correct ! deliv]y ( "o by ^? ( ! o!rs4 ,?is1 ( c\rse1 raises ! "q z to ! necessity ( s5se-exp]i5ce at all "u conditions :]e !re w\ld be no disp>ity betwe5 ! ?+ itself & ! ideal repres5tation ( x 9 ! m9d4 ,! abs5ce ( ?is v>iable quantity w\ld op5 to ! m9d ! possibility ( really kn[+ ! ess5tial nature ( objects 9 ! ph5om5al _w1 a condition ( affairs :i* is admitt$ly n[ )\t ! range ( ! p[]s ( ! m9d4 ,at any rate1 ! ess5tial ?+ness ( objects c nev] be compreh5d$ by ! m9d until ! dim9ution ( ?is disp>ity betwe5 ! object ( s5se & ! m5tal picture ( x :i* exi/s 9 ! consci\sness has proce$$ to su* a limit z ei!r completely to h oblit]at$ x or to su* an ext5t t ! psy*ic fluxion is s slight z n to matt]4 ,x is believ$ t ! results ( m5tal evolution1 z ! m9d approa*es ! transf9ite z a limit1 w op]ate to m9imize ! fluxional quantity :i* subsi/s betwe5 all objects ( s5se & _! ideal repres5tation z data ( consci\sness4 ,! conclusion t ! m9d ( e>ly m5 :o liv$ hundr$s ( ?\s&s & p]haps millions ( ye>s ago on ?is planet consum$ a mu* long] "t 9 le>n+ ! adju/m5ts betwe5 ! objects :i* x contact$ 9 ! s5su\s _w & ! elem5t>y repres5tations :i* 7 regi/]$ 9 its y\?ful consci\sness ?an is to-day requir$ = simil> processes seems to be dem&$1 & sub/antiat$ z well1 by :at is kn[n ( ! phyletic developm5t ( ! m9d 9 ! human race4 ,9 view ( ! above1 x is ?\ght t ! duration ( su* simple m5tal processes s]v$ n only to prolong ! physical life ( ! man ( ^? e>ly days1 b may also acc\nt = ! pu]ility & incapacity ( ! m9d at t /age4 ,n t ! sl[ m5tal processes 7 active causative ag5cies 9 l5g!n+ ! life ( man1 b t !y toge!r ) ! crass physicality ( man necessitat$ a long] physical life4 ,?is1 p]haps 9 a l>g] s5se ?an any o!r consid]ation1 acc\nts = ! fundam5tal discrepancies 9 ! m9d ( ! primitive man 9 comp>ison ) ! effici5cy ( ! m9d ( ! pres5t-day man4 ,9 view ( ! pot5tial "* ( m9d & 9 ! light ( ! well graduat$ scale ( its accompli%m5ts1 x is und\bt$ly safe to conclude t ! quality ( m5tal capacities is proportional to ! psy*ic fluxional :i* may exi/ at any "t betwe5 ! ideal & ! ess5tial or real4 ,m5tal diff]5ces & pot5tialities 9 g5]al may be due to ! magnitude ( ! psy*ic fluxional or diff]5tial t exi/s betwe5 ! conceptual & ! p]ceptual univ]se4 ,9 "s m9ds x may be great] ?an 9 o!rs4 ,! *asm betwe5 ?+s-9-!mselves & ! m5tal notion p]ta9+ !reto may v>y 9 a direct ratio to ! individual m9d's place 9 psy*og5esis1 & !re=e1 be ! key to all m5tal diff]5ces 9 ?is respect4 ,mo/ c]ta9 x is t !re may be m>k$ fluctuations 9 ! judicial approa* ( m9ds t[>ds any psy*ic end4 ,9 o!r words1 !re is n only a fluxional or diff]5tial betwe5 ! object & its repres5tation1 b also a diff]5tial betwe5 ! approa* ( "o m9d & ano!r 9 ! judicial det]m9ation ( notions conc]n+ ideas4 ,9 ?is way1 diff]5ces ( op9ions z to ! "r & wrong ( judgm5ts arise4 ,inde$1 !re seem to be zones ( aff9ity = m9ds ( simil> *>act]i/ics1 or m9ds t h ! same degree ( diff]5tial2 s t1 9 *oos+ among ! _m possible judgm5ts pr$icable ^u a species ( data1 all ^? m9ds hav+ ! same degree ( psy*ic diff]5tial discov] a special aff9ity or agreem5t among !mselves4 ,h5ce1 we h cults1 s*ools ( ?\ght1 & v>i\s o!r sectional bodies t f9d a basis ( agreem5t = _! op]ations 9 ?is way4 ,! outcome ( ?is rem>kable intellectual ph5om5on is t !re are z _m diff]5t k9ds ( judgm5ts z !re are zones ( aff9ity among m9ds4 ,v>i\s sy/ems ( philosophy owe _! exi/5ce to ^! consid]ations1 & ! consid]ations !mselves fl[ f ! fact t all intellectual op]ations are ess5tially sup]ficial2 because !re is no means by :i* !y may p5etrate to ! /eady fl[+ /ream ( reality :i* p]vades & su/a9s objects 9 ! s5sible _w4 ,9 view1 !re=e1 ( ! =ego+ & ) special ref]5ce to geometric con/ructions1 x is necess>y 9 approa*+ a /udy ( ! f\r-space t x be und]/ood at ! outset t ! f\r? dim5sion c nei!r be actualiz$ nor made objectively possible ev5 9 ! slighte/ degree 9 ! p]ceptual _w2 because x belongs to ! _w ( pure ?\ght & exi/s !re z an extra p]sonal affair1 sep>ate & di/9ct f ! _w ( ! s5ses4 ,z says ,,simon ,,newcomb3#af ,! exp]i5ce ( ! race & all ! ref9em5ts ( mod]n sci5ce may be reg>d$ z %[+ q conclusively t1 )9 ! limits ( our exp]i5ce1 !re is no motion ( mat]ial masses1 9 ! direction ( a f\r? dim5sion1 no physical ag5cy :i* we c assume to h its orig9 9 regions to :i* matt] _c move1 :5 x has ?ree degrees ( fre$om4 ,!re is1 h[ev]1 no logical objection to ! /udy ( ! f\r? dim5sion z a purely hypo!tical "q1 if by pursuit ( ! same an improvem5t ( me?ods ( rese>* & ( ! outlook ^u ! field ( ! actual may be ga9$4 ,h5ce1 x is ) ?is attitude ( m9d t we approa* ! consid]ation ( ! f\r? dim5sion4 #af ,vide ,sci5ce1 ,vol4 ,,vii1 p4 #b1 ,no4 #aeh1 #ahih4 ,v>i\s ef=ts h be5 made to r5d] ! conception ( a f\r? dim5sion ( space ?9kable4 ,! /ud5t ( space has reason$3 ,we say t !re are ?ree dim5sions ( space4 ,:y %\ld we /op "h8 ,may !re n be spaces ( f\r dim5sions & m8 ,or he has said3 ,if ',a' may repres5t ! side ( a squ>e1 ,a#b its area1 & ,a#c ! volume ( a cube ) edge equal to ,a2 :at may ,a#d1 ,a#e or ,an? repres5t 9 our space8 ,! conclusion1 ) respect to ! quantity ,a#d1 has be5 t x %\ld repres5t a space ( f\r dim5sions4 ,algebraic quantities1 h[ev]1 repres5t nei!r objects 9 space nor space qualities except 9 a purely conv5tional mann]4 ,all ef=ts to ju/ify ! objective exi/5ce ( a f\r? dim5sion bas$ ^u su* reason+ w1 !re=e1 fail2 because ! basis ( su* argum5ts is itself faulty4 ,9 ! s5t5ce3 ,! man loves 8 bottle1 ! ?+ meant is n ! bottle1 b :at ! bottle conta9s4 ,= ! purpose ( ! figure ! bottle signifies its cont5ts4 ,!re is no m real connection betwe5 ! bottle & :at x conta9s ?an betwe5 any ^w & ! object = :i* x /&s4 ,words are said to be symbols ( ideas4 ,b !y are n natural symbols2 !y are conv5tional symbols1 made = ! purpose ( catalogu+1 index+ & sy/ematiz+ our k4 ,words c be divorc$ f ideas & objects1 or r h nev] _h any real connection ) !m4 ,!re are two classes ( natural symbols1 namely2 objects & ideas4 ,^!1 objects & ideas1 symbolize realities4 ,realities are imp]ceptible & incompreh5sible to ! intellect :i* has aptitude only = a slight compreh5sion ( ! symbols ( realities4 ,= in/ance1 a tree is a natural symbol4 ,x repres5ts an actuality :i* is imp]ceptible to ! intellect4 ,! intellect c deal only ) ! s5sible symbol4 ,x is a natural symbol2 because x is possible directly to trace a liv+ connection betwe5 ! tree & ! tree-reality4 ,t is1 x w\ld be possible s to trace out ! vital connection betwe5 ! tree & its reality if ! intellect _h aptitude = su* trac]y4 ,b1 9 reality1 s9ce x has no su* aptitude1 x rema9s = ! "w ( t high] faculty ?an ! intellect :i* recognizes bo? ! connection & ! intellect's inability to trace x4 ,fur!r1 an object is call$ a natural symbol because x is ! bridge betwe5 s5su\s repres5tation & reality4 ,x is z if "o c\ld beg9 at ! surface ( an object & by a subtle process ( elim9ation & excortication arrive at ! he>t ( ! univ]sum ( reality4 ,no su* consummation may be rea*$ by deal+ ) words :i* h m]ely an artificial relation%ip ) ! objects :i* !y signify4 ,aga91 ideas1 t is1 ideas t are univ]sal 9 application & h _! roots 9 ! great ocean ( reality1 are natural symbols2 because if x 7 possible to h&le an idea ) ! physical h&s x w\ld be possible to arrive at ! he>t ( t :i* x symboliz$ )\t ev] los+ our connection ) ! idea itself4 ,9 o!r words1 ideas & objects1 unlike words1 c nev] be divorc$ f t :i* !y symbolize4 ,bo?1 be+ ( ! same class1 are ! opposite poles ( realities4 ,?is !n is ! diff]5ce betwe5 natural symbols & artificial symbols--t a natural symbol1 su* z objects & ideas1 is copol> ) reality :]eas an artificial symbol1 su* z words1 geometric con/ructions & ! l n only lacks ?is copol>ity b is itself a symbol ( natural symbols4 ,x is1 !re=e1 inconceivable t because ! algebraic quantity ,a#c has be5 arbitr>ily decre$ to be a repres5tation ( ! volume ( a cube1 e su* quantity 9 ! algebraic s]ies %all actually repres5t "s object or set ( objects 9 ! physical _w4 ,ev5 if x be grant$ t su* may be ! case1 is x n c]ta9 t !re is a limit to ?+s 9 ! objective univ]se8 ,yet !re may n be any limit to algebraic or ma!matical det]m9ations4 ,! mat]ial univ]se is limit$ & condition$2 ! _w ( ma!sis is unlimit$ & uncondition$ save by its own limitations & conditions4 ,x is irrational to expect t physical ph5om5a %all ju/ify all ma!matical pr$icates4 ,!re is p]haps no s+le ma!matical desid]atum or consid]ation :i* may be said to be ! natural symbolism ( realities2 = ! :ole ( ma!matical conclusions is a mass ( artificial & arbitr>y b concordant symbols ( ! crass] or ne!r pole ( ! antipodes ( realism4 ,x is exce$+ly dang]\s1 !re=e1 to pr$icate ^u su* a f>-fet*$ symbolism z ma!matics furni%es any?+ purport+ to deal ) ultimate realities4 ,& ^? :o insi/ ^u do+ s are ei!r bl9d !mselves to ^! limitations or are madly endeavor+ to befog ! m9ds ( o!rs :o are dep5d5t ^u !m = lead]%ip 9 que/ions ( ma!matical import4 ,analogies h be5 unsp>+ly us$ 9 ef=ts to popul>ize ! f\r-space conception & mu* ( ! viol5ce :i* has be5 done to ! notion is due to ?is vag>y4 ,! ma!matical publici/1 9 try+ to give a m5tal picture ( ! f\r? dim5sion1 exam9es ! appe>ances ( ?ree dim5sional be+s z !y might appe> to a two dim5sional be+ or duodim4 ,he imag9es a race ( be+s end[$ ) all ! human faculties except t !y live 9 a l& ( b two dim5sions--l5g? & bread?4 ,he ?9ks ( !m z %ad[s ( ?ree dim5sional be+s to :om !re are no su* conceptions z up & d[n4 ,!y c see no?+ nor s5se any?+ 9 any way t is )\t _! plane4 ,!y c move 9 any direction )9 ! plane 9 :i* !y live1 b c h no idea ( any movem5t t might c>ry !m )\t t plane4 ,a h\se = su* be+s might be simply a s]ies ( rectangles4 ,"o ( !m might be z safe beh9d a l9e z a tridim or ?ree dim5sional be+ w\ld be beh9d a /one wall4 ,a bank safe = ! unodim w\ld be a m]e circle4 ,a duodim 9 any two dim5sional prison might be rescu$ by a tridim )\t ! op5+ ( doors or ! break+ ( walls4 ,an action ( a tridim p]=m$ s z to contact _! plane w\ld be to !m a miracle1 absolutely unacc\ntable ^u ! basis ( any kn[n fact to ! unodim or duodim4 ,a tridim might g into a h\se :]e liv$ a family ( duodims1 appe> & disappe> )\t be+ detect$ or its ev] be+ discov]$ h[ he accompli%$ su* a m>vel\s feat4 ,our miracles1 aft] ! same fa%ion1 are said to be ! antics ( "s f\r dim5sional be+ :o has simil> access to our ?ree dim5sional _w & ^: actions are simil>ly inexplicable to u4 ,s ! analogies h be5 multipli$4 ,b ! temptation to apply ! consequ5ces ( su* reason+ to actual ?ree-space conditions has be5 s great t _m h yield$ to x & h consequ5tly s\ght actually to expla9 physical ph5om5a ^u ! basis ( ! f\r? dim5sion4 ,! utilit>ian side ( ! "q ( hyp]space has n be5 neglect$ ei!r4 ,& s1 e>ly 9 ! developm5t ( ! hypo!sis & its v>i\s connotations1 ! att5tion ( inve/igators 0 turn$ to ?is aspect ( ! inquiry4 ,/range possibilities 7 reveal$ z a result4 ,= in/ance1 x 0 f\nd t an exp]t f\r? dim5sional op]ator is possess$ ( extraord9>y advantages ov] ord9>y tridim5sional be+s4 ,op]at+ f 8 my/]i\s hid+ place 9 hyp]space1 he c\ld easily appe> & disappe> 9 s my/]i\s a mann] t ev5 ! mo/ /rongly seal$ *e/s ( treasures w\ld be easily & entirely at 8 disposal4 ,no city police1 ,scotl& ,y>d detective nor g5d>me c\ld h any t]rors = him4 ,,drs4 ,,jekyll & ,,messrs4 ,,hyde might ab\nd ev]y:]e )\t fe> ( detection4 ,objects z well z p]sons might be made to pass into or out ( clos$ rooms )\t p5etrat+ ! walls1 ?us mak+ escape easy = ! imprison$4 ,no tridim5sional /ate1 condition or sy/em ( arrangem5ts1 accord+ly1 w\ld be safe f ! ravages ( evilly incl9$ f\r dim5sional entities4 ,objects t n[ are limit$ to a po9t or l9e rotation c\ld 9 ! f\r? dim5sion rotate ab\t a plane & ?us fur!r increase ! p]plexities ( our eng9e]+ & me*anical problems2 f\r l9es c\ld be erect$ p]p5dicul> to ea* o!r :]eas 9 ?ree space only ?ree su* l9es c be erect$2 ! "r h& c\ld be maneuv]$ into ! f\r? dim5sion & be recov]$ z a left h&2 ! my/]ies ( gr[?1 decay & dea? w\ld f9d a satisfactory explanation on ! basis ( ! f\r? dim5sional hypo!sis & _m1 if n all1 ( ! p]plex+ problems ( physiology1 *emi/ry1 physics1 a/ronomy1 an?ropology & psy*ology w\ld yield up _! my/]ies to ! skill ( ! f\r? dim5sional op]ator4 ,m>vel\s possibilities ^! & mu* to be desir$6 ,b ! mo/ rem>kable ?+ ab\t ^! s-call$ possibilities is _! impossibility4 ,x is ?is k9d ( erratic reason+ t has br\ght ! conception ( a f\r? dim5sion into g5]al disrepute ) ! popul> m9d4 ,x is to be regrett$1 too1 = ! notion is a p]fectly legitimate "o 9 ! doma9 ( ma!sis :]e x orig9at$ & rightly belongs4 ,x is n to be wond]$ at t metageometricians & o!rs %\ld at fir/ surmise t1 9 ! f\r-space1 !y _h f\nd ! key to ! deep my/]ies ( nature 9 all bran*es ( inquiry4 ,= s va/ 0 ! doma9 & s m>vel\s 7 ! possibilities :i* ! new movem5t reveal$ t x 0 to be expect$ t ^? :o 7 privileg$ to get ! fir/ glimpses !re( w\ld n be able to realize fully _! significance4 ,b ! /\nd ( _! m9ds & ! att5dant magnification ( ! elem5ts :i* !y discov]$ 7 b incid5ts 9 ! l>g] & m compreh5sive process ( adju/m5t to ! great out/&+ facts ( psy*og5esis :i* is only fa9tly =e%ad[$ 9 ! s-call$ hyp]dim5sional4 ,! :ole scope ( inquiry connect$ ) hyp]space is n an end 9 itself4 ,x is m]ely a means to an end4 ,& t is ! prep>ation ( ! human m9d = ! inborn+ ( a new faculty & consequ5tly m l>gely ext5d$ p[]s ( cognition4 ,metageometrical discov]ies are !re=e ! excresc5ces ( a deep]1 m significant _w process ( m5tal unfoldm5t4 ,!y belong to ! matut9al ph5om5a incid5t to ?is new /age ( m5tal evolution4 ,all su* inve/igations are b ! prelim9>y ex]cises :i* give bir? to new t5d5cies :i* are de/9$ to fl[] =? into additional faculties & capacities4 ,s t x is well t ! evolution>y aspect ( ! "q be n ov]look$2 = !re is dang] ( ?is on acc\nt ( ! magnitude & kosmic importance ( its scope ( motility4 ,a geometric l9e is said to be a space ( "o dim5sion4 ,a plane is a space ( two dim5sions & a cube1 a space ( ?ree dim5sions4 ,9 figure #g bel[1 ! l9e ab is said to be "o dim5sional2 because only "o cord9ate is necess>y to locate a po9t-position 9 x4 ,! plane1 abcd1 figure #h1 is said to be two dim5sional because two cord9ates1 ab & db are requir$ to locate a po9t1 z ! po9t b4 ,! cube abcdefgh1 figure #i1 is said to be tridim5sional1 because1 9 ord] to locate ! po9t b1 = in/ance1 x is necess>y to h ?ree cord9ates1 ab1 bc & gb4 ,! tess]act is said to be f\r dim5sional1 because1 9 ord] to locate ! po9t b1 9 ! tess]act1 x is necess>y to h f\r cord9ates1 ab1 bc1 bb' & h'b1 figure #aj4 ,a -------------------------------- ,b ,,fig4 #g4 ,a ------------------------------ ,b ,c ------------------------------ ,d ,,fig4 #h4 ,x w be not$ t 9 figures #h1 #i & #aj1 ! elem5t ( p]p5dicul>ity ent]s z a necess>y det]m9ation4 ,9 figure #h1 ! l9es ab & bd are p]p5dicul> to ea* o!r4 ,simil>ly1 9 ,fig4 #aj1 l9es ab1 bc1 bb' & h'b are p]p5dicul> to "o ano!r4 ,t is1 at _! int]sections1 !y make "r angles4 ,simil>ly1 figures repres5t+ any numb] ( dim5sions may be con/ruct$4 ,illu/ration3 ,,fig4 #i4 ,illu/ration3 ,,fig4 #aj4--,! ,tess]act4 ,! l9e ab repres5ts a "o-space4 ,an entity liv+ 9 a "o space is call$ a unodim4 ,! plane1 abcd1 repres5ts a two-space1 & entities liv+ 9 su* a space are call$ duodims4 ,! cube1 abcdefgh1 repres5ts a ?ree-space & entities inhabit+ su* a space are call$ tridims4 ,figure #aj repres5ts a f\r-space1 & its inhabitants are call$ qu>todims4 ,ea* ( ! above-m5tion$ spaces is said to h c]ta9 limitations peculi> to itself4 ,! f\r? dim5sion is said to lie 9 a direction at "r angles to ea* ( our ?ree-space directions4 ,?is1 ( c\rse1 gives rise to ! possibility ( g5]at+ a new k9d ( volume1 ! hyp]volume4 ,! hyp]cube or tess]act is describ$ by mov+ ! g5]at+ cube 9 ! direction 9 :i* ! f\r? dim5sion ext5ds4 ,= in/ance1 if ! cube1 ,fig4 #i1 7 mov$ 9 a direction at "r angles to ea* ( its sides a di/ance equal to "o ( its sides1 a figure ( f\r dim5sions1 ! tess]act1 w\ld result4 ,! initial cube1 abcc'e'fhh'1 :5 mov$ 9 a direction at "r angles to ea* ( its faces1 g5]ates ! hyp]cube1 ,fig4 #aj4 ,! l9es1 aa'1 bb'1 cc'1 dd'1 ee'1 ff'1 gg'1 hh'1 are assum$ to be p]p5dicul> to ! l9es meet+ at ! po9ts1 a1 b1 c1 d1 e1 f1 g1 h4 ,h5ce a'b'1 b'd1 dd'1 d'a'1 ef1 fg1 gg'1 g'e1 repres5t ! f9al cube result+ f ! hyp]space movem5t4 ,c\nt+ ! numb] ( cubes t compose ! hyp]cube we f9d t !re are eight4 ,! g5]at+ cube1 abcc'e'f'hh'1 & ! f9al cube1 a'b'1 b'd1 dd'1 d'a'1 ef1 fg1 gg'1 g'e1 make two cubes2 & ea* face g5]ates a cube mak+ eight 9 all4 ,a tess]act1 !re=e1 is a figure b\nd$ by eight cubes4 ,to f9d ! diff]5t elem5ts ( a tess]act1 ! foll[+ rules w apply3 #a4 ,to f9d ! numb] ( l9es3 ,multiply ! numb] ( l9es 9 ! g5]at+ cube by two1 & add a l9e = ea* po9t or corn] 9 x4 ,e4g41 #b #ab #bd #h #cb4 #b4 ,to f9d ! numb] ( planes1 faces or squ>es3 ,multiply ! numb] ( planes 9 ! g5]at+ cube by #b & add a plane = ea* l9e 9 x4 ,e4g41 #b #f #ab #bd4 #c4 ,to f9d ! numb] ( cubes 9 a hyp]cube3 ,multiply ! numb] ( cubes 9 ! g5]at+ cube1 "o1 by two & add a cube = ea* plane 9 x4 ,e4g41 #b #a #f #h4 #d4 ,to f9d ! numb] ( po9ts or corn]s3 ,multiply ! numb] ( corn]s 9 ! g5]at+ cube by #b4 ,e4g41 #b #h #af4 99 99 99 99 99 ,9 a plane !re may be ?ree po9ts ea* equally di/ant f "o ano!r4 ,^! may be jo9$1 =m+ an equilat]al triangle 9 :i* !re are ?ree v]tices or po9ts1 ?ree l9es or sides & "o surface4 ,9 ?ree-space !re may be f\r po9ts ea* equidi/ant f ! o!rs4 ,at ! v]tices ( a regul> tetrah$ron may be f\nd su* po9ts4 ,! tetrah$ron has f\r po9ts1 "o at ea* v]tex1 #f l9es & #d equilat]al triangles1 z 9 ,fig4 #aa4 ,9 f\r-space1 we h #e po9ts ea* equidi/ant f all ! re/1 giv+ ! hyp]tetrah$ron4 ,?is f\r dim5sional figure may be g5]at$ by mov+ ! tetrah$ron 9 ! direction ( ! f\r? dim5sion1 z 9 ,fig4 #ab4 ,if a plane be pass$ ?r\gh ea* ( ! six edges ( ! tetrah$ron & ! new v]tex !re w be six new planes or faces1 mak+ #aj 9 all1 c\nt+ ! orig9al f\r4 ,f ! new v]tex !re is also a tetrah$ron re/+ ^u ea* base ( ! orig9al tetrah$ron s t !re are five tetrah$ra 9 all4 ,a hyp]tetrah$ron is a f\r-dim5sional figure consi/+ ( five tetrah$ra1 t5 faces1 #aj l9es & #e po9ts4 ,illu/ration3 ,,fig4 #aa4--,tetrah$ron4 ,illu/ration3 ,,fig4 #ab4--;,hyp]tetrah$ron4 ,,paul ,,c>us#ag sugge/s ! use ( mirrors s arrang$ t !y give eight repres5tations ( a cube :5 plac$ at _! po9t ( int]section4 ,he says3 ,if we build up ?ree mirrors at "r angles & place any object 9 ! int]sect+ corn] we %all see ! object n once1 b eight times4 ,! body is reflect$ bel[ & ! object ?us d\bl$ is mirror$ n only on bo? upright sides b 9 addition 9 ! corn] beyond1 appe>+ 9 ei!r ( ! upright mirrors co9cid+ly 9 ! same place4 ,?us ! total multiplication ( our tridim5sional b\nd>ies ( a f\r dim5sional complex is r5d]$ eight-fold4 ,we mu/ n[ be> 9 m9d t ?is repres5tation ( a f\r? dim5sion suff]s f all ! faults ( ! analog\s figure ( a cube 9 two dim5sional space4 ,! sev]al figures are n eight indep5d5t bodies b are m]e b\nd>ies & ! f\r dim5sional space is condition$ by _! int]relation4 ,x is t unrepres5table some?+ :i* !y inclose1 or 9 o!r words1 ( :i* !y are assum$ to be b\nd>ies4 ,if we 7 f\r dim5sional be+s we c\ld naturally & easily ent] into ! mirror$ space & transf] tridim5sional bodies or p>ts ( !m into ^? o!r objects reflect$ "h 9 ! mirrors repres5t+ ! b\nd>ies ( ! f\r dim5sional object4 ,:ile ?us on ! "o h& ! mirror$ pictures w\ld be z real z ! orig9al object1 !y w\ld n take up ! space ( our ?ree dim5sions1 & 9 ?is respect1 our me?od ( repres5t+ ! f\r? dim5sion by mirrors w\ld be q analog\s to ! cube pictur$ on a plane surface1 = ! space to :i* we 7be+ limit$ to our tridim5sional space-conception71 w\ld naturally relegate ! sev5 additional mirror$ images is unoccupi$ & if we %\ld make ! trial1 we w\ld f9d x empty4 #ag ,vide ,f\ndations ( ,ma!matics1 pp4 #ic-id4 ,! utility ( su* a repres5tation z t :i* ,,c>us outl9es 9 ! above is grant$1 i4e41 s f> z ! purpose :i* x s]ves 9 giv+ a g5]al idea ( :at a f\r-space object might be imag9$ to be l1 b ! illu/ration does n demon/rate ! exi/5ce ( a f\r? dim5sion4 ,x only %[s :at might be if !re 7 a f\r-space 9 :i* objects c\ld exi/ & be exam9$4 ,we1 ( c\rse1 h no "r to assume t because x c be %[n by analog\s reason+ t c]ta9 *>act]i/ics ( ! f\r? dim5sional object c be repres5t$ 9 ?ree-space ! possible exi/5ce ( su* an object is !reby e/abli%$4 ,n at all4 ,= !re is no imag9able condition ( tridim5sional me*anics 9 :i* an object may be said to h an objective exi/5ce simil> to t repres5t$ by ! mirror$ cube4 ,b !re are discrepancies 9 ?is repres5tation :i* well might be consid]$4 ,!y h virtually ! =ce ( invalidat+ some:at ! conception :i* ! analogy is design$ to illu/rate4 ,= in/ance1 9 ! case ( ! mirror$ object plac$ at ! po9t ( int]section ( ! ?ree mirrors built up at "r angles to ea* o!r4 ,^u exam9ation ( su* a con/ruction x is f\nd t ! reflection ( ! object 9 ! mirrors has n any p]ceptible connection ) ! object itself4 ,& ?is1 too1 despite ! fact t !y are reg>d$ z b\nd>ies ( ! hyp]cube2 especially is ?is true :5 x is not$ t ^! reflections are call$ ^u to play ! "p ( real1 palpable b\nd>ies4 ,if a f\r? dim5sional object 7 really l ! mirror-repres5tation x w\ld be op5 to s]i\s objections f all viewpo9ts4 ,! replacem5t ( any ( ! b\nd>ies requir$ 9 ! analogy w\ld necess>ily mean ! replacem5t ( ! hyp]cube itself4 ,9 o!r words1 if ! real cube be remov$ f its position at ! int]section ( ! mirrors no reflection w be se51 & h5ce no b\nd>ies & no hyp]cube4 ,! analogy :ile admitt$ly possess+ "s slight value 9 ! direction meant1 is nev]!less valueless s f> z a detail$ repres5tation is conc]n$4 ,s ! analogy falls d[n2 b once aga9 is ! "q rais$ z to :e!r ! s-call$ f\r? dim5sion c be e/abli%$ or prov5 at all ^u purely ma!matical gr\nds4 ,x also emphasizes ! necessity = a cle>] conception ( ! mean+ ( dim5sion & space4 ,! logical difficulties :i* beset ! hyp]space conception are dwelt ^u at l5g? by ,,james ,h4 ,,hyslop4 ,he says3#ah ,! supposition t !re are ?ree dim5sions in/ead ( "o1 or t !re are only ?ree dim5sions is purely arbitr>y1 ?\gh conv5i5t = c]ta9 practical purposes4 ,"h ! supposition expresses only diff]5ces ( directions f an assum$ po9t4 ,?us :at w\ld be said to lie 9 a plane 9 "o relation w\ld lie 9 ! ?ird dim5sion 9 ano!r4 ,!re is no?+ to det]m9e absolutely :at is ! fir/1 second1 or ?ird dim5sion4 ,if ! plane horizontal to ! s5sorium be call$ plane dim5sion1 ! plane v]tical to x w be call$ solid1 or ! ?ird dim5sion1 b a *ange ( position w *ange ! names ( ^! dim5sions )\t involv+ ! slighte/ qualitative *ange or diff]5ce 9 mean+4 ,moreov]1 we usually select ?ree l9es or planes t]m9at+ v]tically at ! same po9t1 ! l9es connect+ ! ?ree surfaces ( a cube ) ! same po9t1 z ! repres5tative ( :at is meant by ?ree dim5sions1 & r$uce all o!r l9es & planes to ^!4 ,b int]e/+ facts are obs]vable "h4 #a4 ,if ! v]tical relation betwe5 two l9es be necess>y = def9+ a dim5sion1 !n all o!r l9es ?an ! specifi$ ones are ei!r n 9 any dim5sion at all1 or !y are outside ! ?ree giv5 dim5sions4 ,?is is d5i$ by all p>ties1 :i* only %[s t a v]tical relation to o!r l9es is n necess>y to ! det]m9ation ( a dim5sion4 #b4 ,if l9es outside ! ?ree v]tically int]sect+ l9es /ill lie 9 dim5sion or are r$ucible to ! o!r dim5sions !y may lie 9 m ?an "o dim5sion at ! same "t :i* aft] all is a fact4 ,?is only %[s t qualitatively all ?ree dim5sions are ! same & t any l9e outside ( ano!r c only repres5t a dim5sion 9 ! s5se ( direction f a giv5 po9t or l9e1 & we are entitl$ to assume z _m dim5sions z we please1 all )9 ?ree dim5sions4 ,?is mode ( treatm5t %[s ! s\rce ( ! illusion ab\t ! 'f\r? dim5sion4' ,! t]m 9 its g5]ic import d5otes comm5surable quality & d5otes only "o su* quality1 s t ! prop]ty suppos$ to det]m9e non-,euclidean geometry mu/ be qualitatively diff]5t f ?is1 if its figures involve ! necess>y qualitative diff]5tiation f ,euclidean ma!matics4 ,b ?is w\ld %ut out ! idea ( 'dim5sion' z its basis :i* is contr>y to ! supposition4 ,on ! o!r h&1 ! t]m has a specific mean+ :i* z diff]5t qualitatively f ! g5]ic includes a "r to use ! g5]ic t]m to describe !m diff]5tially1 b if us$ only quantitatively1 t is1 to express direction z x1 9 fact1 does 9 ^! cases1 involves ! admission ( ! actual1 n a supposititi\s1 exi/5ce ( a f\r? dim5sion :i* aga9 is contr>y to ! supposition ( ! non-,euclidean geometry4 ,/at$ briefly1 dim5sion z comm5surable quality makes ! exi/5ce ( ! f\r? dim5sion a transc5d5tal problem1 b z m]e direction1 an empirical problem4 ,& ! la/ conception satisfies all ! requirem5ts ( ! case because x con=ms to ! purely quantitative diff]5ces :i* exi/ betwe5 ,euclidean & non-,euclidean geometry z ! v language ab\t 'surfaces1' 'triangles1' etc41 9 spite ( ! prefix 'pseudo1' necess>ily implies4 #ah ,vide ,philosophical ,review1 ,vol4 ,v1 #ahif1 p4 #ceb1 et4 seq4 ,?us x w\ld seem t ^? :o h be5 mo/ dilig5t 9 con/ruct+ ! hyp]space conception h be5 ! lea/ c>eful ( ! logical difficulties :i* beset ! elaboration ( _! assumptions4 ,yet x sometimes requires ! illogical1 ! absurd & ! ab]rant to br+ u to a "r conception ( ! tru?1 & :5 we come to a comp>ison ( ! two1 tru? & absurdity1 we are ! m surpris$ t error c\ld h ga9$ s great foo?old 9 face ( s ov]:elm+ evid5ces to ! contr>y4 ,! entire situation is1 accord+ly1 aptly set =? by ,,hyslop :5 he says1 cont9u+3 ,!re are ei!r a confusion ( ! ab/ract ) ! concrete or ( quantitative ) qualitative logic1 444 s t all discussion ab\t a f\r? dim5sion is simply an ext5d$ mass ( equivocations turn+ ^u ! v>i\s mean+s ( ! t]m 'dim5sion4' ,?is :5 once discov]$1 ei!r makes ! controv]sy ridicul\s or ! claim = non-,euclidean prop]ties a m]e truism1 b effectually explodes ! logical claims = a new dim5sional quality ( space z a piece ( m]e juggl]y 9 :i* ! juggl] is z badly deceiv$ z 8 spectators4 ,x simply =ces ma!matics to transc5d its own functions z def9$ by its own advocates & to assume ! pr]ogatives ( metaphysics4 ,%all we1 !re=e1 ass5t to ! imp]iali/ic policy ( ma!maticians :o w\ld fa9 usurp ! pres]ves ( ! metaphysician 9 ord] t !y may exploit a sup]foetat$ hypo!sis8 ,x is n believ$ t ! h>%ness ( ,,hyslop',s judgm5t 9 ?is respect is undes]v$4 ,x is1 h[ev]1 regrett$ t ! notions ( ma!maticians h be5 s in*oate z to ju/ify ?is r cau/ic1 ?\gh appropriate criticism4 ,= x does appe> t ! mom5t ! ma!matician des]ts ! prov9ce ( 8 re/rict$ sph]e ( motility & ent]s ! realm ( ! transc5d5tal1 t mom5t he loses 8 way & becomes an inexp]i5c$ m>9] on an un*>t$ sea4 ,x is int]e/+ to note t ,,cassius ,,jackson ,,keys]1#ai :ile recogniz+ ! purely arbitr>y "* ( ! s-call$ dim5sionality ( space1 nev]!less l5ds himself to ! view t if we ?9k ( ! l9e z g5]at+ elem5t we %all f9d t our space has f\r dim5sions4 ,t fact may be se5 9 v>i\s ways1 z foll[s3 ,a l9e is det]m9$ by any two ( its po9ts4 ,e l9e pi]ces e plane4 ,by jo9+ ! po9ts ( "o plane to all ! po9ts ( ano!r1 all ! l9es ( space are obta9$4 ,to det]m9e a l9e1 x is1 !n1 en\gh to det]m9e two ( its po9ts1 "o 9 ! "o plane & "o 9 ! o!r4 ,= ea* ( ^! det]m9ations two data1 z be=e expla9$1 are necess>y & suffici5t4 ,! position ( ! l9e is ?us se5 to dep5d ^u f\r indep5d5t v>iables1 & ! f\r dim5sionality ( our space 9 l9es is obvi\s4 #ai3 ,vide ,moni/1 ,vol4 ,,xvi1 #ahif1 ,ma!matical ,emancipations4 ,simil>ly he argues = ! f\r dim5sionality ( space 9 sph]es3 ,we may view our space z an assemblage ( its sph]es4 ,to di/+ui% a sph]e f all o!r sph]es1 we ne$ to "k f\r & b f\r indep5d5t facts ab\t x1 z say1 ?ree t %all det]m9e its c5t] & "o its size4 ,h5ce our space is f\r dim5sional also 9 sph]es4 ,9 circles1 its dim5sionality is six2 9 surfaces ( second ord] 7^? t are pi]c$ by a /raight l9e 9 two po9ts71 n9e2 & s on ad inf9itum4 ,! view tak5 by ,,keys] is a typical "o4 ,x is ! ma!matical view & is *>act]iz$ by a c]ta9 lack ( re/ra9t :i* is f\nd to be peculi> to ! :ole s*eme ( ?\ght relat+ to hyp]space4 ,x is cle> t ! k9d ( space t w p]mit ( su* radical *anges 9 its nature z to be at "o "t ?ree dim5sional1 at ano!r "t f\r dim5sional1 !n six1 n9e & ev5 n-dim5sional is n ! k9d ( space 9 :i* ! objective _w is kn[n to exi/4 ,inde$1 x is n ! k9d ( space t really exi/s at all4 ,9 ! fir/ place1 a l9e _c g5]ate p]ceptual space4 ,nei!r c a circle1 nor a sph]e nor any o!r geometrical con/ruction4 ,x is1 !re=e1 n p]missible1 except ma!matically1 to view our space ei!r z an assemblage ( its sph]es1 its circles or its surfaces2 = obvi\sly p]ceptual space is n a geometrical con/ruction ev5 ?\gh ! intellect naturally f9ds inh]+ 9 x a sort ( lat5t geometrism :i* is kosmical4 ,= !re is a wide diff]5ce betwe5 t kosmic ord] :i* is space & ! f9ely elaborat$ ab/raction :i* ! geomet] deceives himself into id5tify+ ) space4 ,!re is absolutely nei!r p]ceptible nor imp]ceptible means by :i* p]ceptual space 9 anywise c be affect$ by an act ( w1 ideation or movem5t4 ,j :y ma!maticians p]si/ 9 vag>iz+ ^u ! g5]ability ( space by movem5t ( l9es1 circles1 planes1 etc41 is confess$ly n easily und]/ood especially :5 ! natural outcome ( su* proc$ure is self-/ultification4 ,x is f> bett] to recognize1 z a guid+ pr9ciple 9 all ma!matical disquisitions respect+ ! nature ( space t ! possibilities f\nd to inh]e 9 an idealiz$ con/ruction _c be objectifi$ 9 kosmic1 s5sible space4 ,! l9e ( dem>kation %\ld be drawn once = all1 & all metageometrical calculations & !ories %\ld be prefac$ by ! rem>k t3 if objective space 7 am5able to ! peculi>ities ( an idealiz$ con/ruction su* & su* a result w\ld be possible1 or words to t effect4 ,?is mode ( proc$ure w\ld s]ve to cl>ify _m if n all ( ! hyp]space conceptions = ! non-ma!matician z well z = ! metageometricians !mselves1 especially ^? :o are unwill+ to recognize ! utt] impossibility ( _! con/ructions z appli$ to p]ceptual space4 ,we %\ld !n cease to h ! spectacle ( o!rwise well-demeanor$ m5 committ+ ! error ( try+ to realize ab/ractions or ab/ractioniz+ realities4 ,h]e9 is ! crux ( ! :ole matt]1 t ma!maticians1 r ?an be cont5t ) realities z !y f9d !m 9 ! kosmos1 %\ld seek to r$uce !m to ab/ractions1 or1 on ! o!r h&1 make _! ab/ractions appe> to be realities4 ,,keys] proce$s to %[ h[ ! concept ( ! g5]ability ( hyp]space may be conceiv$ by beg9n+ ) ! po9t1 mov+ x 9 a direction )\t itself & g5]at+ a l9e2 beg9n+ ) ! l9e1 treat+ x simil>ly1 & g5]at+ a plane2 tak+ ! plane1 mov+ x 9 a direction at "r angles to itself & g5]at+ a cube2 f9ally1 us+ ! cube z g5]at+ elem5t & con/ruct+ a f\r-space figure1 ! tess]act4 ,n[1 z a matt] ( fact1 a po9t be+ intangible _c be mov$ 9 any direction nei!r c a po9t-portion ( s5sible space be remov$4 ,nev]!less1 we q agree ) him :5 he ass]ts3 ,c]ta9ly !re is naught ( absurdity 9 suppos+ t "u suitable /imulation ! human m9d may1 9 ! c\rse ( "t1 spe$ily develop a spatial intuition ( f\r or m dim5sions4 7,! italics 9 ! above quotation are ours47 ,"h we h a tacit implication t ! notion :i* geomet]s h h]et(ore designat$ z dim5sion really is a matt] ( consci\sness1 ( intuition1 & !re=e1 det]m9able only by ! limitations ( consci\sness & ! deliv]ies ( our intuitive cognitions4 ,z a m detail$ discussion ( ?is phase ( ! subject %all be ent]$ into :5 we come to a consid]ation ( ,*apt] ,,vi on ,consci\sness z ! ,norm ( ,space ,det]m9ations fur!r comm5t is def]r$ until !n4 ,n[1 z x appe>s c]ta9 t :at geomet]s are accu/om$ to call dim5sion is bo? relative & int]*angeable 9 mean+--! "o becom+ ! o!r accord+ z x is view$--! conclusion v naturally foll[s t nei!r con/ructive nor symbolic geometry is bas$ ^u dim5sion z comm5surable quality4 ,! real basis ( ! non-,euclidean geometry is dim5sion z direction4 ,= :atev] else may be said ( ! f\r? dim5sion s-call$ x is c]ta9ly un?9kable1 ev5 to ! metageometricians1 :5 x is absolv$ f direction al?\gh no specific direction c be assign$ to x4 ,x is agre$ p]haps among all non-,euclidean publici/s t ! f\r? dim5sion mu/ lie 9 a direction :i* is at "r angles to all ! ?ree dim5sions4 ,b if !y are ask$ h[ ?is direction may be asc]ta9$ or ev5 imag9$ !y are nonplus$ because !y simply d n "k4 ,! difficulty 9 ?is connection seems to h+e ab\t ! "q ( id5tify+ ! conditions ( ! _w ( phantasy ) ^? ( ! _w ( s5se4 ,!re are di/ortions1 ramifications1 subm]sibles1 duplex convolutions & o!r ma!tic acrobatics :i* c be p]=m$ 9 ! realm ( ! conceptual ! execution ( :i* c\ld nev] be actualiz$ 9 ! objective _w4 ,because ^! antics are possible 9 ! premises ( ! ma!matical imag9ation is sc>ce ju/ification = ! attempts at reproduction 9 an actualiz$ & ph5om5al univ]se4 ,"o ( ! pr\de/ boa/s ( ! f\r? dim5sioni/ is t hyp]space (f]s ! possibility ( a new species ( rotation1 namely1 rotation ab\t a plane4 ,he ref]s to ! fact t 9 ! s-call$ "o-space1 rotation c take place only ab\t a po9t4 ,= in/ance 9 ,figure #g1 ! l9e ab repres5ts a "o-space 9 :i* rotation c take place only ab\t "o ( ! two po9ts a & b4 ,9 ,figure #h :i* repres5ts a two-space1 rotation may take place ab\t ! l9e ab or ! l9e cd1 etc41 or1 9 o!r words1 ! plane abcd c be rotat$ on ! axial l9e ab 9 ! direction ( ! ?ird dim5sion4 ,9 tridim5sional space only two k9ds ( rotation are possible1 namely1 rotation ab\t a po9t & ab\t a l9e4 ,9 ! f\r? dim5sion x is claim$ t rotation c take place ab\t a plane4 ,= example1 ! cube 9 ,figure #i1 by manipulation 9 ! direction ( ! f\r? dim5sion1 c be made to rotate ab\t ! side abgf4 ,a v +5i\s argum5t is us$ to %[ h[ rotation ab\t a plane is ?9kable & possible 9 hyp]space4 ,b ) ?is1 z ) ! entire fabric ( hyp]space speculations1 dep5d5ce is plac$ almo/ entirely ^u analog\s & symbolic conceptions = evid5ce z to ! consi/5cy & rationality ( ! conclusions arriv$ at4 ,d ,c ,d#a -------------4444444444444 3 3 3 3 3 -------------4444444444444 ,a ,b ,a#a ,,fig4 #ac4 ,x is urg$ t inasmu* z ! rotation ab\t ! l9e bc 9 ,figure #ac w\ld be incompreh5sible or unimag9able to a plane be+ = ! reason t su* a rotation involves a movem5t ( ! plane into ! ?ird dim5sion1 a dim5sion ( :i* ! plane be+ has no k1 9 l mann] rotation ab\t a plane is also unimag9able or incompreh5sible to a tridim or a ?ree dim5sional be+4 ,x is %[n1 h[ev]1 t ! plane be+1 by mak+ use ( ! possibilities ( an assum$ tridim5sion1 c\ld arrive at a rational explanation ( l9e rotation4 ,illu/ration3 ,,fig4 #ad4 ,figure #ad (f]s an illu/ration by means ( :i* a two dim5sional ma!matician c\ld demon/rate ! possibility ( l9e rotation4 ,he is already acqua9t$ ) rotation ab\t a po9t2 = x is ! only possible rotation t is obs]vable 9 8 two dim5sional _w4 ,by conceiv+ ( a l9e z an inf9ity or succession ( po9ts ext5d+ 9 ! same direction2 by imag9+ ! movem5t ( 8 plane 9 ! direction ( ! ?ird dim5sion !reby g5]at+ a cube & at ! same "t assum+ t ! l9es ?us g5]at$ 7 m]ely successions ( po9ts ext5d+ 9 ! same direction1 he c\ld demon/rate t ! entire cube ,figure #ad1 c\ld be rotat$ ab\t ! l9e ,,bhx us$ z an axis4 ,= ^u ?is hypo!sis x w\ld be arguable t a cube is a succession ( planes pil$ "o ^u ! o!r & limit$ only by ! l5g? ( ! cube :i* w\ld be ext5d+ 9 !1 to him1 unkn[n direction ( ! ?ird dim5sion4 ,he c\ld v logically conclude t z a plane c rotate ab\t a po9t1 a succession ( planes con/itut+ a tridim5sional cube1 c\ld also be conceiv$ z rotat+ ab\t a l9e :i* w\ld be a succession ( po9ts "u ! condition ( ! hypo!sis4 ,8 demon/ration1 !re=e1 t ! cube1 ,figure #ad1 c be made to rotate ar\nd ! l9e ,,bhx w\ld be ?or\ghly rational4 ,he c\ld ?us prove l9e-rotation )\t ev5 be+ able to actualize 9 8 exp]i5ce su* a rotation4 ,analog\sly1 x is s\ght by metageometricians to prove 9 l mann] ! possibility ( rotation ab\t a plane4 ,?us 9 ,figure #af is %[n a cube :i* has be5 rotat$ ab\t "o ( its faces & *ang$ f its initial position to ! position x w\ld occupy :5 ! rotation _h be5 complet$ or its f9al position atta9$4 ,illu/ration3 ,,fig4 #ae4 ,illu/ration3 ,,fig4 #af4--,plane ,rotation ,! gi/ ( ! argum5ts put =w>d z a basis = plane-rotation is briefly /at$ ?us3 ,! face cefg is conceiv$ z consi/+ ( an inf9ity ( l9es4 ,a cube1 z 9 ,figure #ae1 is imag9$ or assum$ to be sect$ into an inf9ity ( su* l9es1 ea* l9e be+ ! t]m9us ( "o ( ! planes :i* make up ! cube4 ,ea* "o ( ! con/itut+ planes is ?\ght ( z rotat+ ab\t its l9e-b\nd>y :i* int]sects ! side ( ! cube4 ,! process is cont9u$ indef9itely until ! entire s]ies ( planes is rotat$1 "o by "o1 ar\nd ! s]ies ( l9es :i* con/itute ! axial plane4 ,h5ce1 9 ord] t ! cube1 ,figure #af1 may *ange f its initial position to its f9al position ea* "o ( ! inf9itesimal planes ( :i* ! cube is assum$ to be compos$ mu/ be made to rotate ab\t ea* "o ( ! inf9itesimal l9es ( :i* ! plane us$ z an axis is compos$4 ,9 ?is way1 x is %[n t ! entire cube has be5 made to rotate ab\t its face1 cefg4 ,?is concisely1 is ! ,,quod ,,erat ,,demon/r&um ( ! metageometrician :o sets out to prove rotation ab\t a plane4 ,?us x is made to appe> t 9 ord] t tridim5sional be+s may be enabl$ to conceive ( f\r-space rotation1 z 9 ,figures #ae & #af1 9 :i* ! rotation mu/ also be ?\ght ( z tak+ place 9 ! direction ( ! f\r? dim5sion1 !y mu/ adopt ! same tactics t a two dim5sional be+ w\ld use to und]/& "s ( ! possibilities ( ! tridim5sional _w4 ,x is1 ( c\rse1 unwise to assume t because a ?+ c be %[n to be possible by analogical reason+ its actuality is !reby e/abli%$4 ,?is consid]ation _c be too emphatically insi/$ ^u2 = _m h be5 l$ into ! error by rely+ too confid5tially ^u results bas$ ^u ?is l9e ( argum5tation4 ,!re is a va/ diff]5ce betwe5 m5tally do+ :at may be assum$ to be possible1 ! hypo!tical1 & ! do+ ( :at is actually possible1 ! practical4 ,9 ! fir/ place1 plane-rotation 9 ! actual univ]se is a /ructural impossibility4 ,! v nature & con/itution ( mat]ial bodies w n admit ( su* contortion z t requir$ by ! rotation ( a body1 say a cube1 ab\t "o ( its faces4 ,let u exam9e "s ( ! results ( plane rotation4 #a4 ,! rotation mu/ take place 9 ! direction ( ! f\r? dim5sion4 ,n[1 z x is utt]ly impossible = any "o1 :e!r layman or metageometrician1 ev5 to imag9e or conceive1 9 any way t is practical1 ! direction ( ! f\r? dim5sion x is also impossible = "o to move or rotate a plane1 surface1 l9e or any o!r body 9 t direction4 ,we are 9 ! v beg9n+ ( ! process ( plane-rotation s-call$ confront$ ) a physical impossibility4 #b4 ,plane rotation necess>ily involves ! orbital div]sion ( e p>ticle 9 ! cube4 ,?is alone is suffici5t to prohibit su* a rotation2 = x is obvi\s t ! mom5t a p>ticle or any s]ies ( p>ticles is div]t$ f its e/abli%$ orbital pa? disruption ( t portion ( ! cube mu/ necess>ily foll[4 ,?is ^u ! assumption t ! p>ticles ( matt] are 9 motion & revolv+ 9 _! corpuscul> orbits4 #c4 ,plane-rotation necessitates a radical *ange 9 ! absolute motion ( ea* individual p>ticle1 electron1 atom or molecule ( matt] 9 ! cube & a consequ5t ret>dation or accel]ation ( ?is motion4 ,?is ^u ! hypo!sis t ! p>ticles ( matt] are vibrat+ at ! rate ( absolute motion4 #d4 ,x presupposes a recon/itution ( ea* atom1 molecule or p>ticle 9 ! cube1 *ang+ ! pa? ( intra-corpuscul> rotation ei!r f a "r to left direction or f a left to "r direction1 z ! case may be4 ,! p>ticles ( matt] 9 ! cube w be act$ ^u 9 mu* ! same mann] z ! p>ticles 9 a glove :5 x is maneuv]$ 9 ! f\r? dim5sion4 ,9 describ+ ?is ph5om5on1 ,,mann+ says3#bj ,e "p by itself1 9 its own place is turn$ ov] ) only a slight possible /ret*+ & slight *ang+ ( positions ( ! diff]5t p>ticles ( matt] :i* g to make up ! glove4 #bj ,vide ,f\r? ,dim5sion1 ,simply ,expla9$1 edit$ by ,h4 ,p4 ,,mann+1 p4 #bh4 ,! slight /ret*+ & slight *ang+ ( ! positions ( ! p>ticles ref]r$ to w\ld be ( small consequ5ce if appli$ to pond]able bodies4 ,b :5 us$ 9 connection ) p>ticles ( matt] :i* are !mselves ( v inf9itesimal size means f> m--en\gh1 z we h said1 to militate sev]ely aga9/ ! integrity ( ! cube4 ,x is n deem$ necess>y to g fur!r into ! physical aspects ( plane-rotation z x is believ$ suffici5t has be5 said to negative ! assumption f a purely /ructural viewpo9t4 ,among ! vag>ies ( hyp]space publici/s none is p]haps m notable ?an ! view tak5 by ,c4 ,h4 ,,h9ton3#ba ,if x c\ld be %[n t ! electric curr5t 9 ! negative direction 7 exactly alike ! electric curr5t 9 ! positive direction1 except = a rev]sal ( ! compon5ts ( ! motion 9 ?ree dim5sional space1 !n ! dissimil>ity ( ! dis*>ge f ! positive & negative poles w\ld be an indication ( ! "o-sid$ness ( our space4 ,! only cause ( diff]5ce 9 ! two dis*>ges w\ld be due to a compon5t 9 ! f\r? dim5sion1 :i* direct$ 9 "o direction transv]se to our space1 met ) a diff]5t resi/ance to t :i* x met :5 direct$ 9 ! opposite direction4 #ba ,vide ,f\r? ,dim5sion1 p4 #ge1 ,c4 ,h4 ,,h9ton4 ,to be sure4 ,& ) equal c]ta9ty x might be said t if ! moon 7 made ( gre5 *eese x might well be ! ambition ( ! _w's *efs to be able at "s "t to flavor mac>oni ) x1 ?us s]v+ a r>e di%4 ,ev5 s1 if !re 7 an actual1 objective f\r? dim5sion to our space we might be able to %ove into x all ! p]plex+ problems ( life & let x solve !m = u4 ,b ! fact t ! f\r? dim5sional hypo!sis is itself a m]e supposition seems to h be5 ov]look$ or r completely ignor$ by ,,h9ton4 ,or else1 ought x n be an obvi\s folly to hope to con/ruct a rational explanation ( p]plex+ physical conditions ^u ! basis ( a purely supposition>y1 & !re=e unprov51 hypo!sis8 ,! recogniz$ doma9 ( ! f\r-space1 ma!matically consid]$1 is accord+ to ! mo/ g5]\s all[ance v small1 s small1 9 fact1 t ! disposition ( "s to cr[d into x ! ess5tial cont5t ( ! manife/$ univ]se is a matt] ( pr(\nd amazem5t4 ,!n1 too1 x _c be d5i$ t !re is no appreciable urg5cy or necessity = hav+ rec\rse to a purely hypo!tical con/ruction = explicatory data reg>d+ a ph5om5on :i* has n be5 %[n to be )\t ! scope ( ord9>y sci5tific me?ods ( proc$ure to unravel4 ,! claim ( c]ta9 spirituali/s1 notably ,,zolln] ( ,leipsig1 t ! ph5om5a ( spiritism is acc\ntable = on ! gr\nds t ! f\r? dim5sion af=ds a resid5tial area = disc>nate be+s :5ce spiriti/ic =ay]s may impose _! pres5ce ^u unprotect$ ?ree dim5sional be+s is no less fatu\s ?an ! orig9al supposition itself4 ,= ^u ?is latt] is built ! entire fabric ( mean+less speculations s gleefully indulg$ 9 by ^? :o glibly proclaim ! reality ( ! f\r-space4 ,inde$1 cle>] second ?\ght w reveal t1 :5 ! p5dulum ( erratic ?9k+ & traffick+ 9 m5tal con/ructions sw+s back1 hyp]spaces1 aft] all1 are b ! ignes fatuii ( ma!tic obscurantism4 ,!n1 :y %\ld x be deem$ necess>y to discov] "s m my/]i\s realm ( f\r dim5sional proportions 9 :i* ! spirits ( ! dead may f9d a habitation8 ,are ! spirituali/s1 too1 r$uc$ to ! necessity ( fur!r my/ify+ _! already adequately my/]i\s ph5om5a8 ,if !re 7 n q en\gh ( physicality ^u ! basis ( :i* all ! antics ( ^! entities c be expla9$1 & t satisfactorily1 "o w\ld1 z a matt] ( c\rse1 be incl9$ to l5d "s cr$5ce to ^! claims2 b z x is cle> t all organiz$ be+s h "s p[]1 if no m ?an t :i* ma9ta9s _! organization1 & z x ought also be an acceptable fact t su* a be+ is direct$ by m9d2 & fur!r1 t ow+ to ! nature ( a _s body x c p5etrate solid matt] or matt] ( any o!r degree ( d5sity bel[ ! coeffici5t ( _s matt]1 x ought likewise be unnecess>y to g )\t ! prov9ce ( /rictly tridim5sional me*anics = an explanation ( spiriti/ic ph5om5a4 ,equally unnecess>y & uncall$ = is ! attempt ( c]ta9 o!rs :o lean t[>d ! view ( speculative *emi/s to acc\nt = ! none too securely e/abli%$ hypo!sis t eight diff]5t alcohols1 ea* hav+ ! =mula ,c#e;,h#ab,o may be produc$ )\t v>iation4 ,?is is said to be due to ! fact t c]ta9 ( ! compon5t atoms1 notably ! c>bon atoms1 take a f\r? dim5sional position 9 ! comp\nd & ?us produce ! unusual spectacle ( eight alcohols f "o =mula4 ,h *emi/s actually exhau/$ all purely physical means ( rea*+ an und]/&+ ( ! c>bon comp\nds & are !re=e compell$ to resort to que/ionable means 9 ord] to make additional progress 9 _! field8 ,x is incr$ible4 ,h5ce ! m faceti\s appe>s ! ma!matical extravaganza 9 :i* orig9ates ! t5d5ce among ! m sangu9e advocates to make ( ! f\r? dim5sion a sort ( jack ( all trades1 a v]itable ,aladd9's lamp :]e) all kosmic pr(undities may be illum9at$ & made pla94 ,n until ! p]fection ( in/rum5ts ( precision has be5 rea*$1 & n until human +5uity has be5 exhau/$ 9 its ef=ts to produce m ref9$ me?ods ( rese>* %\ld x be p]missible ev5 to v5ture into untri$ & m or less debatable fields 9 se>* ( a relief :i* aft] all is unobta9able4 ,not)/&+ ! fact t all attempts at acc\nt+ = physical ph5om5a on ! basis ( n-dim5sionality 7:i* is itself by all ! /&>ds ( objective ref]5ce a non-exi/5t quantity & !re=e irreconcilable ) p]ceptual space requirem5ts7 are to be *>act]iz$ simply z a s5seless dalliance ) o!rwise deeply pr(\nd que/ions1 _m h fall5 into a complete =getfulness ( ! logical b>ri]s inh]+ 9 & h$g+ ab\t ! qu]y & h committ$ o!r & less excusable errors 9 ! premises4 ,take1 = in/ance1 ! sugge/ion t ! action ( a t>trate ^u a beam ( pol>iz$ light is due to ! assumption ( a f\r? dim5sional direction by "s compon5t 9 ! acid4 ,?is = ! reason t exp]im5tation has %[n t t>t>ic acid1 9 "o =m1 w turn ! plane ( pol>iz$ light to ! "r :ile 9 ano!r =m w turn x to ! left4 ,x is n believ$1 h[ev]1 t !re is any w>rant = su* an assumption4 ,!re is also ano!r k9d ( t>trate :i* seems to be neutral 9 t x has no effect :atev] ^u ! beam ( light1 turn+ x nei!r to ! "r nor to ! left nor hav+ o!r visible or det]m9able effect ^u x4 ,inde$1 x is n cle> h[ x is hop$ to prove su* a case by con/itut+ z a norm a hypo!sis :i* is ess5tially indemon/rable4 ,a m logical proc$ure w\ld be fir/ to e/abli% ! objective1 discov]able po/ure ( f\r-space2 %[ ! actual movem5t ( matt] & entities !re92 locate x by empirical me?ods ( rese>*1 & !n1 bas+ our ass]tions ^u apodeictic evid5ces1 assume a new attitude t[>d ^! ph5om5a because ( ! support f\nd 9 e/abli%$ & v]ifiable facts4 ,"s hope ( ga9+ a respectful he>+ might !n be ent]ta9$2 b at lea/ to d s n[ appe>s to be q untimely4 ,,major ,,wilmot ,e4 ,,ellis1 ,coa/ ,artill]y ,corps1 ,unit$ ,/ates ,army1 9 ,! ,f\r? ,dim5sion ,simply ,expla9$1#bb rem>ks3 444 9 ! e!r1 if any:]e1 we %\ld expect to f9d "s f\r? dim5sional *>act]i/ics4 ,gravitation1 electricity1 magnetism & light are kn[n to be due to /resses 91 or motions (1 ! inf9itesimal p>ticles ( ! e!r4 ,! real nature ( ^! ph5om5a has nev] be5 fully expla9$ by ?ree dim5sional ma!matical analysis4 ,inde$1 ! unexpla9$ residuum w\ld seem to indicate t s f> we h m]ely be5 consid]+ ! ?ree dim5sional aspects ( f\r dim5sional processes4 ,z "o illu/ration ( _m1 x has be5 %[n bo? ma!matically & exp]im5tally t no m ?an five corpuscles may h an indep5d5t gr\p+ 9 an atom4 #bb ,q4 v41 p4 #bdb1 edit$ by ,h4 ,p4 ,mann+4 ,! weakness ( ?is view may be due to ! fact t at t "t ,,major ,,ellis 0 emphasiz+ 9 8 own m9d ! necessity ( simplify+ ! conception s z to make x ( easy compreh5sion r ?an ! e/abli%m5t ( any fealty to tru? or ! _s ( ma!sis 9 8 exam9ation ( ! problem4 ,:at !re=e ( reality ! /ud5t fails to f9d 9 8 view may be attribut$ to ! sacrifice :i* ! writ] 7,,major ,,ellis7 felt himself call$ ^u to make = ! sake ( simplicity4 ,h5ce a c]ta9 express$ connivance at 8 position is all[able4 ,b1 on ! o!r h&1 if su* 7 n ! consci\s int5t ( ,,major ,,ellis x is n und]/ood h[ x %\ld appe> t ! unexpla9$ residuum w\ld seem to indicate t s f> we h m]ely be5 consid]+ ! ?ree dim5sional aspects ( f\r dim5sional processes4 ,contr>ily1 x has yet to be prov$ t ?ree dim5sional space does n af=d ample scope ( motility = all obs]vable or recognizable physical processes & t !re is no necessity = ref]5ce to hyp]space ph5om5a = an explanation ( ! unexpla9$ residuum4 ,x is1 ( c\rse1 und]/ood t _m ( ! possibilities pr$icat$ = hyp]space are purely nons5sical s f> z _! actual realization is conc]n$4 ,our conc]n is1 !re=e1 n ) t class ( pr$icates1 b ) ^? :]e9 reside "s slight %[ ( probability ( _! response to ! conditions ( n-dim5sionality ei!r z a sy/em ( space-measurem5t or a s-call$ space or s]ies ( spaces4 ,,major ,,ellis concludes 8 simple /udy ( f\r-space by propos+ ! foll[+ qu]y3 ,may n bir? be an unfold+ ?r\gh ! e!r into ! symmetrical life-cell1 & dea?1 ! rev]se process ( a fold+-up into f\r dim5sional unity8 ,x is confess$ t !re seems to be no?+ to w>rant ! giv+ ( an affirmative reply to ?is qu]y4 ,x is1 p]haps1 s5tim5tally speak+ a v beautiful ?+ to contemplate dea? z a pa9less1 unconsci\s involvem5t into a glori\s "o-ness ) all life1 & bir?1 z ! rev]se ( all ?is4 ,b :]e is ! utility ( su* a dream if x be m]ely a dream & impossible ( realization8 ,,simon ,,newcomb1#bc at "o "t "o ( ! out/&+ figures 9 ! e>ly developm5t ( ! f\r? dim5sional hypo!sis1 op5ly decl>$ t !re is no pro( t ! molecule may n vibrate 9 a f\r? dim5sion4 ,!re are facts :i* seem to indicate at lea/ ! possibility ( molecul> motion or *ange ( "s sort n expressible 9 t]ms ( "t & ! ?ree cord9ates 9 space4 ,( c\rse1 !re is no pro( t a molecule may n at times be ensconc$ 9 a f\r-space nei!r is !re pro( nor probability t x is s hidd54 ,inde$1 !re is no pro( t !re is su* a ?+ z a molecule = t matt]4 #bc ,vide ,sci5ce1 ,vol4 ,,vii1 #aeh1 #ahih1 p4 #d4 ,9 all ( ! =ego+ proposals x is assum$ t ! f\r? dim5sion really exi/s & t x lies j b5ea? ! surface ( ! visible1 palpable limits ( ! mat]ial univ]se2 t ly+ 9 close juxtaposition to all t we are able to see1 to he> or s5se 9 any way is ?is my/]i\s1 et]nally prolific1 all-p[]ful some?+1 hyp]space1 ev]-ready to n\ri% & su/a9 ! =ms :i* h ! ne!r p>ts firmly ency/$ 9 "o or ! o!r ( h] n-dim5sional b]?s4 ,?us x w\ld seem t :ile yet function+ 9 a /rictly tridim5sional atmosph]e1 "s "o1 m reckless ?an ! re/1 %\ld at la/ /umble ^u "s up-ly+ portion ( x & be in/antly trans=m$ into a ma!tic fay ( e!realiz$ f\r-dim5sional /uff4 ,,"p ,,two ,,spatiality ,,an ,,inquiry ,,into ,,! ,,ess5tial ,,nature ,,( ,,space ,,z ,,di/+ui%$ ,,f ,,! ,,ma!matical ,,int]pretation ,,*apt] ,,vi ,,consci\sness ,,! ,,norm ,,( ,,space ,,det]m9ations ,realism ,is ,det]m9$ by ,aw>5ess--,succession ( ,degrees ( ,realism--,suffici5cy ( ,tridim5sionality--,! ,insuffici5cy ( ,self-,consi/5cy z a ,norm ( ,tru?--,g5]al ,=w>d ,movem5t 9 ! ,evolution ( ,consci\sness ,impli$ 9 ! ,hyp]space ,concept--,! ,hypo!tical ,nature ( ,our ,k--,hyp]space ! ,symbol ( a ,m ,ext5sive ,realm ( ,aw>5ess--,v>iations 9 ! ,me?od ( ,int]pret+ ,intellectual ,notions--,! ,tuitional & ! ,intuitional ,faculties--,! ,illusion>y ,"* ( ! ,ph5om5al--,consci\sness & ! ,degrees ( ,realism4 ,?+s h value = u only to ! ext5t to :i* we c become aw>e ( _! be+4 ,! appraisem5t ( all objects1 conditions1 /ates or qualities is det]m9$ directly by ! degree or quality ( aw>5ess ) :i* we appreh5d !m4 ,^? elem5ts :i* are )\t ! intellect's scope ( aw>5ess h no int]e/ & h5ce no value s f> z ! individual intellect is conc]n$4 ,& ?is is true ( all degrees & /ates ( consci\sness f ! l[e/ to ! highe/1 f ! human to ! div9e4 ,!re ent] into all consci\s det]m9ations ?ree factors1 namely3 7a7 ! scope1 or totality1 ( adaptations :i* an organism c make 9 ! s5sible _w1 7b7 ! p[] ( consci\sness to make adaptations & 7c7 environm5t4 ,^! ?ree are int]dep5d5t4 ,! totality ( adaptations dep5ds prim>ily1 ( c\rse1 ^u ! quality ( consci\s p[]s or faculties1 & also1 9 a less] degree1 ^u opportunities af=d$ by environm5t4 ,faculties ( consci\sness are d]iv$ directly f ! influ5ces ex]t$ ^u ! organism by 8 environm5t & ! results ( ! /ruggle to ov]come !m4 ,environm5t is ( two k9ds1 artificial & natural4 ,! artificial environm5t is su* z has be5 modifi$ by our consci\s action ^u ext]nal ph5om5a4 ,! residue is natural4 ,& ?us ! scope ( adaptability becomes an unv>y+ witness to ! quality ( consci\sness manife/+ ?r\gh a giv5 organism4 ,! univ]se is s con/ruct$ t ! ess5tial "* ( its v>i\s /ates & qualities is a fix$ quantity = a giv5 scope ( consci\sness & v>ies only z ! sph]e ( consci\sness v>ies4 ,/ates ( exi/5ce or scopes ( adaptation :i* are regi/]+ ^u a high] plane or 9 a m subtle sph]e ( exi/5ce ?an t 9 :i* we may at any "t be function+ c only appe> evid5tial to u :5 ! me*anism ( our consci\sness becomes congru5tly adju/$ !re)4 ,s t ! focus ( consci\sness mu/ always be a v>iable quantity adaptable1 "u prop] conditions1 to any plane 9 ! kosmos4 ,consci\sness1 !n1 becomes ! sph]e ( limits bo? ( k & adaptability4 ,b le/ we seem to admit implicitly "p ( ! cont5tions :i* ma!matical publici/s h made 9 po/ulat+ ! unodim & duodim consci\sness1 x is necess>y c>efully to diff]5tiate betwe5 ! results arriv$ at z a result ( ! two proc$ures4 ,9 ! fir/ place1 analy/s assume ! exi/5ce ( a unodim & duodim plane ( consci\sness & proce$ to con/ruct !reon an analogy design$ to %[ ! feasibility ( ano!r assumption1 ! f\r? dim5sion4 ,:ile1 9 lay+ ! f\ndation ( consci\sness ^u a tridim5sional plane we d n />t ) an assumption1 b ) a fact4 ,!re9 lies ! diff]5ce4 ,enorm\s advantages inh]e 9 a proc$ure bas$ ^u facts1 b 9 a s]ies ( planes built ^u assumptions no su* advantages are discov]$4 ,= h[ev] mu* ! s]ies ( hypo!tical planes may be ext5d$ or elaborat$ !re mu/ inh]e necess>ily ?r\gh\t ! s]ies an assumptional value :i* vitiates ! conclusions no less ?an ! premises4 ,! sanity & integrity ( intellectual op]ations dep5d almo/ entirely ^u ! diff]5tiation :i* we make betwe5 ! necessities aris+ out ( assumptions & ^? :i* spr+ up empirically f e/abli%$ facts4 ,no proc$ure is necess>y to e/abli% ! value ( su* a diff]5tiation1 nev]!less x may be sugge/$ t x is all[able1 "u ! rules ( logic1 to make any assumption :atsoev] s long z c>e is tak5 to see t ! conclusions embody 9 !mselves ! *>act]i/ics ( ! orig9al premise4 ,= in/ance1 x is p]missible to assume t space is curv$4 ,"u su* an assumption1 x is only necess>y t ! con/ructions :i* foll[ %all be self-consi/5t4 ,b ! case is diff]5t :5 we come to deal ) spatiality & vitality4 ,^! are quantities :i* _c1 9 ! la/ analysis1 be made to con=m to ! rules ( ! game ( logic4 ,?us1 :5 x is intimat$ t realism l5ds itself to an app>5t division into degrees1 & t ea* degree has a correspond+ /ate ( consci\sness1 x is by no means to be inf]r$ t su* app>5t divisions are ( ma!matical import4 ,=1 9 reality1 i4e41 :5 ! consci\sness has exp&$ s z to become congru5t ) ! limits ( ev5 ! space m9d 7vide ,fig4 #bj71 !re appe> to be no divisions 9 realism4 ,x is only because ( ! fragm5t>9ess ( our outlook ^u ! kosmos t realism appe>s to be divid$ into v>i\s planes2 = all ( ^! planes are "o4 ,! divisions exi/ = relative k1 b n = complete k2 !y exi/ = a f9ite intellig5ce1 b n = a transf9ite intellig5ce4 ,t is :y we view realism z a s]ies ( planes4 ,x is because we discov] t1 z we proce$1 z our consci\sness exp&s & we take 9 m & m ( ! vital activities ( ! kosmos & und]/& bett] ! causes und]ly+ t :i* we contact1 we h pass$ f a /ate ( less] k to "o ( great] k4 ,& s we say we h pass$ f "o degree ( realism to ano!r1 :]eas1 really we h n pass$ f "o degree ( realism to ano!r degree4 ,in/ead1 x is our consci\sness t has exp&$4 ,if n[1 we conceive reality to be a scale ext5d+ f "o extremity to ano!r 7t is1 f supreme consci\sness to entire unconsci\sness1 f f9al k to total ignorance71 & ! intellectual consci\sness z ! indicator :i* trav]ses ! scale d5ot+ at all times ! precise degree ( our compreh5sion ( reality1 & h5ce ! degree ( expansion ( consci\sness1 we %all con/itute a similitude closely approximat+ ! real /atus quo ( humanity ) respect to ! s5sible & sup]s5sible worlds4 ,! quantity or =ce :i* causes ! indicator to move along ! scale is ! quality ( aw>5ess4 ,& ?is v>ies directly z ! scope ( adaptability v>ies4 ,realism is homog5e\s ?r\gh\t its ext5t2 b ! scale m>k$ ^u x regi/]s f naught to unity4 ,& betwe5 ^! e conceivable degree ( aw>5ess may be regi/]$4 ,! indicator moves only z ! scope wid5s1 & ?us is %[n a *ange 9 ! quality ( aw>5ess4 ,=1 h[ev] p>adoxical x may seem1 ! wid] ! scope ( k ! bett] its quality3 ! m "o kn[s1 ! m complete & ( high] quality becomes t :i* he kn[s4 ,! intellect is ( sci5tific t5d5ce1 /udi\sly reject+ all ph5om5a :i* d n yield to its s5so-me*anisms4 ,ev5 intuitions suff] ! humility ( rejection & d n escape ! limitations :i* ! intellect imposes ^u !m4 ,?is is s1 because1 z yet1 !re is no adequate p]ceptive & conceptive app>atus = ! propagation & classification ( intuitions1 z ap>t f concepts4 ,! outcome ( ^! proscriptions is t intuitions--free1 mobile1 & m or less =mless 9 !mselves1 mu/ fir/ be rehabilitat$ & ve/ur$ 9 g>m5ts a la intellect to con=m to ! prevail+ mode4 ,b intuitions ?us treat$ are no long] intuitions1 b empirical concepts4 ,true intuitions are l aque\s vapor--amorph\s1 p]meat+1 diffusive3 axioms or empirical concepts are l cakes ( ice--=mal1 inflexible & con=m+ to ! %ape ( ! mold into :i* !y are p\r$4 ,because ( ?is--! sci5tific t5d5ce ( ! intellect & ! consequ5t necessity ( re=m+ s mu* ( ! data :i* con/itute its sub/ructure1 ( press+1 cond5s+ & re%ap+ x to suit its own ready-made patt]ns--x c be p]ceiv$ h[ pr(\nd is ! influ5ce ( ! intellectual consci\sness 9 det]m9+ ! "* ( ! totality ( data :i* ! s5sible _w1 & = t matt]1 ! sup]s5sible1 (f] u4 ,! intellect is ! only means at h& = ! int]pretation ( ! mean+ & significance ( ! _w ( ph5om5a4 ,consequ5tly1 :atev] mean+ or significance we are l$ to atta* to t "p ( ! univ]se :i* we contact1 9 any way1 is dictat$ by ! intellectual consci\sness4 ,!re is no escape f ! decisions ( ! intellect s long z ! pres5t s*eme ( ?+s endures4 ,?us1 by :atev] /&>d ( ref]5ce ! matt] may be det]m9$1 x rema9s indisputably e/abli%$ t ! intellectual consci\sness is ! sole det]m9ant ( ! ph5om5al value ( ev]y?+ )9 our scope ( aw>5ess or adaptability4 ,& :atev] ! fault1 incongruity or discrepancy t may be reveal$ by a m intimate k ( ! g5esis & "* ( ! appe>ance ( ! s5sible _w1 x w be f\nd to be due to ! peculi> cut & mode ( ! intellect & n to ?+s !mselves4 ,! value1 qualitative or exi/5tial1 :i* ! intellect irrevocably assigns to objects & conditions 9 ! _w ( ! s5ses is ! exclusive norm n only by :i* ^! are judg$1 b also1 by :i* our action ^u !m & _! action ^u u are det]m9$4 ,images or objects :i* d n act ^u u & ^u :i* we _c act h no int]e/ = u4 ,b z an integral "p ( ! totality ( images or objects 9 ! s5sible _w1 we mu/ inevitably act ^u all t is outside ( ourselves1 & ^!1 9 turn1 mu/ react ^u u4 ,on ! o!r h&1 !re mu/ be objects & images 9 ! univ]se ( life & =m ^u :i*1 because ( _! inh]5t nature & on acc\nt ( ! lack ( our int]e/ 9 !m & _! int]e/ 9 u1 we c nei!r act nor become ! object ( _! action4 ,b h]e9 is a my/]y4 ,=1 ei!r we act ^u & are recipi5ts ( ! action ( ! totality ( images or objects 9 bo? ! s5sible & sup]s5sible worlds1 or we are s plac$ 9 ! gr& s*eme ( ?+s t bo? ourselves & ! sph]e ( our int]e/s & possible actions are clos$ circuits1 h]metically seal$ & non-communicative ) ! o!r l sph]es1 :i* d n & _c act ^u u4 ,!re is yet a ?ird possibility--t we are s fa%ion$1 9 ! entirety ( our be+1 t "s "p ( u is exactly congru5t ) "s "p ( e sph]e ( possible actions & int]e/s 9 ! kosmos1 & !re=e1 ea* ( u has be+ or consci\sness ( a k9d t is key$ to & regi/]+ 9 ! totality ( su* sph]es2 & t1 at pres5t1 because our int]e/s & possible actions are limit$ to ! plane ( s5sibility1 we are consci\s only !re4 ,& fur!r1 t al?\gh ^? sph]es ( our consci\sness :i* are fix$ to regi/] 9 o!r planes d n answ] to ! l[e/ on :i* we n[ op]ate1 hav+ a "* ( :i* we are unaw>e1 !y nev]!less _c be said n to exi/1 because ( ! lack ( communication betwe5 !m4 ,among ^! ?ree possible *oices1 we h no hesitancy 9 express+ a decid$ pref]5ce = ! la/ m5tion$--t ! range ( our be+ is co-ext5sive ) ! range ( reality1 & l a p5dulum1 we oscillate1 at long int]vals1 betwe5 two kosmic extremities--nesci5ce & omnisci5ce4 ,! intellectual consci\sness is ! t\*-/one ( realism4 ,x is l a spread+ light :i*1 z x exp&s1 reveals previ\sly d>k5$ corn]s & conditions1 only x has p[] bo? to reveal & to br+ into manife/ation4 ,9 its pres5t /ate1 man's consci\sness is l a se>*light4 ,x illum9es & takes cognizance ( ev]y?+ t falls )9 its scope ( motility & is consequ5tly able to /udy 9 detail t :i* x reveals4 ,b t :i* is beyond its scope is z if x nev] exi/$ s f> z ! individual consci\sness is conc]n$4 ,x is n reasonable to pr$ict t ! same *>act]i/ics t are obs]vable 9 any giv5 /ate %all p]si/ ?r\gh\t all ! v>i\s scopes ?r\gh :i* ! consci\sness mu/ proce$ 9 its evolution>y expansion4 ,= ! scale ( kosmic realism is "o gr& panorama ext5d+ f ! grosse/ to ! mo/ subtle & ref9$4 ,:ile 9 g5]al ! ?read ( realism may p]vade ! entire scale x is nev]!less m>k$ by _m & div]se *anges 9 its *>act]i/ics z x is foll[$ f "o /age to ano!r4 ,s t ! reali/ic "* ( "o /age may v>y greatly f t :i* next prec$$ x or f t :i* w succe$ x4 ,x w\ld appe>1 !re=e1 t 9 pass+ f "o /age ( realism to ano!r !re ne$ n rema9 any?+ b ! m]e fact ( reality 9 its connection ) ultimate reality2 = x is obvi\s t 9 e condition ( realism :i* may be enc\nt]$ 9 ! kosmos !re mu/ be a basic ?read ( ultimate reality runn+ ?r\gh ! :ole4 ,! entire gamut ( realism may accord+ly be trav]s$ )\t ! dang] ( be+ div]t$ f ! gold5 ?read ( realism :i* ?us p]meates all4 ,x is always ! ph5om5a ( realism ) :i* we are conc]n$ & :i* we are try+ to und]/& r ?an realism itself4 ,x is ?is t conf\nds u4 ,if x 7 n = ! ph5om5a1 :i* is ! way realism or life pres5ts itself to our consci\sness1 we %\ld exp]i5ce no tr\ble 9 discov]+ ! reality1 all o!r ?+s be+ equal4 ,= ! =m] ev] obscures ! latt]4 ,x is ! supreme task ( m5tal evolution to break ?r\gh ! cl\ds ( ph5om5a 9 ! se>* = ! et]nal sub/ratum ( reality :i* runs ?r\gh ! s5sible univ]se ( ?+s4 ,! fir/ view ( conditions t ! m9d takes ^u awak5+ to consci\sness 9 any new sph]e ( cognition is necess>ily hazy & in*oate4 ,!re is m or less ( a/oni%m5t1 wond] & bewild]m5t ^u fir/ becom+ aw>e ( a new scope ( realism4 ,9 ?is /ate x is natural t ! m9d %\ld ov]look or ignore mu* t is ess5tial & p]haps all t is s ev5 escap+ ! true import ( ! ph5om5a :i* x s5ses4 ,x is reasonable1 too1 t 9 su* a /ate ! ma9 outl9es ( :at is really se5 may be greatly di/ort$ & exagg]at$ s t x is well-nigh impossible to secure a correct compreh5sion ( ! "* ( a new scope ( realism f any e>ly survey4 ,x is n until lat] ye>s1 aft] mu* /udy & circumspection t ! m9d1 becom+ us$ to ! new conditions1 beg9s to get correct impressions & to make valid judgm5ts z to t :i* x disc]ns4 ,& ev5 !n1 x n infrequ5tly happ5s t ! resultant view ( ?+s 9 g5]al is f\nd to be 9 ne$ ( revision & correction4 ,h5ce1 aft] ev]y?+ is sift$ d[n to ! ultimate all[ance = ! illusion incid5t to too mu* en?usiasm & wond] we h only a v small residuum ( tru? ^u :i* to build & ?is latt] we (t5 f9d to be ! s+le ?read ( reality :i* runs ?r\gh all ! ph5om5a & :i* is1 !re=e1 ! only quantity t rema9s wor?y ( mu* consid]ation4 ,?us x is ) religion4 ,! pa? ( progress ov] :i* our religi\s conceptions h come ne$ n be outl9$ "h1 b to any "o at all acqua9t$ ) ! hi/ory ( religi\s ?\ght & ideals x at once mu/ be pat5t t x has be5 "o cont9u\s surr5d] ( ! old = ! new1 ( "o degree ( realism = ano!r new] & high] degree2 t always x has be5 ! ph5om5a1 ! flora ( ! ideals :i* h _h to give way1 :ile no?+ 0 left b ! roots ( realism f :i* !y h sprung4 ,x has be5 ! same ) sci5tific k4 ,facts h be5 collect$ & hypo!ses propos$ to syn!size !m & yet ^! h _h to give way = o!rs1 & o!rs /ill1 until ! data ( sci5tific k to-day are q diff]5t f :at !y 7 9 e>li] days4 ,& yet p]meat+ ! sci5tific k ( all times has be5 ! gold5 ?read ( reality1 & ( all facts & sy/ems ( facts :i* man has successively assum$ & surr5d]$ no?+ has rema9$ b ! reality2 inde$1 no?+ c\ld s rema91 b reality4 ,s x is ) air ph5om5a ) :i* consci\sness has to deal4 ,?is p]haps is due to ! fact t ! m9d int]prets ph5om5a 9 accordance ) ! quality ( its aw>5ess1 & z consci\sness is a v>iable quantity1 its /&>ds ( int]pretation w likewise v>y4 ,ea* new scope ( aw>5ess1 aft] ?is mann]1 yields high] & m exact /&>ds ( int]pretation4 ,& !n1 progress+ 9 aw>5ess f ! segm5t to ! :ole a full] view ( ! ph5om5a z well z ( reality itself is ga9$ & also a m compreh5sive judgm5t ( ! relations :i* exi/ betwe5 ! segm5t & ! :ole4 ,9 o!r words1 z ! scope ( consci\sness wid5s x becomes m & m app>5t t :at 0 fir/ ?\ght to be a sep>ate segm5t is 9 reality id5tifi$ ) ! :ole 9 an indissoluble mann]4 ,= ! ,?9k] is !n n only aw>e ( ! segm5t z su*1 b he is also consci\s ( ! fact t x has def9ite relations ) ! entirety & t :at he ne$s is m]ely a m ext5d$ consci\sness4 ,9 d5y+ ! exi/5ce ( ! f\r-space or spaces ( n-dim5sionality z describ$ & def9$ by geometricians1 we d n !reby d5y ! exi/5ce ( a plane ( consci\sness :i* is z mu* unlike ! conditions ( ! tridim5sional _w z x is said to be unlike ! f\r-dim5sional _w2 b :at we d d5y is t su* a high] plane ( exi/5ce has necess>ily to be condition$ by su* *>act]i/ics z ! metageometricians h propos$4 ,x is ma9ta9$ t !re is no basis 9 consci\sness = a _w ( f\r dim5sions2 t ! consci\sness has no t5d5cy = action 9 f\r-space4 ,nei!r has matt] nor life any incl9ation or pot5cy to behave 9 a f\r-dim5sional mann]4 ,x is inde$ m rational to suppose t !re is a high] plane1 9 fact1 a s]ies ( high] planes1 9 :i* ! ?read ( realism is cont9u\s1 n brok5 z x necess>ily w\ld h to be 9 ext5d+ to hyp]space1 nor curv$ z 9 a manifold2 t ?is s]ies ( subtl] & f9] planes ( consci\sness are m]ely an elongation ( our ?ree dim5sional scope ( realism4 ,x1 !re=e1 rema9s only to ma/] ! ph5om5a ( ea* 9 j ! same mann] z we h1 9 a measure1 ma/]$ ! ph5om5a ( tridim5sionality4 ,= x is easily conceivable t ! quality ( consci\sness is su* t x may adapt itself to a f> wid] range ( possibilities ?an may be discov]$ 9 hyp]space & /ill be a tri-space quantity4 ,x is believ$1 h[ev]1 t 9 all ! new & high] planes ( consci\sness tridim5sionality is ! norm bo? ( ! ph5om5a & ( ! reality peculi> to !m4 ,& t1 be+ su*1 does n *ange or v>y1 b is a fix$ quantity reg>dless ( ! plane ( consci\sness4 ,fur!rmore1 x is believ$ t ! highe/ /ate ( consci\sness 9 ! entire kosmos c\ld easily exi/1 & does s exi/1 ^u ! basis ( ?ree-space z ! norm ( its ext5t4 ,a %>p l9e ( dem>kation %\ld be drawn betwe5 ! reality :i* is life & consci\sness & t :i* belongs to ! realm ( phantasy4 ,= x is ! pr]ogative ( ! intellect to create1 out ( ! rema9s & deposits :i* x f9ds 9 ! pa?way ( life1 :atsoev] x wills4 ,?is x does cont9u\sly2 b x sc>cely c be expect$ t su* creations %all be end[$ ) ! same dynamic "* z t :i* life be/[s ^u its creations4 ,! creations ( ! "o are m]ely dead c>casses :ile ^? ( ! o!r are vital & real4 ,betwe5 !m ! same m>k$ diff]5ce exi/s z betwe5 ! gr[+ tree & ! lumb] :i* ! build] conv]ts into a h\se4 ,! organization :i* we witness :5 we look ^u a build+ made ( ! dead body ( a tree is n ! same k9d ( organization z t :i* we see :5 we view ! liv+1 gr[+1 vital tree4 ,! dead tree is a deposit ( life ca/ (f by x :5 x pass$ on4 ,:atev] ! intellect c d 9 dispos+ ( ! rema9s ( ! tree-life is conv5tional & artificial4 ,if x conv]t x into an edifice x w !n be/[ ^u x a sort ( consi/5cy :i* is q suffici5t = all purposes4 ,b ! consi/5cy :i* holds ! organization ( an edifice toge!r is n ! k9d ( consi/5cy :i* holds a liv+ tree toge!r4 ,9 fact1 !re is a consi/5cy t is n consi/5t4 ,su* is ! consi/5cy ( metageometry4 ,x is self-consi/5t & yet inconsi/5t ) ! consi/5cy ( ! kosmos & its norm ( be+ :i* is consci\sness4 ,self-consi/5cy is "o ?+ & kosmic consi/5cy is q ano!r4 ,x does n necess>ily foll[ t because a giv5 s*eme ( ?\ght is consi/5t 9 all its p>ts t x is also consi/5t ) univ]sal tru? or ) life4 ,?is v vital fact 0 ov]look$ by ,,gauss & all ^? :o foll[$ 9 8 wake :5 he discov]$ t 8 ,a/ral ,geometry 0 consi/5t ?r\gh\t 9 all its p>ts4 ,!re is only "o norm ( tru? & t is kosmic consi/5cy4 ,x matt]s little t a ?+ %all be self-consi/5t2 x matt]s mu* :e!r x is consi/5t ) ! univ]sal /&>d4 ,x has be5 %[n to be logically possible to elaborate at lea/ two diff]5t sy/ems ( geometry1 namely1 ! geometry ( ! acute angle & t ( ! obtuse1 :i*1 :ile ea* ( !m is self-consi/5t ?r\gh\t1 are nev]!less inconsi/5t ) ea* o!r & ) ! geometry ( ! "r angle 7,euclidean74 ,?is1 x w\ld seem1 appe>s to be suffici5t = ! invalidation ( ei!r "o or bo? ( ! non-,euclidean sy/ems ( geometric ?\ght4 ,inde$1 if x c be %[n t ! ,euclidean geometry is m repres5tative ( ! true approa* to ! norm ( space-g5esis & ( creation s f> z its mode ( manife/ation is conc]n$1 & consequ5tly true ( ! norm set up by consci\sness1 ! rejection ( bo? sy/ems ( non-,euclidean geometry seems to be ?or\ghly w>rant$4 ,b ?is is obvi\s & requires no demon/ration nor comm5t to make x cle>4 ,we h only to ask ourselves :e!r x has ev] occurr$ to u t consci\sness has ei!r a t5d5cy to or adaptability = action 9 a curvil9e> mann]2 or1 if :5 we contemplate ideas or idea-relations we h ! impression ( p]ceiv+ a curvil9e> or manifold t5d5ce 9 !m ei!r ( a positive or negative nature1 & also :e!r x has be5 obs]v$ t our ?\ght processes naturally assume f\r-dim5sional attitudes4 ,if we f9d t su* a qu]y mu/ be answ]$ negatively1 & inde$ we mu/ s f9d1 !n1 we h no basis = ! assumption t any "o ( ! sy/ems ( non-,euclidean geometry is valid ei!r = ! pres5t /atus ( consci\sness or = a future exi/5ce1 s9ce x is true t ! future is b an elongation ( ! pres5t4 ,evolution is to br+ no radical *anges 9 ! norms ( reality2 x has m]ely to deep5 & wid5 & make m int5se1 effici5t & compreh5sive ! pres5t scope ( our consci\sness & !reby1 :ile ! ,?9k] is pass+ f "o degree ( realism to ano!r1 to br+ him into a cle>] conception ( :at 8 own limit$ scope ( motility means to ! :ole4 ,! f\r-space is a ma!tic div]tisem5t4 ,t is1 x _c be said to lie 9 ! direction ( a /raight l9e :i* proce$s ei!r 9 a =w>d or lat]al direction4 ,nei!r does x lie 9 a plane :i* is v]tical or horizontal to ! s5sorium4 ,x is1 !re=e1 a fractural dep>ture f any conceivable tridim5sional direction1 a geometric anomaly4 ,evolution1 despite ! m9or aspects ( its movem5t1 und\bt$ly proce$s 9 a /raight l9e & n by a zigzag nor discont9u\s l9e & h5ce x is irrational to assume t x w1 :5 x passes on to ! next advanc$ /age1 em]ge into ! realm ( ! f\r-space4 ,= ! s-call$ hyp]space ( geometry _c by any /&>ds ( ref]5ce be said to lie 9 ! plane ( any /raight l9e :i* c be describ$ 9 ?ree-space4 ,if life is to evolve m effici5t =ms & if ! =ms are to evolve into m p]fect organizations & m9d & consci\sness to become m int5se & compreh5sive expressions ( ! div9e m9d ( ! kosmos x is c]ta9ly n 9 ! doma9 ( hyp]space t ^! %all f9d ! sub/ructure ( _! high] developm5t2 b1 if at all1 x %all be f\nd1 z 9 all times pa/1 9 ! realm ( p]ceptual space :]e bodies are said to h ?ree & only ?ree possibilities ( motion4 ,:at !n is ! significance ( ! m ?an a ?\s& ye>s ( ma!matical labors2 ( all t has be5 said & done 9 an endeavor to br+ into ! popul> consci\sness a conception ( hyp]space8 ,is x a "q ( ,love's ,lab\r's ,lo/8 ,or is x a m]e pro/itution ( ma!matical tal5t8 ,to answ] ^! qu]ies is ! burd5 ( ?is treatise & x is hop$ t z ! text cont9ues ! read] may be able to arrive at 8 own conclusions z to ! relative value ( ! "w ( ! ma!maticians 9 ?is respect & be able to judge = himself ! true significance ( x all4 ,! specific value ( consci\sness z a det]m9ative factor 9 space-measurem5t has be5 recogniz$ by all :o h s\ght to arrive at a logical ju/ification = ! conception ( f\r-dim5sionality by analog\s reason+4 ,! exi/5ce ( ! unodim ) consci\sness limit$ to a l9e or po9t has be5 assum$ & x has be5 %[n h[ greatly su* a be+ w\ld be h&icapp$ by 8 limit$ area ( consci\sness1 x hav+ be5 propos$ to conf9e 8 consci\sness to "o dim5sion4 ,an unodim w\ld1 ( c\rse1 be entirely unaw>e ( any o!r dim5sion ?an t 9 :i* he c\ld consci\sly function4 ,s t ) respect to 8 own consci\sness no o!r dim5sion w\ld be necess>y = ! cont9uance ( 8 life processes4 ,he might live 8 life )\t any k ev5 ( any limitations or b>ri]s to o!r ?+s high] ?an ^? ( 8 plane4 ,he w\ld be cont5t to exi/ 9 ! "o-space & enjoy ! b5efits :i* x (f]$4 ,he c\ld h no notion ( ! two-space1 b x has be5 all[$ t a sup]-unodim1 an unodim metageometrician1 if y please1 c\ld reason out a m5tal conception ( :at ! two-space might be4 ,pass+ on to a space ( two dim5sions1 ! doma9 ( ! duodim1 a great] fre$om ( movem5t is all[$ & in/ead ( be+ able to function 9 only "o dim5sion ! inhabitants ( ?is plane w\ld f9d !mselves able to move ab\t 9 at lea/ two directions4 ,consci\sness w\ld accord+ly enjoy a m compreh5sive scope4 ,b 9 a mann] simil> to t us$ by ! unodim metageometrician x is held t ! duodim c\ld get a conception ( ! ?ree-space by analog\s reason+ & s gradually become consci\s ( a high] degree ( spatiality ?an 8 own4 ,9 ! consci\s reason+ ( bo?1 h[ev]1 is ! condition ( p]p5dicul>ity4 ,t is1 x mu/ be assum$ by bo? ! unodim & ! duodim t ! new dim5sion mu/ lie 9 a plane p]p5dicul> to _! space4 ,s1 ! unodim w\ld po/ulate t ! two-space mu/ lie 9 a direction at "r angles to 8 space1 & yet he w\ld n be able to indicate ! direction ow+ to 8 ignorance ( any exp]i5ce t w\ld acqua9t him ) ! new space z well z ! want ( possibility ( motion !re94 ,simil>ly1 ! duodim w\ld arrive at a conception ( ?ree-space4 ,?us1 x has be5 argu$ t tridims1 or p liv+ 9 our tridim5sional _w1 c\ld1 by us+ a l l9e ( argum5t or reason+1 arrive at a conception or und]/&+ ( ! f\r-space1 :i*1 ( c\rse1 mu/ also lie 9 a direction at "r angles to ?ree-space4 ,! implications ( ?is mode ( ?\ght %[ h[ ?or\ghly ! ma!matician recognizes ! limitations :i* consci\sness imposes ^u our k ( ! _w & ! subtl] conditions ab\t u4 ,b1 moreov]1 x is ev5 obvi\s to all :o /op to ?9k ab\t x2 = x c readily be se5 h[ little ^? ?+s :i* d n ent] our scope ( aw>5ess affect u ei!r physically1 m5tally or spiritually4 ,b no "o c be s bold z to d5y utt]ly t any?+ exi/s b :at is f\nd 9 our consci\snesses4 ,x is ev5 true t 9 ! great c5t]s ( population :]e p are compell$ to live _m families 9 ! same h\se1 x is ! usual ?+ = ^! individual families to live 9 complete =getfulness ( all ! o!rs 9 ! h\se & live _! lives s completely t x w\ld be exce$+ly difficult to measure ! effect ! "o has ^u ! o!r4 ,! ma!matician1 z is %[n by ! hyp]space movem5t1 recognizes t !re are planes ( sup]consci\sness ! nature & "* ( :i* p]sons conf9$ to limit$ areas ( consci\sness c h no k & may only arrive at t k by s]i\s ?\ght & contemplation4 ,9 o!r words1 !y tacitly admit ! exi/5ce ( high] planes ( consci\sness z well z ! necessity ( elevat+ ! p]sonal consci\sness 9 ord] to compreh5d !m4 ,al?\gh x 0 n expressly all[able 9 ! analogy ( ! unodim1 x is nev]!less "o ( ! /ronge/ implications ( ! process ( reason+ t ! unodim c\ld h easily rais$ ! plane ( 8 consci\sness by cont9u+ 8 rese>*es until he1 too1 became consci\s ( ! ?ree-space1 ma!matically1 z well z ! two-space4 ,= x 0 n necess>y = him to raise ! plane ( consci\sness 9 ord] to contact ! two-space4 ,he _h ne$ only to wid5 x4 ,b 9 ord] to compreh5d ! ma!matical ?ree-space x w\ld be necess>y = him to elevate 8 consci\sness4 ,! fundam5tal error 9 ! =ego+ l9e ( ?\ght re/s 9 ! fact t aw>5ess 9 ! human family has n develop$ 9 ! mann] outl9$4 ,! human species has n come into consci\s relations ) ! ?ree-space by outgr[+ ! "o-space & ! two-space 9 succession4 ,! fact ( ! matt] is t :5 consci\sness fir/ dawn$ x mu/ h encompass$ all ?ree dim5sions simultane\sly & equally & !re is no?+ to indicate t its rise 0 o!rwise4 ,!n1 specifically !re is no evid5ce t ! evolution ( consci\sness has proce$$ 9 a rectangul> mann]4 ,inde$1 !re is und\bt$ly no w>rant = ! assumption t x has progress$ 9 ways t are ma!matically det]m9able at all4 ,! "q v naturally rises 9 view ( ! above z to ! relative value ( ma!matical k 9 ! s*eme ( psy*og5esis4 ,c ma!matical k or laws be said actually & f9ally to settle once = all "t any "q 9 :i* consci\sness or life ent]s z a factor8 ,^u ! response to ?is "q h+es unansw]ably ! decision z to ! category :i* ma!matical k %\ld by "r occupy 9 ! entire s*ematism ( life4 ,if x c be successfully ma9ta9$ t f9al judicative p[] abides 9 ma!matics 9 ! det]m9ation ( ^! que/ions1 !n x w\ld be useless to /ruggle aga9/ ! fiat ( ma!matics & ma!maticians2 v]ily1 we %\ld be compell$ to accept nol5s vol5s all t ma!maticians h devis$ ab\t hyp]space & its connotations4 ,if1 on ! o!r h&1 x c be %[n t no su* judicative p[] inh]es 9 ma!matical k we %all !n be able to e/abli% = ma!matics a true category & to dispose ( ! hyp]space movem5t 9 a mann] t %all at once be logical & necess>y4 ,t ! discov]y ( hyp]space by ! ma!matician is m]ely an aspect ( a g5]al =w>d movem5t 9 ! evolution ( consci\sness c be %[n by a brief correlative /udy4 ,hyp]space is ! artificial symbol ( a high] & m ext5sive realm ( aw>5ess4 ,= x _c be d\bt$ t to be able to ?9k 9 ! t]ms ( hyp]space1 to /udy ! v>i\s relations & int]relations upspr++ f ! orig9al premises1 actually to become consci\s 9 ! hyp]spatial realm ?us con/ruct$1 requires a diff]5t species or quality ( consci\sness ?an t requir$ = ord9>y ?9k+4 ,! p]iod cov]+ ! rise ( artificial spatiality is contemporane\s ) ! rise ( ! ph5om5a id5tifi$ ) ! spiritual life ( ,,sw$5borg2 = dur+ ! same "t he began a s]ies ( visions :i* reveal$ to him great k ( ! unse5 & sup]s5su\s realities ( life & exi/5ce4 ,8 consci\sness 0 be+ flood$ ) ! light f s-call$ cele/ial sph]es & he 0 gradually becom+ consci\s ( a new dim5sion1 a new space1 a high] _w t is altoge!r unlike ! _w ( ! s5ses4 ,dur+ ?is p]iod1 too1 ,,dante1 ! great kosmic se] began to jot d[n ! results ( 8 hyp]space exp]i5ces1 aft] :i* he wrote 8 ,div9a ,comm$ia 9 :i* he describes m or less m9utely "s ( ! *>act]i/ics ( ! hyp]space doma9 :i* 0 reveal$ to 8 consci\sness z he saw & int]pret$ x4 ,bo? ,,sw$5borg & ,,dante be+ deeply religi\s & pi\s-m9d$ _h _! reports ( ! new _w color$ by _! own m5tal exp]i5ces & proclivities4 ,,plato _h at an e>li] day set d[n :at he conceiv$ to be ! e?ical & civic *>act]i/ics ( ! new age1 ! ,utopia ( mank9d liv+ on a high] plane4 ,x 0 dur+ ^! days t ! doctr9e ( evolution 0 born1 al?\gh x rema9$ = ,,d>w9 to =mulate & buttress x ) a /up5d\s cong]ies ( facts4 ,,m>t9 ,,lu!r1 ! great religi\s re=m]1 likewise contact$ ! radiat+ light-gl[ ( a high] consci\sness into :i* ! race 0 com+ b ( :i* only ! =emo/ 7 able to get advance glimpses4 ,,kant1 "o ( ! pe]less lead]s ( ! vangu>d ( humanity1 at ?is "t also1 conceiv$ & wrote 8 ,critique ( ,pure ,reason :i* is likewise an evid5ce ( ! upliftm5t ( 8 consci\sness on ! side ( pure intellectuality & ! comm5cem5t ( a g5]al p]iod ( illum9ation4 ,& !n1 lat]1 b embrac$ )9 ! same p]iod1 arti/s began to get glimpses ( ?is high] consci\sness :i* %[$ itself 9 a new & /range dep>ture 9 art4 ,9 rapid succession new s*ools sprang up & came to be kn[n z ! cubi/1 po/-impressioni/1 futuri/1 orphimi/1 ! syn*romi/ & ! vortici/4 ,art really began ! se>* = ! pla/ic ess5ce ( ! _w try+ to portray its conception ( ! real image ( ! _s ( ! _w4 ,color acquir$ a new k9d ( spl5dor & pa9t+ gave bir? to a new intr9sic beauty ( mat]ial & %e] lovel9ess ( texture4 ,all ( :i* 7 evid5ces ( an intellectual up-rea*+ 9 response to ! %>p appulsions f above4 ,,d>w9's m9d1 be+ ( sci5tific b5t1 saw & int]pret$ ev]y?+ 9 ! t]ms ( mat]iali/ic sci5ce2 b !re is no d\bt b t ! expansion ( ! area ( aw>5ess :i* 8 m9d exp]i5c$ 9 8 great conception ( evolution z a cont9u\s process & all t x implies !reby 0 a result ( ! univ]sal appulsion ( ! human intellect aga9/ ! new doma9 ( consci\sness4 ,& ,,kant's conception ( space 9 g5]al p]haps may be said to h be5 ! se$-?\ght = ! metageometrician4 ,b ?us x w be not$ t 9 all ! cases m5tion$ 9 ! =ego+ !re is always pres5t ! p]sonal elem5t ( ! inve/igator1 & t ! reports ( ea* ( ^! h be5 color$ & *>act]iz$ by _! individual consci\sness & exp]i5ces4 ,t all reports w\ld agree ) respect to details connect$ ) ! new doma9 ( consci\sness c\ld sc>cely be expect$ ow+ to ! wond] & bewild]m5t :i* seize ! intellect "u su* circum/ances4 ,no implication t ! ma!maticians h be5 unduly excit$ by :at !y h discov]$ aft] ye>s ( pati5t rese>* 9 ?is direction is indicat$ by ! =ego+ obs]vations2 b x _c be d5i$ t ! en?usiasm ( ! mom5t & ! consequ5t m9imization ( all o!r ph5om5a b ! special l9e be+ inve/igat$ s]ve v effectively to obscure ! m5tal vision ( ! m p>tisan4 ,x p]haps is suffici5t t ! inve/igator %\ld set d[n 9 z ord]ly mann] z possible ! ?+s :i* he conceives1 & t he %\ld int]pret !m accord+ to ! /&>ds ( 8 own intellect4 ,m ?an ?is _c be expect$4 ,moreov]1 x usually suffices t ! future inve/igator1 f> remov$ f ! becl\d+ influ5ces ( p>tisan%ip1 :o successfully raises 8 consci\sness to t high] plane %all be able to syn!size ! f9d+s ( all & !reby ) ! aid :i* comes to him f a m advantage\s position arrive at s\nd] views & a m reliable judgm5t4 ,x w ?us be se5 t ! metageometrician's me?od ( int]pretation is no m entitl$ to f9al cr$5ce & g5]al acceptance ?an t ( ! spirituali/1 ,,sw$5borg1 or ! occult se]1 ,,dante4 ,= 9 _! be/ moods & at _! highe/ po9ts ( m5tal effici5cy ^! h only succe$$ 9 vaguely symboliz+ :at !y h conceiv$ ( ! realities ( ! sup]s5su\s realm 9 t]ms ( _! own exp]i5ces4 ,is !re any m cog5t reason1 !n1 = accept+ ! analy/'s conception ( a _w ( hyp]space peopl$ ) ensembles1 propositions1 spaces ( n-dim5sionality & o!r ma!tic contrivances ?an ! ,inf]no ( ,,dante1 inhabit$ by hide\s %apes & repell5t d5iz5s1 ! rema9s ( ill-sp5t e>?-lives or ,,sw$5borg',s ,cele/ial ,realm1 :]e9 dwell num]\s be+s ( cele/ial "* p]=m+ v>i\s tasks 9 ! "w ( ! _w8 ,^! obs]vations %\ld n lead ! read] to come to ! conclusion t ! visions ( ,,dante & ,,sw$5borg are deem$ to be m wor?y ( cr$5ce ?an ma!matical k :5 t k is limit$ to ! sph]e :]e x rightfully belongs2 b ! prop] view is t :i* w\ld make x appe> t x is ! way ^! widely diff]+ work]s int]pret :at !y h se52 t x is ! adaptation ( ! unse5 realms to ! peculi>ities ( ! m5talities :i* obs]ve !m4 ,! ma!maticians h simply portray$ z well z !y c\ld _! conception ( ! new /age ( consci\sness & its cont5ts1 & foll[+ ! modus viv5di ( all intellects h int]pret$ ^! ?+s 9 ! t]ms ( ma!matics1 m]ely because ma!matics con/itut$ ! be/ available symbology at h& = ! purpose4 ,simil>ly1 ! pa9t] sees a new _w ( color2 ! politician1 a new era ( political fre$om2 ! religi\s en?usia/1 a new religi\s conception2 ! sci5ti/1 a new condition ( matt] & en]gy1 & s on1 to ! mo/ ord9>y m9d1 ea* sees some?+ new :ile at ! same "t is necess>ily limit$ to ! conf9es ( 8 own m5tality :5 he comes to int]pret :at he sees & conceives4 ,h5ce1 !re w\ld appe> to be only "o way to reg>d all ^! advances & t is by syn!siz+ !m1 by correlat+1 & by trac+ !m to a common s\rce1 & f9ally by see+ !m z "o g5]al =w>d movem5t ( intellectual evolution4 ,man1 ! ,?9k]1 :o 9 ess5ce is a pure intellig5ce1 has two m5tal me*anisms or organs ( consci\sness4 ,"o ( ^! is ! bra9-consci\sness or ! egoic4 ,x is s call$ because ! bra9 is its organ ( expression & impression4 ,x manife/s ?r\gh ! bra9 & uses x to fur!r ! v>i\s objective cognitive processes4 ,! bra9-consci\sness is a *ild ( ! physical body & its life is intimately id5tifi$ ) ! life ( ! body4 ,?is consci\sness may be call$ ! a po/]iori/ic me*anism or organ ( ! ,?9k] & is !re=e 8 means ( int]pret+ ! ph5om5a ( ! objective _w4 ,cell-consci\sness is a phase ( ! ergonic functions ( ! a po/]iori/ic me*anism4 ,! o!r organ ( consci\sness is an aspect ( ! intellig5ce ( ! ,?9k] himself & p]haps may be said to be ! active1 organiz$ portion ( t intellig5ce4 ,x is sep>ate & di/9ct f ! a po/]iori/ic consci\sness yet su/a9+ a sub/ructural relation%ip ) x1 be+ ! s\rce ( ! egoic or bra9-consci\sness4 ,x may be call$ ! a priori consci\sness4 ,its roots are buri$ deep )9 ! he>t ( ! space-m9d & x is !refrom n\ri%$ & develop$ by :at x receives 9 ! way ( intellig5ce4 ,x is ! intuitional faculty2 kn[s )\t be+ taught2 conceives )\t reason2 int]prets accord+ to ! norms ( ! space-m9d or ! div9e m9d ( ! kosmos4 ,x always resides on a high] plane ?an t ( ! bra9-m9d or consci\sness1 only at r>e int]vals be+ able to contact x ) fla%es ( its own intellig5ce z intuitions4 ,! a priori consci\sness be+ ! intuitive faculty ( ! ,?9k] is1 !re=e1 a phase ( 8 m5tal life on a high] plane ?an ! s5su\s4 ,all its conceptions con/itute ! a priori k ( ! bra9 m9d s-call$4 ,! a priori faculty ( man's high] consci\sness gives ! "* possess$ by t =m ( k kn[n to philosophy z ! a priori4 ,s t ! a priori has a m sub/antial basis ?an has hi!rto be5 surmis$4 ,x is n only t :i* may be said to transc5d exp]i5ce b t :i* is ! organ ( contact ) ! sup]s5su\s realities z well z ( expression ?r\gh ! bra9-consci\sness4 ,! m9d's me?od ( appreh5d+ objective ph5om5a is n a direct process b an indirect process by virtue ( :i* neurograms or n]ve-impacts regi/]$ 9 ! bra9 are int]pret$4 ,ext]nal s5se-impressions are1 ( c\rse1 convey$ to ! cortical area by means ( appropriate vibrations :i* trav]se ! l9es ( ! neural me*anism4 ,^! are record$ 9 ! bra9 areas j z a telegraphic communication is regi/]$ 9 ! app>atus ( ! receiv+ end1 & 9 be+ s1 !y make t]m9al regi/rations :i* man1 ! ,?9k]1 int]prets aft] a psy*ic code :i* has be5 built up empirically4 ,t is1 he comes to "k t c]ta9 rates ( vibration & c]ta9 peculi>ities !re9 mean c]ta9 ?+s :5 ref]r$ to ! s5sorium4 ,he !n int]prets accord+ to ?is exp]i5ce ! symbolism ( all neurographical impressions4 ,b x is obvi\s t "u su* circum/ances1 :]e ! int]pret] is f> remov$ f ! ?+ itself & f9ds x necess>y to int]pret rates ( vibration or symbols 9 ord] to arrive at a k ( ! intellig5ce :i* is convey$ to him1 ! *ances ( inadequate conception are v great inde$4 ,9 fact1 x is n possible ?r\gh ! use ( neurographical symbols alone to get any complete notion ( ! ph5om5a consid]$4 ,& ?us !re /&s betwe5 ! ,?9k] & absolute k a b>ri] :i* prev5ts 8 arriv+ at a /ate ( c]titude 9 8 k ( ! _w ( s5sible objects4 ,x is1 h[ev]1 a b>ri] :i* w always rema91 *eck+ ev] 8 approa* to f9ality 9 8 und]/&+ ( ! univ]sum ( appe>ances4 ,a m>k$ly diff]5t condition obta9s 9 ! realm ( ! a priori or intuitional = ! reason t ! b>ri]s :i* inh]e 9 ! neurographical or a po/]iori/ic me?od are abs5t & ! ,?9k] has a m direct approa* to ! objects ( cognition4 ,h5ce ! *ance = error is v small inde$4 ,?is w acc\nt1 !re=e1 = ! sup]iority ( ! intuitional ov] ! rational or ! p]ceptual4 ,inde$1 x is d\btful :e!r ! purely rational possesses any value :atsoev] :5 its modus viv5di is unsanction$ by ! intuitional4 ,else :y c we n be c]ta9 t ! results ( our rational processes are correct at all times8 ,is x n because we lack ! p[] to p]ceive :e!r our premises are correct 9 ! fir/ place8 ,q truly4 ,= if ! ,?9k] c intuit ! necessity & c]titude ( any giv5 premise x foll[s t ! consequ5ces ( t premise are true4 ,x w\ld1 !re=e1 appe> t ! m ! intuitional faculty is develop$ ! cle>] w be our p]ceptions n alone ( ab/ract values b ( objective ?+s !mselves4 ,fur!r1 x is d\btlessly true t ! m ! space-m9d is develop$ 9 ! human race ! deep] w become our p]ceptions ( ! ess5tial be-ness ( ?+s s t :atev] may be ! pres5tations ( ! space-m9d to ! bra9-m9d !y w be by f> m accurate ?an ! impressions we receive ?r\gh ! latt] z a m$ium ( appreh5sion4 ,x is b natural1 h[ev]1 t 9 ! pres5t m or less *aotic condition 9 :i* ! faculty ( ! intuitional is f\nd x %\ld be difficult ev5 to int]pret its pres5tations accurately4 ,x is p]haps due to ! fact t we are unus$ to its deliv]ies & mode ( regi/ration z well z to ! fact t x has be5 ov]%ad[$ by ! intellectual or rational faculty4 ,b ! m]e fact t x is pres5t & function+1 ev5 if b rudim5t>ily1 is evid5ce ( its pot5tiality & ! possibility ( its future developm5t to a /ill high] degree ( effici5cy4 ,!re is no d\bt b t ! orig9al impulse :i* result$ 9 ! creation ( ! faculty ( p]ceptibility 9 ! ,?9k] also m>k$ out ! metes & b\nds ( our entire range ( p]ceivability :i* includes n only ! intuitional b some?+ high] /ill4 ,!re is no d\bt+ ei!r ! obvi\s fact t ^! metes & b\nds _c h be5 o!r ?an rudim5t>y or g5]al l9es ( d5otation1 & t ! "w ( _! fur!r elaboration & ref9em5t is a matt] ( evolution>y detail4 ,= if we assume t ! g5]al pr9ciples ( evolution are true we imm$iately recognize ! cog5cy ( ?is view4 ,t :i* we n[ call ! h& has n always be5 ! p]fect in/rum5t t x is nor has ! e> always be5 s ke5ly adju/$ z at pres5t4 ,x has requir$ und\bt$ly _m million ( ye>s = ! eye to rea* its pres5t degree ( complexity & adaptability4 ,yet 9 all ^! cases ! diff]5t organs exi/$ 9 pot5tiality f ! beg9n+2 ! metes & b\nds ( ! h&1 ! e> & ! eye 7 laid out primordially4 ,evolution has specializ$ & adju/$ !m to environm5ts & ne$s4 ,?us x w be se5 t :ile ! intuitional faculty 0 design$ = manife/ation f ! beg9n+ x has nev]!less requir$ ages = its appe>ance ev5 9 ! mo/ rudim5t>y fa%ion4 ,almo/ ! entire cont5t ( human k is bas$ ^u assumptions or hypo!ses2 9 fact1 is b a mass ( ^!1 & especially is ?is true ( ma!matics1 sci5ce & philosophy4 ,( c\rse1 !re are c]ta9 m9or obs]vable facts :i* by reason ( ! seem+ p]man5ce ( _! exi/5ce h be5 elim9at$ f ! category ( assumptions4 ,b ev5 ?is elim9ation :5 x is trac$ to its dep?s may be f\nd to be errone\s1 & p]haps aft] all1 :5 we h really begun to "k some?+ ( ! reality ( ?+s1 may h aga9 to be plac$ 9 ?is category4 ,& !n1 too1 ! hypo!tical nature ( our k is due l>gely to ! ,?9k]'s me?od ( contact+ ! objective _w :i* is ! subject ( 8 k4 ,x is because x is necess>y = him to int]pret ! neurographical symbols :i* s5se-impressions make 9 ! bra9 matt] accord+ to a psy*ic code t r5d]s 8 k ( ?+s 9 g5]al hypo!tical4 ,8 int]pretations are bas$ ^u an assum$ value :i* exp]i5ce has taught him to give to ea* neurogram4 ,b ev5 :5 8 int]pretations leave no?+ to be desir$ 9 respect to _! accuracy ( appreh5sion ( :at ! neurographical vibration implies !re is t fur!r b>ri] to 8 cognition ( reality :i* is due to 8 remote removal f ! object itself & ! consequ5t extreme difficulty1 if n pres5t impossibility1 ( id5tify+ 8 consci\sness ) ! ess5ce ( ! objects :i* he contemplates4 ,:5 ! ,?9k]'s consci\sness is pres5t$ ) a neurograph ( say1 a cube1 x is n ! cube itself :i* he contemplates or obs]ves2 x is ! neurograph or psy*ic symbol :i* ! s5se-impressions make 9 ! bra94 ,8 consci\sness deals n ) ! object b ) ! symbols4 ,x is true t :5 he v]ifies "o neurograph by ano!r1 z ! scopographic or sight impressions by ! tactographic or t\* impressions x is f\nd t ! deliv]y ?us det]m9$ is a true en\gh repres5tation4 ,x is also true t ! ,?9k]1 z a rule1 does n accept a neurograph z valid until x has be5 v]ifi$ by at lea/ "o or m pres5tations ?r\gh 8 out] s5se organs4 ,x occurs1 !re=e1 t all su* deliv]ies are v]ifi$ & correct$ by "o or m s5se witnesses be=e f9al acceptance by ! ,?9k]2 b ev5 !n x _c be said t 8 notions ?us ga9$ are 9 all respects correct & true to ! /&>ds set up by ! bra9-consci\sness n to m5tion high] =ms ( consci\sness4 ,& !n1 :5 we consid] t 9 addition to ! num]\s *ances = error :i* naturally inh]e 9 ?is me?od ( cognition x mu/ also be app>5t t ! ,?9k]'s approa* to ! reality ( ?+s is mu* imp$$ by 8 sep>ation !refrom1 ! unreliability ( our ord9>y me?ods ( cognition is mu* emphasiz$4 ,b aside f ! egoic or bra9-consci\sness !re is ! high] consci\sness ( ! ,?9k] himself4 ,= ! bra9-consci\sness is m]ely 8 me?od ( reg>d+ & compreh5d+ ! neurographical deliv]ies1 ! psy*ic code by :i* he sy/ematizes & organizes 8 cognitions or impressions ( ! s5sible _w4 ,?is high] consci\sness con/itutes ! faculty a priori = ! ,?9k] on a high] plane ( exi/5ce1 & because x deals ) elem5ts altoge!r unlike ^? :i* make up ! data ( bra9-consci\sness is1 accord+ly1 less liable to error 9 its judgm5ts ( ! sup]s5su\s pres5tations ?an is ! objective or bra9-m9d4 ,9 fact1 x is difficult to conceive ( a /ate or conditions :]e91 support$ z ?is view contemplates1 ! intuition %\ld err 9 judgm5t4 ,view$ f ! /&po9t ( ext]nal imp$im5ta1 ?is condition may be said to be due to ! abs5ce ( s5su\s b>ri]s :i* w\ld o!rwise prev5t ! ne> approa* ( ! ,?9k]'s consci\sness to ! ess5ce ( ?+s :i* is ! object ( 8 consci\sness on ?is high] plane4 ,directly1 h[ev]1 x is und\bt$ly due to ! fact t1 foll[+ ! lead ( life itself1 yea1 z ! v]itable h&maid ( life1 x _c err :]e life is conc]n$4 ,:5 deal+ ) notions a priori or intuitograms ! ,?9k] is reliev$ ( ! on]\s necessities & limitations incid5t to ! exam9ation & det]m9ation ( neurographic symbols regi/]$ 9 ! bra9 cortex & s is free to /udy1 to exam9e & judge at fir/ h& ! impressions :i* are receiv$ f 8 own plane ( intuition4 ,! diff]5ce is ab\t ! same z t :i* %\ld exi/ betwe5 ! me?ods ( communication betwe5 two telegraphic op]ators :5 9 "o in/ance !y w\ld h to dep5d ^u ! deliv]ies convey$ ov] ! wires1 :ile 9 ! o!r1 :5 !y /ood face to face ) ea* o!r1 !y c\ld communicate by direct conv]sation4 ,9 ! "o case ! me?od ( communication is direct & simple1 :ile 9 ! o!r x is indirect1 circuit\s & complex4 ,x c1 !re=e1 be readily se5 t 9 all cases :]e ! approa* is made 9 a direct1 simple mann] ! probability ( error is mu* less ?an 9 cases :]e ! intellectual approa* is less direct & m complicat$4 ,h5ce 9 draw+ conclusions z to ! relative importance ( ! two me*anisms ( consci\sness1 ! a po/]iori/ic & ! a priori1 x is necess>y to be> 9 m9d ! comp>ative sup]iority ( ! "o ov] ! o!r z a means ( cognition4 ,x matt]s little t ! intuitional faculty is n s well develop$ z ! tuitional because x is b natural t inasmu* z ! ,?9k]'s ne$s are subs]v$ 9 ! s5su\s realm by ! tuitional consci\sness x %\ld1 f m active use1 ga9 some:at ov] ! intuitional 9 facility ( expression & g5]al utility4 ,& ! m s1 because ! two faculties s]ve diff]5t purposes2 "o is attun$ to receive impressions f a subtl] plane :ile ! o!r is fitt$ = contact ) ! ph5om5al univ]se2 "o is relat$ to ! conceptual :ile ! o!r is relat$ to ! p]ceptual4 ,!y diff] n only 9 function1 b 9 nature z well4 ,!re is1 ( c\rse1 a natural b>ri] consi/+ ( ! inh]5t limitations ( ea* faculty :i* prev5ts ! full m]g5ce or unification ( ! two /ates ( consci\sness s t !re exi/s a /ate ( consci\sness ! data ( :i* ! bra9-m9d is unaw>e1 x be+ able only at r>e int]vals ev5 to receive s mu* z slight impressions f x 9 ! nature ( intuitional fla%es or inspirations & ! l4 ,view$ 9 ?is light x w\ld appe> t ! cognitions :i* are mo/ tru?wor?y are ^? :i* are pres5t$ by ! intuitional faculty because !y are ne>] to ! ess5tial reality ( ?+s2 !y h to d m specifically ) ! nature ( t :i* appe>s :ile ! tuitional m9d c only reg>d t :i* is ! appe>ance4 ,h]e9 lies ! :ole diff]5ce4 ,! natural outcome ( ?is division ( labor betwe5 ! tuitional & ! intuitional is ! e/abli%m5t ( ! fact ( man's relation%ip bo? to ! ph5om5al & ! real2 t 9 8 psy*ic nature mu/ reside ! faculty ( appreh5d+ ! real & t he %all "o day awak5 into activity ?is n[ lat5t faculty :]eby he may make a direct & nak$ contact ) reality4 ,if x be true t1 z ,,plato said1 ,god does geometrize1 & t ! div9e geometry1 z w appe>1 is bas$ ^u a sy/em1 an alphabet :i* tak5 toge!r are ! po9t 4 1 ! l9e ----1 ! triangle ,illu/ration1 ! squ>e ,illu/ration & ! circle ,illu/ration1 !n1 we h 9 ?is geometric alphabet ! v secret ( ! div9e geometry4 ,) ^!1 & 9 ! kosmic laboratory ( *aog5y1 ! ,creative ,logos has measur$ (f ! limits & conf9es ( space2 ) !m ,he has trac$ out its dim5sions ! ar*eological evid5ces ( :i* we may view 9 ! space-m9d itself2 & ) !m he has e/abli%$ ! mann] ( its appe>ance to ! ,?9k]4 ,9 dim5sions1 ?ree1 & yet n ?ree1 b "o1 ,space1 ! et]nal prog5itor ( all =ms & en]gies1 hav+ receiv$ ! div9e fiat 9 ! beg9n+ t ?us f> x %\ld ext5d & no fur!r1 p]si/s 9 fai?ful ob$i5ce to ! law ( its be+--tridim5sionality4 ,x mu/ be s because x is ?us sanction$ by ! highe/ faculty 9 man t c r5d] judgm5t !reon4 ,if tridim5sionality inh]e 9 ! space-m9d1 z ! law ( its be+ & 9 ! intuitional consci\sness z ! norm ( its ess5tial nature & z ! easie/ & simple/ expression ( ! tuitional m9d1 h[ c x be ga9said t ^! consid]ations obviate ! necessity ( ! ma!tical hyp]space8 ,if ! reality ( ?+s is hidd5 f u & if we are1 !re=e1 unable to p]ceive _! real ess5ces x is because our mode ( ?\ght & our consci\sness h obscur$ our vision & limit$ u to ?is /ate ( paucity ( p]ception4 ,x is n because reality is itself a hidd51 inscrutable quantity nor t its modus viv5di is unkn[able2 b because we be+ multi=mly limit$1 cab9$1 cribb$ & conf9$ are resultantly lack+ 9 ! p[] to disc]n t :i* o!rwise w\ld be mo/ obvi\s to u4 ,x may well be set d[n z axiomatic t :51 9 ! process ( our ?9k+1 we arrive at ! inscrutable1 ! unkn[able & ! inf9ite1 x is evid5t t our ?\ght processes are deal+ ) a =m ( realism :i* is high] & beyond ! possibilities ( our l(tie/ ?\ght-rea*es4 ,& 9 ord] to symbolize to itself ?is condition ! intellect poses su* t]ms z inscrutable1 unkn[able & ! inf9ite simply because t is ! be/ x c d4 ,h5ce :5 x is said t space is inf9ite x is app>5t t ! m9d recognizes t :5 x contemplates space x is deal+ ) some?+ ^: degree ( realism transc5ds its p[]s ( compreh5sion4 ,inf9ity is a relative t]m1 & 9 fact1 decreases 9 ext5sity 9 ! proportion t ! consci\sness exp&s & compreh5ds4 ,x is n unlikely t %\ld ! intellect "o day discov] t x _h awak5$ into union ) ! space-m9d x w\ld imm$iately reject its preconceiv$ notion ( ! inf9ity ( space4 ,b we ne$ n wait until ! com+ ( ?is f> (f ev5t 9 ! pa? ( psy*og5esis2 = we c "h & n[ p]ceive ) :at mu/ be a high] faculty ?an ! intellect ! v]ity ( ?is conclusion4 ,b c]ta9 x is t ! intellect1 9 ! pride & arrogance ( its traditional h]itage1 w n )\t a great /ruggle yield ! gr\nd & pre/ige x has held = an aeon ( "t2 & 9 va9 does ! intuition s]ve notice ( dispossessal 9 ^! premises2 b h[ev] /ubbornly f\ght ! battle1 h[ev] t5aci\sly held ! position "t w discov] ! weak5+ ( ! intellect's h&4 ,dea? = ! intellect may ensue z a result ( ! conflict b x w be a dea? :]efrom x w arise1 quick5$1 revivifi$ & uplift$ by its dispos]1 ! intuition1 ^u ! rema9s ( its dead self to a high] & gr&] /ate ?an x has ev] enjoy$ be=e4 ,space is n /atic4 ,x is dynamic1 pot5tial & k9etic4 ,x is a process1 a becom+4 ,its duration z a process is nev] end+4 ,its ext5sity is limit$ & f9ite4 ,! s-call$ inf9ity ( space is "o ( ! capital illusions ( ! intellect :i* c only be remov$ by an expansion ( ! consci\sness1 by a m]g5ce ( ! individual consci\sness ) ! space-consci\sness4 ,9 ! ev]-wid5+ circle ( ! individual consci\sness less] realities give way to great] z ! d>kness rec$es f ! light--! less] appe>+ 9 comp>ison ) ! great]1 z ! consci\sness broad5s1 z matt] to _s1 z night to day or z limitation to non-limitation4 ,?us ! mo/ solid facts & conditions ( our limit$ life are b ! %ad[s ( ! deep] realities :i* %all be reveal$ to ! ,?9k] 9 ! days ( 8 l>g] & m glori\s life ( fre$om f limitations4 ,& n[ x w appe> t ! :ole fabric ( our k %all h to be r$uc$ to ! b>e w>p & wo(2 = no?+ is real b ^!4 ,x is z if ! ,?9k]1 us+ ! tuitional m9d1 _h be5 9 all times pa/ /udy+ ! design wov5 9 ! surface ( a v ?ick plu% c>pet4 ,!re are ! w>p & wo(1 ! long v]tical ?reads :i* make ! plu% & ! intricate design appe>+ on ! surface4 ,our k may be lik5$ to ! design4 ,x repres5ts ! cont5ts ( our k4 ,we h n ev5 s mu* z begun ! /udy ( ! nature ( ! v]tical ?reads z !y appe> b5ea? ! surface to say no?+ ( beg9n+ ! /udy ( ! w>p & wo(4 ,! w>p & ! wo( are ! realism ( ! kosmos2 ! v]tical ?reads are ! roots & /em ( ! ph5om5al _w2 ! design is our s5sible _w z x appe>s to ! intellect4 ,! life ( ! intellect has be5 sp5t 9 contemplat+ ?is design2 :ile ( ! h&s :i* wove ! c>pet1 ( ! m9d :i* direct$ ! h&s & ( ! _s :i* vitaliz$ all1 x kn[s no?+ nor inde$ c x "k any?+4 ,:]e %all we say are ^? h&s1 t m9d & t _s :i* made ! c>pet possible & an actuality8 ,9 va9 d we se>* among ! rema9s1 among ! s(t1 gli/5+ ?reads ( ! c>pet or among ! intricacies ( ! design4 ,= !y are n !re4 ,!y h pass$ on4 ,! intellect looks at ! design or at ! v]tical ?reads & because x is unable to foll[ !m to _! s\rce1 x decides t !y are inf9ite1 inscrutable & unkn[able4 ,b n s4 ,all t is requir$ are eyes to see & a m9d 7or %all we say a m9d vitaliz$ by ! intuition7 tra9$ to disc]n ! ?reads z !y po9t upw>d ) _! t]m9i firmly root$ 9 ! w>p & wo( ( ! fabric4 ,b we mu/ fir/ ma/] ! design1 & !n turn+ to ! ?reads1 ma/] !m4 ,!n %all ! doors ( kosmic reality sw+ wide & ! ,?9k] %all be u%]$ into ! et]nal palace ( kosmic realism :]e9 he %all f9d ! great secret1 ! he>t1 ! purpose1 ! beg9n+ & ! end1 ! v nature ( ?+s-9-!mselves4 ,! nature ( e degree or condition ( realism is s con/itut$ t its qualities1 *>act]i/ics & limitations are exactly adequate = ! satisfaction & fulfillm5t ( all ! requirem5ts & ne$s ( e possible /ate ( normal consci\sness4 ,s t ea* degree ( reality & ea* /ate ( normal consci\sness is suffici5t & complete 9 itself & mutually satisfies ! necessities ( ea* o!r4 ,! sub/ratum ( reality or life :i* ext5ds f ! he>t ( ! kosmos to ! extreme limits ( ! ph5om5al univ]se exi/s 9 degrees1 n discrete1 b cont9u\s4 ,& ^! m]ge into "o ano!r by ins5sible /ages4 ,su* is ! imp]ceptible cont9uity ( ! :ole z ea* degree is gradually imm]g$ into ! o!r t only ! limitations ( consci\sness itself make x to appe> z if x 7 discont9u\s4 ,= e /age ( realism !re is a /ate ( consci\sness :i* answ]s to x completely & suffici5tly4 ,s bo? ! /ate ( consci\sness & t ( reality1 manife/+ at any giv5 /age1 seem to be complete & f9al = t /age4 ,realism or life & consci\sness possess only a relative f9ality fa%ion$ ^u ! necessities & requirem5ts = any giv5 /ate ( be+4 ,consci\sness alone fixes ! app>5t limits ( life2 x also det]m9es ! /ate ( our k ( life4 ,& ?us :5 ! ,?9k] is conf9$ to any /age ( reality & congru5t degree ( consci\sness x appe>s t :at he !re f9ds is ample = all 8 purposes4 ,accord+ly he is conv9c$ t t /age is ! f9al consid]ation ( 8 scope ( motility4 ,x is only :5 he is able to raise 8 consci\sness to a po9t :]e he c contact high] realities t he becomes aw>e t !re are high] /ages 9 :i* 8 consci\sness may manife/4 ,?is peculi>ity ( ! ,?9k]'s consci\sness is acc5tuat$ :5 he all[s himself to become :olly engross$ ) a /udy ( ! ph5om5a ( t /age 9 :i* he c consci\sly function4 ,h5ce x con/antly occurs t m5 exhau/+ ! /udy ( ! ph5om5al f9d !mselves fl\nd]+ ^u ! bea* ( ! outly+ %ores ( consci\sness :]e 9 %e] desp]ation !y fall into ! illusion t !y h inde$ rea*$ ! limits ( manife/$ life & t beyond ^? limits !re is no organiz$ be+4 ,unconsci\s are !y t 9 ev] wid5+ circles ! f]tile l&s ext5d & await ! awak5+ ( _! consci\sness :5 !y may till ! fall[ gr\nd ( ?is new doma9 & beg9 aga9 ! se>* = ! ultimately real4 ,) respect to ! pres5t p[]s ( consci\sness1 x _c be successfully controv]t$ t ! concept ( tridim5sionality ( space is suffici5t = all purposes4 ,x mu/ be s = x is n only an aspect ( ! ph5om5a ( space b ( reality z well4 ,?is fact is atte/$ by ! nature ( m9d t answ]s to ! nature ( space4 ,tridim5sionality *>act]izes ! entire ext5t ( consci\sness & life1 & !re=e1 ( space itself4 ,?is *>act]ization may be trac$ to ! v doors ( ! he>t ( space :]e ! ?ree become "o4 ,nor w\ld ?is conception be 9 ! lea/ vitiat$ if x 7 all[$ t ! mass ( ! ph5om5a ( ! sup]s5su\s _w1 ly+ 9 close proximity to ! s5su\s _w1 does pres5t itself to ! consci\sness 9 a f\r-dim5sional mann] & t ! ph5om5a ( a /ill high] plane pres5t !mselves 9 a five or n-dim5sional mann] to t /ate ( consci\sness :i* may be congru5t ) !m2 because !n we %\ld be mak+ all[ances = ! *anges 9 ph5om5a & _! mode ( pres5tation to ! consci\sness :i* by no means implies a correspond+ *ange 9 reality or life4 ,all ph5om5a are fa%ion$ by ! intellect4 ,! ph5om5al _w is j :at ! intellect int]prets x to be4 ,x is t & no?+ m4 ,its qualities1 attributes & *>act]i/ics are su* z ! consci\sness gives to x4 ,x exi/s only = ! purposes ( ! evolv+ consci\sness4 ,&1 z an in/rum5t ( consci\sness1 its exi/5ce is /rictly subject to ! evolution>y ne$s !re(4 ,9 t mom5t t ! imm$iate ne$s ( ! consci\sness %all no long] be able to f9d satisfaction 9 ! ph5om5a ( any plane ( nature1 9 t mom5t ! ph5om5a ( t plane disappe>1 rec$e & are swall[$ up 9 ! mael/rom ( et]nal reality4 ,9 ! gradual expansion ( consci\sness z x passes ?r\gh ! inf9ite s]ies ( grades ( aw>5ess meantime becom+ deep]1 broad] & m compreh5sive z x proce$s1 !re may be obs]v$ runn+ ?r\gh all ^! planes & ord]s t :i* is nei!r ! ph5om5a ( ! v>i\s planes nor ! consci\sness2 b :i* mu/ be ! sub/ructural basis ( bo?1 rema9+ ! same1 un*ang$ & un*angeable4 ,t is ! ?read ( reality1 ! passage ( life itself :i* is ! et]nal basis ( all4 ,n[ x is to ?is reality1 life1 t ! space-m9d is relat$ & 9 :i* its roots1 its he>t & ! v c5t] ( its be+ are at "o ) ! div9e m9d ( ! kosmos4 ,! "q ( dim5sionality is solely a conc]n ( ! objective or bra9-m9d :i* is ! intellect4 ,x is "o ( ! ways 9 :i* ! intellect endeavors to und]/& ph5om5a4 ,x is an arbitr>y contrivance devis$ by ! intellect = its conv5i5ce 9 /udy+ ! _w ( ?+s4 ,)\t x1 z obvi\sly appe>s1 ! intellect w\ld n be able to g v f> 9 its consid]ation ( ! m9or problems :i* inh]e 9 mat]ial ?+s4 ,! f\r? dim5sion is b ano!r attitude1 ano!r contrivance1 :i* ! intellect has devis$ 9 ord] t x may /udy f ano!r angle ! evanesc5t ph5om5a ( ! _w ( appe>ances4 ,hav+ app>5tly exhau/$ ! possibilities ( motion 9 ?ree dim5sions1 & be+ driv5 on to ! acquirem5t ( m picturesque views by ! v necessity ( its cont9u$ gr[?1 x has betak5 itself to ano!r high] m\nta9 peak1 call$ hyp]space :]e ) l>g] l5ses & high] p[]$ in/rum5ts x is beg9n+ to scan ! l&scapes ( a new intellectual realm ( consci\sness4 ,yet ! cele/ial wond]s ( ?is new-f\nd realm ( consci\sness rema9 9 undi/urb$ =getfulness or neglect4 ,b x is n by a scrut9y ( ma!tic l&scapes nor by a /udy ( ! cele/ial wond]s t ! ,?9k] %all "o day realize ! object ( 8 eag]ly pu%$ que/ aft] ! real2 = he %all f9d x1 if at all1 9 ! temple ( ! kosmic m9d :i* is n made by ! intellect nor met$ & b\nd$ by geometric sy/ems ( space-measurem5t4 ,9 all ! le>n$ po!r incid5t to ! ma/]y ( ! ph5om5al1 ! furniture ( ! _w ( ! s5ses1 x is z if ! self 9 man1 ! ,?9k]1 sat seclud$ 9 a six-wall$ t5em5t1 & h5ce six times remov$ f ! subject ( 8 /udy1 & endeavor$ to int]pret t :i* appe>$ to 8 vision4 ,& ?us1 ?9k+ t :at he sees is ! only reality1 he rema9s 9 +lori\s nesci5ce ( ! reality ( t ^u :i* he himself /&s1 unconsci\s t ! tunnel-%ap$ ap]ture ?r\gh :i* he pe]s leads n outw>d1 b backw>d & )9 to ! habitation ( ! real ( :i* he himself is a "p4 ,m5 are deeply & well-nigh hopelessly conc]n$ ) appe>ances1 ) /atic views ( life1 ) in/antane\s exposures4 ,life1 reality & all ! et]nal v]ities pass on & assume c\ntless po/ures1 attitudes1 moods1 t5ses & nuances4 ,! intellect is cont5t to occupy itself ) a s+le t5se or mood4 ,inde$1 x has no aptitude or p[] to consid] m ?an "o at a s+le "t4 ,x ?us misses ! cont9uity1 ! ceaselessness1 ( life4 ,:at is m1 e s+ul>ity1 e attitude1 mood or t5se :i* ! intellect grasps = consid]ation is imm$iately remade s z to fit its own moods & t5ses4 ,& ^u ea* & e nuance ! intellect imm$iately imposes its own =m--actually & lit]ally rehabilitates !m ) its own habilim5ts4 ,un=tunately1 ?is peculi>ity occludes ! intellect f any approa* to ! true nature ( t phase :i* x c grasp4 ,hyp]space is "o ( ! illusions ( ! ph5om5al2 x is ! dress :i* ! intellect has sup]impos$ ^u a s+le nuance2 x is a mask :i* is an exact replica ( ! mood ( ! intellect4 ,yet ?r\gh ?is mask ! intellect gr&ly hopes to approa* reality4 ,! p]iod ?r\gh :i* ! m9d is n[ pass+ is a repetition ( ! evil days ( s*ola/icism :5 m5 set out to det]m9e ! exact numb] ( cele/ial be+s t c\ld be p]*$ ^u ! extremity ( a ne$le po9t4 ,x is a "t :5 m5's m9ds easily assume grotesque & hide\s %apes & _! ?\ghts become ! embodim5t ( fanta/ic entities4 ,! exclusive occupation ( su* m9ds becomes ! fabrication ( ma!tic mon/rosities :i* rapidly deliquesce ^u ! fir/ approa* ( ! real or ! appe>ance ( ! fir/ ray ( intuition :i* may escape ?r\gh ! dim & mi/y condition ( ! intellectual ov]-hang+s4 ,x w n be ev] ?us2 = ! ,?9k] w "o day pass f a /udy ( ! arrangem5t ( ph5om5a 9 space & by well-ord]$ /eps come once aga9 to himself4 ,& !n ?r\gh ! maze ( x all set out ^u ! true pa?----! tridim5sionality ( space foll[+ :i* he w inevitably approa* ! citadel ( ! real1 ! kosmic space-m9d4 ,,*apt] ,,vii ,,! ,,g5esis ,,& ,,nature ,,( ,,space ,symbology ( ,ma!matical ,k--,manife/ation & ,non-manife/ation ,def9$--,! ,pyknon & ,pyknosis--,! ,kosmic ,eng5d]m5t ( ,space--,on ! ,consub/antiality ( ,spatiality1 ,intellectuality1 ,mat]iality1 ,vitality & ,kosmic ,geometrism--,*aos-,!os-,kosmos--,*aog5y & ,*aomorphog5y--,n4 ,,malebran*e ,on ,god & ! ,_w--,! ,space-,m9d--,space & ,m9d ,are ,"o--,! ,kosmic ,p5toglyph4 ,geometry is conc]n$ prim>ily ) a /udy ( ! measurem5t ( magnitudes 9 space4 ,?ree cord9ates are necess>y & suffici5t = all ( its det]m9ations4 ,metageometry compreh5ds ! /udy ( ! measurem5t ( magnitudes 9 conceptual space4 ,= its purposes f\r or n-cord9ates are necess>y & suffici5t4 ,p]ceptual space is t =m ( ext5sion 9 :i* ! physical univ]se is recogniz$ to h be5 creat$ & 9 :i* x n[ exi/s4 ,conceptual space is an idealiz$ conception belong+ to ! doma9 ( ma!sis & has no actual1 physical exi/5ce outside ( ! m9d4 ,ma!matical space repres5ts ! idealism ( p]ceptual space4 ,geometrical magnitudes may be def9$ z symbols ( physical objects & geometry z a treatise on ! symbology ( =ms 9 space4 ,9 fact1 all cognitive processes are simply ef=ts at int]pret+ ! symbolism ( s5se-deliv]ies2 & ! diff]5ce betwe5 m]e k & wisdom1 :i* is ! ess5ce ( all k1 is ! diff]5ce betwe5 ! und]/&+ ( a symbol & ! compreh5sion ( ! ess5tial nature ( ! ?+ symboliz$4 ,s long z k ( space is limit$ to ! und]/&+ ( a symbol or symbols by :i* x is pres5t$ to ! consci\sness s long w x fall %ort ( ! compreh5sion ( ! ess5tial nature ( space4 ,9 va9 h we s\ght 9 times pa/ to und]/& space by /udy+ relations1 positions & ! *>act]i/ics ( =ms 9 space2 9 va9 h we bas$ our conclusions z to its real nature ^u ! fragm5t>y evid5ces :i* our s5ses pres5t to our consci\snesses4 ,x is z if "o _h busi$ himself ) "o ( ! me%es 9 a great net & conf9$ 8 entire att5tion to :at he f\nd !re1 mean:ile rema9+ 9 complete ignorance ( ! nature ( ! net1 h[ x came to be !re1 ( :at x is made & h[ great its ext5t may be4 ,!re is ev] a m>k$ diff]5ce betwe5 a symbol & ! ?+ :i* x symbolizes4 ,words are ! symbols ( ideas2 ideas1 z !y exi/ 9 ! m9d1 are ! symbols ( et]nal v]ities z !y exi/ 9 ! consci\sness ( ! ,logos ( ! univ]se4 ,!re may be a wide div]sity ( symbolic =ms :i* repres5t "o s+le idea2 z1 = in/ance1 ! v>iety ( ^w =ms :i* repres5t ! idea ( deity 9 ! v>i\s languages4 ,likewise !re may be a multiplicity ( ideas :i* repres5t a s+le v]ity4 ,b nei!r is ! idea nor ! ^w ! real ?+ 9 itself4 ,t quality ( a life-aspect :i* we call its ?+ness has an ess5tial nature :i* _c become ! object ( consci\sness except by virtue ( its repres5tation ?r\gh ideas & _! symbolisms1 & ev5 !n1 ! ?+ :i* we conceive is n ! nature ( a quality ( ! life-aspect b an idea ( x--a symbol :i* /&s = t idea4 ,9 ord]1 !re=e1 = ! m9d to arrive at an und]/&+ ( an et]nal v]ity1 su* z space1 x mu/ fir/ be able to syn!size all ( ! repres5tative ideas & !n ab/ract f _! composit5ess a notion ( its ess5tial nature4 ,b ?is c be done only by id5tify+ ! consci\sness ) ! ess5tial be+ ( ! object consid]$4 ,9 o!r words1 ! consci\sness & ! intr9sic be+ ( =ms1 pr9ciples1 =ces & processes mu/ embrace ea* o!r 9 ! intimacies ( direct cognition2 ! life :i* is consci\sness & t life :i* is ess5tial be+1 be+ coeval1 cord9ate & mutually responsive1 mu/ 9 s close a contact z "h intimat$ rea* an und]/&+ ( ! realism %>$ by bo?4 ,t is1 ! human consci\sness1 foll[+ 9 ! wake ( life & consi/+ ( a specializ$ aspect ( life itself1 w1 by su* an intimate approa* to ! life-pr9ciple ( =ms1 readily und]/&2 = x has only to recognize a replica ( itself 9 r5d]+ its judgm5t4 ,b x is n claim$ t su* a /ate ( recognition by ! consci\sness ( life itself c be atta9$ at all by ord9>y means1 nei!r is x believ$ t x is ! next /age 9 consci\s evolution4 ,h[ev]1 x is n d\bt$ b t su* an exaltation ( ! consci\sness is possible1 yea practical2 b ! difficulties :i* beset ! pa? ( atta9m5t 9 ?is direction are s great t x may z well be consid]$ unatta9able4 ,! m]e fact ( ^! difficulties1 h[ev]1 only re-emphasizes ! insuffici5cy ( ! intellectual me?od4 ,! id5tification ( consci\sness ) ess5tial be+ is a proc$ure :i* _c be accompli%$ by an act ( w directly & imm$iately4 ,because x is a process1 a s]ies ( unfoldm5ts1 an adju/m5t ( ! focus ( consci\sness to ! kosmic ess5tialities :i* con/itute ! sub/ructure ( ! manife/$ univ]se4 ,9 ! v nature ( ?+s1 a kosmic ess5tiality _c be view$ z be+ 9 manife/ation especially 9 ! same degree z ord9>y physical objects are manife/4 ,! =m] is a /ate1 a pot5tiality1 a dynamic =ce1 an exi/5ce :i* %\ld be ?\ght ( z an extra-kosmic affair dwell+ on ! plane ( unity or kosmic orig9s2 :ile ! latt] are ! exact opposite ( ?is4 ,! "o c be se51 felt & s5s$ :ile ! o!r is ! roots :i* are n se5 b lie buri$ deeply 9 ! he>t ( ! univ]sal plasm ( be+ & beyond ! k5 ( s5su\s app]ception4 ,! t]m manife/ation is bo? relative & flexible 9 its use4 ,x is relative because x w apply equally to all /ages ( cognition4 ,a ?+ is 9 manife/ation :5 x is pres5table to ! ord9>y means ( cognition belong+ to any /age ( consci\s function+2 x is n 9 manife/ation :5 x is beyond ! scope ( ! ,?9k]'s s*ematism ( cognitive p[]s4 ,its flexibility is se5 9 its ready yieldance to ! entire range ( implications inh]+ 9 ! process ( cognition1 fitt+ ! simple/ z well z ! highe/ & mo/ complex4 ,great is ! gulf :i* is int]pos$ betwe5 manife/ation & non-manife/ation2 & yet ! two1 9 ess5ce1 are "o4 ,!y are l9k$ toge!r z ! /em ( a fl[] is jo9$ to its roots4 ,likewise "o is visible1 palpable :ile ! o!r is invisible1 impalpable ?\gh no less real & abid+4 ,z ! ?9 cru/ ( e>? sep>ates ! /em1 leaves & fl[]s f ! roots s ! limitations ( man's consci\sness sep>ate ! manife/ f ! unmanife/4 ,simil>ly1 z :5 ! surr\nd+ e>? is remov$ f ! roots & !y are laid b>e reveal+ _! cont9uity & unity ) ! outputt+ /em & fl[]s1 s1 :5 ! limitations ( consci\sness are remov$ by ! subtle process ( expansion to :i* ! consci\sness is am5able s t x c encompass ! er/:ile unmanife/1 x1 too1 w reveal ! et]nal unity ( ! kosmic pol>s--manife/ation & unmanife/ation4 ,!re is b "o b>ri] to ultimate k & t is ! human consci\sness h[ev] p>adoxical ?is may seem4 ,! unutt]able d>kness :i* %uts out ! s-call$ unkn[able f our cognition is ! limitation ( man's uprea*+ consci\sness4 ,^! limitations con/itute ! diff]5ce betwe5 ! human intellect & ! m9d ( ! ,logos4 ,nev]!less ! outly+ fronti]s ( man's consci\sness gradually are be+ pu%$ f>!r & f>!r )\t4 ,e new idea ga9$1 ea* new emotion indulg$1 ea* new conception conqu]$1 & e m5tal =ay :i* ! ,?9k] makes into ! realm ( ! conceptual1 e exploration into ! abysmal labyr9? ( man's inn] nature are ! self's exp$ition>y =ces :i* are gradually annihilat+ ! fronti] b>ri]s ( consci\sness & ?us approa*+ m closely ^u ! ,ultima ,?ule ( man's spiritual possibilities4 ,space is 9 manife/ation4 ,x exi/s & has be+ :e!r x is view$ z an object1 an entity or ! m]e possibility ( motion4 ,t x (f]s an opportunity ( motion & r5d]s x possible = objects to move freely f po9t to po9t _c be d5i$ & yet ?is fact has no be>+ :atev] ^u ! ess5tial nature ( space4 ,! v fact ( its appe>ance1 its manife/ation1 makes x obvi\s t x is ! ne!r pole ( t et]nal pair ( opposites--manife/ation & non-manife/ation1 be+ & non-be+1 :i* are ess5tially "o4 ,x w be se5 f figure #ag t ! p]iod ( involution embraces sev5 sep>ate /ages1 ! monopyknon1 duopyknon1 tripyknon1 etc41 be+ ! unit pr9ciple or eng5d]+ elem5ts ( ! respective /ages4 ,involution comprises all creative activity f ! fir/ fa9t /irr+s ( ! void & =mless *aos until ! univ]se has actually become manife/ & d5se physical matt] has appe>$4 ,x is divid$ into two c>d9al p]iods1 namely1 ! *aog5ic p]iod dur+ :i* primordial *aos is giv5 its "* & directive t5d5cies = ! _w age4 ,x is a phase ( duration :]e9 ! fiat ( kosmic ord] is promulgat$1 & consi/ ( ?ree /ages1 monopyknosis1 duopyknosis1 tripyknosis#bd gradually1 ins5sibly1 gradat+ into ! f\r? or qu>topyknotic2 ! *aomorphog5ic p]iod is likewise divid$ into ?ree /ages--qu9topkynosis1 sextopyknosis & septopyknosis1 develop+ out ( ! f\r? gradually4 ,! qu>topyknotic /age is ! /age ( metamorphosis or transmutation :]e9 ! transition f non-manife/ation to manife/ation is complet$2 x is also ! /age ( kosmic causation1 because f x spr+ ! matur$ causes or vital impetus :i* eng5d] all t foll[4 #bd ,see ,fig4 #ah4 ,illu/ration3 ,,fig4 #ag4--;,involution & ,evolution ,! close ( ! involution>y phase ( ! _w age is m>k$ by ! f9al deposition ( d5se physical matt] & ?is is closely foll[$ by ! beg9n+s ( ! evolution>y movem5t :i*1 l ! involution>y movem5t1 is divid$ into two c>d9al p]iods1 namely1 ! morphog5ic 7dur+ :i* are produc$1 9 turn1 ins5sible =ms1 s5sible =ms & spiritual =ms7 & ! ka!kotic p]iod :i* m>ks ! p]fection1 ! consummation ( ! evolution>y movem5t4 ,^! two c>d9al p]iods ( ! evolution>y phase ( duration & ! two c>d9al p]iods ( ! involution>y phase complete ! kosmic age1 ! ,great ,day ( ,brahma4 ,! conc5tric circles1 beg9n+ ) ! dot & end+ ) ! sev5 conc5tric circles1 & designat$ z a1 b1 c1 d1 e1 f1 g1 are repres5tations ( ! con/itution ( ! respective units correspond+ to ea* ( ! sev5 subdivisions4 ,!y symbolize ! sev5 degrees ( cond5sation or pyknosis :i* comprise ! g5esis ( space1 on ! "o h&1 & on ! o!r1 ! /ages ( unfoldm5t4 ,because1 dur+ involution all pot5cies1 p[]s & *>act]s 7 be+ infold$1 involv$2 b dur+ evolution1 ^! are be+ unfold$1 express$1 evolv$4 ,! figure #ah is ano!r view ( ^! two major movem5ts1 involution & evolution4 ,! g5esis ( space is "h %[n symboliz$ by ! ,kosmic ,egg4 ,! sev5 /ages ( involution are ref]r$ to z1 ! monopyknotic1 duopyknotic1 tripyknotic1 qu>topyknotic1 qu9topyknotic1 sextopyknotic & ! septopyknotic2 :ile ! correspond+ /ages ( evolution are ref]r$ to z1 ! physical1 ! s5ti5t1 m5tal1 causative or spiritual1 ! triadic1 duadic & monadic1 indicat+ t ! pr9ciple ( physicality is succe$$ by ! pr9ciples ( s5ti5ce1 m5tality1 spirituality1 & ! ?ree =ms ( ka!kotic be+4 ,?is symbolism1 x %\ld be /at$1 is design$ ) respect to ! univ]se & man & has no ref]5ce to o!r possible evolutions ?an ! human & contemporane\s animal1 plant & m9]al evolutions4 ,illu/ration3 ,,fig4 #ah4--,! ,g5esis ( ,space ,to foll[ ! ramifications ( ! symbolism above w\ld involve a survey ( all bran*es ( k1 & inde$1 w\ld be out ( place 9 ?is book4 ,only ! wide/ g5]al outl9es c be sugge/$ "h & x is believ$ t ?is is suffici5t to enable ! read] to grasp ! magnitude ( ! symbol & to und]/& its purpose & int5t4 ,x w\ld appe>1 !re=e1 t if x is possible = ! intellect to trav]se by means ( a /udy ( kosmic symbolism1 us$ z a /&>d ( ref]5ce1 ! entire l5g? ( ! bridge :i* engages ! antipodes into an et]nal unity1 some?+ may be ga9$ 9 ! way ( a m def9ite & cle>] und]/&+ ( ! ess5tial nature ( space 9 its relation to kosmog5esis4 ,9 ! diagram1 figure #ag1 is %[n a table :i* repres5ts ! /ages ( space-g5esis4 ,x w be not$ t ! :ole s*eme is divid$ into sev5 /ages4 ,x is n an arbitr>y division simply b a symbolic "o & repres5ts fullness1 complet5ess1 entirety4 ,! names giv51 namely1 monopyknotic1 duopyknotic1 etc41 repres5t ! symbolic *>act]i/ics ( ea* /age 9 its relation to ! univ]se 9 ! process ( becom+4 ,! t]ms monadic1 duadic1 triadic1 etc41 are repres5tative ( ! sev5 planes ( matt] 9 ! univ]se4 ,a pyknon is a kosmic pr9ciple & repres5ts ! typal aspect ( kosmog5esis4 ,x is a g5]ic t]m & may be id5tifi$ 9 its relation to ! v>i\s /ages by ! prefix4 ,! monopyknon belongs to ! ult]ior pole ( ! antipodes on ! side ( non-manife/ation4 ,s d ! duopyknon & ! tripyknon4 ,pyknosis is a process ( kosmic cond5sation1 or limitation = purposes ( manife/ation4 ,x is a /age 9 ! desc5t ( ! kosmic ,_s-,life1 a degradation ( non-manife/ation into manife/ation1 & is1 !re=e1 ! c>d9al causative pr9ciple ( creation4 ,! t]m pyknon be+ g5]ic is applicable alike to a p>ticle ( matt]1 a /ate ( be+1 a condition ( exi/5ce1 a process or a pr9ciple4 ,! monopyknon is1 accord+ly1 ! prim>y aspect ( ! process ( kosmic pyknosis4 ,x is ! ar*etype & !re=e all inclusive & omnipot5tial4 ,b :e!r reg>d$ z a s+ul>ity or z a :ole x %\ld nev] be divorc$ 9 ?\ght f ! primal act ( creation4 ,x repres5ts ! fir/ act ( mat]ial diff]5tiation 9 ! be+ ( ! creative ,logos on ! plane ( non-manife/ation4 ,x is ! beg9n+ ( e great planet>y or kosmic manvant>a or p]iod ( manife/ation4 ,dur+ ei!r a planet>y1 sol> or kosmic pralaya1 or ge/atory p]iod1 ! kosmic plasm is 9 a quiesc5t1 undiff]5tiat$ condition4 ,?is undiff]5tiat$ plasm :5 act$ ^u by ! w ( ! ,creative ,logos1 ,fohat1 z ,he is sometimes call$ 9 ,ea/]n ,philosophies1 beg9s to become condition$1 beg9s to diff]5tiate4 ,! primal act or /age 9 su* a process is ! =mation or appe>ance ( a monopyknon4 ,x !n becomes ! *>act]i/ic aspect ( t /age4 ,monopyknons are ! quiesc5t1 unawak5$1 ?\gh pot5tial & ar*etypal pr9ciples peculi> to ! monopyknotic p]iod ( space-g5esis :i* are ultimately to become1 on ! physical plane1 s+ul>ities ( life ( :atsoev] k9d4 ,?us ! l9eage ( e s+le life-=m or pr9ciple 9 ! univ]se runs unbrok5 back f ! pres5t ( ! ,n[ to ! pres5t ( monopyknosis4 ,s great is ! design ( ! kosmos t ! entity :i* is n[ man or ! atom 0 />t$ on its j\rney to ?is culm9ation at ! break ( ! ,great ,kosmic ,day :5 ! omni-pregnant :eels ( monopyknosis fir/ began to turn4 ,duopyknons & tripyknons con/itute ! two rema9+ /ages on ! plane ( non-manife/ation4 ,& _! correspond5ces 9 e /age ( involution or ! desc5t ( _s into matt] are et]nal & kosmic4 ,likewise ! l9eage ( ! dual & triple aspects ( all life =ms on ! pa? ( evolution may be trac$ re>w>d to ! duopyknotic & tripyknotic /ages ( kosmog5esis4 ,! metamorphosis by :i* ! monopyknon becomes a duopyknon contrives ! diff]5tiation ( ! pri/9e plasm ( kosmic be+ s t ! fir/ becomes ! ens\l+ or vitaliz+ pr9ciple ( ! second2 &1 9 turn1 ! second becomes ! vitaliz+ or inn] pr9ciple ( ! ?ird2 ! ?ird ( ! f\r? & ! f\r? ( ! fif? & s on ?r\gh\t ! s]ies until ! la/ is rea*$ :i* is ! septopyknon4 ,! septopyknon is1 !re=e1 a sev5-pr9cipl$ =m4 ,x is bo? unit>y & sept5>y--unit>y 9 ! s5se t ! sev5 are really "o & sept5>y = ! reason t ea* ( ! sev5 pr9ciples1 9 ! c\rse ( evolution1 becomes a sep>ate process specially adapt$ to function+ ^u its peculi> plane ( matt]4 ,?us x is se5 t ! utmo/ significance atta*es to ?is sept5>y pyknosis ( ! kosmic plasm ( life4 ,! implications ( ?is conception are1 ( c\rse1 too va/ & multif>i\s to be set d[n "h4 ,we %all h to dismiss x ) "o obs]vation only1 & t is3 e s+le appe>ance ( life & =m 9 ! totality ( su* appe>ances is root$ 9 kosmic pyknosis :]e x has receiv$ its inn] vitaliz+ =ce1 its =m & ! law ( its mode & mann] ( appe>ance toge!r ) ! metes & b\nds ( its exi/5ce4 ,^! processes1 monopyknosis & duopyknosis1 are to be reg>d$ z tak+ place1 ea* 9 its own p]iod1 ev]y:]e ?r\gh\t ! ,body ( ,be+ ( ! ,logos b on ! plane ( non-manife/ation4 ,!y are /ates ( prep>ation = manife/ation analog\s to ! g]m9ative p]iod ( ! se$ or ! egg4 ,!y repres5t ! fir/ /irr+s ( ! kosmic plasm & conta9 ! promise & pot5cy ( all t is to succe$ !m4 ,!re is "o o!r /age1 cord9ate ) ^! two1 & t is ! tripyknotic :i* completes ! unmanife/ tr9ity & con/itutes ! ar*etypal vehicle :5ce proce$s ! manife/$ univ]se4 ,! ens\l+ pr9ciple ( ! tripyknon is ! duopyknotic pr9ciple4 ,b :5 ! desc5t has rea*$ ! tripyknotic /age ! ?ree h be5 m]g$ into "o & ! *>act]i/ics :i* 7 peculi> to ea* z a sep>ate pyknon are !n fus$ into a s+le quality hav+ ?ree aspects :i* are mutually int]dep5d5t & cord9ate4 ,! unmanife/ tr9ity1 n[ complete z a result ( ! triple pyknotic process1 is ! imp]i%able & ev] su/a9+ radix1 ! all-"m ( ! manife/$ univ]se4 ,x is ! ,gold5 ,egg laid by ! god ,seb at ! beg9n+ ( a great life-cycle4 ,x is also ,*aos-,!os-,kosmos1 i4e41 kosmic disord]1 div9e w or g5]at+ elem5t1 & kosmic ord] or space4 ,9 x1 z 9 an egg1 resides 9 kosmic pot5cy all t ! univ]se is to become 9 any ,great ,day ( ,brahma or any ,great ,kosmic ,life ,cycle4 ,its elde/ born is ,,space1 physiological & p]ceptual1 & ! latt] is ! et]nal fa!r-"m ( ! univ]se4 ,space is1 !re=e1 ! male-female pr9ciple ( manife/ation2 9 its kosmic womb all =ms are creat$1 develop$1 evolv$ & su/a9$4 ,into x aga91 at ! close ( ! ,great ,day1 all exi/5ces1 =ms & all pr9ciples matur$ & rip5$ by ! vicissitudes ( kosmic evolution w be inhal$ ) ! return ( ! ,great ,brea? ( ,life4 ,! unmanife/ tr9ity is ! ar*etype1 & !re=e1 ! patt]n or model = ! manife/1 embody+ 9 pot5cy all t ! manife/ may ev] become4 ,=? f ! unmanife/ proce$s space z a dynamic process endu$ ) ! pot5tiality = g5]at+ all t ! manife/$ univ]se conta9s4 ,! t]ms unmanife/1 uncondition$ & unlimit$ h a special mean+ "h & are us$ 9 ! same s5se z ! ma!matical t]m transf9ite1 & !re=e1 imply a transc5d+ ( any f9ite or assignable degree or quality ( manife/ation4 ,h5ce !y %\ld be di/+ui%$ f ! t]m absolute :i* has a diff]5t implication4 ,s t al?\gh ! triple process outl9$ above may n be view$ except z a *>act]ization ( ! plane ( non-manife/ation1 & h5ce ( ! primordial activity ( ! ,creative ,logos1 !re is no?+ 9 ! symbolism to w>rant ! id5tification ( ?is process 9 any way ) ! ,logos 9 absolution4 ,= on ?is view ,absolute ,be+ is1 9 a l>ge measure1 sacrific$ :5 ! monopyknotic process is begun & ! monopyknon 7kosmic pr9ciple7 beg9s to appe>4 ,absolute ,be+1 :ile x may n be def9$1 del9eat$ or describ$ may be symboliz$ by ! ideograph3 action 9 inaction2 be+ 9 non-be+2 manife/ation 9 non-manife/ation2 = ^! are symbols m]ely & d n describe or del9eate4 ,we h obs]v$ ! subtle connection :i* exi/s betwe5 manife/ation & non-manife/ation & h se5 h[ t1 z ! roots ( a plant su/a9 ! out] gr[? ( /em & fl[]s1 ! =m] be+ ! matrix out ( :i* proce$s ! latt]1 & t 9 l mann] does ! unmanife/ su/a9 ! manife/2 x %\ld1 !re=e1 be cle> t ! ,body ( ,be+ ( ! ,unmanife/ ,logos1 9 a simil> mann]1 is ! basis & cause ( all t is manife/ or 9 exi/5ce2 & yet x is m1 x is ess5tially all t is & all t ! all is to be 9 manife/ation at any "t ?r\gh\t ! immeasurable process ( kosmog5esis4 ,x is ! ,self ( ! ,univ]se1 ! meta-self ( ! great div]sity ( selves4 ,! ,self1 h[ev]1 al?\gh x _c be said to exi/ except z a simple1 homog5e\s quantity is nev]!less1 9 ! v nature ( ?+s1 a triunity1 & 9 ess5ce1 n only ! basal elem5t ( ! ,all-,space & ! concrete =ms :i* exi/ !re91 b is also id5tical 9 ess5ce & sub/ance ) space4 ,a /age has n[ be5 rea*$ 9 ! description ( our symbolism :5 x may be assum$1 ^u ! basis ( ! =ego+1 t ! meta-self has become manife/1 i4e41 9 pot5tial & dynamic appe>ance1 z a result ( ! triple process ( pyknosis h]e9be=e outl9$4 ,! meta-self may !n be id5tifi$ ) ! ,supreme ,manife/ ,deity2 = !re is ev] a subtle id5tification ( ! manife/ ) ! unmanife/4 ,out ( _! action & int]action ! univ]se is made manife/ & ph5om5al & is !reby su/a9$4 ,! reciprocity ( action betwe5 ^! two kosmic pol>s1 is ! metamorphotic key to creation2 x is ! symbol ( ! proc$ure ( ,creative ,w 9 ! act ( creat+4 ,x is ! transitional process :]eby ! passage is made f non-be+ to be+2 f ! uncondition$ to ! condition$2 f undiff]5tiation to diff]5tiation & is reflect$ & symboliz$ 9 e natural process :]e9 matt] is trans=m$ f "o /ate to ano!r1 or life & m9d & _s diffus$1 c5traliz$ & organiz$ into ev] new & high] =ms & expressions4 ,ano!r important notion to be ga9$ 9 ?is connection is ! fact t x appe>s z a logical sequ5ce to ! =ego+ t ! be+ ( ! manife/$ ,logos mu/ necess>ily fill all space1 yea m1 is t space 9 e conceivable ess5tiality4 ,8 limitations are ! limitations ( space4 ,8 qualities1 prop]ties & attributes are ! qualities1 prop]ties & attributes ( space & are only diff]5t f ! orig9al spatial "* :5 manife/$ ?r\gh a div]sity ( =ms by ^: v inn] con/itution & ext]ior =m ! modifications are accompli%$4 ,all matt] 9 ! univ]se1 all en]gy1 & inde$1 all manife/ations or emanations ( :atsoev] "*1 hue1 tone or quality are1 9 reality1 ,8 be+ & no?+ b ,8 be+4 ,!re is1 !re=e1 no =m nor ens\l+ pr9ciple :e!r ( life1 m9d or %e] dynamism :i* c exi/ outside ( ,8 be+ & be1 ev5 9 ! slighte/ degree1 absolv$ f an et]nal id5tity !re)4 ,once ?is idea is grasp$ & its v>i$ implications not$ x !n is no long] conceivable t any o!r ord] or s*ematism c be possible 9 our univ]se1 & t1 too1 despite ! multi=m conceptions peculi> to ! v>i$ sy/ems ( philosophy4 ,! matut9al dawn ( creation came at ! close ( ! tripyknotic movem5t :i* result$ 9 ! elaboration ( mat]ials1 ! initiation ( pr9ciples1 processes & types1 & ! f9al prep>ation ( ! field ( evolution4 ,! ?ree processes or aspects ( non-manife/ation project$ 9 prep>ation = manife/ation1 namely1 monopyknosis1 duopyknosis & tripyknosis repres5t ! e>lie/ /ages ( g]m9al developm5t4 ,:5 ^! _h clos$1 ! ,great ,kosmic ,egg began to g]m9ate2 ! fir/ fa9t1 indescribable signs ( manife/$ life began to appe>4 ,involution set 94 ,! f\r? or qu>topyknotic /age1 ?\gh only slightly diff]5tiat$1 or r repres5t+ t p]iod ( kosmic involution :5 t :i* is to become ! manife/$ univ]se fir/ beg9s to fall "u ! sway ( kosmic ord]1 is nev]!less ! basis ( all great _w processes4 ,x is j midway betwe5 ! poles--manife/ation & non-manife/ation4 ,dur+ ?is /age ! life elem5ts are receiv+ ! impr9ts ( "*1 be+ end[$ ) directive t5d5cies & /or$ ) su* dynamism z w p]si/ ?r\gh\t ! ,great ,life ,cycle 9 :i* !y are to manife/4 ,x is "h t beg9s ! movem5t ( involution1 ! /or+ away ( ^? elem5ts & factors1 no m & no less1 t are to %[ =? on ! upw>d pa? ( evolution2 x is "h t matt] beg9s to assume =m2 electrons1 ions & atoms creat$1 or1 t ^? m9ute processes :i* on ! evolution>y side are to culm9ate 9 ^! are orig9at$4 ,?is is ! metamorphotic /age4 ,x is ! laboratory ( ! univ]se :]e9 ,fohat1 ! ,creative ,logos1 prep>es ! mat]ials out ( :i* & 9 :i* ! va/ div]sity ( morphons or =ms is creat$4 ,qu>topyknosis1 accord+ly1 is ! fir/ active /ep1 on ! plane ( manife/ation1 :i* results 9 ! appe>ance ( p]ceptual space & consequ5tly ( physical matt] itself z well z all ! o!r grades ( matt] 9 ! kosmos4 ,space1 br\ght into exi/5ce by ! act ( ! ,creative ,logos 9 impos+ limitation ^u ,8 be+1 is 9 its primordial =m compos$ ( qu>topyknons or quadruplicate pr9ciples & t5d5cies :i* act 9 unison & to ! accompli%m5t ( a s+le end or purpose4 ,on ?is plane or dur+ ! cont9uance ( ?is p]iod ( space-creation1 ! roots ( univ]sal law & ord] are produc$4 ,9 x are plant$ ! pr9ciples ( good & evil & a %>p l9e ( dem>kation e/abli%$ betwe5 all ! conceivable pairs ( opposites :i* exi/4 ,x acc\nts = ! duality ( life & =m4 ,male-female2 fa!r-"m2 positive-negative2 ,rajah-,tamas 7action-inaction7--all ^! f9d 9 ?is process _! et]nal orig9ation4 ,x is ! /age ( h>mony1 bliss1 ideality1 p]fection1 p]fect equilibrium & balance4 ,"h1 innum]able ages be=e !y actually appe>1 ! gl[-worm & ! daisy1 ! amoeba & ! dynosaur1 man & ! planet>y gods alike abode _! "t await+ ! toppl+ ( ! scales ( kosmic pot5cy :5 all w\ld be plung$ headlong into ! endless labyr9? ( becom+4 ,! qu>topyknotic process is simil> 9 all details to ! ?ree prec$+ processes1 ^! latt] be+ prototypes ( all succe$+ /ages ( involution4 ,! qu9topyknon1 accord+ly1 symbolizes ! qu9tuplicative action ( life 9 its desc5d+ movem5t t[>d ! creation ( matt] 9 its d5se/ =m4 ,t is1 x is a five-fold pr9ciple act+ 9 unison & kosmic consi/5cy1 infold+ 9 ! univ]sal :]e)al t :i* is to become m5tal matt] on ! side ( evolution4 ,j1 z may be se5 9 ! diagram1 ,figure #ag1 ! qu>topyknotic process symbolizes1 on ! involution>y side ( ! life curr5t t :i* is to become on ! evolution>y side1 spiritual ess5ce1 s ! qu9topyknotic deposits ! se$s ( t :i* is to become m5tal matt]4 ,dur+ bo? ! qu>topyknotic & ! qu9topyknotic processes all ! pot5cies & promises1 resid+ on ! plane ( non-manife/ation & de/9$ to %[ =? z _s & m9d are br\ght into a full] & m m>k$ degree ( manife/ation & become ! se$s ( spirituality & m5tality :i* are to rip5 & be lad5$ ) ! fruitage !re( _m ages h5ce4 ,! read] %\ld be> 9 m9d t ! processes "h describ$ are ?\ght ( z tak+ place at ! beg9n+ & z hav+ _! roots plant$ 9 et]nal duration2 t !y ref] to a p]iod long be=e ! univ]se ev5 resembl$ any?+ l its pres5t aspect2 at a "t ev5 be=e !re 7 individual m9ds to p]ceive x1 be=e ev5 ! gods--sol>1 planet>y1 sup]-sol> & sup]-planet>y 7 9 exi/5ce to take "p 9 ! matut9al c]emonials ( creation's va/ h\r ( /illness4 ,! m9d mu/ accu/om itself to g back ( appe>ances1 back ( "t1 back ( space itself & disc]n ! f\ndations ( "t1 space & appe>ances be+ laid & to p]ceive t :i* is no less ?an ! action ( ! ,supreme ,deity ,himself 9 brood+ ov] ! primordial =mlessness :i* is ,himself1 & f :i* w gradually evolve ! univ]se ( qualities1 conditions & appe>ances4 ,! qu9topyknon is1 !re=e1 ! base ( ! m9d-pr9ciple 9 ! kosmos4 ,all ! qualities ( m9d :e!r 9 man or 9 ! planet>y gods1 :e!r 9 ! mon]on or ! tyrannosaur1 9 ! m\nta9 or ! oak1 reside 9 kosmic pot5cy 9 ! qu9topyknon4 ,,ni*olas ,,malebran*e1#be 9 "o ( 8 v lucid mom5ts1 beheld ! ess5tial "* ( ! symbology ( space & 0 l$ to ! conclusion t ,god is space itself4 ,to him x 0 equally c]ta9 t all our ideas ( space1 geometrical or purely physiological1 z well z our notions ( ! great supras5sual doma9 ( ideas1 exi/ 9 ! kosmic dei=m1 or body ( ! ,logos ( ,be+4 ,he saw all ?+s 9 ,god4 ,god did n create ideas2 !y are a "p ( ,god ,himself2 ,god did n create m9d2 x is a "p ( ,himself2 no k9d ( matt] did ,he create2 x is a v]itable "p ( ,himself & indissoluble f ,himself4 ,! great out/&+ implication ( ?is philosophy is t our consci\sness ( ,god is b a "p ( ,god's consci\sness ( ,himself2 our consci\sness ( self & ! n-self is b ,god's consci\sness ( ^! ?+s4 ,!re is no exi/5ce ( any?+1 ei!r ( ! self or ! n-self1 except 9 ?is consci\sness4 ,x is refre%+1 !re=e1 to note t al?\gh ! approa* is made f ano!r & entirely diff]5t direction1 almo/ ! same conclusion z to ! ultimate resolution ( all *aog5etic elem5ts into :at is ! v sy/asis or consi/5ce ( ! great kosmic dei=m1 is rea*$4 #be ,vide ,re*]*e1 ,*ap4 ,,vii1 also ,philosophical ,review1 ,v4 #ae1 p4 #dja4--,,malebran*e4 ,b a m>vel\s vision comes ) ! dawn ( ?is tru? ^u ! l[] m9d4 ,x e/abli%es cle>ly ! tru? ( ,,kant',s notion :5 he said3 ,s9ce ev]y?+ we conceive is conceiv$ z be+ 9 space1 !re is no?+ :i* comes be=e our m9d f :i* ! idea ( space c be d]iv$2 x is equally pres5t 9 ! mo/ rudim5t>y p]ception & ! mo/ complete4 ,! m9d _c get away f ! conception ( space1 because1 out ( ! v ess5ce ( space1 z a result ( ! qu9topyknotic process1 x 0 produc$1 creat$ & organiz$4 ,! idea ( space is1 !re=e1 n d]iv$ f ?+s 9 space nor f _! relations 9 space4 ,x sprang up ) self-consci\sness4 ,z soon z ! ,?9k] became consci\s ( himself he became aw>e ( space4 ,! v /ate ( self-consci\sness implies space4 ,! self 9 man is a specializ$ aspect ( space4 ,inde$1 x is a projection ( space4 ,! mom5t ! self c say3 ,i am1 x also c complete ! decl>ation by say+3 ,i am ,space4 ,:5 ! self looks out f 8 six-wall$ cab9 ( imprisonm5t into ! imm5sity ( :at we call space he looks out into t :i* is himself & 8 imm5sity2 he p]ceives ! s\rce & ! ev]-pres5t su/5ance ( 8 be+ & recognizes 8 id5tity !re)1 provid$ he does n all[ himself to become entangl$ 9 ! philosophical difficulties :i* ! intellect is prone to ?r[ ar\nd ! simple1 yet m>vel\sly complex1 notion ( self-consci\sness4 ,?is %\ld settle1 once = all1 ! "q ( apriority4 ,! a priori inh]es 9 qu9topyknosis or kosmic psy*og5esis4 ,x is ! ess5tial nature ( m9d2 x is ! m9d's l9es ( organization2 x is ! law ( ! m9d's be+ & action4 ,all m5tal p]ception orig9ates f ?+s 9 space4 ,no ?\ght ( any detail1 ( any /ate or condition1 :e!r limit$ or unlimit$1 relat$ or isolat$ c be conceiv$ except x be ( ?+s 9 space4 ,& ?is is s1 because m9d & space are "o4 ,x is n s ) our conception ( "t4 ,"t is m]ely an aspect ( consci\sness 9 its limitation & does n inh]e 9 ! m9d 9 ! same mann] t does space4 ,9 fact1 x is n a "p ( ! m9d's nature z x has be5 %[n t space is4 ,x w\ld1 !re=e1 seem to be a grave mi/ake s to cord9ate ! two notions4 ,space is ! prog5itor ( m9d & is cont9ually id5tifi$ ) m9d4 ,"t is ! *ild ( consci\sness4 ,t is1 x is "o ( ! illusions ( consci\sness :i* ! ego w %$ z 8 consci\sness exp&s4 ,duration alone is a cord9ate ( space4 ,! m9d n[ recognizes space z some?+ ap>t & sep>ate f itself only because ( its unconsci\sness ( ! id5tity exi/+ betwe5 x & space4 ,j s1 x is n by m9d alone t ! at-"o /ate ( consci\sness %all be atta9$2 = al?\gh 9 "o =m or ano!r x is able to ga9 "s k ( ! app>5t on5ess ( all life x _c directly realize ?is on5ess4 ,9 ord] to d ?is fully x mu/ be able consci\sly to id5tify itself ) ! life1 feel :at x feels & exp]i5ce :at x exp]i5ces & o!rwise come into a consci\s relation%ip ) ! root & s\rce ( life4 ,space-consci\sness is a simple1 direct cognitive process2 :ile "t-consci\sness is a complex1 & !re=e1 indirect process4 ,! =m] _c be analyz$4 ,t is1 no analysis is necess>y to its suffici5t compreh5sion2 ! latt] mu/ always be analyz$ & categoriz$ = its suffici5t appreh5sion4 ,e mom5t ( "t :e!r pa/1 pres5t or future1 :5 pres5t$ to ! consci\sness1 is det]m9$ by its relation%ip to "s o!r mom5t ( "t4 ,space is indivisible2 "t is divisible4 ,space is an intuitional concept2 "t is an intellectual concept4 ,"t belongs to ph5om5a4 ,space is ! root & s\rce ( ph5om5a4 ,"t is ! leaves ( a tree :ile space is ! life ( ! tree4 ,space-consci\sness1 9 its relation to ! pres5t /atus ( m9d-developm5t1 is itself an illusion2 = despite ! fact t ! ,?9k]'s app]ception ( x z a /ate is simple1 direct & fundam5tal1 x is only s because ( ! inability to realize to itself ! unity ( ! seem+ two4 ,! atta9m5t ( space-consci\sness or ! space m9d1 :i* contrives ! und]/&+ ( ! id5tity ( m9d & space also annihilates ! consci\sness ( space z a sep>ate notion f ! m9d4 ,once ! ,?9k]'s consci\sness has aris5 to t /ate :]e x p]ceives its unity ) space all s5se ( sep>at5ess is lo/4 ,j z :5 two molecules ( hydrog5 unit+ ) "o molecule ( oxyg5 to =m a new comp\nd lose _! id5tity 9 ! new realization ( unity1 s does ! consci\sness :5 by ! al*emy ( psy*og5esis x becomes id5tifi$ ) space1 n only lose its id5tity z su*1 b also any consci\sness :atev] t space exi/s z some?+ sep>ate & di/9ct f itself4 ,imag9e ! :ole ( ! duration aspect ( kosmog5esis cr[d$ into an inf9itesimal in/ant & ! bulk ( all matt]1 suns1 />s1 worlds & planets1 cond5s$ into a space less ?an ! magnitude ( an hydrog5 ion & 9 ?is way a symbol ( :at x may mean to atta9 unto absolute k or unto ! space-m9d1 may be obta9$4 ,recurr+ to ! process ( qu9topyknosis1 x may be not$ t ! qu9topyknon or five-fold kosmic pr9ciple ( life :i* we h se5 to be id5tical to ! se$s ( m5tal matt] br\ght into exi/5ce by ! reaction ( ,fohatic en]gy or ! ,w ( ! ,creative ,logos ^u ! sub/ance ( ! qu>topyknotic /age1 is1 symbolically speak+1 m d5se & compact ?an ! pyknons ( ! prec$+ /ages4 ,x is ens\l$ by ! qu>topyknon4 ,x is a r complex /ate ( ens\lm5t consi/+ ( f\r cond5sations or pyknoses4 ,! next /age 9 ! process ( kosmic involution :i* is also conc]n$ ) ! prep>ation ( ! evolution>y field is t ( sextopyknosis & implies ! s5>y cond5sation ( ! orig9al _w-/uff ) ! view to ! =mation ( emotional or a/ral matt]4 ,id5tically ! same process ( ens\lm5t or involution obta9s ^u ! plane ( sextopyknosis z h be5 obs]v$ to obta9 ^u ! prec$+ planes ( involution4 ,involution mu/ necess>ily prec$e evolution4 ,t :i* has n be5 involv$1 enfold$ or ens\l$ _c be evolv$ or unfold$4 ,:atev] pot5cies1 p[]s & capabilities or qualities & *>act]i/ics t may appe> at any "t 9 ! univ]se ( life & =m mu/ h fir/ be5 involv$ or enfold$ or else !y c\ld n h be5 evolv$4 ,space itself is an evolution4 ,x is a process ( becom+1 ( unfold+1 ( fl[]+ =?4 ,z x evolves m & m !re w appe> new & add$ *>act]i/ics & qualities ( life & =m4 ,new possibilities w arise & 9 ! end a sup]nal vision ( a glorifi$ univ]se w bur/ into view4 ,! s*eme ( space-g5esis is complet$ dur+ ! septopyknotic process :]e9 ! basal elem5ts ( d5se physical matt] & its v>i\s gradations are produc$ & giv5 "*1 =m & direction4 ,b ?is completion means m]ely a tempor>y e/opm5t 9 ! process ( kosmog5esis :i* actually results 9 ! =mation ( physical matt] 9 its crasse/ /ate4 ,x does n mean a f9al arre/ ( ! entire process :i* is conceiv$ ( z cont9u+ only 9 a regressive mann] back to a ka!kotic#bf condition :]e9 x embodies ! fruitage ( ! entire s*eme4 ,! septopyknon1 accord+ly1 is a sev5-ply pyknon 9 :i* are embodi$1 9 v>y+ degrees ( manife/ation & phan]obiog5ic 7life-exhibit+7 quality1 ! ess5tialities ( all t has prec$$ on all planes & dur+ all /ages ( space-g5esis4 ,t is to say--9 ! physical life ( ! univ]se is conf9$ ! ess5ce ( all ! s]ies ( grades ( life 9 ! kosmos4 ,9 man's physical body are wrapp$ up all ! glories atta9able 9 8 long1 almo/ un5d+ pilgrimage ( evolution2 9 x are /or$ all ! possibilities ( ! _s2 all p[]s1 all qualities1 all *>act]i/ics1 ev] int5d$ = man's atta9m5t are 9 ! physical4 ,b !y mu/ be evolv$1 !y mu/ be unfold$ & express$4 ,! physical mu/ be glorifi$1 spiritualiz$1 deifi$4 ,= by ! way ( ! glorification & spiritualization ( ! fle% man may atta9 unto on5ess ) ! div9ity 9 himself & consequ5tly ) ! div9e life ( ! _w4 #bf ,ka!kosis 7f ,*aos-,!os-,kosmos7 is to evolution :at *aog5y is to involution4 ,x is ! end ( evolution1 b also ! beg9n+ ( involution1 & 9 ! latt] function is kn[n z *aog5y4 ,see diagram ,no4 #ag4 ,to summ>ize3 ,! g5esis ( space embraces sev5 /ages1 namely1 ! monopyknotic1 ! duopyknotic & ! tripyknotic :i* belong to ! plane ( non-manife/ation & are ! primordial _w-/uff & toge!r make up ! unmanife/ body ( ! ,logos ( ,be+4 ,^! become ! se$-g]m ( ! univ]se ( spatiality4 ,! qu>topyknotic is ! f\r? /age 9 ! process ( space-g5esis & is ! metamorphotic or crucial /age dur+ :i* non-manife/ation is metamorphos$ into manife/ation4 ,9 x ! unmanife/ becomes ! manife/4 ,x corresponds to ! plane ( pure _s1 & inde$1 embodies )9 itself all ! qualities :i* spirituality is to %[ =? dur+ ! life ( ! kosmos4 ,! qu9topyknotic is ! fif? /age & corresponds to ! m5tal plane1 embody+ 9 itself all qualities ( m5tality 9 ! univ]se & furni%+ ! basis & ess5ce ( t :i* is to become ! kosmic m9d 9 manife/ation4 ,! sextopyknotic is ! six? process & symbolizes ! six? /age :i* embodies all ! *>act]i/ics & prop]ties ( emotional matt] 9 ! univ]se & is ! basal elem5t ( ! pla/ic ess5ce ( s5ti5t exi/5ce 9 ! kosmos4 ,! septopyknotic is ! sev5? & f9al /age correspond+ to ! physical plane ( ! kosmos & conta9s 9 its sev5-fold con/itution ! se$s & pot5cies ( all ! prec$+ /ages1 z well z all ! *>act]i/ics & prop]ties :i* physical matt] is de/9$ to %[ =? dur+ ! manvant>a or _w age4 ,^! sev5 processes result 9 ! dynamic appe>ance ( space1 ! "m & conta9] ( all ?+s1 & complete ! involution>y aspects ( kosmog5esis4 ,evolution began :]e involution ceas$ & w end = ?is manvant>a :5 ! la/ ve/ige ( ^? p[]s1 capabilities & pot5cies :i* 7 involv$ %all h be5 evolv$ unto kosmic p]fection4 ,! measure ( ! ,great ,kosmic ,space-=m 0 seal$ at ! close ( ! involution>y movem5t ( ! ,great ,life ,wave4 ,!n its metes & b\nds 7 fix$ by ! fr+e ( ka!kosity :i* circumscrib$ x4 ,if x be true t ! read] f\nd x extremely difficult to grant ! connotations ( ! symbolism :5 ! m5tal or qu9topyknotic /age 0 rea*$ :5 illative cognizance 0 giv5 to ! fact t space is also compos$ ( m5tal matt]1 x may be /ill m difficult to grant ! claim t physical matt] is also ess5tially a "p ( space4 ,b ?is is ! implication4 ,&1 !re=e1 x foll[s t all matt]1 all en]gy1 all life & all m9d :]ev] x may be f\nd 9 ! ,great ,space-,=m is space itself & no?+ b space4 ,h5ce1 x appe>s t space is inde$ ! dynamism ( ! univ]se4 ,9 its kosmic womb ! great _w egg 0 =m$ ( its own sub/ance solely & 9 x /ill ! univ]se ( =m p]si/s & evolves )al4 ,if x be suitable = ! physici/ to talk ( gravitation1 electricity1 magnetism & =ce let him d s1 = ^! t]ms s]ve ! pres5t category ( human k2 b ! human m9d w n lam5t ! day :5 x comes to recognize t ^! ?+s1 ^! =ces1 ^! aspects are no?+ m ?an space-activities & space-ph5om5a4 ,if a planet's place be pres]v$ 9 space x is because space1 vital1 dynamic1 creative space1 su/a9s x & f its g5tle1 yet et]nally firm grasp !re is no escape4 ,all t ! planets1 suns & worlds are & all t !y may ev] become 9 ?is manvant>a or _w age h be5 d]iv$ f space1 yea1 are ( ! v ess5ce ( spatiality4 ,if ! *emi/ *oose to talk ( *emism1 negative & positive1 ( comb9+ prop]ties & dissociative ph5om5a let him also become aw>e t ^! ph5om5a are b ! ext]nal aspects ( ! inn] & ephem]al life-processes ( space-=ms & t ultimately ^!1 too1 may be trac$ back into an et]nal orig9ality )9 ! bosom ( ! all-"m1 spatiality4 ,d5se physical matt]1 su* z con/itutes ! physicality ( cele/ial bodies 9 its ultimate dissociation w\ld1 accord+ly1 be resolv$ into ! orig9al *aog5etic =mlessness :i* m>k$ ! *aog5y ( non-manife/ation al?\gh x w\ld naturally be ord]ly & progressive pass+ ?r\gh ! sev5 /ages1 septopyknosis1 sextopyknosis1 qu9topyknosis1 etc41 until ! end _h be5 rea*$1 mean:ile exhibit+ 9 ea* plane ! ph5om5a peculi> to ! dissociative processes !re(4 ,on ?is view space is a pl5um ( matt] ( v>y+ degrees ( int5sity1 rang+ f ! d5se/ physical to ! mo/ t5u\s & =mless matt] ( ! highe/ levels ( ! manife/$ univ]se4 ,b z nei!r ! d5se mat]ial =ms nor ! o!r grades ( matt] h an et]nally endur+ quality1 be+ alike subject to mutation1 space likewise falls "u ! law ( becom+ :]eby x1 too1 mu/ yield to ! edict ( kosmic disord]4 ,"s may be incl9$ to argue t s9ce space & m9d are "o & ! same ?+ x mu/ necess>ily foll[ t :atev] possibilities ( measurem5t may be f\nd to exi/ 9 ! m9d w\ld logically be f\nd to exi/ 9 space2 & t s9ce all ! necess>y conditions ( hyp]spatial op]ations are prov$ to be exi/5t 9 ! m9d ! case ( ! hyp]spatiality ( p]ceptual space is prov$ !reby4 ,9 o!r words1 if ! f\r? dim5sion c be prov$ to be m5tally con/ruable x is also possible 9 p]ceptual space4 ,b ^! hypo!ses are n grant$1 & nei!r w !y be acceptable to ^? m9ds :o *oose to take t view :5 x is kn[n t !re is a m>k$ diff]5ce betwe5 ! m9d t is purely intellectual & m9d t is purely intuitional or m9d a priori4 ,! intellect is fa%ion$ = matt] only2 x is s con/ruct$ z to fit squ>ely into e nook & cranny1 e groove & int]/ice 9 matt]2 yet = ! g5]at+ elem5t1 life1 x has no aptitude nor suitable congru5ce4 ,! atta9m5t ( ! space-m9d or kosmic consci\sness w\ld !n imply a ma/]y ( all fundam5tal possibilities p]ta9+ to all degrees ( matt]4 ,?us by becom+ consci\s 9 ! matt] ( all ! planes "o makes a c]ta9 def9ite approa* to ?is ultimate /ate ( consci\sness until all ! b>ri]s betwe5 ord9>y self-consci\sness & ! consci\sness ( ! space-m9d h be5 entirely oblit]at$4 ,pyknosis1 9 all ( its sept5>y aspects1 is conc]n$ prim>ily ) involution or ! prep>ation ( ! *aog5etic elem5ts = ! "w ( kosmic evolution4 ,x may be ?\ght ( z be+ divid$ into two great divisions1 namely3 *aog5y & *aomorphog5y4 ,x is conc]n$ ) ! organization ( *aos1 ! e/abli%m5t ( kosmic geometrism 9 ! =mless1 void1 arupic sub/ance & prep>ation = evolution4 ,*aog5y1 ( c\rse1 is t kosmic process by virtue ( :i* space itself becomes manife/ & 9 :i* !re is no e/abli%$ ord]4 ,*aomorphog5y 7f ,*aos ,morphe ,g5y7 signifies ! activities ( ! creative ,logos 9 lay+ ! f\ndations 9 primordial space-matt] ( ! v>i\s />-=ms1 includ+ nebul1 worlds1 planets1 suns1 etc41 ( :i* ,canopus1 ,jupit]1 ,fomalhaut & ,sirius & our own sun are examples1 giv+ direction & g5]al t5d5ce to _! v>i$ life-processes4 ,bo? ^! processes are conc]n$ ) ! prep>ation ( ! field & its consequ5t f]tilization 9 anticipation ( its cultivation & h>ve/4 ,^! two con/itute kosmic involution or ! great life wave's passage on ! d[nw>d arc ( ! ,great ,_w ,egg or ,circle4 ,x is dur+ ! *aomorphog5ic cycle t ! con/itution ( ! univ]se ( manife/ation is promulgat$2 :5 laws = its gov]nm5t dur+ t manvant>a are sket*$ out 9 ! _w ( nasc5t spatiality2 :5 ! ar*etype ( e imag9able or possible =m is project$ ^u ! impregnat$ scre5 ( creation1 !n fold$ 91 pu%$ t[>d ! c5t]1 involv$1 await+ t "t :5 ! life wave beg9s its passage ^u ! upw>d arc & evolution ensues1 call+ =? all t has be5 enfold$ 9 ! bosom ( ! pyknotic c5t]s ( manife/ation4 ,x is easily conceivable t "h dur+ ! tr\bl\s times ( ! *aomorphog5ic enfoldm5t ! n[ kn[n six directions ( space 7 among ! et]nal edicts ( space-g5esis & t t law :i* n[ makes x appe> t ?ree cord9ates1 & only ?ree1 are suffici5t = ! det]m9ation ( a po9t position 9 space 0 impr9t$ 9 ! v nature ( t :i* 0 to become space4 ,! kosmic field hav+ be5 prep>$ z a result ( ! *aomorphog5ic activities1 l[ly & sc>cely organiz$ =ms beg9 to appe> & ! asc5t ^u ! upw>d arc ( ! ,great ,cycle comm5ces4 ,evolution beg9s4 ,its scope is likewise divid$ into two great /ages1 namely3 7a7 ,morphog5y1 ! purpose ( :i* is ! developm5t ( life-=ms or pyknons :i* are to appe> on ! v>i\s planets1 />s1 worlds & suns ( ! univ]se4 ,x embraces ! :ole span ( ! life-aspect on ! evolution>y side ( manife/ation4 ,9 ?is aspect is includ$ also e conceivable adaptation ( ! univ]sal pr9ciple ( life f ! beg9n+ ( its movem5t to ! end4 ,! univ]se is n[ function+ 9 & progress+ ?r\gh ! vicissitudes ( ?is /age4 ,t is1 all ! pres5t obs]vable adaptations :i* ! life-pyknon or pr9ciple is mak+1 has made or w make1 are embrac$ )9 ! scope ( :at is "h designat$ z ! morphog5etic aspect ( evolution4 7b7 ,! second & la/ division ( ! arc ( evolution is call$ ,ka!kos1 ?us symboliz+ ! syncretism ( ! tr9it>ian aspects ( kosmog5esis1 ,*aos-,!os-,kosmos1 p]fect$ & unit$ z a result ( ! labors ( manife/ation4 ,9 ?is f9al summation ( ! labors ( ! life-wave z x has progress$ f involution ?r\gh all ! devi\s manife/ations ( evolution are embodi$ ! p]fection & ultimate elaboration & expression ( all ! pyknotic t5d5cies :i* 7 e/abli%$ dur+ ! entire scope ( space-g5esis4 ,?us x w be se5 t ! fir/ ?ree /ages ( space-g5esis1 call$ *aog5y1 encompass ! fir/ ?ree pyknotic processes or are analog\s !reto :ile ! latt] call$ *aomorphog5y1 ! organization & ens\lm5t ( space-=ms1 embraces ! latt] f\r1 qu>topyknosis1 qu9topyknosis1 sextopyknosis & septopyknosis4 ,?is division obta9s on ! involution>y side ( ! great life-cycle4 ,! upw>d arc ( ! ,great ,kosmic ,egg or ,cycle is also divid$ into two great /ages1 namely1 ,morphog5y 7manife/ation ( life ?r\gh ! v>i\s =ms :i* x assumes7 & ,ka!kos1 or ! ka!kotic plane ( p]fect$ triunity :i* is repres5t$ by ! evolution>y union ( ,*aos-,!os-,kosmos4 ,ka!kos w\ld1 !re=e1 symbolize ! ultimate elaboration ( ,*aos into a well-ord]$ kosmos :]e9 are express$ all ! possibilities :i* inh]$ 9 ! ar*etypal plan ( ! ,creative ,logos or ,!os & 9 :i* all _h rea*$ ! ultimate p]fection 9 ! body ( be+ ( ! ,logos ,himself4 ,b ! ka!kotic plane is to be di/+ui%$ f ! orig9al ,*aos-,!os-,kosmos repres5t$ z functionat+ ^u ! plane ( non-manife/ation dur+ *aog5y4 ,ka!kos symbolizes ! p]fect$ manife/ations ( ! triune aspects ( ! ,creative ,logos ?r\gh ! p]fect$ =ms result+ f ! labors ( kosmic evolution1 :ile ,*aos-,!os-,kosmos symboliz$1 z a triune glyph1 ! ,unmanife/ ,tr9ity 9 ! primordial beg9n+s ( space-g5esis4 ,"o is ! se$2 ! o!r ! fully matur$ plant2 "o ! egg2 :ile ! o!r is ! full gr[n bird2 "o ! root2 ! o!r ! fruitage2 "o ,alpha1 ! o!r ,omega2 "o ! beg9n+1 ! o!r ! end4 ,! end1 h[ev]1 is rea*$ only t1 9 due "t1 ! entire s*eme may be comm5c$ aga91 once m utiliz+ ! results ( ! prec$+ s*eme ( evolution z ! basis ( ! ensu+ "o4 ,?us aft] e ,kosmic ,day1 comm5ces ! ,kosmic ,night4 ,! succession ( kosmic days & nights is inf9ite4 ,?is inf9ity ( becom+s 9 ! life ( ! kosmos is a necess>y outcome ( et]nal duration4 ,! above1 ?us briefly set d[n1 is ! symbolism ( space-g5esis4 ,x is comm5d$ to ! read] z a basis = ! conception t ! real1 ess5tial1 p]ceptual space is some?+ f> m wond]ful1 m fundam5tal ?an ei!r ! geometrician or ! metageometrician has ev] dream$ (1 & yet ! latt]'s consci\sness is und\bt$ly be+ appuls$ by ! f+]s ( a new species ( conceptualizations :i*1 "o day 9 ! n too di/ant future1 w ar\se 9 x ! fa9t hung]+s aft] ! realization ( ! real space-nature4 ,^! ma!tic appetites ?us br\ght into be+ w f9ally lead ! human m9d into ! ,elysian fields ( kosmic consci\sness :]e = ano!r million ye>s1 p]haps1 x may fe$ ^u ! my/]ies & hyp]my/]ies to be f\nd 9 ! gran>ies ( ! ,space-,m9d4 ,! /udy ( space 9 its wid] & deep] mean+s is necess>y 9 ord] t a cle>] und]/&+ ( its true significance1 z ! subject ( geometric rese>*es1 may be ga9$4 ,x is confess$1 h[ev]1 t !re is nei!r direct evid5ce nor implicative au?ority = any assumption t ! view h]e9 outl9$ af=ds any ju/ification = ! notion ( ! n-dim5sionality ( space4 ,=1 al?\gh ! l9e ( reason+ indulg$ 9 mu/ lead inevitably to ! conclusion t ! worlds ( spatiality1 mat]iality1 intellectuality & spirituality1 ess5tially & fundam5tally "o s f> z orig9s & qualities are conc]n$1 7 alike eng5d]$ by ! same g5]at+ elem5t1 life2 & t spatiality be+ ! primal basis ( ! o!rs is1 nev]!less1 "u ! exig5cies ( ?is aspect ( ! kosmos1 highly susceptible to ! m5surative requirem5ts ( ! grosse/1 !re appe>s to be no necessity = call+ ^u extrane\s consid]ations = assi/ance 9 our ef=ts to compreh5d ! v>i\s connotations ( ! symbolism4 ,!n1 too1 x is easily conceivable t "u conditions :]e ^! elem5ts1 spatiality1 intellectuality & mat]iality1 are n only co-ext5sive b int]p5etrative1 !re is no ju/ification = ! assumption t !y mu/ exi/ 9 lay]s or manifoldnesses or 9 discrete degrees1 sep>at$ f "o ano!r z if !y 7 con/itut$ ( diff]5t sub/ances & occupi$ diff]5t sph]es4 ,= e s+le po9t 9 p]ceptual space is a focus = l9es drawn ?r\gh e conceivable grade ( mat]iality1 spatiality or intellectuality 9 ! kosmos4 ,& ! same sy/em ( cord9ates :i* is necess>y & suffici5t = ! localization ( a po9t 9 our space is also suffici5t = ! location ( a po9t any:]e 9 ! entire _w ( spatiality1 intellectuality or spirituality4 ,9 fact1 ! ext]nal1 visible worlds ( mat]iality & spatiality are no?+ m ?an ! mass-t]m9i ( l9es ext5d+ f div9ity to physicality2 f primordial orig9ality to kosmic mod]nity & x is intellectually conceivable t progression back ov] ! grooves made by ^! mass-t]m9i ( l9es w\ld lead directly & un]r+ly to orig9ality itself4 ,9 spite ( ! manifold pyknoses :i* we h %[n to *>act]ize ! symbolism ( space-g5esis x is a v simple matt]2 = ! entire s*eme c\ld & mu/ h proce$$ along /rictly tridim5sional l9es4 ,tridim5sionality mu/ h inh]$ 9 ! primeval ar*etype ( space or else x c\ld n appe> z an out/&+ fact ( p]ceptual space n[2 = all t we c n[ obs]ve 9 space z *>act]i/ics mu/ h fir/ be5 includ$1 enfold$1 involv$1 be=e x c\ld h be5 evolv$4 ,h5ce1 x is to be rememb]$ t we are to-day deal+ ) ! expressions ( t5d5cies & pr9ciples :i* inh]$ 9 ! manife/$ univ]se z pot5tialities 9 ! v beg9n+4 ,! alphabet ( space-g5esis consi/s ( five *>act]s1 namely1 ! po9t1 ! l9e1 ! triangle1 ! squ>e & ! circle4 ,^! are ! p5tagrammaton ( space1 ( intellectuality1 mat]iality & ( spirituality4 ,!y con/itute ! basis ( kosmic geometrism4 ,) ^! all geometrical figures may be con/ruct$2 ) !m all magnitudes may be del9eat$ & project$4 ,!y describe e conceivable activity ( ! ,creative ,logos & designate ! b\nds ( ! entire scope ( motility ( kosmog5esis4 ,9 figure #ai1 are %[n ! dot1 ! l9e1 triangle1 squ>e & ! circle :i* toge!r =m ! kosmic p5toglyph4 ,! po9t symbolizes kosmic in]tia1 inactivity or ! beg9n+ ( motion2 ! l9e is ! fir/ aspect ( motion1 ! beg9n+ ( creation2 ! triple aspect ( kosmog5esis is symboliz$ by ! triangle1 ,*aos-,!os-,kosmos1 ! ,unmanife/ ,tr9ity2 ! squ>e emblematizes kosmic be+ 9 evolution2 :ile ! circle is ! syncretism ( all ^! & /&s = ! p]fect$ kosmos1 or ! kosmos 9 process ( p]fection4 ,v truly did ,,plato rem>k3 ,god geometrizes2 = ! p5tagrammaton--! po9t-l9e-triangle-squ>e-circle--is ! deity's way ( manife/+ ,himself4 ,b !re is "h no ne$ = space-curvature nor = triangles ^: value is great] or less ?an #ahj degrees2 !re is no ne$ ev5 = ! ma!matical f\r? dim5sion4 ,illu/ration3 ,,fig4 #ai4--,kosmic ,p5toglyph ,x _c be believ$1 h[ev]1 t metageometricians are really 9 e>ne/ 9 :at !y sugge/ ( hyp]space & n-dim5sionality2 x _c be believ$ t !y are entirely satisfi$ ) :at !y h f\nd ( ! s-call$ hyp]spatial1 & yet1 "s ( !m are fanatically patriotic ov] ! new-f\nd doma92 "s are ev5 intol]ant4 ,b !re are o!rs :o look ^u ! fabric ( metageometry z a /epp+ /one to space-realities1 a mile-po/ on ! pa? to ! realization ( a high] consci\sness1 ! consci\sness ( ! space-m9d or kosmic consci\sness4 ,& may ?is n1 aft] all1 be ! goal ( ! human intellect1 n[ slightly di/raught by ! exub]ances ( y\? & ! joys ( a new m5tal fre$om8 ,! "w ( ! future ma!maticians w be ! de/ruction ( ! tumor\s inconsi/5ces to be f\nd 9 ! v>i\s non-,euclidean sy/ems ( geometrical ?\ght1 ! elim9ation ( ! novelties & ! nons5sicals1 ! syn!siz+ ( ^? elem5ts :i* are sanction$ by ! space-m9d & ! build+ !reon a sane int]pretation ( space-ph5om5a 9 ! light ( illum9ations receiv$ f greatly ext5d$ faculties & a p>ticipation 9 t l>g] consci\sness into :i* ! human race seems sl[ly to be imm]g+4 ,! doma9 ( hyp]space is b ! fairy-l& ( ma!sis1 peopl$ ) gobl9s1 gnomes1 kobolds1 elves & fays :i* are ! spaces1 dim5sions1 propositions1 ensembles & !orems ( ! metageometrician4 ,b l ! fairies & nature spirits ( ! unse5 ab\t u1 !y h _! bases 9 ! real1 objective _w ( facts h[ev] difficult x may be to e/abli% _! direct connection ) x4 ,z ! gay1 invisible sprites ( phantom-l& repres5t intellig5t natural =ces at "w 9 ! fur!rance ( ! evolution ( =ms1 s ! impalpable ?+s ( ma!sis are emblems ( kosmic =ces at "w 9 ! upbuild+ ( /ructures ( high] consci\sness :i* %all be t[]s ( vision = ! human s\l :5ce x may view ! hill-cre/s ( inf9ite k & ! l[-ly+ pla9s ( kosmic my/]ies4 ,f9ally1 x has be5 not$ t space is ! v consi/5ce ( ! kosmos2 x is ! life1 ! =m & bo? ! out] & ! inn] manife/ation ( ! comb9$ life & =m2 x is reality1 also illusion2 x is concrete1 also ideal4 ,we h not$ also t m9d is consub/antial ) space & t space gives x its inn] life & nature z well z n\ri%es its out] gr[? & developm5t4 ,9 fact1 we h se5 t space & m9d are "o ess5tially & t !y exi/ z aspects ( ! same ?+1 life4 ,9 :atev] way1 !n1 t ! m9d normally views space t is ! natural way4 ,all attempts to deviate f ! natural way are1 !re=e1 unsanction$ by ! nature ( ?+s4 ,s long z geometry rema9s true to ! nature ( m9d & space s long w x be valid univ]sally & possess$ ( kosmic necessity & inv>iance4 ,x behaves mo/ unseemly :5 x dep>ts f its fealty to ! nature ( ?+s p] se4 ,bo? ! outlook ( ! m9d ^u ! objective _w z well z its inlook ^u its own /ates ( consci\sness or ! subjective _w are tridim5sional4 ,its gr[? is tridim5sional1 its nature is likewise tridim5sional1 & !re is n ev5 ! slighte/ t5d5ce ei!r to p]ceive1 conceive or p]=m 9 a f\r-dim5sional mann]1 ma!matically speak+4 ,trace out ! biologic developm5t ( ea* m5tal faculty1 f ! m9d ( ! mon]on to ! m9d ( ! mo/ highly develop$ man & x w be f\nd t ev]y:]e & always1 )\t v>iation or exception1 ! nature ( ea* ( ^! has be5 to express itself tridim5sionally & naturally4 ,!re is n ev5 ! slighte/ sign ( s mu* z a g]m9al appet5ce = ! f\r-space2 x w\ld1 !re=e1 seem almo/ a pro/itution ( m5tal faculty to div]t m5tal en]gy into ! seem+ly useless *annel ( pres5t-day metageometrical rese>*es2 yet1 x mu/ be admitt$ t ev5 ?\gh ! end s\ght _c be atta9$1 ! f9al results ( ! intellectual delv+s into ! dread homog5eity ( kosmic orig9s & ! consequ5t realization ( ! awesome coevalism ( m9d & space :5ce %all arise ! recognition ( ! wondr\s unit>9ess ( all exi/5ces1 w be t we %all come ^u t ?rice my/]i\s contrivance--! ,he>t ( ,div9ity1 ! ,kosmic ,space-,c5t] 9 :i* abide ! roots ( ! ,great ,all 9 a m>vel\sly indescribable unity & inf9ite orig9ality4 ,we may conclude1 !n1 t hyp]spatiality & all its appurt5ances are b ! toys ( ! *ildhood ( humanity4 ,b1 z ! ye>s pass & ! days ( maturity come on apace1 x1 toy-l1 w also be disc>d$4 ,& ! m9d w seize !n ^u ! s]i\sness ( reality j z ! matur$ y\? responds to ! /]n realities ( life & manhood responsibilities4 ,b no "o c say t ! toys ( *ildhood are :olly useless2 no "o c say t ! joys :i* !y br+ are entirely fatu\s & unreal nor %all we attempt to intimate t ma!tic contrivances are )\t utility1 )\t purpose & significance 9 ! life ( ! gr[+ m9d ( humanity4 ,b !y1 too1 w pass away4 ,,*apt] ,,viii ,,! ,,my/]y ,,( ,,space ,! ,?9k] & ! ,ego--,incresc5t ,automatism ( ! ,intellect--,! ,egopsy*e & ! ,omnipsy*e--,kosmic ,ord] or ,geometrism--,life z ,eng5d]+ ,elem5t--,! ,my/]y ( ,space ,/at$--,ka!kos & ,ka!kotic ,consci\sness--,function ( ! ,ideal--,! ,pa? ( ,se>* = an ,und]/&+ ( ! ,nature & ,ext5t ( ,space ,mu/ ,proce$ 9 an ,inv]se ,direction4 ,! fragm5t>9ess ( ! ,?9k]'s outlook ^u ! univ]se ( spatiality is due to ! inhibitive action set up by ! con/rictive bonds :i* 8 complicate me*anism ( intellectuality int]poses betwe5 himself & reality4 ,! ,?9k]1 :o /&s back ( & uses ! v>i\s m$ia ( objective consci\sness1 su* z ! neural me*anisms1 bra91 emotions1 8 individualiz$ life-=ce & ! m9d :i* toge!r make up ! in/rum5ts ) :i* he contacts ! s5su\s doma91 by adapt+ 8 consci\sness to ^! means1 z ! artisan utilizes 8 tools1 con/itutes 8 own intellectuality4 ,! intellectuality1 !n1 is ! totality ( m$ia by :i* consci\sness effects its entrance into ! s5su\s _w & by :i* x receives impressions !refrom4 ,9 o!r words1 x is ! sum ( all ^? qualities1 op]ations1 processes & me*anisms :i* are recogniz$ z con/itut+ ! modus viv5di ( man's intellectuality1 & ^! are1 9 reality1 no?+ m ?an ! ego himself4 ,_m h be5 incl9$ to reg>d t :i* has be5 call$ ! ego z ! highe/ sov]eign p[] 9 ! /ate ( manhood4 ,he has be5 look$ ^u z ! f9al consid]ation 9 ! con/itution ( ! human be+4 ,b ! ego is an evolution>y product & ! concomitant ( self-consci\sness :i* is ! ,i-mak+ faculty 9 man's psy*ic life4 ,x is t quality ( consci\sness :i* makes man conceive ( himself z a sep>ate1 deta*$ & indep5d5t be+4 ,x is a purely intellectual or tuitional product1 &1 z su*1 is to be diff]5tiat$ f ! intuitional or life-quality :i* is ! ess5ce ( man's real selfhood4 ,) respect to ! ,?9k]1 ! ego occupies precisely ! same /atus z ! ag5t to 8 pr9cipal4 ,z ! ag5t is ! repres5tative ( ! pr9cipal 9 all matt]s :i* come )9 ! scope ( 8 prescrib$ jurisdiction s is ! ego ! ag5t ( ! ,?9k] :o is a spiritual intellig5ce4 ,accord+ly1 f an e?ical viewpo9t ! ,?9k] is responsible = ! acts ( ! ag5t & c 9 no wise escape ! p5alties accru+ z a result ( ! ag5t's violations4 ,j z a comm]cial firm s5ds out a repres5tative = ! collection ( data conc]n+ c]ta9 phases ( its bus9ess or x may be ( any bus9ess or ! entire _w m>ket s ! ,?9k] projects 8 own consci\sness into ! me*anisms :i* are 9 _! totality ! egoic life4 ,t is1 he s5ds out 8 ag5t1 ! ego1 into life & into ! objective _w ( facts & dem&s t he %all convey to him1 f all po9ts ( ! t]ritory :i* he is expect$ to cov]1 reports ( 8 f9d+s4 ,( c\rse1 ^! reports :i* are transmitt$ by ! ego 7! intellectual me*anism ( ! ,?9k]7 are m or less well prep>$ summations ( 8 individual obs]vations & d$uctions4 ,^! are ! p]cepts :i* ! ego pres5ts to ! ,?9k]'s consci\sness4 ,concepts are =m$ by ! ,?9k] 9 8 treatm5t ( ^! s5se-pres5tations4 ,x v frequ5tly happ5s t ! ego transmits reports :i*1 = "o reason or ano!r1 give v imp]fect k ( ! matt] :i* 8 reports are design$ to cov]4 ,(t5 x is necess>y t additional & supplem5tal reports be made ab\t ! same ?+1 & ev5 !n1 x is well-nigh impossible1 if n q s1 = him fully to cov] e detail ( ! matt] "u consid]ation & 9 no case is x possible = him to d m ?an report on ! sup]ficialities ( ! "q "u scrut9y4 ,if ! ego1 9 8 op]ations1 be imag9$ to be hamp]$ by simil> circum/ances & difficulties z ^? :i* w\ld ord9>ily beset a comm]cial atta* x w !n be cle> t 8 reports mu/ ev] be fragm5t>y because ( ! inaccessibility ( mu* ( ! data :i* w\ld be necess>y = a full report1 & fur!r1 because ( ! inadequacy ( 8 me?ods & means ( ga!r+ data due to ! inh]5t limitations ( 8 capabilities1 endurance & p]spicacity & innum]able o!r limitations & difficulties :i* mu/ be fac$ 9 all se>* = ! real4 ,s t1 :ile ! suffici5cy ( ! means :i* ! ego enjoys at ?is /age = all practical purposes is grant$ no hesitancy is ent]ta9$ :5 x comes to a discov]y ( ! reals ( k 9 decl>+ _! insuffici5cy4 ,!n1 too1 :5 x is rememb]$ t ^! egoic reports are 9 ! nature ( neurographical communications :i* are simil> to telegraphic despat*es & mu/ pass ?r\gh sev]al /ations1 z ganglia1 etc41 (t5 be+ relay$ f "o to ano!r1 x w be q app>5t t mu*1 ev5 ( ! orig9al quality ( ! missives =w>d$1 w h be5 lo/ or radically *ang$ 9 "s way be=e x is f9ally deliv]$ = ! inspection ( ! ,?9k] himself4 ,x n infrequ5tly happ5s1 ev5 9 p]fectly normal be+s1 t ! ego 9 fil+1 record+1 transcrib+1 int]pret+1 translat+ & o!rwise prep>+ ^! data = ! ,?9k]'s use1 lets a cog slip1 misplaces "s ( ! data1 loses or de/roys fragm5ts ( x & s is unable to ma9ta9 a complete portfolio ( 8 mat]ials4 ,z ! ,?9k] is entirely dep5d5t ^u 8 ag5t1 ! ego1 = ! tru/wor?9ess ( 8 in=mation cov]+ ! matt] ( ! s5su\s _w x is obvi\s t at be/ 8 in=mation is v fragm5t>y inde$1 & necess>ily s :5 x is consid]$ t ! modus op]&i ( 8 ag5t & ! difficulty ( 8 op]ations are s complicate z to magnify ! ob/ructions 9 ! way to complete fre$om 9 ?is reg>d4 ,to cont9ue ! similitude ( pr9cipal & ag5t x may be ass]t$ t x is also true t ! comm]cial h\se t s5ds out its atta*es frequ5tly w s5d lett]s conta9+ directions z to proc$ure1 sometimes c5sur+ = pa/ del9qu5cies & sometimes comm5d+ = praisewor?y de$s2 & ?is1 too1 9 addition to ! orig9al in/ructions :i* 7 giv5 at ! outset4 ,x ev5 comes to pass t ! home (fice1 because ( "s m]etrici\s accompli%m5t1 z ! m>k$ increase ( effici5cy %[n by ! ag5t's close application to 8 duties & ! consequ5t success ( 8 op]ations1 conf]s c]ta9 favors ^u ! ag5t or removes "s ( ! re/rictions :i* 7 orig9ally impos$1 gives an increase 9 sal>y or promotes ! ag5t to a high] & m lucrative (fice ) l>g] p[]s & great] au?ority4 ,?is is analog\s to :at ! ,?9k] does = ! ego4 ,= he n only receives reports f ! ego1 b (t51 9 ! %ape ( intuitions1 gives additional in=mation z to ! prop] mann] ( do+ ?+s1 %$s m light ^u "s obscure op]ation1 comm5ds = duty well p]=m$1 condemns = failures or = wrong-do+1 rew>ds ardu\s toil ) great] p[]s ( vision1 ke5] insight1 great] capabilities2 9 fact1 promotes ! ego 9 ! sight ( o!r egos by m>k+ him out z an exceptional ego4 ,b ! curi\s aspect ( ?is proc$ure is t1 9 "t & aft] ! ego has be5 repeat$ly comm5d$ & promot$ & o!rwise favor$ by ! ,?9k]1 he beg9s to ?9k t he owns ! firm1 t he is ! life & ma9 support ( ! :ole corporation4 ,he becomes arrogant1 self-will$ & f9ally falls into ! illusion t he alone is responsible = ! ph5om5al success ( ! firm4 ,?is is ! s\rce ( t illusion ( ! intellect :i* makes itself ?9k t x1 ! ego1 is all !re is to man1 t 8 in/rum5ts ( op]ation 9 ! objective _w are ! only k9d ( in/rum5ts t may be us$2 t 8 me?od ( ga!r+ data ab\t ?+s is ! only safe & sure me?od2 & s x develops t ! intellectuality is ! s\rce ( man's sep>at5ess1 8 individuality & 8 app>5t alo(ness f o!r m5 & ?+s4 ,x is1 ( c\rse1 ne$less to po9t out t 9 ?is way ! intellect comes to be ! tyrant ( man1 rul+ ) a rigid monopoly & z an all-exclusive autocracy4 ,f ! above implications x w\ld appe> t ! intellect & ! intuitive faculty are two sep>ate & di/9ct processes1 & s !y are4 ,"o is ! inv]se ( ! o!r4 ,! t5d5ce ( ! egoic life or ! intellect is = ! ext]nal :ile ! intuition is an int]nal process4 ,! intellect acts f )\t t[>ds ! int]ior :ile ! intuition acts f )9 outw>d4 ,! intellect is ! product ( ! intuition :i* is ano!r t]m = ! consci\sness ( ! ,?9k] on 8 own plane4 ,j z ! *ild lives a sep>ate & di/9ct1 ?\gh dep5d5t1 life f ! p>5ts s ! intellect has a modus viv5di :i* is di/9ct & sep>ate f t ( ! ,?9k]1 & yet x is 9 all po9ts dep5d5t ^u ! life ( ! ,?9k]4 ,"h aga91 we f9d an analogy 9 ! relation ( ! *ild to ! p>5t4 ,z "s *ildr5 are m am5able to ! w ( ! p>5t ?an o!rs1 s1 9 "s p]sons1 ! intellect is m am5able to ! action ( ! intuition ?an 9 o!rs4 ,yet x is a c]ta9 fact t ! m ! outw>d life is gov]n$ by ! intuition1 i4e41 ! m ! intellect responds to ! intuitive faculty ( ! ,?9k]1 ! high] ! ord] ( ! life ( ! ego & ! m accurate 8 decisions & judgm5ts4 ,9 fact1 x assur$ly may be ass]t$ t ! place ( e individual 9 ! scale ( evolution is det]m9$ 9 a v l>ge measure by ! degree ( agreem5t betwe5 ! intuition & ! intellect or by ! ease ) :i* ! intuition may op]ate ?r\gh ! intellect z a m$ium4 ,at lea/1 ! quality ( "o's life may be det]m9$ directly by ^! consid]ations4 ,! ,?9k] be+ himself a pure spiritual intellig5ce1 liv+ ^u ! plane ( _s & !re=e unhamp]$ by ! difficulties :i* ! ego meets 9 8 op]ations 9 ! objective s5sorium1 & possess$ ( f> great] k1 is correspond+ly free f ! limitations ( ! ego & v naturally clos] to kosmic realities4 ,h5ce1 he is bett] situat$ = ! procurem5t ( correct notions ( relations1 ess5tialities & ! l4 ,x is believ$1 !re=e1 t 9 ! proportion t ^! two processes1 ! intellectual & ! intuitional1 are br\ght1 9 ! c\rse ( evolution1 to a clos] & m rigid agreem5t1 9 ! proportion t ! ,?9k] is able to transmit ! intuitograms 9 ! %ape ( concepts or t ! intuition is made m & m conceptual1 9 j t proportion is humanity becom+ p]fect & its evolution complete4 ,! difficulty f\nd to inh]e 9 ! conceptualization ( intuitions s t !y may be propagat$ f man to man seems n to lie 9 ! ,?9k] himself1 b m ess5tially 9 ! ego1 9 ! intellectuality & its complicate s*ematism or plan ( action4 ,x w\ld appe>1 !re=e1 t ! only way ( escap+ or transc5d+ ?is difficulty is = ! ego s to ref9e 8 vehicles or s facilitate 8 plan ( action by elim9at+ ! num]\s relays or sub-/ations int]v5+ betwe5 ! consci\sness ( ! ,?9k] & t :i* may be said to be 8 own t ! transmission ( intuitograms may be accompli%$ ) ! greate/ ease & cle>ness4 ,:ile no attempt w be made to indicate ! probable l9e ( action :i* ! ego or objective man w adopt = ?is purpose1 x is believ$ t x may be said )\t p$anticism t ! only true me?od ( atta9+ unto ?is mu* desir$ /ate ( ?+s is1 fir/ ( all1 by assum+ a sympa!tic attitude n only t[>ds ! "q ( ! intuition itself b to all ph5om5a :i* are an outgr[? (1 or incid5t to1 ! manife/ations ( ! intuitive faculty ?r\gh ! intellectuality1 & second1 by ! practice ( prolong$ ab/ract ?\ght1 ?is latt] proc$ure effect+ a susp5sion ( ! intellectuality tempor>ily at ! same "t all[+ x to exp]i5ce an undi/urb$ contact ) ! intuitional consci\sness1 !reby lay+ ! basis = future recognition ( its nature & quality4 ,x w\ld seem t ^! two conditions are absolutely necess>y 9 ord] t a m congru5t relation%ip may be promot$ betwe5 ^! two cognitive faculties4 ,ord9>ily1 x w\ld appe> t ! philosoph] :o is und\bt$ly inur$ to ! necessities ( cont9u\s ab/raction or ! ma!matician ^: mo/ common tasks naturally fall 9 ?is category w\ld be among all m5 mo/ apt to develop to ! po9t ( conceptualiz+ intuitograms readily1 yet x seems t ?is is n ! case4 ,& !re is good reason = x4 ,! m9d ( ! philosoph] & ! ma!matician is intellectual r ?an intuitional & is1 !re=e1 w$d$ to matt]1 to ! action & reaction ( matt] aga9/ matt] & h5ce op]at+ 9 a direction at v>iance ) ! tr5d ( an intuitional m9d4 ,& ?is condition is und\bt$ly due to a lack ( a sympa!tic attitude t[>ds ?is species ( consci\sness4 ,at any rate1 x is ?\ght t a too great anxiety 9 ?is respect ne$ n be ent]ta9$ by humanity at all1 = ! reason t 9 ! case ( a faculty1 ! rudim5t>y outcropp+s ( :i* are s m>k$ & univ]sally obs]vable & exi/+ 9 great] or less] degrees 9 v>i\s human be+s1 !re is ample evid5ce = ! belief t x is be+ c>efully & duly promot$ by a well-direct$ evolution ( psy*ic faculties & p[]s1 s t at ! prop] "t1 det]m9able by ! /ate ( p]fection rea*$ by ! intellectuality or ! ego 9 ! op]ation ( 8 cognitive processes1 ! mu* desir$ agreem5t ( ^! two faculties w h be5 realiz$ & ! conceptualization ( intuitograms into propagable conceptions an accompli%$ fact4 ,until ?is goal %all h be5 rea*$ & ! intuition %all h ov]%ad[$ ! intellect z ! intellect n[ ov]%ad[s ! intuition2 or ! consci\sness ( ! ego1 d]iv$ f ! int]play ( ! ,?9k]'s consci\sness among ! v>i\s elem5ts :i* con/itute ! ego himself1 %all h be5 m]g$ ) t ( ! ,?9k]1 ! outlook mu/ rema9 fragm5t>y1 only becom+ a well-ord]$ :ole z ! b>ri]s ( dissid5ce are brok5 d[n 9 succession4 ,! evolution ( consci\sness1 f ! simple1 undiff]5tiat$ mon]on to ! diff]5tiat$ cell & f t to ! cell-colony & f ! cell-colony to ! organism1 trav]s+ 9 successive paces ?r\gh all ! /ages ( l[] life--m9]al1 vegetable & animal--to ! /ages ( ! simple1 communal consci\sness ( ! high] animals1 to ! self or individual consci\sness ( ! human be+1 ea* requir+ millions ( ye>s = its p]fection be=e a m advanc$ /age is ent]$1 has be5 "o cont9u\s rel9qui%m5t ( ! l[] & less complicate = ! high] & m complex expression ( itself ?r\gh ! giv5 m$ia4 ,:5 a new] & high] /age ( consci\sness is be+ ent]$ by humanity its appe>ance or manife/ation is fir/ made 9 ! mo/ advanc$ ( ! race & t only 9 a dim1 vague way4 ,?is rudim5t>y condition p]si/s = "s "t1 p]haps _m ?\s&s ( ye>s1 !n ! faculty becomes m g5]al 9 appe>ance1 ! numb] ( advanc$ individuals increases1 & consequ5tly1 z 9 ! case ( ! intuitive faculty1 x becomes univ]sally preval5t 9 all humanity2 becomes transmissible z s-call$ acquir$ *>act]s1 & !n appe>s z ! normal faculty ( ! entire human family cropp+ out 9 ea* individual4 ,?us1 9 pass+ f ! few advanc$ ones 9 ! beg9n+ to t /age :]e x becomes ! common possession ( all1 a faculty requires _m ?\s&s ( ye>s = its p]fection1 & especially has ?is be5 true 9 ! pa/ hi/ory ( ! developm5t ( human faculties4 ,b x is believ$ t ! sweep ( ! life curr5t z x proce$s f =m to =m1 f faculty to faculty1 ga9s 9 mom5tum z x proce$s1 s t 9 ^! latt] ye>s due to ! already highly develop$ vehicul> me*anisms at its disposal n s great a p]iod ( "t z =m]ly is requir$ = ! out-br++ ( a new faculty4 ,x might well be t :ile 9 ! pa/ hundr$s ( ?\s&s ( ye>s 7 necess>y 9 ! p]fection ( organs & faculties1 9 ^! latt] days only a few ?\s&1 p]haps hundr$s1 may be necess>y & t 9 ! days ( ! future n ev5 s _m ye>s may be requir$ to univ]salize a faculty4 ,& especially does ?is appe> to be true 9 a /ate ( affairs :]e s l>ge a numb] ( p]sons are beg9n+ consci\sly to take _! evolution 9 h& & by volitional activities are supply+ greatly increas$ impetus to _! psy*ic processes :i* "u ord9>y1 natural me?ods w\ld be consid]ably sl[] 9 _! developm5t4 ,x is q obvi\s t all cultural ef=ts :5 appli$ to ! bett]m5t ( a giv5 plant1 animal or faculty result 9 a correspond+ ha/5+ ( ! process ( gr[? f> 9 excess ( :at t gr[? w\ld be "u normal1 natural conditions4 ,all ! pres5t faculties possess$ by man are rem>kably susceptible to cultural influ5ces2 9 fact1 ! /&+ edict ( e?ical & social law is t ! human faculties mu/ be cultivat$ z highly z possible1 !reby giv+ ! _s a m p]fect m$ium ( expression4 ,^! obs]vations1 !re=e1 lead irresi/ibly & unavoidably to ! conclusion t ! "t = ! upspr++ ( ! intuitional faculty 9 ! human organism is ev5 n[ ^u u1 t und\bt$ly 9 c]ta9 v advanc$ ones x has already rea*$ a notable degree ( p]fection & is r m g5]al ?an w\ld appe> 9 ! abs5ce ( c>eful inve/igation4 ,n[1 j z ! intellect has made = individuality1 has emphasiz$ ! sep>at5ess ( ! ,?9k]'s exi/5ce f t ( o!r ?9k]s1 has develop$ self-consci\sness to a v high degree1 ev5 pu%+ x f> ov] into ! doma9 ( ! high] consci\sness to ! tempor>y obscuration ( ! latt]1 s ! intuitional w make = union1 = ! bro!rhood ( man1 = co-op]ation & = ! common weal4 ,?r\gh x man w come gradually into ! consci\sness t fundam5tally1 9 8 inn] nature1 9 e respect ( vital conc]n1 he is at-"o ) 8 fell[m5 & n only ) ! app>5t units ( life b ) all life z express$ 9 :atsoev] =m ?r\gh\t ! univ]se4 ,!n1 too1 he w be clos] to ! reality ( ?+s1 ( actions & natural processes2 9 f9e1 he w h begun ! developm5t ( ! space-m9d :i* w br+ him to ! k t he is "o ) space also &1 !re=e1 ) ! div9e life ( ! _w4 ,"o ( ! peculi>ities ( ! vital =ce :i* %[s itself 9 ! consci\sness z man's intellect1 is its gr[+ automatism1 or t t5d5cy :i* enables ! consci\sness to p]=m its functions automatically & ?us all[ opportunity = ! developm5t ( new] & high] faculties4 ,actions1 (t repeat$1 t5d to become automatic4 ,?is is also true ( ?\ght & consci\sness4 ,x is "o ( ! b5efic5t results ( ab/ract ?\ght t x develops1 or t5ds to develop1 a k9d ( automatism :]eby a m>k$ sav+ 9 "t & en]gy is effect$4 ,?is af=ds opportunity = o!r ?+s4 ,x is und\bt$ly true t 9 ! days ( ! truly primitive man 8 consci\sness 0 m completely engag$ 9 ! execution ( ! ergonic functions ( cells1 organs & tissues2 t all ^? processes :i* are n[ said to be involunt>y & reflexive 7 at "o "t1 9 ! di/ant pa/ ( man's evolution1 ! results ( consci\s volitions4 ,?is is a condition :i* mu/ h prec$$ ev5 ! developm5t ( ! intellect itself4 ,inde$1 !re c\ld be no intellect 9 a /ate :]e ! entire modicum ( consci\sness 0 be+ utiliz$ 9 ! p]=mance ( cellul> & hi/ologic functions4 ,! rise ( ! intellect mu/ h be5 9 direct ratio to ! developm5t ( automatism among ! cells1 tissues & organs1 s t z ^! came gradually to p]=m _! special labors reflexively ! intellect began to be =mulat$ & to gr[1 at fir/ only incipi5tly1 !n m & m completely until x rea*$ its pres5t /ate4 ,at ! pres5t /age ( its evolution1 a great deal ( ! labor ( ! intellect is beg9n+ to fall into a k9d ( incresc5t automatism1 al?\gh only rudim5t>ily1 9 _m in/ances4 ,yet1 z a result ( ?is t5d5cy1 q ! :ole ( ! ph5om5a ( p]ception is *>act]iz$ by a sort ( automatic action4 ,& ! m9d p]ceives )\t consci\s volition4 ,_m ( ! /eps ( conceptualization are automatic1 9 "p1 if n :olly4 ,c]ta9 x is t impulses once set 9 op]ation :e!r consci\sly or unconsci\sly cont9ue to act along ! same l9e until exhau/$ or until ! end has be5 atta9$4 ,consequ5tly1 x is a prov5 fact t (t5 s]i\s ma!matical & philosophic problems h be5 solv$ by ! m9d long aft] any consci\s ef=t to solve !m _h ceas$4 ,(t5 solutions h be5 arriv$ at dur+ sleep4 ,_m su* cases might be cit$1 b ! ph5om5on is n[ s common t almo/ e "o c cite "s exp]i5ce 9 8 own life t w sub/antiate ! claim4 ,!re is no d\bt b t ^! ph5om5a are evid5ces ( a reflexive developm5t 9 ! intellect4 ,! "t w come und\bt$ly1 & necess>ily s if ! intellect is to give way to a high] faculty1 :i* %all be z mu* above ! intellect 9 its grasp ( ?+s z ! intellect is n[ above ! simple consci\sness ( ! l[] animal1 :5 q ! entirety ( our intellectual processes w become automatic or self-p]=m+4 ,:at !n rema9s ( ! egoic s*ematism1 aft] its transmutation or elevation z ! organ ( ! intuitional consci\sness w be utiliz$ z ! organ ( ! ,?9k]'s involunt>y cognitive processes4 ,?is w mean t all ( t labori\s ideation :i* is n[ ! ab/ract ?\ght ( ! ,?9k] w be p]=m$ automatically1 leav+ ! high] aspect ( ! egoic consci\sness free to conceptualize or intuitograph ! intuitions4 ,p]ceptualization !n w be replac$ by conceptualization4 ,?is latt] w occupy ab\t ! same /atus z ! =m] does n[4 ,& necess>ily1 p]ception w become m complex4 ,9 o!r words1 :ile we n[ p]ceive simple p]cepts :i* are aga9 arrang$ into concepts mak+ a composite picture ( ! object1 we %all !n be tak+ 9 ! composite picture ( ! object at fir/ h&1 !reby disp5s+ ) ! r sl[ process ( p]ception z x n[ op]ates4 ,we %all /ill be p]ceiv+1 b :at we p]ceive w be concepts r ?an p]cepts1 z at pres5t4 ,! increas$ p[]s ( intellection ga9$ z a result ( ! incresc5t automatism 9 ! intellect1 ! fl[]+ =? ( ! intuitive faculty & ! g5]al enhancem5t ( ! intellect ?r\gh\t all its processes w enable x to ent]ta9 concepts or composite picture ( ?+s j z readily & z p]fectly z x c at pres5t deal ) a s+le p]cept4 ,concepts w be replac$ by sup]-concepts or intuitographs4 ,increas$ p]spicacity w enable ! ,?9k] to manipulate ! concepts & intuitographs ) ! same ease & read9ess & )al ! m9d w h atta9$ unto an almo/ unrealizable fre$om 9 its se>* aft] tru?4 ,! outcome ( ?is new adju/m5t :i*1 ( c\rse1 w n spr+ up at once1 b by ins5sible degrees1 w be ! cl>ification & unification ( our k4 ,x w mean also ! simplification ( x2 ! obviation ( div]sities ( op9ions1 ! spr++ up ( a new & w9n[$ sy/em ( philosophy :i* %all be ! true "o2 fur!r1 x w imply ! less5+ ( ! probability ( error 9 our judgm5ts & conclusions2 ! removal ( illusion to a mu* l>g] degree ?an to-day is possible & ! realization by e "o ( some?+ ( ! ess5ce ( ?+s1 ( causes & effects1 ( actions1 op]ations1 natural =ces & laws2 9 fact1 a condition ( m9d :i* w pres5t to ! consci\sness ! simple tru? above e conceivable phase ( kosmic life :i* may come )9 ! scope ( ! ,?9k]'s obs]vation4 ,! fur!r implications ( ?is view are t !re is a diff]5ce betwe5 ! ,?9k] & ! intellectuality4 ,! ,?9k] is et]nal & p>takes1 !re=e1 ( ! v ess5ce ( primordial orig9ality :ile ! m5tality is an artificial process1 ! resultant ( ! adaptation ( ! ,?9k]'s consci\sness to 8 vehicul> contrivances ( objective cognition & ! int]play ( 8 life among !m4 ,if ! appe>ance ( a *oppy sea di/urb$ by ! passage ( a brisk breeze ov] its surface be imag9$1 a similitude ( ! great ocean ( life may be envisag$4 ,! wavelet cre/s symbolize ! egos2 ! base ( ! wavelet :i* is "o ) ! great sea ( wat] repres5ts ! ,?9k] :i* is "o ) ! div9e life & consci\sness ( ! kosmos4 ,j z wavelet cre/s are cont9ually spr++ up & fall+ back into ! sea1 s are egos cont9ually be+ ca/ =? & reabsorb$ into ! univ]sality ( life only to be reca/1 z a wavelet cre/ or ego1 ^u ! surface ( ! mov+ ocean ( life4 ,& s1 9 ?is respect1 ! univ]sum ( life & consci\sness :i* are ess5tially "o is 9 a con/ant /ate ( ev]-becom+1 un-becom+ & re-becom+4 ,ano!r implication is t1 on acc\nt ( ! div]sity & complexity ( ! means ( contact ) ! ext]nal _w1 x is n possible = ! ego to arrive at m ?an a fragm5t>y und]/&+ ( ev5 ! lat5t geometrism ( life1 m9d & mat]iality4 ,9 our exam9ation ( ! s5su\s _w1 we are v mu* l ! ?ree bl9d m5 set to exam9+ an elephant4 ,"o set to scrut9iz+ 8 trunk by means ( 8 s5se ( feel+4 ,:5 ask$ = 8 judgm5t z to :at ! elephant 0 he decl>$ x 0 a snake2 a second :o began ) ! legs f\nd x to be l huge pill>s2 & a ?ird :o caught hold ( ! elephant's tail & decl>$ ! elephant to be l a rope4 ,ea* "o ( ! bl9d m5 describ$ :at he 0 able to p]ceive4 ,to ea* :at he felt 0 all !re 0 ^u :i* he c\ld r5d] judgm5t4 ,& s1 arti/s1 philosoph]s1 ma!maticians1 musicians1 me*anicians1 religi\s se]s1 metaphysicians & all o!r types ( m9d1 are j s _m bl9d m5 set to ! exam9ation ( an elephant1 or ! s5su\s _w4 ,ea* "o confid5tly believes 8 view to be correct2 ea* "o is satisfi$ ) ! deliv]ies ( 8 s5ses4 ,yet no "o ( !m is :olly correct1 no "o ( !m has se5 e phase & aspect ( ! problem4 ,does x n1 !re=e1 appe> to be ! m reasonable & urg5t t ! view :i* syn!sizes ! judgm5ts ( all ! possible exam9]s !reby con/ruct+ a composite idea ( ! entire mass ( judgm5ts is ! m reliable & ! m correct8 ,ref]r+ aga9 to ! dual intellig5ce1 ! ego & ! ,?9k]1 :i* toge!r con/itute man1 x is deem$ necess>y1 9 ord] to pres5t ! concept ( ?is duality to ! m9d ( ! read] 9 ! way t %all enable him easily to recall x1 to designate ! egoic intellig5ce z ! egopsy*e1 & ! ,?9k]'s intellig5ce z ! omnipsy*e4 ,! egopsy*e is ! ,i-mak+ faculty1 ! faculty ( self-consci\sness & ! syn!sis ( all ^? psy*ic /ates & functions kn[n z ! intellect or m9d & includes ! e?ical aspect ( man's nature4 ,! omnipsy*e is ! organism ( kosmic consci\sness1 ! space-m9d1 or man's high] self & t :i* connects ) or allies him to all life2 x is ! basis ( human unity & ( unity ) div9ity1 j z ! egopsy*e is ! basis ( sep>ation & individuality2 x is ! organ ( direct & in/antane\s cognition & ! p]man5t ess5ce :i* has p]si/$ ?r\gh e =m :i* ! be+1 man1 has ev] assum$ & ?r\gh e /age ( human evolution4 ,9 x are /or$ up ! memories ( ! ,?9k]'s pa/1 ! secrets ( life1 m9d1 be+1 reality1 & ! hi/ory ( life f ! beg9n+2 9 x also ! plan ( action = ! future ( ! life-wave z x passes f plane to plane1 f /age to /age1 & f =m to =m4 ,x is ! sp>k f ! flame t is nev] q free f its s\rce2 x is ! cont9u\s sp>k1 ! prolong$ ray :i* does n g out & _c be ext+ui%$4 ,x is t 9 man :i* :5 full union !re) has be5 atta9$ makes him a god 9 full consci\sness4 ,! omnipsy*e is really a neglect$ & ov]look$ factor 9 ! doctr9e ( evolution4 ,evolutioni/s1 :ile !y claim life to be cont9u\s & t man has come ?r\gh all ! k+doms ( nature 9 succession & has sp5t millions ( ye>s 9 ! p]fection ( 8 v>i\s organs1 faculties & /ages ( consci\sness1 make no ample all[ance = :at is 9 reality ! basal elem5t 9 evolution--a cont9u\s1 p]si/+1 p]man5t life-=ce :i* does n lose its id5tity f ! beg9n+ to ! end ( ! process4 ,?is fact--t t sp>k ( life :i* set out ^u ! evolution>y j\rney z a mon]on has gl[$ /eadily f t /age to manhood1 ma9ta9+ meantime its orig9al purposiv5ess & int5t--seems to be ! mo/ obvi\s consid]ation ( ! :ole doctr9e1 yet x has be5 m or less completely ignor$4 ,! elem5t>y requirem5ts ( evolution w\ld seem to e/abli% cle>ly ! necessity = "s su* et]nally p]si/+ pr9ciple z ! omnipsy*e :i* is capable ( su* subtle adaptations to e conceivable =m ( life & 9 :i* %\ld be ga!r$ up ! evolution>y results ( e life-cycle4 ,= ?is purpose ! omnipsy*e or unify+ pr9ciple 9 man 0 design$ f ! beg9n+ & x is t :i* con/itutes ! basis ( 8 intellectual nature :ile 9 a f> l>g] s5se x is ! div9ity 9 man himself4 ,x is inde$ /range t s important a factor z ! omnipsy*e %\ld h be5 omitt$ by evolutioni/s4 ,yet x c be acc\nt$ = ^u ! gr\nds ( ! purely me*ani/ic "* ( all intellectual attempts at solv+ ! problems ( vital manife/ations4 ,b s long z m5 rely ^u me*anical explanations ( su* ph5om5a s long w !y be prone to ov]look ! v ess5tialities ( ! problems :i* !y dev\tly wi% to solve4 ,! cont9uity ( ! physical g]m-plasm ( ! human species1#bg n[ q g5]ally admitt$1 w\ld sugge/1 x seems1 an analog\s condition to ! cont9uity ( ! psy*ic plasm call$ ! omnipsy*e1 ! only diff]5ce be+ t ! omnipsy*e is an intellig5t factor :ile ! physical plasm is a m$ium ( transmission ?\gh non-intellig5t4 ,! omnipsy*e is1 !re=e1 ! psy*ic res]voir ( evolution into :i* are /or$ ! transmut$ psy*ics ( mon]on1 amoeba1 jellyfi% & e o!r =m :i* x has ens\l$ & acts z ! /or]oom ( man's psy*ic op]ations z well z ! s\rce ( 8 intellectuality4 ,we turn n[ f ! /udy ( a sket* ( ! me*anism ( man's consci\sness :i* gives at its be/ only a fragm5t>y view ( ! univ]se ( spatiality to a consid]ation ( space itself 9 ! light ( its int]relational be>+s ^u ! "q ( intellectuality4 #bg ,see ,! ,g]m ,plasm2 ,a ,!ory ( ,h]$ity1 by ,a4 ,,weissman4 ,9 ! *apt] on ! ,g5esis & ,nature ( ,space we h1 9 trac+ out ! eng5d]m5t ( space1 prov$ x to be basically "o ) matt] 7& inde$ ! prog5itor ( matt]71 also ) life & consci\sness4 ,fur!r1 x has be5 %[n t all ! *>act]i/ics ( mat]iality are due to ! adaptation ( consci\sness to x & t out ( ?is adaptation grew ! intellectuality4 ,a close approximation to ?is view 0 ma9ta9$ by ,,kant :5 he discov]$ t our faculty ( ?9k+ or ! intellect only f9ds aga9 9 matt] ! ma!matical ord] or prop]ties :i* our faculty ( p]ceiv+ or consci\sness has depos$ !re4 ,x appe>s1 !re=e1 t :5 ! intellect approa*es matt] or spatiality x f9ds always a ready yieldance to its dem&s simply because intellectuality has previ\sly e/abli%$ !re9 ! del9eation or map ( ! pa? ov] :i* x necess>ily mu/ trav]se 9 its exam9ation ( ! object ( its pursuit4 ,9 o!r words1 ! kosmic m9d 9 eng5d]+ mat]iality & spatiality has set up !re9 a kosmic ord] or geometrism4 ,bo? motor & intellectual progress1 !re=e1 c be made ?r\gh ! _w ( spatiality because ( ! imman5ce ( ?is kosmic geometrism :i* lies lat5t 9 ! v fabric ( ! _w ( sub/ance fa%ion+ bo? ! "* & ! nature ( ! intellect z well z ( space itself4 ,s t !re is a p]fect congruity subsi/+ betwe5 spatiality & intellectuality4 ,accord+ly x is impossible = ei!r "o or ! o!r to transc5d ! grim grasp ( ! ma!matical ord] :i* b9ds !m 9 su* la/+ & fundam5tal agreem5t4 ,extra-spatiality may degrade itself into spatiality1 & inde$ 9 ! v nature ( ! case1 does s degrade itself1 yet spatiality c nev] raise itself beyond ! limits set by its eng5d]+ p>5t4 ,mat]iality may become m & m spatializ$ & consci\sness m & m intellectualiz$1 b !y mu/ proce$ h&-9-h& "o n sup]s$+ ! o!r4 ,be+ ! ess5ce ( ! natural geometry :i* is ev]y:]e imman5t 9 ! univ]sum ( matt]1 space becomes an organiz$ & ord]$ ext5sion1 9 fact is ! totality ( su* organiz$ & ord]$ ext5sion1 :i* con=ms to ! lat5t geometrism ! eng5d]m5t ( :i* x is ! sole cause 9 ! la/ analysis4 ,does x n appe> !n t all t mass ( artificial geometry :i* has sprung up z a result ( dep>tures made f ?is natural geometry is utt]ly baseless & mo/ c]ta9ly lack+ 9 ! kosmic agreem5t :i* spatiality l5ds to our prim>y conceptions8 ,( c\rse1 x is admitt$ly possible to devise c]ta9 conv5tional =ms ( logic & end[ !m ) all ! evid5ces ( a rigid consi/5cy b :i*1 because ( _! purely artificial "*1 w fall f> %ort ( any real con=mity to ! pot5tial geometrism :i* has be5 e/abli%$ 9 spatiality4 ,& ?is fact is ( utmo/ significance = all ^? :o seek to f9d ju/ification ei!r logically or naturally = ! exi/5ce ( a multi-dim5sional quality 9 space2 =1 if a cle>1 discrim9ative conception z to ! categorical relation%ip1 ea* to ea*1 ( ! two k9ds ( geometry be c>ri$ 9 m9d1 x w n be easy to conf\nd !m nei!r w x be difficult to disc]n :]e ! "o ends & ! o!r beg9s4 ,n[1 ! f\r? dim5sion & ! entirety ( ^? ma!matical speculations t\*+ ^u ! "q ( hyp]space1 dim5sionality1 space-curvature & ! manifoldness ( space are purely conv5tional & arbitr>y contrivances & d n meet ) any agreem5t or au?ority 9 ! native geometrism :i* we f9d inh]+ 9 space & :i* ! intellect recognizes !re4 ,?is conclusion seems to be obvi\s = ! reason t1 9 ! fir/ place1 ! non-,euclidean geometries h be5 con/ruct$ ^u ! basis ( a negation ( ! lat5t geometrism ( space & intellectuality2 & if s1 is x reasonable to expect t ei!r !y or any ( _! conclusions %\ld accord ) ! nature ( t =m ( geometry s admirably del9eat$ by ,,euclid8 ,obvi\sly n4 ,x is a matt] ( hi/orical k t ! :ole ( ! artificial non-,euclidean geometries consi/s ( ^? purely conv5tional results :i* inve/igators arriv$ at :5 !y d5i$ or controv]t$ ! norms suppli$ by ! natural geometry4 ,:5 metageometricians f\nd t !y c\ld nei!r prove nor disprove ! ,euclidean p>allel-po/ulate !y !n set ^u ! exam9ation ( idealiz$ con/ructions :i* negativ$ ! po/ulate4 ,! results1 ?us obta9$1 al?\gh self-consi/5t en\gh1 7 compil$ into sy/ems ( geometry :i* naturally 7 at v>iance ) ea* o!r & ) ?is inh]5t geometrism :i* is f\nd 9 spatiality & answ]$ to by ! intellect bo? normally & logically4 ,fur!rmore1 !re is ano!r consid]ation :i* to u seems to be equally if n m =bidd+1 9 its objections to ! cord9ation ( ! two sy/ems ( geometry1 & t is ! fact t ! geometry ( hyp]space is d5i$ ! corroborative te/imony ( exp]i5ce & ?is is true ( practically ! :ole ( its data4 ,inde$1 !re is p]haps no s+le elem5t 9 its entire con/itution :i* claims ! au?ority ( exp]i5ce4 ,?is is und\bt$ly ! weake/ po9t 9 ! /ructure ( ! hyp]spatial geometries4 ,contr>ily1 su* is n ! case ) ! natural geometry2 =1 9 ?is1 ! intellect 9 retrac+ its /eps ov] ! pa? laid out by t movem5t :i* has at ! same "t creat$ bo? ! intellect & spatiality1 f9ds an ord]ly & commodi\s arrangem5t into :i* x naturally & easily falls4 ,s exact is ?is agreem5t ( ! intellect ) ! kosmic ord] t if x 7 possible to remove ! :ole ( spatiality & mat]iality !re w\ld /ill be left ! frame "w :i* is ?is lat5t geometrism ( kosmog5esis4 ,b ! fact t ! intellect naturally fills all ! int]/ices ( mat]iality & spatiality1 fitt+ snugly into all ( !m z if mold$ = j t purpose1 by no means w>rants ! assumption t x w\ld or does also fit ! eng5d]+ factor :i* has creat$ ^! int]/ices4 ,! frame "w1 ! ord] or ! geometrism ( ! kosmos has be5 e/abli%$ by life act+ consci\sly ^u ! univ]sum ( mat]iality4 ,& 9 ord] to e/abli% ?is geometrism life _h to be mobile1 active1 creative4 ,x c\ld n rema9 /atic1 immobile1 & accompli% x4 ,be+ mobile1 dynamic1 creative1 x passes on4 ,x is l a fa%ion+ tool :i* ! cab9et mak]s use 9 cutt+ out designs ^u a piece ( wood4 ,x moves1 & keeps mov+ until ! design is f9i%$1 & !n x is ready = m design+4 ,life is l t4 ,x cuts out ! designs 9 mat]iality1 fa%ions ! =m1 molds ! mat]ial1 & passes on to o!r =ms4 ,! intellect fits into ^! designs gracefully4 ,b :at x f9ds is n life itself1 only ! design :i* life has made4 ,h5ce1 z !re is nei!r an empirical spatiality nor mat]iality 9 con=mity ) :i* ! artificial geometry ( ! analy/ may be said to exi/1 & z x may n be said to con=m to ! pa? :i* life has made 9 pass+ ?r\gh ei!r ( ^!1 x is absurd to pr$icate x ^u ! same basis z ! natural geometry4 ,& s1 we are =c$1 9 ! light ( ^! consid]ations to d5y ! validity & h5ce ! acceptability ( ! non-,euclidean geometries z ei!r reasonable or w>rantable sub/itutes = ! ,euclidean1 & d5y+ :i* we also =mally ignore ! claims ( ! f\r? dim5sion1 z ma!matically design$1 to any legitimate an*orage 9 ei!r our vital or intellectual movem5ts4 ,x has be5 %[n t ! fl[ ( life1 z x describes t movem5t :i* we call evolution1 eng5d]s simultane\sly & consub/antially spatiality1 mat]iality & intellectuality1 & ^!1 9 turn1 ! natural ord] or geometrism ev]y:]e imman5t 9 ! univ]se2 & t automatically1 "o out ( ! o!r & ea* out ( ! all1 ^! con/itute ! totality ( kosmic fundam5tals4 ,also we h sket*$ ! me*anism ( man's consci\sness & discov]$ h[1 9 its evolution>y developm5t x has divid$ into two aspects1 ! egopsy*ic & ! omnipsy*ic1 & ^! two factors ally him def9itely & adequately to ! _w ( ! s5ses & to ! _w ( sup]s5su\s cognitions4 ,& ?us we h cle>$ up "s ( ! misconceptions :i* _h to be confront$ & made m easy ! approa* to ! c5tral idea1 !reby cons]v+ ! sub/antiat+ influ5ce :i* a g5]al & m compreh5sive view ( ! :ole w\ld naturally give4 ,! totality ( kosmic ord] is space4 ,x is circumscrib$ by an ord]less envelope ( *aos j z ! g]m ( an egg is surr\nd$ by ! egg-plasm4 ,! organiz$ kosmos is ! g]m1 k]nel or c5tral1 nucleat$ mass1 endur+ 9 a /ate ( becom+4 ,involution>y ka!kos or primordial *aos is ! egg-plasm :i* n\ri%es ! g]m or ! kosmos & is t out ( :i* ! g]m evolves4 ,ka!kos or *aos is ! unmanife/1 unorganiz$1 uncondition$1 unlimit$ & undiff]5tiat$ plasm4 ,space is ! manife/1 limit$1 f9ite1 organiz$ g]m t1 fe$+ ^u ! envelop+ *aos1 exi/s 9 a p]petual /ate ( alt]nate manife/ation & non-manife/ation--appe>+1 disappe>+ & reappe>+ indef9itely4 ,! appe>ance ( ! kosmos z an ord]ly elaboration ( ! involution>y phase ( kosmog5esis1 9 s f> z kosmic ord] may be said to be an accompli%$ fact1 m>k$ ! turn+ po9t 9 t proc$ure ^: function x 0 to make manife/ a univ]se possess+ c]ta9 def9ite *>act]i/ics ( ord]l9ess2 b ! kosmos1 z x n[ /&s1 may n be ?\ght ( z hav+ atta9$ unto a /ate ( ultimate ord]l9ess4 ,! idea meant to be convey$ is t betwe5 ! po9t ( becom+ & ! actually pyknos$1 or solidifi$ /age 9 ! process ( creation !re is a m or less well def9$ l9e ( dem>kation cutt+ (f t :i* is spatiality f t :i* is non-spatiality4 ,beyond ! limits ( spatiality is an abs5ce ( geometric ord]4 ,"h geometry breaks d[n1 becomes impot5t1 because x is an intellectual con/ruction2 at lea/1 x is n s app>5t z 9 ! manife/$ kosmos4 ,x is a /ate ab\t :i* x is utt]ly futile to pr$icate any?+2 because no words c describe x4 ,! mo/ t may be said is t x is abs5ce ( geometric ord] z x inh]es 9 space4 ,& if s1 all ^? movem5ts compreh5d$ "u ! g5]al notions ( spatiality1 mat]iality1 intellectuality & geometricity h bo? _! ext5sive & det5sive or inv]se movem5ts nullifi$ 9 _! approa* to x4 ,involution>y ,ka!kos1 !re=e1 may be said to be ! primordial wild]ness ( disord] :i* outskirts ! well laid-out & c>efully plann$ g>d5 ( ! spatial univ]se4 ,we may excogitate ^u "s ( ! obvi\s functions ( ?is ka!kotic _w-plasm2 b 9 do+ s we mu/ leave (f all attempts at a description ( its appe>ance1 its magnitude1 ext5t or o!r qualities1 & ?9k only ( its kosmic function4 ,we _c say t !re is back ( x a spatiality nor c we say t x is a spatiality2 = :atev] may be its ext5t or volume1 x suffices t x may n be said to be space4 ,x is *aos4 ,space is ord]1 organization1 geometricity4 ,x _c be said t !re is a lat5t geometrism 9 *aos2 because geometric ord] is f\nd only 9 spatiality & is t :i* di/+ui%es spatiality f ka!kosity or non-spatiality4 ,*aos is ! lack ( spatiality4 ,?is1 ( c\rse1 implies t x is imp5etrable to ! intellectuality or to vitality4 ,all inv]se movem5t su* z is discov]$ z tak+ place 9 spatiality & :i* results 9 ! ph5om5alization ( space runs agr\nd :5 x /rikes aga9/ ! rock-b\nd coa/ ( ka!kosity4 ,we c only say t x is bo? ! po9t ( orig9 = ! evolv+ univ]se ( life & =m & its t]m9us4 ,x is ! nebulosity out ( :i* ! :ole came & into :i* all is ultimately occlud$4 ,a great & f>-rea*+ error is made 9 all our ?9k+ ) respect to ! kosmogonic processes :5 we po/ulate ! complete absorption ( *aos z an e>ly act ( kosmogony4 ,cu/om>ily1 we ?9k ( kosmic *aos z a primordial condition ^: exi/5ce 0 done away z soon z ! univ]se came into active manife/ation4 ,?is because x has be5 exce$+ly difficult1 if n q impossible1 = ^? ^: privilege x 0 to det]m9e ! tr5d ( philosophic ?\ght to free !mselves f ! bondage ( a dogma :i* ow$ its exi/5ce to a traditional or leg5d>y int]pretation ( facts t ought nev] h be5 s int]pret$4 ,*aos ,,is & ,,ev] ,,%all ,,be1 s long z ! univ]se itself lacks completion1 fullness or p]fection 9 purpose1 ext5t & possibility4 ,x is und\bt$ly be+ dim9i%$1 h[ev]1 9 proportion z ! kosmos is approa*+ absolute p]fection4 ,& :5 ! la/ ve/ige ( *aos disappe>s f ! out]skirts ( ! matur+ kosmos !re %all appe> a glorifi$ univ]se ( indescribable qualities4 ,space be+ a p]ception a priori _c be det]m9$ :olly by purely objective me?ods4 ,! y>d-/ick1 ! telescope & ! light-ye> are objects :i* belong exclusively to ! ph5om5al & ) !m alone nev] c we arrive at a true conception ( ! nature ( space4 ,we c no m demon/rate ! nature ( space by ! use ( objective in/rum5ts & movem5ts ?an we c measure ! _s 9 a balance4 ,c]ta9ly1 !n1 x _c be hop$ t by tak+ ! measurem5t ( space-di/ances 9 light-ye>s1 or /udy+ ! nature ( mat]ial bodies1 we %all be able to fa?om ?is mo/ objectively incompreh5sible & ineluctable ?+ :i* we call space4 ,x is su* t e ,?9k] mu/1 9 8 own inn] consci\sness1 come into ! realization ( t awfully my/]i\s some?+ :i* is ! nature ( space bo? z to exi/5ce & ext5t by 8 own subjective ef=ts unaid$1 un*>t$ & alone4 ,:5 we measure1 weigh1 apportion & o!rwise try to det]m9e a ?+ we are deal+ ) ! ph5om5al :i* is no m ! ?+ itself ?an a %ad[ is ! object :i* ca/s x4 ,:at does x matt] t metageometricians %all be able to demon/rate t space exhibits itself to ! s5ses 9 a f\r-or n-dim5sional mann]8 ,grant+ t !y may be able to d ?is1 if m]ely = ! sake ( ! discussion1 :5 !y h f9i%$1 x w n be space t !y h det]m9$1 b ! ph5om5a ( space1 its arboresc5ce1 :ile space itself rema9 indet]m9ate & unapproa*able by ph5om5al me?ods4 ,if !re are curvature1 manifoldness & n-dim5sionality ^! are n prop]ties ( space1 b ( intellectuality 9 its cultur$ /ate & :5 x is1 !re=e1 remov$ f ! native /ate ( conception4 ,sci5ti/s may be able to weigh ! human body1 c\nt e cell1 "n & describe e n]ve1 muscle & fib]2 !y may ev5 be able to "k x 9 e conceivable "p & f e physical angle & relation%ip1 & yet "k no?+ ( ! life :i* vitalizes t body & makes x appe> ! ph5om5al ?+ t x is4 ,s x is n by in/rum5ts :i* man may devise t we %all be able to det]m9e ! true nature & purpose ( space4 ,we mu/ adopt o!r me?ods & means & assume o!r angles ( approa* ?an ! purely objective 9 ord] to compreh5d space :i*1 be+ ! sole inh]5t aspect ( consci\sness1 c be und]/ood be/ by apply+ ! measures :i* ! latt] provides = its und]/&+4 ,x w\ld appe>1 !re=e1 t ! be/ /udy ( space is ! consci\sness itself1 kn[+ :i* we %all "k space4 ,! univ]sum ( space1 includ+ ! ph5om5al univ]se1 & its relation to consci\sness may be lik5$ to a conical funnel ^: base repres5ts ! ph5om5al _w ( ! s5ses & ^: apex or smalle/ po9t repres5ts ultimate reality4 ,9 ,figure #bj1 we h endeavor$ to symbolize graphically ?is conception ( space4 ,! base m>k$ ,s5sorium repres5ts ! s5sible _w4 ,t m>k$ ,realism symbolizes ! ultimate plane ( reality1 ! inn] ess5ce ( ! _w1 ! plane ( ?+s-9-!mselves4 ,! cone aris+ f ! base s5sorium symbolizes ! objective _w z comp>$ ) consci\sness2 ! subv]t$ cone1 ) apex 9 ! s5sorium1 repres5ts ! evolv+ human consci\sness4 ,! successive bases h ! foll[+ symbology3 ,self-consci\sness1 ,communal ,consci\sness1 ,mikrocosmic ,consci\sness1 ,makrokosmic or ,univ]sal ,consci\sness1 ! ,plane ( ! ,space-,m9d ,consci\sness1 ,div9e ,consci\sness1 ,ka!kotic ,consci\sness1 or ! ,plane ( ,f9al ,union ) ! ,manife/ ,logos4 ,self-consci\sness is t =m ( consci\sness :i* enables ! ego to become aw>e ( himself z di/+ui%$ f o!r selves or ! ,n-self2 ! ,omnipsy*ic or ,communal ,consci\sness is t =m ( consci\sness f :i* arises ! realization by ! ,?9k] ( 8 on5ess ) all o!r ?9k]s & ) o!r =ms ( life4 ,mikrocosmic consci\sness d5otes a /ill high] =m ( consci\sness1 z t :i* enables ! ,?9k] to become consci\s ( 8 liv+ id5tity ) ! life ( ! _w or ! planet on :i* he lives4 ,x repres5ts a /age 9 ! expansion ( consci\sness :5 x becomes "o ) ! consci\sness ( ! planet ^u :i* x may be function+4 ,makrokosmic consci\sness accompli%es ! aw>5ess ( ! ,?9k]'s unity ) ! life ( ! kosmos or univ]se4 ,! space-m9d & ! consci\sness :i* con/itutes x enable ! ,?9k] to compreh5d ! orig9ality & ! t]m9ality ( kosmic processes4 ,x is ar*etypal s f> z ! life-cycle ( ! univ]se is conc]n$ because ! beg9n+1 ! int]m$iate portion & ! end+ ( ! kosmos are encompass$ )9 x4 ,div9e consci\sness is t =m ( consci\sness :i* arises ^u ! unification ( ! ,?9k]'s consci\sness ) t ( ! manife/ deity2 x is1 9 fact1 omnisci5ce4 ,! ka!kotic consci\sness belongs to ! ultimate plane ( reality2 to kosmic orig9s & *aog5y1 & !re=e1 p]ta9s to ! plane ( non-manife/ation4 ,illu/ration3 ,,fig4 #bj4--,kosmos & ,consci\sness ,! implications are t 9 comp>ison ) ! s5sorium1 ! ,?9k]'s consci\sness is a m]e po9t 9 space4 ,x is1 9 reality1 s small & insignificant t ! ext5sity ( ! physical _w or univ]se seems unlimit$1 unfa?omable 9 mean+ & inf9ite 9 ext5t4 ,b z 8 consci\sness exp&s1 z x passes1 9 evolution>y succession f "o plane ( reality to ano!r & high] "o1 ! illimitability1 ! incompreh5sibility & inf9ity ( ! univ]se gr[ ev] small] & small]1 until ! plane ( div9e consci\sness is rea*$4 ,!n ! previ\sly incompreh5sible dw9dles into insignificance1 lo/ 9 ! real illimitability1 inf9ity & unfa?omability ( consci\sness itself4 ,kosmic psy*og5esis1 z exhibit$ & specializ$ = ! purposes ( ! evolution ( ! ,?9k]1 c h no o!r de/9y ?an ! fl[]+ =? z ! ne plus ultra ( manife/ation :i* is no?+ %ort ( unification ) ! highe/ =m ( consci\sness exi/5t 9 ! kosmos4 ,x is n to be consid]$ really t ! scope ( space is dim9i%$ b t ! gr[+1 exp&+ consci\sness ( ! ,?9k] w s r$uce ! relative ext5sion ( x t illimitability w be swall[$ up 9 its ext5sity4 ,consci\sness1 9 becom+ inf9ite 9 compreh5sion1 annihilates ! imag9>y inf9ity ( space4 ,accord+ly1 t :i* n[ appe>s to be beyond m5tal encompassm5t und]goes a correspond+ dim9ution 9 e respect z ! consci\sness exp&s & becomes m compreh5sive4 ,! my/]y ( space decreases z ! scope ( consci\sness increases4 ,z ! ,?9k]'s consci\sness exp&s ! ext5sity ( ! manife/$ univ]se decreases4 ,?us ! my/]y ( e aspect ( kosmic life less5s1 & fades away1 z ! intimacy ( our k conc]n+ x becomes m & m complete4 ,!re is no my/]y :]e k is4 ,my/]i\sness is a symbol ( ignorance or unconsci\sness1 & t :i* we d n und]/& acts z a ,flam+ ,sword keep+ ! way ( ! ,temple ( ,reality le/ ignorance break 9 & despoil ! treasures !re(4 ,figure #ba is a graph %[+ a sectional view ( consci\sness on all planes repres5t$ z sev5 conc5tric circles4 ,?is describes ! analog\s enveilm5t ( ! consci\sness :5 x ens\ls a physical body or :5 b\nd to ! purely objective _w ( ! s5ses4 ,! ov]com+ ( ! b>ri]s ( reality1 repres5t$ by ! circumscrib+ circles is ! "w ( ! ,?9k] :o is =ev] seek+ to exp& & to "k4 ,= only at its c5t]1 z symboliz$ "h1 is ! consci\sness at "o ) ! highe/ aspect ( kosmic consci\sness & !re alone is ! my/]y ( space despoil$ ( its habilim5ts4 ,illu/ration3 ,,fig4 #ba4--,sept5>y ,enveilm5t ( ,consci\sness ,accord+ly1 z consci\sness or ! ,?9k] is m & m dive/$ ( c>nal b>ri]s & illusions !re develops a gradual recognition ( ! unit>9ess ( spatial ext5t & magnitude2 !re arises ! c]ta9 k t space has b "o dim5sion & t dim5sion is %e] ext5sion4 ,! ,?9k]'s sph]e ( aw>5ess is repres5t$ z if x beg9s z a po9t 9 space & develops into a l9e :i* divides into two l9es1 ! b\nd>ies ( ! space cones4 ,?us x may be p]ceiv$ t ! anci5ts _h a simil> conception 9 m9d :5 !y symboliz$ kosmog5esis ) ! dot 7471 ! l9e1 & ! circle ) diamet] inscrib$1 :i* toge!r repres5t ! univ]se 9 manife/ation4 ,we realize ! impossibility ( adequately depict+ ! full significance ( ! inv]se ratio exi/+ betwe5 ! ext5sity ( space & ! incresc5t inclusivity ( consci\sness by means ( graphs2 = nei!r words nor diagrams c portray ! scope & mean+ ( ! conception 9 its entirety4 ,yet !y aid ! intellect to grasp a ray ( light1 an intimation ( :at ! ,?9k] sees & und]/&s int]iorly4 ,9 ?is connection x is int]e/+ to note ! function ( ! ideal 9 ! evolution & expansion ( consci\sness4 ,! ideal has no p]ceptual value2 x has no /atus 9 ! _w ( ! s5ses4 ,x is unapproa*able ei!r 9 ?\ght or action1 & !re=e1 lies beyond ! grasp ( bo? ! intellectuality & ! vitality4 ,x is indescribable1 inconceptible & se>*less2 = ! mom5t t we describe1 def9e1 or approa* ! ideal1 ei!r intellectually or vitally1 9 t mom5t x ceases to be ideal1 b actual4 ,x flees f ev5 ! slighte/ approa*2 x nev] rema9s ! same2 x _c be atta9$1 at lea/ its atta9m5t causes x to lose its idealty4 ,x is !n no long] ! ideal4 ,x is l an ignis fatuus2 ! clos] we come to x ! f>!r away x rec$es4 ,x hangs susp5d$ be=e ! m9d l ! lusci\s grapes :i* hung be=e ! m\? ( ! hungry ,tantalus4 ,z ! grapes & ! wat] rec$$ f 8 rea* at e ef=t he made to seize !m s ! ideal rema9s et]nally unseizable & unatta9able4 ,:atev]1 !re=e1 is 9 our ?\ght processes1 or 9 our k1 t may be said to be ideal1 does n really exi/4 ,! ideal is a phantom gr[+ out ( ! nature & ess5ce ( ! intellectuality4 ,its purpose is to lead m]ely ! m9d on2 to allure x1 to tantalize1 & compel x to gr[ by ex]tion1 by ! /ruggle to atta91 by ! desire to ov]come4 ,9 ?is respect1 x s]ves well its function 9 ! economy ( intellectual evolution4 ,x is a my/]i\s aspect ( ! orig9al & et]nal desire to live :i* is ! kosmic urge pres5t 9 all organiz$ be+ & has its roots hidd5 9 ! div9e purpose ( creation4 ,idealiz$ con/ructions1 !n1 are l ,arabian fea/s conjur$ up by a fami%+ m5tality4 ,!y are l ! dreams ( a />v+ man 9 :i* he actualizes 9 phantom-/uff ! *oice/ vi&s 9 abundant supply = 8 imag9>y delectation4 ,! m9d t is satisfi$ nev] idealizes1 nev] makes an idealiz$ con/ruction4 ,x is only :5 an a*+ void is felt1 :5 a long+ = ! realization ( t :i* x has n arises )9 itself1 :5 a feel+ ( di/9ct lack1 a want1 a hank]+ aft] some?+ n 9 its rea*1 takes possession ( ! m9d t x beg9s to idealize4 ,t is :y "s m9ds are )\t ideals4 ,x is because !y are satisfi$ ) :at !y h & c und]/&4 ,!y feel no hung]+ = bett] & gr&] ?+s2 !y h no desire to und]/& ! unkn[n & ! my/]i\s2 h5ce !y d n idealize2 !y make no attempt to repres5t unto !mselves a picture ( t :i* is beyond !m4 ,su* m9ds are dormant1 hib]nant1 asleep1 unfeel+ & unresponsive to ! div9e urge4 ,b ! ideal is nei!r obta9able objectively nor subjectively1 nei!r ph5om5ally nor really1 s t :5 we come ^u ! ideal 9 our mode ( ?9k+ we h arriv$ n at a f9ality or end1 b at t :i* is design$ to lead u on to some?+ high]1 to nobl] accompli%m5ts & m ext5sive conque/s4 ,:5 we h devis$ idealiz$ con/ructions1 !re=e1 we %\ld n !re) be cont5t b %\ld scrut9ize !m1 exam9e & /udy !m = _! implications2 = !reby we may discov] ! pa? & ! guide-po/s to a new doma91 a new ideal1 foll[+ :i* we %all1 9 "t1 come to a po9t 9 our se>* = ! real :]e ! fluxional is at a m9imum2 we %all rea* t some?+ :i* w admit ( no fur!r /ruggle--! la/ *asm betwe5 ! ph5om5al & ! real--& /&+ on ! bridge1 consci\sness1 :i* engages ! twa91 %all h a complete view ( t ,sacr$ & ,imp]i%able ,l& ( ,kosmic ,realism :]e l a fleet+ cl\d ( %e]e/ vapor %all be se5 ! phantom-ideal deliquesc+ & disappe>+ 9 ! cold1 ?9 air ( ! real & ! et]nal4 ,s9ce space is judg$ to be inf9ite by ! intellect occlud$ 9 su* cl\ds ( illusion & hamp]$ by su* con/rictive bonds ( limitations1 z x n[ endures1 we h no "r to conclude t ! concept ( inf9ity w\ld /ill l+] be=e ! m9d's eyes :5 ! illusion>y veil is remov$2 9 fact1 !re is ample reason to believe1 nay = ! ass]tion1 t ! recession ( ! veil w reveal j ! opposite ( ?is illusion1 namely t space is f9ite1 & ev5 b\nd$ by ! fr+e ( *aog5etic disord]l9ess4 ,ei!r we p]ceive ! real or we d n2 ei!r ! pure ?+ness ( all objects c be p]ceiv$ or x _c be p]ceiv$4 ,if n1 grant+ t !re is su* a ?+ z ! real1 x mu/ be )9 ! ultimate range ( conceivability4 ,x also seems reasonable t realism exi/s some:]e1 & if s1 mu/ be s\ght 9 a direction inv]se to t 9 :i* we f9d ! ph5om5al & ! approa* !reto mu/ necess>ily be gradual1 cont9u\s & direct & n by abrupt breaks1 by twi/s & turns4 ,! ph5om5al mu/ lie at ! t]m9us ( ! real1 & vice v]sa4 ,s t by retrac+ ! pa? blaz$ out by ! real 9 com+ to ph5om5alization we %all p]haps f9d t :i* ca/s our %ad[y _w1 j z by trac+ a %ad[ 9 a direction inv]se to t 9 :i* x ext5ds we may f9d ! object :i* projects x4 ,x is n out & beyond t we %all f9d ! end ( space2 x is n by c\nt+ t5s ( ?\s&s ( light-ye>s t ! suppos$ limits ( space %all be atta9$4 ,! pa? ( se>* mu/ project 9 an opposite direction--n />-w>d b ,?9k]-w>d1 t[>d ! subtle habitation ( ! consci\sness itself4 ,we err greatly :5 we ?9k t by measur+ di/ances we %all encompass space2 = t :i* we measure & det]m9e is b ! cl\ds caus$ by ! vapor ( reality4 ,x is1 !re=e1 n )\t1 b )91 9 an inv]se direction t ! se>* mu/ proce$4 ,go+ back ov] ! life-/ream1 beg9n+ :]e x /rikes aga9/ ! %ores ( solid objectivity1 deep] & deep] /ill1 pa/ ! inn]mo/ mile-/one ( ! self-consci\sness1 back into ! v he>t ( ! imp]turbable int]ior ( be+ :]e ! ,?9k]'s ca/le op5s its doors to ! ,great ,kosmic ,self1 f t op5 door-way we may /ep out into t great my/]y ( space--limit$1 yet n limit$1 multi-dim5sion$1 & yet hav+ only "o dim5sion1 v]itably real & fundam5tal1 ! ,fa!r-,"m ( all ph5om5a4 ,"h ! great my/]y ( my/]ies is reveal$ z ! citadel ( ! univ]sal & ! ultimate real4 ,9 ?is citadel1 ! plane ( kosmic consci\sness1 space loses its spaci\sness & "t its timel9ess1 div]sity its multiplicity & on5ess alone reigns supreme4 ,b ! movem5t t[>ds ! c5t] & circumf]5ce ( space1 aft] ?is mann]1 requires aid nei!r f ! notion ( space-curvature nor t ( ! space-manifold1 except1 inde$1 only 9 s f> z a /ate ( consci\sness or a degree ( realism may be said to be a tridim5sional manifold4 ,! feel+ t space is s+le-po9t$1 & yet ubiquit\sly c5t]$1 has be5 indulg$ by ma!maticians & o!rs 9 a m or less modifi$ =m2 b !y h imag9$ x 9 ! t]ms ( an indef9ite proce$+ outw>d until 9 "s mann] unacc\ntable alike to all we come back to ! po9t ( orig94 ,x has be5 express$ by ,,pick]+ :5 he says t if we g f> en\gh ea/ we %all arrive at ! we/2 f> en\gh nor? we %all come to ! s\?2 f> en\gh into ! z5i? we %all come to ! nadir4 ,b ?is conception is bas$ ^u a notion ( space :i* is ! exclusive result ( ma!matical det]m9ations & subject to all ! re/rictions ( ma!tic rigor\sness4 ,x requires t we %all all[ space to be curv$4 ,?is we decl9e to d = ! reason t x is bo? unnecess>y & contr>y to ! mo/ fundam5tal affirmations ( ! a priori faculty ( ! ,?9k]'s cognitive app>atus4 ,x w\ld seem to be necess>y only t we %\ld ext5d our consci\sness backw>d1 rev]t x into ! direction :5ce life came to f9d t :i* we seek4 ,by ext5sion ( consci\sness is meant ! ability to function consci\sly ^u ! v>i\s sup]kosmic sph]es or planes j z we d on ! physical4 ,yet x %\ld be q z easy to devise an idealiz$ con/ruction :i* w\ld imagify ! results ( ?is +ressive movem5t ( ! consci\sness z to repres5t ! results ( a progressive outw>d movem5t />-w>d4 ,hav+ done s ! exam9ation ( !m c\ld be conduct$ along l9es simil> to ^? foll[$ 9 ! scrut9y ( objective results4 ,:at w\ld x mean to ! ,?9k] if he 7 able to id5tify 8 consci\sness ) ! e!r 9 all its v>y+ degrees2 :at w\ld x mean if he 7 able to id5tify 8 consci\sness ) life & ) ! pure m9d-matt] ( ! kosmos2 & la/ly1 ) ! spiritual ess5ce ( ! univ]se8 ,:at if 8 v>i\s vehicles ( aw>5ess 7 available = 8 purposes ( cognition8 ,:at1 inde$1 if he c\ld trav]se consci\sly ! entire gamut ( realism & consci\sness f man to ! div9e consci\sness8 ,does x n appe> reasonable t z he assum$ ea* ( ^! v>i\s ve/ures ( consci\sness1 9 succession1 he w\ld gradually & f9ally1 come to a full und]/&+ ( reality itself8 ,x seems s4 ,?is view is ev5 m cog5t :5 x is consid]$ t ! limitations1 & consequ5t obscuration ( consci\sness are proportional to ! numb] ( vehicles or b>ri]s ?r\gh :i* ! ,?9k] is requir$ to act 9 contact+ ! ph5om5al univ]se4 ,common s5se sugge/s t fre$om ( motility is det]m9$ by ! pres5ce or abs5ce 7m p>ticul>ly ! latt]7 ( bonds & b>ri]s2 t ! less ! numb] ( su* b>ri]s ! great] ! scope ( motility & consequ5tly great] ! k4 ,,plato evid5tly _h ?is 9 m9d :5 he imag9$ ! life ( m5 sp5t 9 cave-wall$ prisons 9 :i* _! bodies 7 s fix$ t !y 7 compell$ to sit 9 "o prescrib$ position1 & !re=e1 be unable to see any?+ except ! %ad[s ( p]sons or objects z !y pass$ by4 ,he conceiv$ t m5 ?us condition$ w\ld1 9 "t1 suff] ! dim9ution ( _! scope ( consci\sness to su* an ext5t z to r$uce x to id5tification ) ! %ad[s on ! walls4 ,_! consci\sness w\ld be m]e %ad[-consci\snesses ! entire data ( :i* w\ld be %ad[graphs4 ,s t = !m ! only reality w\ld be ! %ad[s :i* !y con/antly saw4 ,a simil> ?+ really happ5s to man's consci\sness limit$ to ! plane ( ! objective _w4 ,?+s :i* are n objective d n appe> z real to him1 if !y d appe> at all4 ,x is n t !re are no o!r realities ?an ^? :i* appe> to ! egopsy*ic consci\sness or t fall )9 its scope2 b t ?is =m ( consci\sness is incompet5t to judge ( ! nature & appe>ance ( ^? realities :i* d n answ] to ! limitations "u :i* x exi/s4 ,& s1 ) m5 ^: data ( consci\sness or ^: outlook ^u ! _w ( facts1 or r life1 are conf9$ to ! n>r[ b\nds ( ma!matic rigor & exclusiv5ess1 !re may appe> to exi/ no realities :i* may n be def9$ 9 ! t]ms ( ma!matics4 ,simil>ly1 to ! empirici/1 us$ to measurem5ts ( magnitudes1 weights1 & rates ( motion1 !re may also appe> to be no realities :i* are n am5able to ! mold ( 8 empirical contrivances--! balance1 ! *romatic & ! scalpel4 ,all ( ^! are %ad[ m5 con/rict$ to ! metes & b\nds ( %ad[s :i* !y obs]ve only because !y are ignorant ( ! realities :i* lie )\t _! plane4 ,life has s _m ways ( exhibit+ its rema9s to ! intellect2 & ^! rema9s h s _m facets or viewpo9ts f :i* !y may be /udi$1 t no?+ %ort ( a panoramic view ( all ! modes ( exhibition & ( all ! facets & angles ( appe>ances w suffice to pres5t a tru/wor?y & compreh5sive view ( ! :ole4 ,!n1 life itself is s illusive1 s unseizable by ! intellect t ! te/imony ( all inve/igators are requir$ to summ>ize its modes ( appe>ance4 ,&1 !re=e1 ev5tual cont5tm5t %all be secur$ only :5 ! mass ( div]se te/imonies is r$uc$ to ! l[e/ common divisor1 & = ?is purpose ! op]ations ( e class ( inve/igators mu/ be view$ z ! "w ( speciali/s ^u sep>ate phases1 facets & angles ( life's rema9s4 ,& s x is manife/ly absurd = ! empirici/s1 by tak+ note ( ! dim5sion1 ext5t1 quality & "* ( ! %ad[s1 or "o s+le class ( angles1 to hope to pr$icate any tru/wor?y judgm5ts ab\t ei!r ! realities :i* ca/ ! %ad[s or und]lie ! angles2 because :atev] notion or conception !y may be able to ga9 mu/ ( necessity be m]ely fragm5t>y & entirely inadequate4 ,despite ?is fact1 h[ev]1 we /ill h ! spectacle ( m5 :o1 /udy+ ! s5sible univ]sum ( space-cont5t1 endeavor ei!r to make x appe> z a f9ality 9 itself1 or t ! _w ( ! real mu/ necess>ily be con=mable to ! precise /&>ds :i* !y arbitr>ily set up 9 _! exam9ation ( ! objective _w4 ,x c be said ) assurance t we %all nev] be able ev5 s mu* z to approa* a true und]/&+ ( ! unse51 real _w until we %all h *ang$ our m5tal attitude t[>ds x & ceas$ to expect t x %all necess>ily be fa%ion$ & ord]$ 9 exactly ! same way z ! _w ( our s5ses1 or t x %all be und]/ood by apply+ ! same me?ods ( proc$ure z ^? :i* we use 9 our exam9ation ( ! ph5om5al1 s5su\s _w4 ,x is a matt] ( logical necessity t1 z !re are no s5ses :i* c respond to ! real1 z !re are no organs :i* vibrate 9 accord ) ! rates ( vibration ( ! real1 !re c be no reasonable hope ( und]/&+ x by means ( s5su\s contrivances & /&>ds4 ,let ! consci\sness1 !re=e1 be turn$ n outw>d1 b inw>d :]e is situat$ ! temple ( div9e life2 let !re be tak5 away ! outw>d %ea?s :i* en%r9e ! pure intellig5ce ( ! ,?9k]2 let him gr[ & exp& 8 sph]e ( aw>5ess2 let !re be an exploration ( ! abysmal deeps ( m9d1 ( life & consci\sness2 = buri$ deeply 9 man's own inn] nature is ! answ] to all qu]ies :i* may vex 8 impuissant intellectuality4 ,,*apt] ,,ix ,,metageometrical ,,ne>-,,tru?s ,realism is ,psy*ological & ,vital--,! ,imp]man5ce ( ,facts--,on ! ,t5d5cy ( ! ,intellect to ,fragm5tate--,! ,intellect & ,logic--,! ,passage ( ,space1 ! ,kosmomet] & ,zoomet]1 ,in/rum5ts = ! ,measurem5t ( ! ,passage ( ,space & ! ,fl[ ( ,life--,! ,disposal ( ,life & ! ,p[] to ,create--,space a ,dynamic1 ,creative ,process--,numb]s & ,kosmogony--,! ,kosmic ,significance ( ! ,circle & ! ,pi-,proportion--,me*anical ,t5d5ce ( ! ,intellect & its ,inaptitude = ! ,und]/&+ ( ,life--,! ,crit]ion ( ,tru?4 ,kosmic tru? has _m facets4 ,! rays ( light :i* we see d>t+ f its surface d n always come f ! core4 ,(t5 !y are reflections ( rays ^: light /ops %ort at ! sup]fice2 & ^!1 9 turn1 are reflections ( deep] realities4 ,?us ! reflect$ light may be trac$ to its s\rce by foll[+ ! lead ( ext]nal reflections4 ,x is n[ kn[n t moonlight1 & p]haps1 9 _m cases1 />light1 are reflections ( sunlight1 if n ( our sun1 "s o!r 9 ! univ]se4 ,b x is only at c]ta9 times & "u c]ta9 conditions t we c see ! sun :i* is ! s\rce ( ! o!r k9ds ( light4 ,! />s :i* owe _! light to suns are s _m facets ( sunlight4 ,! moon is a facet ( sunlight also4 ,facts are facets ( tru?4 ,!y are s _m faces ( et]nal tru?4 ,!y repres5t ! _m ways reality exhibits itself1 or r its effects1 to ! consci\sness4 ,:5 we1 !re=e1 become aw>e ( facts we h n 9 virtue !re( become aw>e ( ! reality :i* produces ! facts4 ,we h come to "k only some?+ ( ! t]m9i ( realism :ile ! complexities & int]nal ramifications :i* lie betwe5 realism itself & ^! t]m9i altoge!r elude our cognition4 ,let u exam9e briefly an icosah$ron1 = in/ance4 ,an icosah$ron is a figure compreh5d$ "u tw5ty equal sides4 ,^! v>i\s sides are s _m faces by means ( :i* ! figure pres5ts itself to ! consci\sness4 ,^! faces1 h[ev]1 are n ! real object4 ,! figure may be exam9$ by view+ x f any "o ( its sides2 yet1 by simply exam9+ a s+le face1 or any numb] ( faces1 less ! total numb]1 we arrive at no satisfactory k ( ! magnitude or its sub/ance4 ,we mu/ fir/ become consci\s ( all ! faces1 hold+ !m 9 m9d z a composite picture1 be=e we c ev5 beg9 to h any?+ l a complete notion ( ! icosah$ron4 ,!n by cont9u+ ! exam9ation we may f9d t ! magnitude is compos$ ( wood fib] or /one or metal1 z ! case may be4 ,9 ?is way we might c>ry ! exam9ation to indef9ite limits & f9ally arrive at a v compreh5sive k ( ! icosah$ron & yet be unaw>e altoge!r ( ! =ces :i* h be5 at "w 9 ! production ( ! magnitude or ( ! reality :i* lies back ( x4 ,realism is psy*ological & vital4 ,9 ess5ce x is m9d1 _s1 life4 ,yet ^! ?ree are "o4 ,m9d is ! outw>d vehicle ( life2 _s is ! =m or ! int]ior vehicle :i* life assumes 9 ord] to express itself4 ,realism1 !n1 is life4 ,is ! logician deal+ ) reality :5 he collects & cord9ates ! v>i\s modes ( int]pretation by :i* we le>n to und]/& ! symbolism ( life8 ,obvi\sly n4 ,! data ( logic are simply a collection ( rules = int]pret+ concepts4 ,x is a comp5dium ( indices = ! ,book ( ,life4 ,x is no m ! book itself ?an a table ( cont5ts is a book4 ,b logic occupies ab\t ! same category z does an index to a volume4 ,a book1 h[ev]1 is m ?an its conv5tional cont5ts4 ,x is ! ?\ght t is symboliz$ !re94 ,! book ( life1 accord+ly1 is ! sum total ( life's expressions2 b x is n life itself4 ,t is ! subtle1 evasive some?+ :i* ! cont5ts ( ! book ( life symbolize4 ,nature1 bo? 9 h] palpable & impalpable aspects1 may be said to be ! book ( life :]e9 are record$ ! movem5ts1 ! expressions1 & ! diacritics ( life4 ,! :ole is a magnitude ( _m facets 7little faces74 ,we %all h to "k all ! faces be=e we c say t we h a compreh5sive k ( nature4 ,= s long z we h only a fragm5t>y k ( ! :ole1 s long ev5 z we h m]ely a sup]ficial k ( any aspect ( nature1 j s long w our k be 9 va94 ,j z x frequ5tly happ5s t1 on acc\nt ( ! p>tial view ( ?+s1 we are l$ to make incorrect judgm5ts conc]n+ !m1 s :5 we come to make ass]tions ab\t life or nature 9 g5]al1 we are apt to fall into ! error ( r5d]+ judgm5ts ^u insuffici5t data4 ,& x is n at all likely t judgm5ts ?us arriv$ at c possess true validity because x may happ51 & und\bt$ly does always s happ5 "u ! pres5t limitations ( human k1 t ! v elem5ts :i* are ignor$ or neglect$ 9 =m+ a judgm5t possess en\gh ( virtue to alt] ! intr9sic value ( det]m9ations bas$ ^u o!rwise insuffici5t data4 ,h5ce x develops n infrequ5tly t our judgm5ts repeat$ly h to be *ang$ 9 proportion z our data are made m & m compreh5sive4 ,m5 se>*+ eag]ly = ! tru? sometimes all[ !mselves to be c>ri$ away by ! en?usiasm ( ! mom5t :i* arises ^u ! discov]y ( a new facet ( tru?2 b if all se>*]s 7 to be> 9 m9d ! fact t reality pres5ts itself to consci\sness 9 myriad ways & t !re are innum]able facets all lead+ ev5tually back to ! s\rce ( all !y n s easily w\ld be induc$ to jump to ! conclusion t !y _h cov]$ ! entire gr\nd4 ,= :5 we h discov]$ a million facts1 or _m millions ( !m1 ab\t nature we may say t we h only m]ely begun & t :at we h f\nd is n to be comp>$ ) ! totality ev5 ( ! directly obs]vable phases ( nature4 ,logic1 !re=e1 deals ) ! symbolism exi/+ betwe5 & among facets ( tru?1 & n directly ) tru? itself1 al?\gh ! conclusions rea*$ by ! logicians may be true en\gh f an intr9sic /&po9t4 ,logic is n tru?1 h[ev]2 x is m]ely ! consi/5ce ( relations & int]-relations betwe5 facts & among gr\ps ( facts4 ,tru? is n e/abli%$ by logic2 x /&s 9 no ne$ ( ! light ( logic = its revelation2 inde$1 m apt ?an n is logic to obscure tru?4 ,tru? is its own pro(2 x is self-evid5t4 ,logic is a m]e model] ( facts2 x is /atic1 immobile1 fix$4 ,all truly logical processes ne$ a />t+ po9t1 a f\ndation1 a premise1 a base4 ,tru?1 be+ et]nal1 mobile1 dynamic1 vital1 ne$s no />t+ po9t2 ne$s no f\ndation because x is itself fundam5tal2 x requires no premise because no premise is compreh5sive en\gh to encompass x4 ,!re is only "o way ( arriv+ at tru? & t is n to arrive at all--j to recognize x )\t proc$ure4 ,! fact t facts are1 & ! fact ( _! relations & int]-relations1 _! sequ5ce & implications1 c be arriv$ at only by logical processes4 ,life1 9 its passage ?r\gh ! univ]sum ( spatiality1 c>efully diacriticizes betwe5 ! realm ( facts & ! doma9 ( tru?1 m>k+ ea* (f f ! o!r by unmi/akable signs & b>ri]s4 ,tru? is p]ceiv$ z an axiomatic1 self-evid5t pr9ciple & no am\nt ( logic c\ld prove or e/abli% its v]ity4 ,facts are intellectual creatures2 tru? is intuitional1 vital4 ,! intellect conceives ! consi/5ce ( facts :ile ! intuition recognizes tru?--is tru?1 & !re=e1 foll[s 9 ! wake ( life z consci\sness4 ,!re is no p]man5ce 9 facts & ! intellectual recognition ( _! consi/5ce4 ,! discov]y ( a s+le new fact may de/roy ! consi/5ce ( a :ole mass ( previ\sly correlat$ facts4 ,?us is reveal$ ! miracle p[] ( logic ov] facts4 ,x c take a mass ( facts1 relat$ or unrelat$1 mold !m into hypo!ses1 end[ !m ) a sort ( int]ior consi/5cy1 & make ^! hypo!ses take ! po/ure ( tru?4 ,h5ce logic is (t5 an effective mask :i* ! intellect commonly imposes ^u its mat]ial2 b x does s in/9ctively & c no m escape ! rigor\s compulsion ( ?is in/9ctive function+ ?an wat] c escape its liquidity4 ,:]e=e1 we conclude t true p]man5ce abides alone 9 tru? because tru? is duration itself4 ,= ! f\ndations ( ! :ole /ructure ( facts 9 religion1 sci5ce1 art & philosophy :i* man has toilfully built up 9 ! la/ million ye>s might easily be de/roy$ or ov]turn$ by ! discov]y ( "s great fact or by appreciat+ ! true value ( tru?4 ,let u suppose x %\ld sudd5ly be realiz$ by m5 t !y are really & truly gods capable ( creat+ & possess+ all ! o!r virtues1 p[]s & capabilities :i* we are accu/om$ to impute to supreme div9ity2 & suppose t ! fact ( _! omnipot5ce & div9e omnisci5ce always _h be5 obvi\s b t m5 7 s engag$ ^u details & ! non-ess5tials ( life & matt] t !y _h n notic$ nor realiz$ x be=e1 w\ld n ?is realization make a va/ diff]5ce 9 ! "* ( our k & ! attitude :i* we w\ld necess>ily assume !reaft] t[>ds matt]1 life & ! problems :i* !y pres5t8 ,w\ld n x completely revolutionize our arts1 our sci5ces & our philosophies8 ,h[ mu*1 !n1 ( ! facts ( ^! w\ld be left :5 ! light ( omnisci5ce _h be5 turn$ on--:5 tru? itself c\ld be p]ceiv$ & int]iorly realiz$8 ,n mu*1 to be sure4 ,we %\ld und\bt$ly h to disp5se ) ! entirety ( our fact-mass1 = x %\ld !n be entirely useless & mean+less 9 ! light ( ! respl5d5t omnisci5ce ( tru?4 ,z at pres5t con/itut$ consci\sness is focus$ ^u ! mat]ial plane = ! purposes ( sup]ficial obs]vances4 ,b if ! focus ( consci\sness %\ld be *ang$ s z to reveal conditions ^u :at mu/ be a high] & m int]ior level1 ! aspect ( ?+s w\ld be entirely *ang$ & ! :ole ( our !ory ( k w\ld h to be recon/itut$4 ,x is conceivable1 yea obvi\s1 t ! /]n reality ( be+ is f> remov$ into ! ,great ,int]ior ( t :i* is2 & !re is a po9t 9 ! pa? to ! int]iority ( be+ :]e !re is no illusion1 no appe>ance1 inde$1 no?+ b ! cold1 illum9at+ body ( reality itself4 ,x mu/ appe> also t along ! j\rney int]ior-w>d !re are _m app>5t levels or planes1 ea* ( :i* requires a new focus4 ,x is unreasonable1 !n1 to suppose t ! conclusions arriv$ at z a result ( purely logical processes1 conf9$ to ! l[e/ levels ( reality1 are p]t95t & valid = ! entirety ( realism :i* is nei!r ( ma!matical nor logical import4 ,= in/ance1 if we take ! purely axiomatic ass]tion3 x equals x1 ! intellect is at once c]ta9 t ?is is s1 & _c be o!rwise1 & yet a proposition ( ?is k9d is purely conceptual1 conv5tional & arbitr>y4 x may also equal #a1 #b1 #c1 #d1 or any o!r quantity4 ,!n1 if ea* x 9 ! above equation be replac$1 by say1 a horse1 !re imm$iately arises a difficulty4 ,= x is n possible to f9d two horses :i* are 9 all respects mutually equal4 ,s t z soon z we pass f ! conceptual into ! actual1 :e!r on ! side ( objective reality or t ( absolute reality1 ! validity ( ! axiom is imm$iately expos$ to s]i\s que/ion+4 ,! tru? ( ! matt] is t on bo? sides ( ! conceptual x is always f\nd t !re is a v>iance f ! /&>ds set up by ! conceptual1 ?is v>iance be+ m m>k$ on ! side ne>e/ to absolute reality ?an on ! side ( objectivism4 ,objectively1 ! con=mity ( ! s5sible ) ! conceptual is ( su* approximation z to l5d tru/wor?y utility to ! conceptual 9 its application to ! s5su\s4 ,?us by simply elim9at+ ! vital factors f our equations we are enabl$ to proce$ 9 a reasonably safe mann] ) our judgm5ts4 ,really1 h[ev]1 no su* approximate congru5ce c be f\nd2 = on ! side ( reality we are deal+ ) an indivisible some?+--some?+ t is et]nally & absolutely unit>y 9 its con/itution :ile :5 we transf] ! sc5e ( our obs]vations to ! objective _w we discov] a contr>y situation4 ,"h we are ev]y:]e beset by div]sities1 multiplicities & dissimil>ities4 ,?is is s because ! intellect naturally t5ds t[>d ! objective :]e x f9ds a mo/ com=table atmosph]e = its op]ations4 ,! conceptual is relat$ to ! objective z a tra9 ( c>s is relat$ to ! railway4 ,t is to say1 ! con/itution ( ! intellect is su* t x f9ds its mo/ facile expression 9 ! objective _w & is ab\t z com=table 9 ! doma9 ( realism z ! same tra9 ( c>s w\ld be on ! ocean4 ,! intellectuality is design$ to deal ) facets ( tru?2 x is made to manipulate segm5ts1 p>ts1 fractions1 & _c *>t its way ?r\gh a cont9uum su* z reality4 ,be+ con/itutionally a conv5tionality ( ! ,?9k]'s own contrivance1 & aris+ out ( ! subtle adaptation ( 8 vehicles to ! environm5t af=d$ by ! s5su\s _w1 x c only f9d congru5ce 9 t conv5tionality :i* is ! in/rum5tality ( a high] intellectuality express$ 9 a div]sity ( =ms1 into :i* reality divides itself = manife/ation4 ,! human intellect is1 !re=e1 ! bridge ov] :i* is made ! passage f ! individual consci\sness to ! ,all-,consci\sness2 simultane\sly1 ! m$ium :]eby ! physics ( ! bra9 are conv]t$ into ! psy*ics ( unconsci\sness4 ,x may be lik5$ to a pair ( specially con/ruct$ tongs :i* are s =m$ z to fit exactly ! objects :i* a high] intellectuality has made4 ,x is )\t ! prov9ce ( ! intellect to take note ( :at int]v5es betwe5 physics & psy*ics2 x is always oblivi\s ( int]/ices :ile tak+ cognizance ( objects or ?+s4 ,9 ?is respect1 ! intellect is mu* l a /e]age pass5g] on bo>d an ocean l9] :o sees only 8 port ( dep>ture & port ( arrival1 kn[+ no?+ 9 ! meantime ( :at happ5s dur+ ! voyage1 no?+ ( :at ! o!r pass5g]s on ! upp] decks may exp]i5ce & tak+ no "p 9 any ( ! pass+ %[ until he l&s4 ,s t ! passage ( ! intellect f fact to fact is an altoge!r un9t]e/+ voyage2 x may z well be made unconsci\sly1 & to all int5ts & purposes1 is s made4 ,accord+ly1 ! advocates ( n-dim5sionality f9d x q impossible to pr$icate any?+ :atsoev] ( ! passage1 say1 f tridim5sionality to qu>todim5sionality4 ,!y f9d !mselves at ease 9 tridim5sionality & h ev5 contriv$ to f9d pleasant environs 9 ! f\r-space hav+ made !re9 su* idealiz$ con/ructions z w af=d ample hospitality to ! intellect4 ,b ! que/ions z to h[ ! passage f ! ?ree-space to ! f\r-space is to be made & h[ ! intellect %all demean itself dur+ ! passage h be5 completely ignor$ &1 !re=e1 left unansw]$4 ,:at1 !n1 %all be said ( an explor] :o says he has f\nd a new l& & yet c give no intimation z to h[ "o may proce$ to arrive at ! new l&1 :at *anges are to be made en r\te1 nor ! slighte/ sugge/ion z to ! direction "o %\ld take 9 sett+ out = x8 ,x is n likely t ! report ( su* an explor]1 9 practical life1 w\ld be tak5 s]i\sly2 & yet1 !re are ^? :o1 rely+ utt]ly ^u simil> reports made by c]ta9 en?usia/ic analy/s1 d>e to place cr$5ce 9 _! assev]ations4 ,n only h !y giv5 wide cr$5ce to ^! reports1 b h1 inde$1 s\ght to rehabilitate _! own t]ritory 9 accordance ) ! /range descriptions giv5 by unhappy analytical explor]s4 ,n[ ! "q ( greate/ conc]n1 grant+ = ! nonce t !re is su* a doma9 z hyp]space1 is ! passage4 ,h[ %all we make ! passage8 ,or1 is ! passage possible8 ,9 va9 d we int]rogate ! analy/2 = he does n "k1 nor does he confess to "k4 ,evid5tly x is impossible = him to "k by means ( ! intellect alone2 = ! intellect n be+ fitt$ to take cognizance ( ! passage1 b only ! />ts & /ops1 has no aptitude = su* que/ions4 ,h5ce1 :at seems to be ! mo/ important phase ( ! entire "q w h to rema9 utt]ly inscrutable until ! intellect n\ri%$ by ! intuition %all be ar\s$ f its le?>gy & br\ght to a c]ta9 high po9t ( illum9ation :]e x1 too1 may take note ( ! passage4 ,space is ! pa? :i* life makes 9 its d[nw>d sweep ?r\gh all ! /ages ( pyknosis or kosmic cond5sation by virtue ( :i* x accompli%es ! eng5d]m5t ( mat]iality z also ! pa? m>k$ out by x 9 its upw>d sw+ :]eby x accompli%es ! spiritualization ( matt]4 ,x is ! kosmic ord] :i* life e/abli%es by means ( its outgo+s & incom+s4 ,:5 we look out into space we p]ceive t :i* is a dynamic appe>ance ( life itself1 & n a pure =m4 ,no?+ t is a pure =m c exi/ 9 nature & 9 z mu* z space is n only indissoluble f nature b p>takes ( its v ess5ce x _c be said to be a pure =m4 ,! intellect1 h[ev]1 prone to foll[ ! grooves laid out by pure logic1 nev] fails to seek to make ev]y?+ t x contacts con=m to ^! logical necessities4 ,b1 if ! analy/ 7 to make c>eful discrim9ation z to ! respective categories--t into :i* life falls & t 9 :i* ! intellect is =c$ by its nature to proce$--he n s easily w\ld be l$ into ! fault ( attempt+ to %ape realities ^u models :i* be+ /rictly conv5tional 7 n meant = su* uses4 ,b nei!r ! logician nor ! ma!matician c be condemn$ = su* g5]osity if su* condemnation 7 ju/ifiable4 ,= !y ev]y:]e & at all times insi/ ^u realiz+ ab/ractions & ab/ractioniz+ realities1 & !y d ?is ) an ins\ciance t is at times surpris+4 ,yet x is 9 ?is v vag>y t is discov]$ ! true nature ( ! intellect4 ,!re is a sort ( dual t5d5ce obs]v$ 9 ! me?od ( ! intellect's op]ation4 ,a pol>ity is ma9ta9$ ?r\gh\t3 ! ab/ractive & ! concretional4 ,x vacillates cont9ually betwe5 ! ab/ract & ! concrete & no soon] has x f\nd a concrete ?an x beg9s to set up an ab/ract = x2 & vice v]sa--z soon z x is has con/ruct$ an ab/ract x imm$iately seeks ei!r its concrete or sets out to hew "s o!r concrete into su* %ape z w fit x4 ,& betwe5 ^! two extremes num]\s excuses are f\nd = ex]cis+ ?is peculi> *>act]i/ic1 & t too1 )\t reg>d to consequ5ces4 ,x w\ld seem t ! intellect1 9 ?us function+1 0 really engag$ at a sort ( s5su\s play out ( :i* x d]iv$ an int5se & n altoge!r unselfi% pleasure4 ,( c\rse1 x mu/ be grant$ t div]sity has its specific & )al necess>y uses 9 t x af=ds a field = ! op]ation ( human intellectuality & repres5ts ! adaptation ( ! kosmic intellect to ! human = ! purposes ( evolution4 ,?is adaptation :ile necess>y = ! intellectual developm5t is1 h[ev]1 n an end 9 itself4 ,x is m]ely a means to a high] purpose4 ,9 fact1 if we reg>d mat]iality z a deposit ( life1 c>ri$ by x z a k9d ( imp$im5tum1 & consci\sness1 :i* is life1 z be+ id5tical ) ! intellectuality :i* makes ^! adaptations1 !re %\ld be no gr\nds = ! /atem5t t ! "o is adaptable to ! o!r at all4 ,& z ?is is really ! view :i* we assume x w\ld p]haps be m /rict to reg>d ! adaptation z subsi/+ betwe5 ! human intellect & mat]iality bo? ( :i* hav+ be5 con/ruct$ by kosmic intellectuality4 ,pursuant to ! div]sity ( uses to :i* mat]iality l5ds itself !re arises 9 ! intellect a supreme t5d5cy to segm5t1 to break up into sep>ate p>ts1 to multiply & div]sify4 ,x is n cont5t unless x is at ?is favorite & natural pa/ime4 ,x delights 9 tak+ a :ole & divid+ x into innum]able p>ts4 ,?is x w d aga9 & aga92 because all its muscles1 s9ews & n]ves are mold$ 9 t mold & c no m cease 9 _! t5d5cy to fragm5tation ?an c ! muscles ( a danc+ m\se cease 9 _! circul> twirl+ ( ! m\se's body4 ,yet1 9 ?is x is b creat+ a well-nigh endless task = itself--:i* task mu/ be p]=m$ to ! utt]mo/4 ,b 9 its p]=mance1 t is1 9 ! intellect's complete und]/&+ ( ! div]sity ( p>ts1 9 ! k ( _! relations & int]-relations & 9 _! syn!sis1 x may arrive at t "o ineluctable some?+ :i* is call$ unity4 ,& s do+1 become ultimately free4 ,9 view ( ! =ego+1 x is n surpris+ t ! intellect %\ld h1 f9ally1 fall5 ^u ! notion ( n-dim5sionality4 ,x has come to t z naturally z x has p]=m$ its mo/ common task4 ,left alone & unhamp]$ 9 its movem5ts1 x has simply foll[$ ! lead ( ! ,great ,highway ?r\gh ! doma9 ( mat]iality4 ,& n[ x has arriv$ at a /age :]e x ?9ks x has succe$$ 9 fractionaliz+ space4 ,"t has long ago yield$ to fragm5tation1 be5 divid$ into m9ute p>ts & ea* "p c>efully measur$4 ,space1 n hav+ a visible indicator l "t to d5ote its passage or p>ts1 suff]$ a long & t$i\s delay be=e x c\ld boa/ ( a measur]4 ,z ! sun-dial measur$ "t 9 ! pa/ & became ! =]unn] ( ! mod]n clock s n-dim5sionality measures space = ! ma!matician4 ,:at m practical in/rum5t = ?is purpose may yet be devis$ is n ours to prophesy2 yet x is n to be despair$ ( t "s "o %all f9d a suitable means = ?is purpose4 ,s]i\sly1 h[ev]1 x is n )\t possibility t %\ld "s subtle m9d devise an in/rum5t = m>k+ ! passage ( space z we h = d5ot+ ! passage ( "t a great /ride =w>d w\ld be accompli%$ 9 ! evolution ( ! human intellect4 ,= ! g5]al outcome ( ! intellect's att5tion be+ turn$ to ! passage ( space w\ld und\bt$ly be to recognize n only its dynamism b its becom+-ness1 z a process ( kosmog5esis4 ,because su* an in/rum5t w\ld h to be s con/ruct$ z to take note ( ! movem5t ( life1 & = ?is reason1 x w\ld h to be extremely s5sitive necess>ily & key$ to ! subtleties ( vitality & n to mat]iality4 ,ma!matics %all h fail$ utt]ly 9 ! utilit>ian aspects ( ?is phase ( its late/ div]sion if x d n ju/ify its claims by cr[n+ its "w 9 ! field ( hyp]space ) a ,kosmomet]1 an in/rum5t devis$ = ! measurem5t ( ! movem5t ( space or a ,zoomet]1 an in/rum5t devis$ = ! measurem5t ( ! passage ( life4 ,we %\ld l to enc\rage inv5tive m9ds to turn _! att5tion life-w>d & space-w>d ) ! end 9 view ( con/ruct+ su* an in/rum5t4 ,:5 once we h le>n$ accurately to measure life we %all !n be able to dispose ( x--to create4 ,x is n d\bt$ t if ev] humanity is to arrive at t po9t 9 its evolution :]e x c und]/& life2 if ev] x is to atta9 unto ! supreme ma/]y bo? ( vitality & mat]iality & to come to ! ultimate atta9m5t ( div9e consci\sness 7all ( :i* we confid5tly believe to be 9 /ore = humanity7 x mu/ be accompli%$ aft] ?is mann]3 fir/1 by syncretiz+ mat]iality ) vitality1 & !n1 by intuitionally recogniz+ ! tru? ( ! implications ( ! syncretism4 ,! hi/ory ( consci\sness 9 ! human family is id5tical ) ! hi/ory ( man's conque/ ov] matt] & physical =ces4 ,& ?is is cle>ly indicat$ 9 ! incid5tals cont+5t ^u ! toilsome rise ( ! g5us homo f ! e>lie/ caveman ^: /atus d5ot$ a comp>atively negligible transc5d5ce ( mat]ial =ces1 to ! pres5t-day man :o has ga9$ a m>k$ly notable conque/ ov] ^! =ces4 ,always consci\sness seeks ! means ( adequately express+ itself 9 ! s5sible _w4 ,& to ?is end x eng5d]s faculties1 organs & processes 9 ! bodily me*anism1 &1 9 matt]1 devises in/rum5ts ( application :]eupon & :]e) x may te/1 analyze1 comb9e & recomb9e ! =ces & mat]ials x f9ds4 ,! unlimit$ range ( expressions ly+ op5 to ! consci\sness makes x necess>y cont9ually to devise high] & high] grades ( appliances to meet its ne$s z x exp&s4 ,x w n be ga9said t ! telescope has s]v$ actually to lay b>e to ! consci\sness an immeasurable realm ( k nor t ! microscope1 turn+ its att5tion 9 an opposite direction1 m>vel\sly has enl>g$ & enri*5$ our k ( ! _w ab\t u4 ,& simil> decl>ation may be made an5t almo/ e inv5tion1 discov]y & conque/ :i* man has made ov] natural ph5om5a4 ,?us1 by ext]nally apply+ me*anical implem5ts to ! subject ( 8 consci\sness1 man has ext5d$ actually 8 consci\sness1 8 sph]e ( k2 has greatly enhanc$ its quality1 &1 9 ! process1 has urg$ ! intellect to endeavors t h wr\ght its pres5t unequal$ ma/]y ( ?+s4 ,nor h ! spiritual aspects ( our advance along ^! l9es be5 ! lea/ notable4 ,= ^! h enjoy$ ! ess5ce ( all t has be5 ga9$ 9 ! process & h1 !re=e1 kept pace ) ! onw>d movem5t ( ! intellectual consci\sness4 ,b h]et(ore no advance has be5 made z a result ( me?odic or reflexive det]m9ations4 ,t is1 m5 did n set out f ! beg9n+1 equipp$ ) =ekn[l$ge ( :at _! ef=ts w\ld br+1 to develop ! pres5t quality ( human consci\sness4 ,!y simply work$ on1 _! att5tion be+ absorb$ by ! problems t lay ne>e/ & dem&$ e>lie/ consid]ation4 ,s ! advance has come z a resultant ( man's close application to 8 ev]-pres5t ne$s--%elt]1 clo?+1 food1 protection & o!r pres]vative measures--& x has come naturally & inevitably & )\t prep5se4 ,nev]!less1 if man1 kn[+ :at to expect f ! syncretization ( matt] & m9d1 aft] ?is fa%ion1 %\ld set out delib]ately to accel]ate ! int5sification1 expansion & gr[? ( 8 consci\sness1 !re is no d\bt b t ! consequ5ce w\ld be mo/ f>-rea*+ & satisfactory4 ,b ! pa? t leads to ?is gr& consummation does n lie 9 ! direction ( div]sity2 x lies 9 ! opposite direction4 ,9 va91 !n1 does ! intellect fractionalize 9 ! hope t by do+ s x %all come to ! solid sub/ructure ( life2 9 va9 does ! analy/ segm5t space into any numb] ( p>ts or ord]s2 9 va9 does he ask h[ _m & h[ mu*2 = by answ]+ none ( ^! qu]ies w he f9d ! satisfaction :i* he vaguely seeks4 ,if x be true t x is n by analysis b by syn!sis t ! true norm ( life1 & !re=e1 ( reality %all be f\nd x is futile to ent]ta9 s]i\s hope ( f9d+ x 9 any o!r way4 ,z a p]isophism or ne>-tru?1 !n1 n-dim5sionality takes =emo/ rank4 ,& ?is is s = ! reason t :5 we proce$ 9 ! direction ( multiple dim5sions1 t is1 "o dim5sion pil$ ^u ano!r dim5sion or ins]t$ betwe5 two o!rs we are travel+ 9 a direction :i*1 ! m we multiply our dim5sions1 leads u f>!r & f>!r away f ! tru?4 ,?is is a simple truism4 ,if we take1 = in/ance1 a wood5 ball & cut x up into f\r qu>t]s1 & divide ea* "o ( ^! qu>t]s into eigh?s1 into sixte5?s1 ?irty-seconds1 sixty-f\r?s1 etc41 indef9itely1 we %all h a multiplicity ( p>ts1 ea* "o unlike ! orig9al ball4 ,b f no exam9ation ( ! multip>tite segm5ts c we d]ive any?+ l an adequate conception ( ! orig9al ball4 ,some?+1 ( c\rse1 c be le>n$1 b n en\gh to enable ! r5d]+ ( a correct judgm5t z to ! nature1 size1 %ape & g5]al appe>ance ( ! ball4 ,b ?is is precisely :at happ5s :5 ! analy/ divides space into _m dim5sions4 ,he cuts x up into n-dim5sional p>ts & ! m m9utely he divides x into p>ts ! m remote w ea* "p be 9 its simil>ity to ! orig9al %ape & =m ( space1 & ! f>!r away f ! true conception ( ! nature ( space he is l$ !reby4 ,n[1 n-dim5sionality or t phase ( metageometry :i* reg>ds space z be+ divisible into any numb] ( dim5sions or sy/ems ( cord9ates is a direct & inevitable product ( t t5d5cy ( ! intellect to individuate & to s+ul>ize ph5om5a4 ,biologically speak+1 x is a peculi>ity :i* h>ks back to ! "t :5 life 0 manife/$ ?r\gh ! cell-colony & :5 ! individual cells began1 because ( increas+ consci\sness1 to deta* !mselves f ! colony & set out = !mselves1 & ?us ea* intellect recapitulates 9 its modus viv5di ! sali5t t5d5cies ( phylog5esis4 ,let x suffice1 !n1 to po9t out t ?is univ]sal t5d5cy to segm5t & fragm5tate :i* rigor\sly *>act]izes intellectual op]ations ^u e ph5om5on ) :i* x deals is a culm9ation ( ! primordial t5d5cy among cells to divide1 inasmu* z ?is phase ( cell life mu/ be ! "w ( ! kosmic intellect4 ,! natural inf]5ce is t f ! extreme ( individualization !re %all be a gradual turn+1 :e!r ( ! intellect p] se or ( ! intellect jo9$ to ! intuition does n matt]1 t[>ds t o!r extreme ( communalization4 ,& f ?is latt] %all gr[ up1 z "o ( ! inevitable & ineluctable t5d5cies ( ! ,?9k]'s consci\sness a torr5ti\s movem5t 9 human society t[>ds cop]ation1 bro!rhood1 mutuality & union 9 ev]y?+4 ,s t :]eas 9 ! pa/ & at ! pres5t "t ! intellect has be5 develop+ "u ! dom9ant note ( individuality x w !n be com+ gradually "u ano!r dom9ant note--communality4 ,! result ( ?is developm5t w be ! unification ( all ?+s1 & in/ead ( _m dim5sions ( space1 _m measures ( "t1 & a g5]al div]sification ( all ph5om5a1 we %all come to ! only true notion ( ^! ?+s & realize pragmatically ! true value & ext5t ( unity 9 ! univ]se4 ,x is admitt$ t ! intellect1 9 treat+ objects s+ly & deal+ only ) ! />ts & /ops ( a movem5t1 is )al loyal to ! kosmic ord]1 design & purpose :i* h priorly *>act]iz$ manife/$ ph5om5a by segm5tation4 ,& 9 ?is loyalty x has be5 foll[+ m]ely a natural lead :i*1 :ile admitt+ ( ! wide/ developm5t & exp]i5ce1 nev]!less at ! same "t b5efic5tly obscures ! und]ly+ reality 9 ord] t 9 its adaptation to ! s5su\s _w ! intellect might h ! greate/ fre$om = ! developm5t suit$ to ! giv5 /age ( its evolution4 ,b 9 ?us admitt+ ! natural congru5ce betwe5 ! intellectuality & ! ph5om5al or s5su\s we d n !reby unite ) ^? :o already believe t ?is kosmic agreem5t is ! ne plus ultra ( psy*og5esis4 ,on ! o!r h&1 x is ma9ta9$ t ?is is m]ely a phase ( psy*og5esis :i* %all be outgr[n 9 j ! same measure z o!r phases h be5 outgr[n4 ,& not)/&+ ! fact t judgm5ts ( ! intellect ) respect to int]-factual relations or ! ens ( facts !mselves are z valid z its judicial det]m9ation ( self-consci\sness1 no m & no less1 we are1 by ! v rigor & exclusiv5ess ( ?is logical necessity & inh]5t limitation1 l$ to view ! intellect's int]pretation ( ph5om5a z p>tial & fragm5t>y2 = ! reason t ! necessit\s conf9em5t ( its und]/&+ & int]pretative p[]s to fact-relations q effectively inhibits ! use ( ^! p[]s = ! contemplation ( ! deep] causative ag5cies :i* h op]at$ to produce ! ph5om5a4 ,b x is app>5t t j z ! transmut$ results ( o!r phases ( psy*og5esis are n[ be+ utiliz$ z a basis = ! effici5t op]ation ( ! intellect 9 ! s5su\s _w1 !reby enabl+ ! atta9m5t ( a v high ma/]y ov] matt]1 s w ! functional dynamism acquir$ by x 9 ! pursuit & compreh5sion ( div]sity s]ve well :51 9 lat] days1 x has acquir$ ! p[] to deal directly ) reality1 to create & dispose ( life j z ! kosmic intellect has & is n[ us+ x 9 ! execution ( ! inf9ite process ( becom+ ?r\gh :i* creation is proce$+4 ,x w\ld seem t ! necess>y pr]equisite to ! developm5t ( any high] functional capability is t ! intellect %\ld be capable ( dispos+ ( innum]able details1 inde$ ! totality ( kosmic detail1 be=e x c come :olly into ! p[] & capacity to und]/& & manipulate life4 ,fur!rmore1 x appe>s t ! acquirem5t ( ?is p[] q necess>ily has be5 delay$ await+ t "t :51 dom9at$ by ! intuition1 ! intellect %all h atta9$ ! requisite manag]ial ability = m>%al+ an exce$+ly l>ge numb] ( details4 ,! supreme t5d5cy ( life is expression4 ,& ?is expression1 s+ul>ly en\gh1 rea*es its mo/ p]fect ph5om5alization by means ( t movem5t :i* results 9 ! multiplication ( =ms4 ,despite ! fact1 !re=e1 t ! compreh5sion ( reality involves a gradual turn+ away f ! exclusive occupation ( organiz+ a multitude ( sep>ate & app>5tly unrelat$ facts to a moni/ic view :i* at once recognizes ! unit>9ess & co-orig9ality ( all ?+s1 ( life1 m9d & =m1 ! intellect w ne$ ! tra9+ & developm5t :i* come f ! ma/]y ( div]sity4 ,x is1 !n1 n difficult to p]ceive ! wise utilit>ianism ( ! pres5t s*ematism ( ?+s z %[n 9 ! univ]sal t5d5cy 9 ! intellect to devote itself exclusively to p>ts or segm5ts ( tru?4 ,:5ev] an individual intellectuality1 on acc\nt ( prolong$ ?\ght & ! consequ5t inurem5t ( ! m9d to high] & high] vibrations ( ! kosmic intellect1 br+s itself to su* a high po9t ( s5sitiv5ess t x c receive s mu* z an intimation ( "s great tru?1 x beg9s to s5se1 9 a m or less vague way1 some?+ ( ! sub/ance & g5]al t5d5ce ( ! und]ly+ reality ( t :i* =e%ad[s its appe>ance4 ,!n1 conf\nd$ by ! multi=mal *>act]i/ics ( kosmic tru? because ( ! fact t x pres5ts itself 9 su* num]\s ways & =ms1 m5 (t5 are induc$ to attempt ! re=mation ( all facts1 or a great mass ( k9dr$ facts1 9 accordance ) ! newly-f\nd fact or pr9ciple4 ,!y =get evid5tly t no fact 9 ! univ]se c be at v>iance ) any o!r fact & /ill be a fact4 ,s t 9 ! totality ( facts e sep>ate & di/9ct fact mu/ be congru5t ) e o!r fact =m+ a beautiful1 h>moni\s & symmetrical :ole2 b (t5 ! :ole is made to suff] 9 ! attempt at mak+ x con=m to ! sub/ance ( a m]e intimation4 ,moreov]1 x is conceivable t ev5 ! totality ( facts may lack a rigid con=mity ) reality 9 all its p>ts & t hav+ compass$ ! entire mass ( facts "o may fall %ort ( ! und]/&+ ( realism4 ,?is is practically :at has happ5$ 9 ! m9d ( ! metageometrician :o hav+ receiv$ an intimation z to ! real nature ( space z t ^: c5t] is ev]y:]e & yet n[h]e & ^: nature is psy*ological & vital r ?an ma!matical & logical1 misses ! great out/&+ facts & cl+s to ! intimations :i* he exp]i5ces z to ! nature ( space4 ,he1 !re=e1 concludes t ! =m ( space is t ( a flexure or curve4 ,!re is a valid elem5t 9 ! notion ( ! curvature ( space b n en\gh ( tru? :olly to validate ! notion4 ,s9ce ! v reality ( space is a matt] :i* c be det]m9$ only by ! con=mance ( ! consci\sness ) x 9 su* a mann] z to r5d] ! conception ( x entirely un9telligible to ! intellect except 9 s f> z x may be able to id5tify itself ) ! space-process1 !re is mu* room = ! s]i\s que/ion+ ( ! ma!matic conclusion ^u ! gr\nds ( its fragm5t>9ess if n entirely ^u ! basis ( its invalidity4 ,:]e=e x may be se5 t any se>* = ei!r ! c5t] or ! extreme out] limits :i* proce$s 9 a mann] con=mable to ! ext]nal indications ( ! intellectual ord] is va91 inde$4 ,al?\gh x is und\bt$ly true t ! atta9m5t ( a c5tral or fronti] position 9 space does n involve any l9eal progression :atsoev]1 ! same be+ atta9able1 n by progression nor by ov]com+ di/ances1 b by a subtle adju/m5t1 yea1 a sort ( atta*m5t ( ! consci\sness to ! ord] ( becom+ :i* b9ds ! appe>ance ( space1 :]ev] "o may be1 x is nev]!less difficult & pa9ful = ! intellect to grasp ! totality ( ?is tru? at "o sweep4 ,inde$1 x is n possible = x1 alone & unaid$ by ! intuition1 to grasp x at all4 ,h5ce1 ! ma!matician :o dep5ds entirely ^u ! deliv]ies ( ! intellect :i* con=m1 9 _! passage f ! conceptual to ! writt5 or spok5 ^w1 to all ! rigors ( ma!tic requirem5ts1 fails utt]ly 9 p]ceiv+ ! magnitude ( ?is conception & all its connotations2 he fails because 8 prejudices & ! wo( & w>p ( 8 intellectual habits prev5t 8 assum+ a sympa!tic attitude t[>d x & !reby preclud+ at ! />t any calm consid]ation ( x4 ,& n only is ?is true ( ! ma!matician b ( all ^? ^: endeavors are conf9$ to ! plane ( purely s5su\s & logical data4 ,x w\ld1 !re=e1 appe> t our entire attitude t[>ds ?+s spatial mu/ be *ang$ be=e we c ev5 beg9 to p]ceive ! reality :i* is really ! object ( all rese>*es 9 ?is doma94 ,b1 on ! surface1 !re is aft] all little diff]5ce betwe5 ! ultimate facts involv$ 9 ^! two totally diff]5t conceptions4 ,ma!matically speak+1 all progression ea/w>d w\ld t]m9ate at ! we/1 & vice v]sa2 & ! same w\ld be true reg>dless ( ! po9t f :i* progression might orig9ate4 ,always ! t]m9us w\ld be ! opposite ( ! />t+ po9t4 ,!n1 too1 x might be said t if we s\ght ! space-c5t] we %\ld arrive at ! circumf]5ce4 ,! difficulty ) ?is view is t !re is a v remote1 ?\gh important1 connection betwe5 x & ! tru? ( ! matt]4 ,b ! p>tiality ( ?is view1 & ! abs5ce ( ei!r exp]i5ce or intuition to intimate a m reasonable view1 s]ve effectively to buttress x z a hypo!sis acceptable to _m4 ,?us x is ev] m difficult to supplant a ne>-tru? ?an x is to ga9 cr$5ce = ! :ole tru?4 ,on ! o!r h&1 accord+ to ! view :i* we ma9ta9 "h1 x is q true t ! seek+ ( ! kosmic space-c5t] w reveal ! circumf]5ce2 t ! se>* = ! nadir w uncov] ! z5i?2 ! ea/ effloresces z ! we/1 & a nor?w>d j\rney w w9d up at ! s\?1 etc41 b 9 q a diff]5t mann] f t :i* ! ma!matician has 9 m9d :5 he po/ulates ! curvature ( space4 ,our view involves no space curvature nor any o!r spatial di/ortion4 ,x deals ) space z reality1 z a dynamic process1 a flux :i*1 l ! sea1 is cont9ually ca/+ itself ^u ! %ores ( *aos & fall+ back ^u itself only to be reca/ aga9/ ! rock-b\nd coa/ ( its *aotic limits4 ,n[1 t :i* falls back ^u itself & rolls 9 a recurr5t movem5t ^u its own surface is life :i*1 9 its recession is ! natural & kosmic limitations ( itself1 g5]ates matt] 9 all its v>i$ expressions4 ,space1 9 its ext5sity1 _c transc5d life2 = x is ! pa? :i* life makes 9 its out-com+1 its manife/ation4 ,( ! *aotic fr+e :i* circumscribes ! manife/$ univ]se x is absurd to say t x is vital or psy*ological 9 any s5se ( ^! t]ms4 ,= not)/&+ ! fact t out ( its v sub/ance are eng5d]$ life1 intellectuality1 spatiality & mat]iality1 x is nev]!less none ( ^! 9 its prim>y ess5ce4 ,x is ,*aos-,kosmos2 because f its cont5t ! kosmos is evolv$1 & x /ill rema9s2 x is *aos-spatiality2 *aos-mat]iality2 *aos-intellectuality2 *aos-geometricity2 because ^! are eng5d]$ by ! movem5t ( life 9 *aos :ile at ! same "t !re rema9s a residuum ( ! *aog5etic sub/ance :i* con/itutes ! limitations ( all ^! subsequ5t processes4 ,9 ?is s5se1 ! *aog5etic fr+e becomes ! limits ( ! manife/$ univ]se s t x w\ld appe> t all ^? major processes outl9$ above are f9ite manife/ations ( ! et]nal *aos4 ,b none ( ^? possibilities ( motion :i* are f\nd 9 ^! major movem5ts ( ! kosmos c be logically said to exi/ 9 *aos4 ,x is ! embodim5t ( ev]y?+ t is ! opposite ( ^? qualities :i* may be f\nd 9 !m1 t is1 9 mat]iality1 vitality1 spatiality1 intellectuality & geometricity4 ,apropos to ?is phase ( ! discussion let u exam9e briefly "o ( its mo/ significant implications1 bo? ma!matical & kosmic1 :i* arises out ( ! fact t space is an eng5d]$ product ( life t is b\nd by ! fr+e ( *aos :i* su/a9s & limits x4 ,! *aotic fr+e plus manife/+ kosmos con/itute ! absolute magnitude ( ! kosmos4 ,! manife/ation factor is complem5t$ by ! *aos factor & toge!r ! two def9e ! full univ]se4 ,kosmogony is ! univ]sal movem5t ( all kosmic elem5ts or factors 9 dim9i%+ ! *aotic complem5t & r$uc+ x to kosmic ord] or geometrism4 ,x is und\bt$ly impossible to det]m9e ma!matically ! exact volume ( ei!r complem5t or ! ratio ( ! "o to ! o!r2 yet x is conceivable t ! *aotic fr+e is great] 9 ext5t ?an ! ord]$ portion ( ! kosmic uni-circle or univ]se4 ,x is ev5 conceivable t ! diff]5ce1 ^u ! basis ( ! mean+ ( ! ,py?agorean ,tetragrammaton & ! view outl9$ 9 ! ,*apt] on ! ,my/]y ( ,space1 is z sev5 to ?ree :]efrom ! conclusion might be drawn t ! univ]se has yet sev5 complete /ages m or less ( evolution be=e ! close ( ! ,great ,cycle ( ,manife/ation :5 ! fr+e ( *aos %all h be5 totally us$ up 9 ! "w ( creation4 ,b = ^? :o may exp]i5ce impati5ce at ! inf9itude ( ! process :5 view$ 9 ?is light ! t]ms may be rev]s$ & ! diff]5ce may be conceiv$ z ! ratio ( ?ree to sev5 :]efrom ! conclusion w\ld foll[ t ! kosmogonic process is sev5-t5?s complete1 z x w n v>y ! seem+ inf9itude ei!r way x may be det]m9$4 ,! notion1 despite its speculative "*1 (f]s an explanation ( o!rwise inexplicable conditions1 &1 on acc\nt ( its pr(\nd connotations1 may ev5 be f\nd to be productive ( ! highe/ good 9 its equilibrat+ influ5ce ^u our mode ( ?9k+4 ,9 any ev5t1 !re does appe> to be a subtle relation subsi/+ betwe5 true numb]s & kosmogony4 ,numb] is a phase ( ! kosmogonic movem5t1 a measur] ( ! intellect & ! e/abli%] ( ! geometrism ( space1 answ]+ t5tatively to ! num]icity ( pure be+4 ,9 fact1 be+ actually expresses numb] & numb] itself is an evolution & n a ?+ posit$ once = all z a pure1 inv>iable =m 9 ! univ]se4 ,x is1 l ! kosmos1 9 a /ate ( becom+ & !re may yet appe> to our cognitive p[]s a :ole s]ies ( new numb]s pure 9 itself & altoge!r con=mable to ! conditions reign+ at ! "t4 ,! symbology ( ! circle1 9 all times recogniz$ z ! true symbol ( ! kosmos 9 et]nity1 ( et]nity itself1 ( ! ar*etypal1 ( space1 duration & ,ultimate ,p]fection1 is replete ) pr(\nd significations4 ,b x %\ld be und]/ood t ! circle is a symbol ( ! p]fect$ univ]se & n ! univ]se 9 a /ate ( evolution4 ,x symbolizes p]fection1 completion & ! ultimate union ( ! manife/+ ) ! ar*etypal :i* results 9 ! cr[n+ de$ ( ,p]fection4 ,! circle is1 !re=e1 n a symbol ( ! univ]se z x n[ /&s2 x does n repres5t a snap%ot view ( ! kosmos b ! univ]se z a full4 ,x _c be a full until x has atta9$ ! ne plus ultra ( completion2 = a kosmic full is t /ate to be atta9$ by ! manife/$ kosmos ^u ! t]m9ation ( all ! fundam5tal processes n[ 9 op]ation4 ,b x is ?is /ate t ! circle really repres5ts1 & by virtue ( :i* x possesses its intr9sic qualities & also 9 virtue ( :i* ! intellect recognizes ^! qualities4 ,! prop]ties ( und]/&+ & recognizance 9 ! intellect are v]itably fix$ by ! /atus quo ( ! univ]se dur+ e /age4 ,t is1 ! focus ( ! intellect1 l ! focus ( a *romatic l5s1 is adju/$ by ! fiat ( ! nature & et]nal fitness ( ?+s to correspond exactly ) e /ate ?r\gh :i* ! kosmos itself passes4 ,?is is "o ( ! obvi\s implications ( ! phan]obiog5ic behavior ( ! kosmos & is necess>ily resid5t 9 ! notion ( ! g5esis ( space & intellectuality z consub/antial & cord9ate factors4 ,:]e=e ! m cog5t is ! reason = ! belief t ! inh]5t qualities ( ! kosmogonic fundam5tals2 z1 vitality1 mat]iality1 spatiality1 intellectuality & geometricity1 are true v>iants1 & t _! v>iability is proportional to ! progress ( ^! major movem5ts t[>d ! ultimate satisfaction ( ! orig9al creative impulse4 ,may x n be1 !re=e1 t ! indet]m9ate "* ( ! ratio ( ! diamet] to ! circumf]5ce 7#c4adaeibf44471 is due to causes f> m pr(\nd ?an ! crudity ( our micromet]s or ! m]e suppos$ fact ( ! circle's peculi>ity8 ,may x n also be true t ! pi proportion %all become a :ole numb]1 & 9 its integration1 keep apace ) ! p]fect+ process ( ! kosmos1 dim9i%+1 by retrogression to "o or increas+1 by progression1 to t5 :i*1 aft] all1 is ess5tially unity1 be+ ! p]fect num]al8 ,x is n )\t ! utmo/ assurance t ^! qu]ies w be categorically que/ion$ by ! or?odox1 cre$-loyal1 /rictly intellectual type t we sket* ^! implications1 b x is felt to be an urg5t duty to rem9d all su* t ! mo/ effective b>ri] to realization 9 ! field ( philosophy is an intol]ant attitude t[>ds all l9es ( ?\ght :i* sugge/ ! imp]man5ce ( conditions z we f9d !m 9 ! kosmos at ! pres5t "t4 ,! fact is t our lives are s di/ress+ly %ort t we h nei!r "t nor opportunity to wat* ! *ang+ moods ( ! kosmos nor disc]n ! gradual r$uction ( m]e appe>ance to ! firm basis ( reality1 & accord+ly1 ! intellect t5aci\sly cl+s to ^? notions :i* x d]ives f ! in/ant-exposure :i* ! l5s ( intellectual conceivability allots to x4 ,once ! view is tak5 x is imm$iately inve/$ ) ev]la/+ness4 ,?is ev]la/+ness is !n imput$ to ! kosmos 9 t p>ticul> pose1 attitude or /ate4 ,always ! intellect beholds 9 t pass+ view1 snat*$ f ! fleet+ panorama ( et]nal duration1 a picture ( itself :i* x mi/akes = ! reality ( ! n-self4 ,! incl9ation ( ! axis ( ! e>? t[>d ! plane ( its orbit is approximately tw5ty-?ree & "o-half degrees4 ,no well-in=m$ a/ronom]1 h[ev]1 d\bts n[ ! fact t ?is ecliptic angle is be+ gradually less5$2 because1 z a result ( c5turies ( obs]vation1 x has be5 f\nd to be decreas+ at ! rate ( ab\t #df4c seconds p] c5tury4 ,yet no intellect is able to p]ceive 9 any giv5 lifetime ! actual decrem5t ( ?is angle4 ,x is only by c>eful measurem5ts aft] c5turies ( wait+ t a diff]5ce c be discov]$ at all4 ,?us x may ev5 be s ) ! ratio ( ! diamet] to ! circumf]5ce ( a circle1 ! only diff]5ce be+ t x has n yet be5 det]m9$ :e!r !re is a decrem5t or an increase 9 ! size ( ! ratio4 ,! pi proportion is1 !n1 a regi/] or measur] ( ! sl[1 measur$ approa* ( ! manife/+ kosmos to ! /&>d ( ultimate p]fection4 ,!re=e1 & 9 view ( ^! consid]ations1 we may n hesitate to confirm our belief 9 ! validity ( ! notion t x actually & lit]ally expresses ! key to ! evolution>y /atus ( kosmogony4 ,! ma!matical det]m9ation :i* limits x z an un*angeable1 inela/ic quantity is1 consequ5tly1 only p>tially true & leads to ! inclusion ( ?is quantity "u ! category ( ma!matical ne>-tru?s1 = su* x appe>s to be 9 spite ( its rigor\s e/abli%m5t4 ,! =mal topography into :i* ! intellect spreads :5 seek+ ! ideal & ! ab/ract is n a condition :i* is d]ivable f ! real ess5ce ( life or matt]1 b1 on ! o!r h&1 is a product ( ! intellect itself p>tak+ ( its nature r ?an ( ! nature ( reality4 ,!re is1 !re=e1 a v important di/9ction to be made betwe5 all deliv]ies ( ! intellect & ! realism bo? ( ! objects & conditions to :i* ! intellectual deliv]ies p]ta94 ,"o ( ! mo/ m>k$ peculi>ities ( ! human intellect is ! fact t x always unavoidably /amps its own nature & features ^u e datum :i* passes ?r\gh x to ! consci\sness4 ,! utmo/ importance atta*es to ?is ph5om5on1 = ! reason t x po9ts to ! necessity ( c>efully scrut9iz+ intellectual deliv]ies & ! mak+ ( all[ances = ^? ev]-pres5t *>act]i/ics :i* ! intellect sup]imposes ^u its data4 ,p]haps ! inh]5t colorific quality :i* x imposes ^u our k w\ld be bett] und]/ood if a similitude 7 indulg$ at ?is juncture4 ,! intellect may be lik5$ to a color-be>+ in/rum5t :i*1 :5 x has once h&l$ an object1 leaves =ev] its own color transfus$ into e cell & fib] ( ! object s t :5 ! same object is pres5t$ to ! consci\sness = purposes ( cognition x be>s always ! same peculi> m>ks & colorations :i* ! intellect1 9 its manipulation ( x1 places !reon4 ,9 ?is respect ! intellect may also be said to be l a pott] :o has b "o mold & t ( a peculi> =mation4 ,h5ce1 :atev] w>es x pres5ts to ! consci\sness w inv>iably be f\nd to be mold$ 9 con=mity ) t p>ticul> mold4 ,if x 7 possible to view reality or ! ess5tial nature ( ?+s ! difficulty :i* n[ ! intellect lays 9 ! pa? ( direct & uncolor$ cognition w\ld be obviat$2 = !n !re no long] w\ld be any necessity ( view+ ?+s z !y are color$ or mold$ by ! intellect4 ,! intuition1 be+ a process ( pure consci\sness1 w1 :5 x has aris5 to a position :]e x may dom9ate ! intellect z ! intellect n[ dom9ates x1 s modify ?is t5d5cy :i* we see s in]adicably b\nd up 9 ! v nature ( ! intellect t ! app>5tly insurm\ntable difficulties :i* x has int]pos$ betwe5 m]e p]ception & a direct cognitive op]ation w be q completely ov]come4 ,?us1 9 ! above1 is discov]$ ano!r ob/acle :i* posits itself betwe5 ! notion ( space z reality & ! intellectual det]m9ation ( x :i* ! ma!matician exam9es & to :i* 8 consci\sness is necess>ily limit$4 ,fur!rmore1 x may be p]ceiv$ also h[ easily ! m9d may be delud$ into ?9k+ t ! intellectual notion :i* x ent]ta9s ( space is necess>ily correct1 :5 obv]sely1 x is simply exam9+ a concept :i* has be5 remade by ! intellect into a =m :i* is n at all unlike its own peculi> nature1 & !re=e1 z mu* %ort ( reality z ! intellect itself is4 ,simil>ly1 if ! ma!matical m9d succe$ 9 cat*+ a glimpse ( ! reality ( space 9 ! =m ( an intimation1 :i*1 9 itself ?\gh fragm5t>y1 is nev]!less true1 its consci\sness is f9ally depriv$ ( ! true validity !re( simply because ( ! behavior ( ! intellect 9 its manipulation ( x4 ,! importance ( ^! intellectual difficulties _c be ov]-e/imat$ = !y furni% ! gr\nds = ! ineptitude ( intellectual det]m9ations made 9 a sph]e ( motility to :i* ! intellect is a /rang]4 ,& ?is fact w appe> m evid5t :5 x is p]ceiv$ t q ! entire cont5t ( human k has be5 ?or\ghly vitiat$ by !m4 ,s t only 9 ^? v r>e mom5ts :i* 79 a highly s5sitive m5tality7 enable ! intuition to ga9 a mom5t>y asc5dancy ov] ! intellect is x possible = ! ,?9k] to cat* hold ( realism itself1 & project ! tru? ( :at he sees into ! l[]1 intellectual consci\sness4 ,b s small is t portion ( our k :i* owes its orig9 to ! intuition t :5 comp>$ ) ! totality ( t :i* we seem to und]/& x is well-nigh negligible4 ,& !n1 :5 x is consid]$ t at pres5t !re is no way ( conceptualiz+ adequately ! intuitograph s z to make x propagable ! insignificance ( ?is =m ( k is ev5 m notable4 ,x c n[ be se5 9 h[ l>ge a measure ! notion ( ! curvature ( space is m]ely an intellectual translation ( a true intuition into ! t]ms ( ! intellect :i*1 9 ! v nature ( ! case1 c only approximate ! tru? because ( its colorific habits4 ,a simil> decl>ation may be made ( t o!r datum ( metageometrical k :i* po/ulates ! ultimate conv]g5ce ( p>allel l9es4 ,9 fact1 :at has be5 said z to ! p]isophical nature ( ! notion ( space-curvature w apply ) equal =ce to ! idea ( p>allel conv]g5ce s9ce ! latt] is a d]ivative ( ! =m]4 ,b !re is yet ano!r consid]ation1 ap>t f ! colorific influ5ce ( ! intellect1 :i*1 al?\gh x p>takes ( ! nature ( ?is quality1 is nev]!less a ne>-tru? ( q a diff]5t ord]4 ,?is may be bett] und]/ood by ref]r+ to ! graph %[+ ! inv]se ratio ( objective space to ! consci\sness4#bh ,let u suppose t ! graph may also repres5t ! ,?9k]'s outlook into ! _w ( spatiality4 ,x !n appe>s t1 because ( t movem5t ( consci\sness 9 its pursuit ( life :i*1 z x exp&s1 makes ! objective _w to appe> to be dim9i%$ 9 proportion to ! ext5t ( its expansion1 x is q natural1 "u su* circum/ances1 t p>allel l9es drawn any:]e 9 ! limits ( ! objective _w %\ld seem to come to a po9t 9 ! ultimate ext5sion ( !mselves4 ,:ile ?is graph is n meant to depict su* a view1 x may be f\nd nev]!less1 to be a true del9eation ( ! topography ( t /ate ( m9d into :i* ! metageometrician br+s himself :5 he visualizes space z curv$2 = !re is no d\bt b t a /ate ( intellectual ec/asy1 su* z t 9 :i* ! m9d ( ! metageometrician mu/ be function+ 9 ord] to p]ceive space 9 t =m1 is q diff]5t f ! normal &1 !re=e1 9 ne$ ( a diff]5t topographical survey4 ,b1 if we grant t 9 ! creational aspects ( space !re is conceivable an ev]-pres5t t5d5cy to convolution1 or a roll+ back ^u itself1 x is imag9able t p>allel l9es inscrib$ ei!r ^u its surface or 9 its texture ne$ n necess>ily meet b ma9ta9 _! p>allelism reg>dless ( ! complexity ( ! convolutions4 ,! conv]g5ce ( p>allel l9es is mu* l a tang5t 9 ! outgr[? ( ! idea f ! notion ( space-curvature4 ,! m a tang5tial l9e is ext5d$ ! f>!r away f ! circumf]5ce x becomes & consequ5tly less 9 agreem5t !re)4 ,! m subsidi>y propositions or coroll>ies are multipli$ ! m remote f ! tru? ! det]m9ations become & especially is ?is true ( ! hypo!sis ( space curvature4 #bh ,figure #bj4 ,9 ! notion ( ! manifoldness ( space1 by virtue ( :i* x is conceiv$ z exi/+ 9 a s]ies ( sup]imposable & g5]able manifolds ( v>y+ degrees ( complexity1 are disc]nible traces ( t intuitional intimation :i* und]lies ! ass]tion t because ( ! necess>y ph5om5alization ( reality = ! purpose ( manife/ation to ! intellect x appe>s to exi/ 9 a s]ies ( sep>ate degrees1 ea* "o m ref9$ & subtle ?an ! prec$+ "o & requir+ a m highly develop$ species ( consci\sness = its compreh5sion4 ,9 o!r words1 t intuitional glimpse ( ! ess5tial "* ( reality1 z view$ by ! human consci\sness1 :i* imp+$ ^u ! m9ds ( ,,riemann & ,,beltrami lead+ !m to po/ulate z a coroll>y proposition to space-curvature1 its manifoldness1 is no?+ m nor less ?an ! intuition t ! univ]sum ( spatiality _c o!rwise pres5t itself to ! intellect1 ow+ to its peculi> adaptation to ! s5su\s1 except by a s]ies ( cont9u\s degrees :i* are p]ceptible only 9 proportion z ! und]/&+ is magnifi$ to con=m ) x4 ,aft] all1 h[ev]1 x is n improbable t ! v objectivism ( ! univ]se 9 manife/ation subsi/s 9 j ! mann] 9 :i* ?is intuitive glimpse implies & t ! wisdom & utilit>9ess ( ! kosmogonic process :i* eng5d]$ spatiality are cle>ly demon/rat$ 9 t arrangem5t ( ! cont5ts ( ! kosmos :i* pres5ts ! grosse/ elem5ts ( ph5om5a fir/ to ! intellect 9 its mo/ impot5t /ate :ile res]v+ ! less crass = t "t :5 ! ,?9k] %all h evolv$ a cognitive organ adaptable to its pres5tations4 ,^? metageometricians :o cl+ to ! idea ( ! manifoldness ( space1 bas$ z we h %[n ^u ! pseudo-int]pretation ( a r vague h9t aris+ out ( an unque/ionably true intuition1 h all[$ !mselves to fall into ! unconsci\s error ( magnify+ ! importance ( ! m]e ins9uation z to ! space-nature to su* an ext5t z :olly to obscure 9 _! own m9ds & 9 ! m9ds ( ^? :o ?9k aft] !m :atev] ( ! true vision t may h be5 grasp$ by !m4 ,fur!rmore1 x is indubitably true t t same peculi>ity ( arrangem5t by :i* impalpable & invisible =ces really subt5d gross matt] produc+ t subtle s*ematism 9 virtue ( :i* ! visible is subjo9$ to ! invisible1 ! s5su\s to ! non-s5su\s1 _s to matt]1 etc41 also *>act]izes ! appe>ance ( spatiality to ! human und]/&+4 ,:ile !re is a sup]ficial semblance ( sep>ate & discrete manifolds into :i* space may be divid$ !re are1 9 reality1 no su* %>p l9es ( dem>kation betwe5 ! subtle & ! gross1 betwe5 ! visible & ! invisible or betwe5 _s & matt]1 ea* ( ^! be+ capable ( r$uction1 by ins5sible degrees1 into ! o!r reg>dless z to :e!r ! r$uctional process orig9ates on ! side ( ! mo/ ref9$ or on t ( ! grosse/4 ,accord+ly1 !re are no reasonable gr\nds ^u :i* ! notion ( a space-manifold may be ju/ifi$ except z a metageometrical ne>-tru?4 ,9 addition to ! =ego+1 !re are yet o!r v fundam5tal consid]ations :i* w\ld seem to deb> ! totality ( analytical conclusions z to ! nature ( space f any claim to ultimate reliability & tru/wor?9ess4 ,^! are fir/3 ! fact t analyses are absolutely incapable ( deal+ ) life2 t be+ ! direct product ( a sort ( me*anical consi/5cy :i* m>ks ! intellectual op]ations x has adaptability only = deal+ ) fragm5ts or disconnect$ p>ts1 & t )\t any ref]5ce :atsoev] to ! curr5t ( life or ! fl[ ( reality :i* has produc$ ! p>ts4 ,?is fact is cle>ly %[n 9 t attitude ( ! und]/&+ :i* inevitably leads x to ! decl>ation t a l9e is an inf9ite s]ies ( po9ts1 a plane an inf9ite s]ies ( l9es1 & a cube1 an inf9ite s]ies ( planes1 & s on1 indef9itely4 ,to d ?is1 to look ^u all ph5om5a z a s]ies ( p>ts simil> to ea* o!r & pil$1 "o ^u ! o!r1 or juxtapos$ 9 ! mann] :i* !y are discov]$ 9 ! s5sible _w1 is ! natural t5d5cy ( ! intellect & ?is t5d5cy f9ds its mo/ facile expression 9 analytics4 ,inadaptability ( ?is sort is especially obs]vable 9 all problems ( ari?metical analysis 9 :i* ! vital elem5t is a factor4 ,:5 ^! analyses are c>ri$ to _! logical conclusion1 z has be5 %[n 9 ! *apt] on ,! ,f\r? ,dim5sion1 inv>iably !y end 9 an evid5t absurdity4 ,b x is at _! v conclusion :]e ! life-elem5t is enc\nt]$1 :]e reality is approa*$1 t !y break d[n4 ,! failure ( analysis1 !n1 to encompass life1 to fit into its requirem5ts & to satisfy its natural outcome seems cle>ly to e/abli% ! basis ( ! p]isophical nature ( ! entirety ( analytical claims1 especially t species ( analysis :i* seeks ! remot] fields ( ! conceptual = its det]m9ations4 ,second3 ! close connection :i* has be5 se5 to subsi/ betwe5 space & life z jo9t products ( ! same movem5t makes x obvi\s t ! same ultimate rule ( int]pretation mu/ be appli$ to bo? 9 ord] to insure correct & dep5dable judgm5ts reg>d+ !m4 ,h[ diff]5t w\ld be ! intellectual attitude t[>ds space if x 7 consid]$ 9 ! same light z vitality1 provid$ "o really und]/ood any?+ ab\t vitality6 ,moreov]1 z x appe>s c]ta9 t ! pa? ( ! intellect does n run 9 ! same direction z ! pa? :i* life makes1 b 9 an inv]se direction1 x is cle> t ! judgm5ts ( ! =m]1 z to ! action & ess5ce ( ! latt]1 mu/ necess>ily be ultimately unreliable4 ,x c readily be se51 h[ev]1 t %\ld ! intellect be focus$ s z to foll[ ! pa? ( life1 to atta* itself to ! v /ream ( life1 x w\ld h necess>ily to neglect mat]iality4 ,& su* an adju/m5t w\ld1 ( c\rse1 obviate ! ne$ ( a mat]ial life at all = humanity4 ,9 fact1 a physical life ) an intellect w\ld be impossible "u su* conditions4 ,x is well to recognize ! suitability ( ! pres5t s*ematism & n to become unwisely re/ive because ( x2 b x is also fitt+ t we %\ld discrim9ate betwe5 t :i* is possible = ! intellect *a9$ to mat]iality & t :i* is impossible = x1 9 su* a /ate1 :5 =ay+ 9 a t]ritory =eign to its nature1 & beyond its p[]s to ma/]4 ,! pr$om9at+ t5d5cy 9 ! intellect to acc\nt = ! univ]se ( life1 m9d & matt] ^u a /rictly me*anical basis is und\bt$ly due to ! con/itution ( ! intellect :i* does n admit ( its direct consid]ation ( ! vital ess5ce ( ?+s4 ,we are b\nd ineluctably to ! surface ( ?+s4 ,all our k is !re=e sup]ficial4 ,we are ev5 b\nd to ! surface ( ideas1 & _c p5etrate to ! int]ior ( ^! realities4 ,our art is ! reproductions ( sup]fices2 our philosophies are ! husks ( et]nalities2 our religions1 ! habilim5ts ( relations1 & :ile x _c be d\bt$ t ?is arrangem5t is pre-em95tly ! be/ possible "o = ! pres5t /age ( man's evolution1 x is nev]!less wor? :ile to note t x is ?is v re/rict$ activity ( ! intellect :i* %uts out f man's consci\sness ^? v elem5ts ab\t :i* he is mo/ conc]n$ :5 he goes into ! field ( philosophy 9 se>* ( a solution to 8 unansw]able qu]ies4 ,b "s progress mo/ surely is made :5 ! m9d is enabl$ to see its plight & recognize :at are ! difficulties & limitations t lie 9 its pa? ( ultimate atta9m5t4 ,x is believ$ t ! me*ani/ic1 or true1 "* ( ! intellect rea*$ its z5i? 9 ! m9d ( ,,lagrange :5 he succe$$ 9 r$uc+ ! entirety ( physics to c]ta9 me*anical laws & =mul :i* he embodi$ 9 8 ,mecanique ,analytique ,?is "w is und\bt$ly ! cap/one ( intellectual endeavors & /&s z a monum5t :i* m>ks ! culm9ation ( ! pres5t /age ( intellectual developm5t4 ,9 ?us plac+ ! ,mecanique at ! apex ( intellectual endeavors x is n !reby meant to be impli$ t ! intellect %all n make m progress nor t o!r =mul1 equally z m>vel\s z ^? :i* ,,lagrange discov]$1 may be devis$1 nor t o!r laws1 h]et(ore undream$ (1 may be f\nd2 b :at is ma9ta9$ is ! fact t :ile !re w be gr[? & developm5t ^! w run along o!r *annels1 p]haps 9 ! realm ( ! intuitable1 & n any long]1 especially s notably z n[1 9 an opposite direction aga9/ ! curr5t ( life & reality2 & fur!r1 t !re w be a gradual turn+ away f me*anics to biog5etics1 f div]sity to unity1 f ! purely intellectual to ! intuitional1 & )al a f9al gett+ rid ( ! bonds ( illusion1 ( t ?ralldom ( me*anics1 :]eupon w sl[ly arise ! obsolesc5ce ( all ^? disp>ities :i* may n[ be recogniz$ 9 our k & 9 ! applications ( ! intellect to ! data ( ! objective _w4 ,because ! intellect is unsuit$ to deal ) reality1 & because ( its peculi> adaptation = div]sity1 = multiplicity1 due to its me*ani/ic modus viv5di1 !re has gr[n up a volum9\s catalogue ( sy/ems ( philosophy4 ,^! embody su* a multitud9\s array ( beliefs1 ideas1 conceptions1 !ories & conjectures & con/itute a movem5t 9 human ?\ght :i* oscillates betwe5 ! empirici/ on ! "o h& & ! transc5d5tali/ on ! o!r2 betwe5 ! ideali/ & ! reali/1 lean+ sometimes t[>ds ! ,platonic1 ! ,c>tesian & ! ,kantian & at o!r times t[>ds ,,sp9oza1 ,,ari/otle1 ,,sp5c] & ,,socrates1 always t]m9at+ by multiply+ ! numb] ( div]se beliefs r ?an unify+ !m t ! conclusion is unavoidable t s m>k$ a lack ( unanimity is indicative ( a pr(\nd m5tal pre/riction4 ,x 01 !re=e1 inevitable t ma!matics %\ld fall "u ! same spell & brook no let nor h9drance until x _h succe$$ 9 devis+ sev]al div]se sy/ems ( geometry :i* x has done = ! m]e joy ( do+ some?+1 ( foll[+ its in/9ctive aptitudes4 ,!re is no o!r basis = ! het]og5eity ( our philosophies1 our ma!matics1 inde$ our beliefs ?an ?is me*anical1 & h5ce1 radically illusion>y "* ( ! intellect 9 consequ5ce ( :i* we h _h to be satisfi$ ) m]e glimpses1 h9ts1 intimations & fa9t glimm]+s ( reality1 ( life1 & ( ^? kosmic movem5ts :i*1 if we _h ! ability to trace !m f _! s\rce outw>d1 w\ld lead u un]r+ly to a tru] & deep] k ( ^? ?+s t "u ! pres5t s*ematism mu/ rema9 = u a clos$ book4 ,! crit]ion ( tru? = u1 con/itut$ z we are & w$g$ 9 betwe5 ! /ream ( life & its %ore ( mat]iality1 mu/ be t :i* relates our k bo? to ! /ream & to ! %ore4 ,x mu/ be s t all pr$icates :i* purport to approa* x %all exhibit a dual ref]5ce--"o t relates to mat]iality & ano!r t relates to vitality1 & yet a ?ird t %all comb9e ^! two relations into "o4 ,all ass]tions1 !re=e1 :i* p]ta9 exclusively to ei!r ( ^! elem5ts--to mat]iality or to life--are necess>ily p>tial1 fragm5t>y & p]isophical 9 nature4 ,ma!matics1 because x relates to matt] & ! me*anical =ces set up by matt] act+ aga9/ matt] _c be said to agree ) su* a crit]ion2 art1 because x relates to snap%ots or /atic views ( matt] is ev5 m remote 9 its agreem5t2 philosophy1 z x has be5 kn[n 9 ! pa/ & is kn[n to-day1 because x seeks to deal ) a vitality fa%ion$ aft] ! image ( mat]iality has fail$ :5 posit$ alongside ( ?is crit]ion2 & ?us1 ! intellectual toil ( millions ( ye>s has be5 9 va9 9 s f> z x has n succe$$ ev5 9 rais+ a corn] ( ! cov] :i* hides reality f our view4 ,a ne>-tru? is any v>iation f ?is /&>d1 ?is norm or crit]ion4 ,x may be ei!r logical1 cognitive1 sci5tific or ev5 metaphysical4 ,to def9e3 a logical tru? is a pr$icate bas$ ^u & involv+ ! coh]5cy & consi/5cy ( ?\ghts !mselves2 a cognitive tru? is ! con=mity ( k ) s mu* ( reality z is kn[n2 sci5tific tru? is ! con=mity ( ?\ghts to ?+s & conditions4 ,all ( ^! are obvi\sly ne>-tru?s4 ,!n1 too1 a ne>-tru? may be def9$ z an ass]tion bas$ ^u ! crit]ion ( tru? b fall+ )9 ! category ( cognitive tru?s ow+ to insuffici5cy ( data or vision4 ,su* inde$ are ^? metageometrical pr$icates--n-dim5sionality1 space-flexure1 space-manifoldness & all o!r ass]tions bas$ ^u ^! 9 g5]al & specifically4 ,any recognition ( tru? mu/ cle>ly embrace bo? ! vital & mat]ial aspects ( its subject 9 ord] to be adequately inclusive1 t is1 x %\ld include ! causative1 ! su/5tative1 ! relational & ! developm5tal factors4 ,^! f\r factors are consid]$ necess>y & suffici5t to det]m9e ! con=mity ( any view to ! crit]ion ( tru? = :5 we are cognizant ( ! cause ( a subject1 und]/& ! su/5tative factors :i* keep x 9 exi/5ce1 are conv]sant ) its relations to o!r subjects & c foll[ its developm5tal v>iations until we come to its f9al /atus1 :y !n1 our k is bo? suffici5t & ultimate s f> z t subject is conc]n$4 ,is x ask+ too mu* ( ma!matics or ( philosophy or any sy/em ( ?\ght t x con=m to ^! /&>ds or to ?is crit]ion be=e we %all accept x z f9al8 ,or %all we be satisfi$ ) less ?an ?is8 ,let u hope n4 ,9 ! =ego+ pres5tation /ress has be5 plac$ ^u ! fragm5t>y1 & !re=e1 illusion>y "* ( ! intellect 9 ord] to arrive at an und]/&+ ( ! difficulties "u :i* real k has to be acquir$ & to indicate ! inanity ( all attempts to resolve ! riddle ( space by means ( ma!matics ?\gh reg>d$ z ! mo/ typical exemplification ( ! me*ani/ic nature ( ! intellect4 ,& fur!r1 to %[ t1 on acc\nt ( ! radical incongruity :i* e/ranges life1 ! produc] ( spatiality1 f ! intellect :i* returns aga9 to scrut9ize ! passage ( life 9 its outw>d expressions1 no hope ( ev] ga9+ ! true viewpo9t by means ( ! intellect ne$ be ent]ta9$4 ,b 9 do+ s1 x is deem$ fitt+ t a note ( w>n+ %\ld be s\nd$ aga9/ any abortive attempts t may be made to obscure or di/ort ! results ( su* a close discrim9ation le/ ! true import ( ! exam9ation be lo/ =1 if we emphasize ! vanity ( ! intellect 9 ! pursuit ( t :i* x is by nature unsuit$ to atta9 we also equally /ress ! wise utilit>ianism :i* limits x to ! p]=mance ( ! tasks assign$ :ile at ! same "t res]v+ = ! function ( m highly evolv$ p[]s1 & inde$1 = ! intuition itself1 ! solution ( ! riddle ( spatiality4 ,& if we decl>e ! futility ( ! ma!matical me?od 9 all endeavors aim$ at unveil+ ! my/]ies ( life & m9d1 & ( t movem5t :i* has its roots set 9 et]nal duration f :i* x proce$s 9 an endless cont9uity ( purpose & promise1 we d also recognize t 9 ! sci5ce ( ma!matics ! intellect %all1 z 9 no o!r me?od ( cognition1 mo/ fully fulfill ! kosmic int5t ( its exi/5ce2 & moreov]1 9 ! pursuit !re( x %all pu% ! fronti]s ( its possibilities outw>d until x c be said almo/ to be able to make disposition ( life itself--at lea/ to t po9t :]e1 :5 ! intuition %all h come into its own1 ! passage f ! me*anics ( matt] to ! dynamics ( life1 %all be comp>atively easy & natural4 ,,*apt] ,x ,,! ,,m$ia ,,( ,,new ,,p]ceptive ,,faculties ,! ,spiritualization ( ,matt] ! ,end ( ,evolution--,sequ5ce & ,design 9 ! ,evolution ( ,human ,faculties--,! ,upspr++ ,intuition--,evid5ces ( ,sup]normal ,p[]s ( ,p]ception & ! ,possibility ( ,atta9m5t--,! ,influ5ce & ,place ( ! ,pituit>y ,body & ! ,p9eal ,gl& 9 ! ,evolution ( ,additional ,faculties--,! ,skeptical ,attitude ( ,empirical ,sci5ce & ! ,ne$ = a ,m ,lib]al ,po/ure--,! ,g5]al ,results ( ,pituit>ial ,awak5+ ,^u ,man & ! ,!ory ( ,k4 ,evolution is a cont9u\s process & ! primal impetus back ( ! great on-fl[+ ocean ( life acts inf9itively4 ,x is n t]m9at$ :5 life has succe$$ 9 p]fect+ a =m = ! p]fection ( =ms 9 !mselves is n ! end ( vital activity4 ,! end ( evolution is ! complete spiritualization ( matt]4 ,s t x does n matt] h[ p]fect a =m may be ei!r subjectively or 9 its adaptation to environm5ts2 x does n matt] h[ faultless a m$ium = ! ens\l+ life x may be1 !re is ev] ! et]nal necessity t life mu/ drive x back ov] ! pa? ( its g5esis until x %all be transmut$ into pure _s4 ,adaptation succe$s adaptation & ) ea* !re is a *ange 9 ! =m & ?is process cont9ues until !re is a m or less p]fect congru5ce betwe5 =m & juxtapos$ environm5tal conditions4 ,b no soon] ?an agreem5t has be5 atta9$ "u "o set ( conditions new conditions arise & require a new sett+1 new adaptative movem5ts4 ,?us !re is a cont9u\s proce$+ f /age to /age1 go+ f ! grosse/ to ! subtle/ & mo/ ref9$1 always ! =m is be+ pu%$ onw>d & upw>d by life4 ,b adaptation is n und]gone = ! b5efit ( ! =m1 b m truly = ! in=m+ pr9ciple4 ,x is ! progression ( ! life-elem5t :i* con/itutes ! adaptation ( =m to =m & to _! peculi> environs4 ,! =m is a tool or in/rum5t ( life :i* x disc>ds ! mom5t x fails to respond to its requirem5ts4 ,?us =ms are con/antly be+ assum$ & z con/antly be+ rel9qui%$4 ,b no ef=t ( life is lo/ reg>dless z to :e!r ! action is p]=m$ 9 "o or ano!r =m4 ,! totality ( matt] is p]petually be+ act$ ^u by ! totality ( life4 ,e appulse ( life aga9/ matt] means an add$ pu% 9 ! direction ( spiritualization4 ,! totality ( su* appulses ( life aga9/ matt] may seem inf9itely small 9 ! visible results :i* !y produce 9 ! process ( spiritualization2 b ) ea* !re is an et]nal ga9 9 t movem5t t %all end 9 ! complete transmutation ( mat]iality into spirituality4 ,?is action ( life 9 metamorphos+ matt]1 ! ne!r pole ( ! great pair ( opposites1 into spirituality1 its copol> factor1 9 its outw>d1 visible effects1 is :at we vaguely call evolution4 ,& su* x is2 = life is m]ely unfold+ t :i* x has enfold$4 ,matt]1 hav+ be5 involv$ z a phase ( kosmic involution1 is n[ be+ evolv$4 ,9 ! g5esis ( ! kosmos !re appe> to be ?ree great undulations 9 ! univ]sal curr5t ( life4 ,! fir/ ( ^! prep>es ! field by deposit+ t elem5tal ess5ce :i* is to become ! _w-plasm2 ! second precipitates ! univ]sum ( mat]iality1 spatiality & intellectuality1 n z we n[ "k !m1 ( c\rse1 b z pot5cies2 ! ?ird great undulation 9 ! curr5t ( life effects ! end[m5t ( ! _w-plasm ) ^? t5d5cies t are to build ar\nd !mselves =ms appropriate to _! fulfillm5t4 ,?is ens\lm5t ( ! _w-plasm ) t5d5cies & ! consequ5t segm5tation ( x into sep>ate =ms by ^! t5d5cies con/itute ! prim>y /ages ( t proc$ure ( life :i* results ultimately 9 ! up-raisem5t ( matt] & its f9al exaltation into pure _s4 ,h5ce1 ! entire mass ( mat]iality is besieg$ on all sides by ! sum-total ( life & ! =m] is be+ rais$ sl[ly & irresi/ibly to heights t are immeasurably m sublime ?an its pres5t degree ( grossness4 ,x appe>s p>adoxical1 !re=e1 t life1 al?\gh 9 all respects va/ly sup]ior to matt]1 %\ld become ! app>5t vassal ( mat]iality & give itself up to all ! /rict rules ( imprisonm5t :i* are impos$ ^u x by ! prop]ties & qualities :i* we obs]ve 9 matt]4 ,x seems s subject to e :im & fancy ( matt] t "o is incl9$ to ?9k t matt] & n life is ! *ief design] ( univ]sal de/9y4 ,?is is n a condition to be wond]$ at s mu*1 = ! reason t ?is app>5t vassalage1 ?is seem+ enslavem5t ( life by matt]1 is due to t sup]ior & mo/ m>vel\s adaptability ( life :i* x enjoys 9 contradi/9ction to ! relative unpliability ( matt]1 & due also to ! fact t life is k9etic & matt]1 be+ a m]e deposit ( life1 is /atic4 ,life is mobility :ile matt] is immobility & ?us 9 possess+ a great] range ( fre$om is1 ( c\rse1 correspond+ly sup]ior2 b 9 ?is adaptation ( itself to ! labyr9?9e cavities & multi=m$ int]/ices 9 matt] x exhibits b a seem+ s]fdom :i* is really n a s]fdom b a ma/]y4 ,x is z if a man _h tak5 lumb]1 h>dw>e & /one & built a h\se :]e9 he might dwell--life has m]ely us$ matt]1 mold$ & fa%ion$ x s z to make = itself a m$ium1 a dwell+-place :]e9 x op]ates1 n z a slave b z a ma/] possess+ unlimit$ fre$om ( motility4 ,9 ! production ( a =m life /amps ^u x1 once = all "t1 ! pa? ( its eng5d]+ action4 ,x leaves its f+]-pr9ts ^u ! mold :i* x makes = itself4 ,s t if we w\ld "k :]e life has be5 or :]e x is we %\ld look = its f+]-pr9ts 7organization72 we %\ld obs]ve ! s9uosities :i* m>k its pa?way1 rememb]+ always t x is life t has =m$ ! intricacies & complexities ( ! =m into :i* x p\rs itself s accommodat+ly 9 ord] t x may raise t =m1 develop & transmute x into some?+ high] & bett]4 ,:5 we speak ( =m x mu/ n be und]/ood !reby t ref]5ce is made only to ! gross physical =m1 b to ! entire range ( vital assumptions or vehicles :i* life ens\ls = purposes ( manife/ation4 ,?is range we believe to cov] ! :ole pa? ( kosmog5esis s]iat+ f ! d5se/ to ! mo/ subtle4 ,our *ief conc]n1 h[ev]1 is ! imm$iate effect :i* ! totality ( life's op]ations w h ^u humanity or ! =m :i* x ens\ls z ! human organism4 ,= x is impossible t humanity %all escape ei!r ! g5]al or ! specific results ( ! exalt+ p[] :i* life ex]ts ov] mat]iality & its appurt5ances4 ,x is1 ( c\rse1 impossible "h to g into ! v>i\s implications ( ?is g5]al =w>d movem5t ( ! univ]sum ( mat]iality or ev5 to outl9e briefly ! div]g5t l9es ( op]ation into :i* a satisfactory exposition ( ?is view w\ld naturally lead4 ,& !n to d s w\ld be inappropriate 9 a volume ( ?is k9d4 ,s we %all h to be cont5t at ?is juncture to limit our /udy to a consid]ation ( :at we believe to be "s ( ! imm$iate indications ( ?is va/ & mo/ f>-rea*+ ph5om5on4 ,9 ! *apt] on ! ,g5esis & ,nature ( ,space x is %[n t ! mat]ial univ]se is eng5d]$ at ! same "t & by ! same movem5t or process z ! univ]sum ( spatiality & intellectuality & t z ! passage f *aos to kosmos proce$s ! function ( ?is movem5t is *ang$ gradually f eng5d]m5t to exaltation :]e9 mat]iality is transmut$ into spirituality4 ,x is1 ( c\rse1 obvi\s t z mat]iality is exalt$ s are spatiality & intellectuality2 & t z ! "o becomes m & m ref9$1 capable ( answ]+ to high] & yet high] requirem5ts s d all ! o!rs4 ,=1 at "w 9 all & ?r\gh all ( ^!1 is ! curr5t ( life :i* p]vades !m1 eng5d]+1 su/a9+ & elevat+ z x proce$s4 ,s t z matt] has evolv$ add$ *>act]i/ics & prop]ties1 ea* answ]+ to a giv5 ne$ & aris+ out ( ! necessities inh]+ 9 ! /age at :i* x appe>$1 s has ! intellect evolv$ faculties to correspond !re)4 ,9 o!r words1 ! evolution ( faculties = ! expression ( ! human intellect has proce$$ syn*ron\sly ) ! evolution ( mat]ial qualities4 ,& :5ev] a new faculty or an additional scope ( motility is a*iev$ by humanity !re is always f\nd a set ( kosmic conditions :i* answ]s !reto4 ,! c>d9al pr9ciples ( ! doctr9e ( evolution are n1 !re=e1 adv]se to ! conclusion t ! organs ( s5se-p]ception--he>+1 t\*1 sight1 ta/e & smell--h n be5 end[$ ^u ! human race or atta9$ by x at "o "t2 b r t ea* answ]+ to a newly acquir$ ne$ & op5+ a wid] scope ( motility = ! intellect has be5 evolv$ sep>ately & 9 due ord]4 ,x w\ld also seem t ! quality ( consci\sness1 z x has be5 manife/$ 9 ! v>i\s /ages ( life ?r\gh :i* x has pass$1 & especially ! m9]al1 vegetal & l[] animal1 has n always be5 ( ! same degree ( effici5cy4 ,nor has x enjoy$ ! same k9d ( fre$om :i* x n[ enjoys 9 ! highly evolv$ g5us homo4 ,x is equally app>5t t matt] itself has n always be5 9 possession ( ! same qualities & *>act]i/ics :i* x n[ exhibits2 b t x1 too1 has gone ?r\gh v>i\s /ages ( evolution br++ =w>d into ea* new /age ! transmut$ results ( ea* prec$+ "o z a basis = fur!r evolution & expansion4 ,! innum]able ar*ological evid5ces :i* support ?is view make x unnecess>y to d m ?an /ate ! facts1 z !y appe> to be sub/antiat$ by indubitable te/imonies4 ,fur!rmore1 x is believ$ t ! out/&+ implications ( ^! ph5om5a w n be successfully controv]t$ by ^? :o are dis9cl9$ to see su* implications 9 ! evolution>y process4 ,9 a previ\s *apt] we h briefly sket*$ ! *>act]i/ics :i* m>k ! upspr++ ( a new faculty %[+ h[1 at fir/1 x appe>s z an abnormality :i* exhibits itself 9 a v few individuals only1 & t 9 a m or less indef9ite mann]2 & h[ lat] ! numb] ( individuals 9 :i* x appe>s gradually increases1 ! def9it5ess ( ! faculty1 at ! same "t1 appe>+ m m>k$2 !n1 l a tidal wave1 x recurs 9 a /ill l>g] numb] ( p]sons until1 at la/ aft] a long p]iod ( "t usually sev]al ?\s&s ( ye>s1 x becomes univ]sal exhibit+ itself 9 e individual & appe>+ z a h]$it>y *>act]i/ic ( ! entire human race4 ,x is1 !re=e1 n )\t assurance z to ! ultimate s\ndness ( ?is view t we make ! ass]tions :i* foll[ ?is brief introduction4 ,x has already be5 /at$ t = a v obvi\s reason1 namely1 ! satisfaction ( ! ne$s ( our pres5t humanity1 ! intuition is = ! "t dom9at$ by ! intellect & held 9 subjugation by x s t all ( man's ext]nal op]ations are gov]n$ & dictat$ almo/ entirely by ! intellectuality1 all[+ ! intuition only r>e mom5ts :5 x c come to ! =e at all4 ,?is is ! rule 9 ! evolution ( faculties & *>act]i/ics4 ,! high] faculty1 al?\gh pot5tially pres5t 9 e way1 is ev] held 9 abeyance :ile ! l[] is br\ght1 "u ! rigors ( its own evolution1 to a po9t :]e its jo9t op]ation ) ! high] may be execut$ ) ! lea/ possible friction & ret>dation z also ) ! greate/ possible cord9ation & cop]ation4 ,accord+ly1 not)/&+ ! fact t mat]iality mu/ possess 9 pot5tiality all ! qualities :i* x w at any "t reveal1 x is nev]!less necess>y t ^! qualities %all come =? gradually & 9 due ord]4 ,simil>ly1 humanity has come into possession ( its v>i\s faculties ( m9d1 & p[]s ( physiological functions1 by ins5sible degrees1 ! high] always be+ held 9 abeyance until ! l[] is fully develop$4 ,^? faculties :i* are to be/[ add$ p[]s1 additional fre$om & a great] scope ( motility are ! ones :i* appe> lat] ?an ^? :i* are truly primitive 9 "*4 ,^! facts h be5 amply demon/rat$ by ! sci5ce ( embryology :]e9 x is %[n t ontog5y is a recapitulation ( phylog5y4 ,t is1 ! hi/ory ( ! developm5t ( ! individual is a recapitulation ( ! developm5t ( ! species4 ,?us ! v>i\s /ages ( developm5t ?r\gh :i* ! human embryo passes :ile 9 ut]o are b a repetition ( simil> /ages ?r\gh :i* ! entire human species has pass$ 9 its phylog5etic developm5t4 ,:]e=e1 x is c]ta9 t humanity has n atta9$1 at "o & ! same "t1 all ! p[]s ( m9d & body :i* x n[ possesses2 t ! *ildhood ( ! human race repres5t$ a "t :5 x _h b few faculties or organs ( s5se-p]ception--inde$ a "t :5 ! high] s5se-organs ( smell1 ta/e & sight 7 entirely lack+ al?\gh resid+ 9 pot5tiality !re94 ,x is und\bt$ly true t ! e>? has pass$ ?r\gh a simil> evolution ) respect to its own mat]ial *>act]i/ics1 t its *ildhood 01 9 all po9ts1 analog\s to ! *ildhood ( humanity2 t ! air1 e>? & wat] 7 :olly abs5t1 except 9 pot5tiality1 dur+ ! nebul\s y\? ( its g5esis4 ,x is ev5 probable t !re are at "w to-day processes :i* 9 ! future %all culm9ate 9 ! evolution ( new]1 high] & m complicately organiz$ species ( plants1 animals & m9]als4 ,e ye> br+s fre% evid5ces t cry/allize ! conviction t ! e>? has be5 ! sc5e = ! appe>ance ( _m /range ord]s ( animal life4 ,fossilif]\s /rata are cont9ually yield+ inconte/able te/imonies ( *ang+ flora & fauna4 ,we c\nt ! animal & vegetal life ( to-day z be+ m highly develop$ ?an t ( any o!r previ\s age1 & x is well t ?is is s1 = simplicity ( organization & primality ( manife/ation are always succe$$ by complexity & a great] scope ( adaptability4 ,we h said t ! :ole ( t movem5t ( ! intellect :i* has br\ght =? ! metageometrical creations ( hyp]spaces1 ! curvature ( space & its manifoldness toge!r ) ! entire assemblage ( ma!tic contrivances are m]ely ! e>ly evid5ces ( ! appe>ance 9 ! human race ( a new faculty1 a new m$ium ( p]ception :]eby ! ,?9k] %all acquire a /ill great] range ( motility ?an t n[ (f]$ by ! intellect4 ,att5tion has be5 call$ also to ! fact t ?is ph5om5on has be5 manife/$ n alone 9 ! field ( ma!matics1 b 9 art1 religion1 politics & also 9 sci5ce 9 :i* we h only to witness ! m>vel\s /rides already made 9 ! discov]y ( radio-active sub/ances1 ! ,,ro5tg51 ,,becqu]el1 ,,leon>d & o!r k9ds ( rays4 ,x ,is q confid5tly believ$ t ^! =w>d movem5ts 9 e bran* ( intellectual pursuit1 ^! comb9$ ef=ts ( ! intellect1 9 pe]+ into ! occult side ( mat]ial ?+s1 are 9 response to ! evolution>y ne$s ( ! ,?9k]1 & 9 addition1 are ! evid5ces1 & %all 9 "t be ! cause1 ( ! developm5t ( an additional set ( faculties4 ,function1 or ! p]=mance ( acts1 det]m9es faculty or ! p[] ( action & ultimately ! organ itself4 ,?us ! m]e wi% to p]=m ar\s$ by desire & vitaliz$ by ! w actually t]m9ates1 9 ! c\rse ( "t1 9 ! g5esis ( a faculty1 or ! p[] to p]=m4 ,! con/ant uprea*+ ye>n+s ( ! ,?9k] ?r\gh 8 intellect = great] fre$om & a l>g] scope ( action1 ! desire to pe] into ! my/]ies ( life & m9d1 ! infantile out-feel+s ( ! m5tality aft] "s saf] & sur] basis = its !ory ( k _c fail 9 produc+ n only ! faculty or p[] to satisfy ^! crav+s b ! v organ or m$ium by virtue ( :i* ! satisfaction may be atta9$4 ,x is n /range t 9 ma!matics ! intellect %\ld h f\nd fir/ ! clue to ! exi/5ce ( a high] sph]e ( intellectual rese>* :]e9 x might become ! creator ( ! v>i\s entities :i* peopl$ ! new f\nd doma92 x is n /range t ! ma!matician %\ld1 9 ?is in/ance1 h assum$ ! role ( ! prophet proclaim+ by v>i\s ma!tic contrivances 7al?\gh unconsci\sly7 t ! human race is ne>+ t "t :5 x %all actually be able to function consci\sly 9 "s high] sph]e2 nei!r is x to be wond]$ at t ! voice ( ! prophet is he>d & respect$ ?r\gh\t ! e>?2 =1 inde$ ! ma!matician is a spokesman :o1 z a rule1 is unmov$ by sudd5 outbur/s ( passion & ec/atic fr5zies ( emotions b calmly & dispassionately v]ifies 8 conclusions1 te/s !m = consi/5cy & hav+ f\nd !m to satisfy ! mo/ rigor\s ma!tic requirem5ts hesitates n to prop\nd !m4 ,= ?is cause humanity respects ! ma!matician1 & :5 he speaks li/5s to 8 voice4 ,x is well1 too1 t ?is is s2 = ! hi/ory ( ma!matics is cle>ly ! hi/ory ( ! developm5t ( ! intellect4 ,s exact a det]m9ator ( ! quality ( intellectual effici5cy is x t its reign may be said to be an absolute mon>*ism ^: l9es ( dom9ance ext5d to ! m9ute/ desire or appet5cy4 ,x has always be5 ! guide ( ! intellect1 go+ be=e1 z x 71 blaz+ ! trail1 pu%+ back ! fronti]s ( ! intellect's doma9 & cle>+ away ! debris s t ! intellect ) its ret9ue ( s]vitors might h an easy pa? ( progress4 ,ma!matics1 h[ev]1 has n ! aptitude to s]ve ! intuition z x s]ves ! intellect4 ,s ! pa? into :i* ! intuition w\ld lead humanity ! ma!matician1 because ( 8 tra9+ & peculi> functions1 is unprep>$ to ent]4 ,x is = ?is reason t :5 ma!matics leads ! intellect up to t po9t :]e x enc\nt]s life x fails1 x becomes confus$ & its dictator%ip becomes a mock]y1 its decrees rema9 unexecut$ & futile4 ,9 tak+ ?is view we h c]ta9ly no desire to (f5d ! ma!matician or to detract f ! glory ( 8 mon>*i/ic rul]%ip ov] ! intellectual progress ( ! race2 =1 9 tru?1 ma!matics is ! diadem ( gold :]e) man has cr[n$ 8 intellect4 ,yet x is well1 yea imp]ative 9 ! light ( rec5t developm5ts 9 ! realm ( hyp]space1 t a c>eful discrim9ation %\ld be made z betwe5 ! sph]e ( ! intellect & t to :i* ! intuition %all atta94 ,! intuition1 long held 9 abeyance until ! intellect %\ld be fully cr[n$ & rea* ! z5i? ( its p[]s1 is n[ com+ to ! front4 ,x w be _m c5turies p]haps be=e x %all h gr[n to su* proportions z ^? already atta9$ by ! intellect2 p]haps a few ?\s& ye>s may pass be=e ! intuition %all h evolv$ to t po9t :]e x may labor z coadjutor to ! intellect2 b und\bt$ly ! "t w come :5 x1 too1 %all rew>d ! ,?9k]'s labors ) t :i* %all be m preci\s ?an ! cr[n ( gold :i* ! intellect has won4 ,!n1 ! intellect1 gr[n old & decrepit ) ye>s ( reign+ %all become dim & cry/al-%ap$ & f9ally pass into automatism or reflexive movem5ts :]e )\t ! urge ( volitional impulses x w p]=m ) exactness1 precision & utt] loyalty ! tasks :i* x has le>n$ s well to execute 9 ! days ( its =gott5 glory4 ,mank9d w !n be free4 ,a new fre$om1 :]e9 ! er/:ile lightn+ fla%es ( intuition w become fus$ into "o glori\s %e5 ( all-reveal+ light1 %all come to m5 & ?us ! race respl5d5t w walk ! e>? en%r9$ 9 ! maje/y ( div9e p[]s atta9$ z a result ( millions ( ye>s ( aspiration4 ,t !re are sup]s5su\s realms s f> above ! range ( our s5ses z to be entirely beyond _! k5 ne$s n[ no pro( or argum5t2 = ! sci5ti/ has demon/rat$1 by ! inv5tion ( in/rum5ts ( extreme delicacy & precision1 t su* a _w does really exi/4 ,already we "k ( />s s di/ant t1 ?\gh light trav]ses 9 ! brief space ( an h\r six hundr$ million miles1 !y might h ceas$ to %9e be=e ! pyramids 7 built & yet be visible to u 9 ! skies4 ,if ! human eye 7 z s5sitive z ! spectroscope _m ?\s& t9ts & %ades might be add$ to ! _w ( color2 if !y possess$ ! magnify+ p[]s ( ! microscope we %\ld live 9 con/ant t]ror & awe ( ! mon/r\s entities t teem 9 ! wat] :i* we dr9k & 9 ! air :i* we brea!2 & if our e>s c\ld detect ! microphonic vibrations :i* regi/] 9 ! delicate app>atus ( "s microphones ! dead1 vacuum-/illness ( nature's great sil5ces w\ld appe> z a babel ( voices by ! seaside4 ,! s5se ( t\*1 respond+ to ! same range ( vibrations z ! micromet]1 w\ld reveal actually ! int]/ices betwe5 p>ticles ( ! d5se/ elem5ts2 & gold1 silv]1 plat9um & m]cury w\ld seem b honeycombs ( matt]4 ,b1 to ! =w>d-look+ !re is no elem5t ( absurdity 9 ! expectation t all ^! s5ses %all1 "o day1 be able to disp5se ) ! artificial aid ( physical app>atus & p]=m1 ) ev5 great] precision & fai?fulness1 ! task :i* !y n[ p]=m s crudely & ineffectively4 ,!re are )\t d\bt vibrations ( ta/e & smell :i* are s f> above ! range ( ^! s5ses t !y h no effect ^u !m :atsoev]4 ,not)/&+ ! fact1 h[ev]1 t ! galvanomet]1 microscope1 ! microphone1 ! spectroscope & ! telescope h ext5d$ ?us ! sph]e ( s5se-k !re are yet subtl] vibrations to :i* ^! delicate in/rum5ts d n & ought n be expect$ to respond4 ,b to say1 z d _m empirici/s1 t s9ce ^! ph5om5a _c be detect$ by sci5tific in/rum5ts !y d n1 !re=e1 exi/ seems to be expect+ too mu* ( mat]ial means z well z expos+ oneself unnecess>ily to criticism on ! gr\nds ( extreme mat]iali/ic appet5ces4 ,!re is inde$ ne$ ( a m lib]al attitude among m5 ( sci5ce t[>ds ! _w ( ! unse54 ,intol]ance ( ! data :i* x (f]s w = a "t p]haps pres]ve ! alo(ness ( sci5tific dogmatism inviolate b !re w mo/ surely come a reaction aga9/ ! dogmatism ( sci5ce & m5 w seek fre$om & atta9 x despite _! fett]s4 ,sir ,,oliv] ,,lodge1 9 8 book1 ! ,survival ( ,man1#bi says3 ,man's outlook ^u ! univ]se is ent]+ ^u a new phase4 ,simultane\sly ) ! beg9n+ ( a revolution>y increase 9 8 p[]s ( physical locomotion--:i* w soon be ext5d$ to a ?ird dim5sion & no long] limit$ to a solid or liquid surface--8 p[] ( reciprocal m5tal int]c\rse is also 9 process ( be+ enl>g$2 = !re are signs t x w "s day be no long] limit$ to contempor>y d5iz5s ( e>?1 b w p]mit a utilization ( k & p[]s sup]ior to 8 own1 ev5 to ! ext5t ( ultimately atta9+ tru/wor?y in=mation conc]n+ o!r conditions ( exi/5ce4 #bi ,see pp4 #cch1 #cda4 ,x is ! au?or's good =tune t he has = a p]iod ext5d+ ov] sev]al ye>s be5 able to v]ify ! conclusions :i* ,sir ,,oliv] ,,lodge expresses 9 ! above1 & ?us to satisfy 8 own m9d t ! process by :i* man's m5tal p[]s are be+ enl>g$ is inde$ demon/rable by actual obs]vation & exp]im5tal me?ods4 ,,lodge cont9ues3 ,! b\nd>y betwe5 ! two /ates--! kn[n & ! unkn[n1 is /ill sub/antial1 b x is we>+ ?9 9 places1 & l excavators engag$ 9 bor+ a tunnel f opposite ends amid ! ro> ( wat] & o!r noises1 we are beg9n+ to he> n[ & aga9 ! /rokes ( ! pick-axes ( our comrades on ! o!r side4 ,,camille ,,flamm>ion#cj cites #dcf cases ( psy*ic manife/ations exam9$ by himself & :i* e/abli% beyond any reasonable d\bt t !re are c]ta9 p]ceptive faculties1 namely1 clairvoyance & clairaudi5ce1 t crop out 9 c]ta9 individuals1 sometimes 9 abnormal conditions & sometimes normally1 ! v unusual "* ( :i* proves _! rudim5t>y nature & ! pot5cy ( _! maturesc5ce 9 ! humanity ( ! future4 ,among ! cases cit$ by ,,flamm>ion are #ahf in/ances ( manife/ations f ! dy+ receiv$ by p]sons :o 7 awake2 #gj cases 7 manife/ations receiv$ by p]sons asleep2 #eg 7 obs]vations ( direct transmission ( ?\ght )\t ! aid ( sight1 he>+ or t\* or o!r physical means2 #di 7 cases ( sight at a di/ance or clairvoyance by p]sons awake1 9 dreams or 9 somnambulism & #gd cases ( premonitory dreams or pr$ictions ( ! future4 ,inde$1 !re are few p]sons n[ liv+ :o h n _h simil> exp]i5ces1 if n exactly l ^!1 ( ! same nature4 ,^! examples1 ( c\rse1 may be greatly multipli$ 9 e c\ntry 9 ! _w1 & x is unnecess>y to enum]ate !m fur!r2 =1 :5 once ! exi/5ce ( su* faculties has be5 demon/rat$ 9 p]sons1 ei!r 9 a normal or an abnormal condition1 _! pres5ce c no long] be que/ion$ by ! fair-m9d$4 ,x is1 !n1 only a "q ( evolution be=e !y w appe> 9 ! normal way & _! univ]salization1 z transmissible *>act]s1 be an accompli%$ fact4 ,:5 we are br\ght face to face ) ?is sort ( ph5om5on :i* seems to be increas+ rapidly ! conclusion is inevitably =c$ ^u u t s9ce evolution mu/ be a cont9u\s process & matt] de/9$ to yield high] & m ref9$ p[]s & humanity to come into a f> m ext5sive scope ( motility because ( ! op5+ av5ues ( k1 x is n impossible t ^! acut] s5ses1 ^! new faculties are n[ exi/+ 9 ! human race 9 a rudim5t>y /age & are design$ to become ! univ]sal possession ( all4 ,t ?is is to be ! almo/ imm$iate outcome ( ! p]petual exalt+ p[] :i* life ex]cises n alone ov] mat]iality b ov] human organs & faculties z well1 seems to be ! "o big1 out/&+ implication ( ! evolution>y process4 ,! pres5ce ( su* functions z ! ability to s5se ! invisible & ! inaudible1 to answ] to vibrations f> subtl] ?an any?+ 9 ! scope ( our ext]nal s5se-organs1 c]ta9ly indicates ! exi/5ce ( rudim5t>y faculties :i* make ^! functions possible4 ,back ( ^! vague1 indef9ite functions1 back ( e sup]normal or abnormal manife/ation ( man's m5tality & back ( all t class ( ph5om5a :i* take _! rise out ( sup]s5su\s areas mu/ lie1 9 ev] increas+ pot5cy1 faculties & organs1 h[ev] rudim5t>y1 :i* are ! s\rce ( ^! manife/ations4 ,life1 t ineluctable ag5t ( creation1 :i* is incessantly pu%+ outw>d ! conf9es ( ! intellect's scope ( motility1 nev] we>y+1 nev] tir+ nor sleep+1 has long ago1 9 ! dim & di/ant pa/ ( man's evolution1 laid ! f\ndations2 & 9 fact1 ) "o /roke ( its creative h&1 has mold$ ! organs :i* are to become ! active m$ia ( ^! new faculties4 ,& n[1 ^! incipi5t demon/rations1 ^! infantile /ruggles :i* we see n[ & aga9 outputt+ f !m1 are b ! specializ+ processes ?r\gh :i*1 9 _! lat] developm5t1 ^! organs are proce$+4 ,^! are ! outw>d signs :i* %\ld tell u t life is break+ up ^! organs into special p>ts1 assign+ to ea* a c]ta9 division ( labor & mak+ ( ea* a p]fect cord9ate ( all ! o!rs4 ,x is1 by ^! v dispread exhibitions1 cutt+ up1 specializ+ & by sl[ degrees det]m9+ ! function1 "* & g5]al t5d5ce ( ! organs ( expression :]e) ^! manife/ations %all be c5traliz$ & put into effective op]ation4 ,9 do+ ?is1 x is b foll[+ its accu/om$ proc$ure1 ! proc$ure :i* x adopt$ :5 x produc$ ! eye1 ! e>1 ! he>t & ! sple54 ,we %all1 !re=e1 gauge our und]/&+ ( ! purport & end ( evolution2 9 fact1 we %all det]m9e our exact intellectual compreh5sion ( life itself1 by ! attitude :i* we adopt t[>ds x & ! mode ( its appe>ance4 ,mu* dep5ds1 accord+ly1 ^u ! po/ure :i* we assume t[>ds life--:e!r we %all say ! totality ( life's creative p[]s has be5 dissipat$ 9 ! br++ ( ! human body to its pres5t degree ( p]fection2 :e!r we %all say t x is nei!r necess>y nor possible = life to produce o!r organs & faculties :i* %all respond to ! unse5 _w ab\t u reveal+ its glories 9 a way f> m p]fect ?an d our ext]nal s5se-organs reveal ! wond]s ( ! _w ( s5sation2 or1 :e!r we %all conclude f ^! mo/ palpable evid5ces t life has yet o!r p[]s & faculties :i* x designs to be/[ ^u ! human m9d & o!r organs & capabilities ) :i* x %all end[ ! human body s t man1 9 8 evolution1 %all be enabl$ to rise to /ill high] sph]es :ile yet inc>nate4 ,!re may be1 & und\bt$ly are1 ^? :o1 = v>i\s reasons pref] to take ! =m] positions & !re are c]ta9ly ^? :o l ,,lodge1 ,,flamm>ion1 ,,hudson1 ,,crookes & a ho/ ( o!rs1 pref]r+ ! latt] view1 w\ld r believe 9 ! /r5g? ( ! great mass ( corroborative te/imonies t we are ev5 to-day 9 ! mid/ ( ! matut9al h\rs ( a new]1 a bett] & a f> m effici5t era ( human evolution ?an any ?r\gh :i* we h hi!rto come4 #cj ,see ,unkn[n1 p4 #dhe1 et4 seq4 ,already1 rec5t sci5tific inve/igations & ! results obta9$ !refrom h begun to turn ! att5tion ( m$ical au?orities to ! activities ( two v small organs situat$ 9 ! mid-bra9 & kn[n z ! p9eal gl& & ! pituit>y body4 ,^! organs1 & especially ! p9eal gl& hi!rto suppos$ to be a ve/ige ( ! pa/1 are n[ beg9n+ to be recogniz$ z rudim5t>y organs belong+ to ! future evolution ( humanity4 ,dr4 ,,*>les ,,de ,m4 ,,saj\s1 :o is an au?ority on ! pituit>y body1 believes t x has no active int]nal secretions b is an epi!lio-n]v\s organ :i* controls1 ?r\gh n]ves lead+ to ! adr5als & ?yroid bone1 ! processes ( g5]al oxyg5ation1 metabolism & nutrition4 ,little is kn[n ( ! functions ( ! p9eal gl& except t x is an ovoid1 r$di% organ atta*$ to ! po/]ior c]ebral commissure project+ d[nw>d & backw>d betwe5 ! ant]ior pair ( ! corpora quadrigem9a4 ,x is o!rwise kn[n z ! con>ium ! p9us or epiphysis4 ,situat$ at ! base ( ! bra91 x is held 9 position by a fold ( ! pia mat] :ile its base is connect$ ) ! c]ebrum by two p$icles4 ,x conta9s amylace\s & gritty1 calc>e\s p>ticles con/itut+ ! bra9 s&4 ,!re are1 h[ev]1 m>k$ /ructural resemblances betwe5 ! p9eal gl& & ! pituit>y body & _! =mation is p]haps ! mo/ int]e/+ feature ( ! developm5t ( ! ?alam5cephalon or mid-bra94 ,! hypophysis c]ebri or pituit>y body is a small1 ovoid1 pale1 r$di% mass v>y+ 9 weight f five to t5 gra9s & situat$ at ! basal extremity ( ! bra9 9 a depression ( ! cranium kn[n z ! sella turcica1 a configuration v mu* l a ,turki% saddle 9 %ape4 ,x is a composite1 ductless gl& & consi/s ( two divisions1 an ant]ior & a po/]ior1 connect$ by an int]m$ial portion--all ( :i* are atta*$ to ! base ( ! c]ebrum by ! infundibulum4 ,! ant]ior lobe is l>g] ?an ! po/]ior & v vascul>1 spr++ 9 its developm5t f ! buccal cavity ( ! embryo2 ! po/]ior lobe is situat$ 9 a depression ( ! ant]ior & is a bra9-process4 ,! pituit>y body itself is lodg$ 9 a cavity ( ! sph5oid bone call$ ! pituit>y fossa4 ,?is is a mo/ rem>kable position1 = ! reason t ! sph5oid1 or w$ge-%ap$1 bone :i* lies at ! base ( ! skull articulates f beh9d ) ! occipital & 9 front ) ! frontal & e?moid bones & by lat]al processes ) ! frontal1 p>ietal & temporal bones4 ,f ?is position x b9ds toge!r all ! bones ( ! cranium1 & moreov]1 articulates ) _m bones ( ! face4 ,x is ^u ! upp] surface ( ! sph5oid bone :i* occupies su* a prom95t & comm&+ position 9 ! cranium1 9 a deep depression1 t ! pituit>y gl& is locat$4 ,ea* nasal *amb] is l9$ by a muc\s membrane call$ ! pituit>y or ,s*neid]ian4 ,?is membrane is prolong$ into ! meatuses & air s9uses :i* op5 into ! nasal *amb]s4 ,! pituit>y membrane is ?ick & s(t & dim9i%es ! size ( ! meatuses & air s9uses4 ,x is cov]$ by a ciliat$ column> epi!lium & conta9s num]\s racemose gl&s = ! secretion ( muc\s or pituita4 ,x is also vascul> & ! ve9s :i* ramify x h a plexi=m or net-"w l arrangem5t4 ,x divides into two membranes--a respiratory1 :i* is conc]n$ 9 brea?+1 & an olfactory region4 ,! respiratory region corresponds to ! floor ( ! nose1 to ! inf]ior turb9at$ bone & to ! l[] ?ird ( ! nasal septum4 ,! olfactory region is ! seat & di/ribution ( ! olfactory n]ve & corresponds to ! base ( ! nose1 to ! sup]ior & middle turb9als & ! upp] two-?irds ( ! nasal septum4 ,rec5t developm5ts prove t ?is gl& has a pr(\nd influ5ce ov] ! animal economy4 ,x is believ$ by "s t ! pituit>y body actually de/roys c]ta9 sub/ances :i* h a toxic influ5ce on ! n]v\s sy/em2 o!rs believe t x secretes mat]ial m$ia = ! prop] action ( ! trophic or nutritive app>atus2 /ill o!rs believe t x influ5ces blood-pressure4 ,x is kn[n1 h[ev]1 f exp]im5tation1 t its removal 9 dogs1 cats1 mice & gu9ea pigs causes a fall ( temp]ature1 lassitude1 muscul> twit*+s1 dyspnoea or difficult brea?+1 & ev5 spe$y dea?4 ,hyp]trophy ( ! gl& is directly associat$ ) c]ta9 diseases1 su* z giantism & acromegaly4 ,! latt] is a disease :i* causes a g5]al enl>gem5t ( ! bones ( ! head1 feet & h&s1 usually occurr+ betwe5 ! ages ( tw5ty & =ty ye>s1 & mo/ frequ5tly 9 females4 ,! fact t ^! diseases are s closely associat$ ) a hyp]trophic condition ( ! pituit>y gl& has l$ to ! conclusion t p]haps ! giants or ,cyclops ( anci5t times 7 cases ( giantism or acromegaly4 ,?is view1 :ile int]e/+ f ! /&po9t ( ! functions ( ! pituit>y gl&1 is n necess>ily a correct "o2 = ! age ( giants1 :5 m5 atta9$ to a mu* l>g] /ature ?an at pres5t1 c be acc\nt$ = on o!r gr\nds1 namely2 t ! e>ly mesozoic man1 on acc\nt ( 8 hav+ to live among animals1 trees & o!r vegetation ( su* huge size1 _h naturally to be fitt$ ) a frame proportional to o!r animals 9 ord] t he might successfully cope ) 8 environ+ conditions4 ,nature ?us wisely fitt$ him = ! conditions :i* %e _h prep>$ = ! sc5es ( 8 life4 ,! facts adduc$ 9 ! =ego+ description are purely empirical & may be v]ifi$ by any :o seek to e/abli% _! correctness or incorrectness4 ,b we are ab\t to introduce a species ( te/imony :i* :ile x may also be v]ifi$ w n be f\nd s easy ( v]ification z ! above-m5tion$ physiological facts1 & n by ! same means2 yet !y are nev]!less des]v+ ( a place "h4 ,x is ! lib]al attitude t we mu/ adopt t[>ds all ph5om5a1 exclud+ none t give promise ( ! wid5+ & deep5+ ( our k & an explanation ( mu* t has seem$ h]et(ore unacc\ntable4 ,we h not$ h[ subtle is ! physical connection betwe5 ^! two bodies1 ! p9eal gl& & ! pituit>y body2 we h se5 h[ pr(\nd is ! effect :i* ! latt] has be5 demon/rat$1 9 a measure1 to h ov] ! entire bodily economy2 b !re is ev5 o!r te/imony to ! effect t ^? gift$ ) ! inn] vision c obs]ve ! pulsat+ aura 9 ea* body1 a movem5t :i* is n unlike ! pulsations ( ! he>t & :i* nev] ceases ?r\gh\t life4 ,9 ! developm5t ( clairvoyance x is kn[n t ?is motion becomes int5sifi$1 ! auric vibrations becom+ /rong] & m pron\nc$4 ,! pituit>y body is ! en]giz] ( ! p9eal gl& &1 z its pulsat+ arc rises m & m until x contacts ! p9eal gl&1 x awak5s & ar\ses x into a r5ew$ activity 9 mu* ! same mann] z curr5t electricity excites n]v\s tissue4 ,:5 ! p9eal gl& is ?us ar\s$ clairvoyant p]ception is said to become possible4 ,^! are facts :i* _c be prov$ by ! mat]iali/ic man ( sci5ce nor c !y be demon/rat$ to ! layman :o has to dep5d alone ^u s5se-deliv]ies = 8 k4 ,?is is true = ! reason t1 9 ! fir/ place1 x is necess>y t he %all ei!r feel 9 8 own mid-bra9 ! en]giz+ activity ( ^! two organs & h 8 entire n]ve-body %ak5 f cr[n to toe by ! d[n ru%+ curr5ts ( t subtle en]gy ) :i* ! pituit>y body floods x or be himself ! p]ceiv] ( its activities4 ,nev]!less att5tion is "h call$ to ^! ph5om5a & ! conclusions drawn !refrom are (f]$ z a means ( d5ot+ ! probable l9e ( inve/igations :i* w e/abli% ! directions :i* we %\ld pursue & ! s\rce :5ce we %all f9d outcropp+ ! new faculties & _! organs ( expression4 ,we confess to a k ( ! fact t m5 ( empirical sci5ce h long ma9ta9$ a r skeptical1 if n contemptu\s1 attitude t[>ds all ^! ph5om5a b x is also felt t !re is f> m ( discr$it 9 _! attitude ?an ( cr$it2 =1 9 s do+1 !y h volunt>ily adopt$ measures by means ( :i* ! k t !y s eag]ly seek is %ut out f _! atta9m5t4 ,9 va91 !n1 is appeal made to ! intellect to remove ! b>ri]s :i* x unconsci\sly int]poses betwe5 itself & ! goal ( its pursuit2 9 va9 d we appeal to ! mat]iali/ to give e> to te/imony ! data ( :i* _c be made am5able to 8 knife & scalpel nei!r to ! microscope nor microphone2 9 %e] vanity is he adjur$ to look )9--into ! int]ior ( life1 ( m9d & ! ?+s :i* he h&les ) 8 in/rum5ts--= ! answ]s to 8 qu]ies1 = ! pa? :i* leads into ! wake ( life & consci\sness4 ,because 8 utt] loyalty & devotion to ! modus viv5di ( ! intellect w n p]mit ?is2 b1 aft] all1 x is n :olly wise to allure him away unbetimes f 8 se>* aft] tru? ?r\gh sup]ficialities nor to inveigle him into giv+ up 8 t5aci\s prosecution ( ! physically det]m9able4 ,we w\ld n h x s2 =1 p]*ance1 he1 too1 "o f9e day1 9 ! quiet ( 8 laboratory %all come ^u ! data :i* may sub/antiate 9 8 own m9d ! long settl$ conclusions ( ! occulti/ :o1 frequ5tly & n )\t cause1 gr[s impati5t at ! sci5ti/'s ob/9ate delay4 ,^! two work]s1 ! empirici/ & ! occulti/1 mu/ ultimately come toge!r z collaborators--! "o work+ ^u ! =m1 ! vehicle1 physical matt] & ! o!r seek+ to und]/& ! life1 ! int]ior =ces :i* produce1 ! creative elem5t4 ,!y _c rema9 always alo( f "o ano!r2 = !y1 too1 are z m5 digg+ a tunnel f opposite ends4 ,f9ally1 ! p>tition w break & ?us w dawn a new day = ! k ( humanity & m5 w see ! rationale1 ! tru? & good s5se ( cop]ation 9 ?is respect4 ,x c be said ) confid5ce t :atev] 9 ! future may be le>n$ z to ! physiologic functions ( ! pituit>y body & ! p9eal gl&1 x suffices to "k t x is life :i* !y express & t1 too1 9 a f> sup]ior mann] ?an any ( ! o!r s5se organs4 ,! modus ( ^! two gl&s diff]s 9 a v m>k$ way f t ( ! organs ( sight1 he>+1 ta/e1 smell & feel+4 ,= ^! latt] are design$ = contact ) ! ext]nal1 objective _w ( s5sations1 _! gr[? & evolution be+ dep5d5t ^u /imuli receiv$ f )\t :ile ) ! =m] ! case is f> diff]5t1 9 fact1 j ! opposite4 ,! mode ( life ( ! pituit>y body & ! p9eal gl&1 in/ead ( receiv+ su/5ance & impetus f ext]nal /imuli1 is r dep5d5t ^u impacts receiv$ f ! ,?9k]'s own consci\sness & made to imp+e ^u !m by an exclusively int]ior process4 ,situat$ 9 ! mid-bra91 safely seclud$ f all ext]nal int]f]5ce1 !y are naturally limit$ to /imuli :i* come f )91 or x may be said1 !y are responsive to excitations t are m spiritual ?an ^? :i* come ?r\gh ! ext]nal s5se-organs4 ,if1 z has be5 said !y control ! int]nal processes ( metabolism 7anabolism & katabolism71 oxyg5ation1 nutrition1 & o!r important int]nal movem5ts1 none ( :i* c be said to be "u ! control ( ! intellect1 is x n1 !re=e1 ju/ly assum$ t _! response is direct$ t[>ds /imuli :i* arise int]iorly or ^u a plane high] ?an ! intellectual8 ,x is a matt] ( sci5tific k t ^? p]sons gift$ ) clairvoyance1 & commonly kn[n z s5sitives are f> m responsive to n]v\s excitation ?an ^? :o are n s gift$4 ,?is w\ld seem to imply t1 on acc\nt ( ! sup]activity ( ^! two organs1 ! entire n]ve-body has1 9 consequ5ce1 become m delicately & subtly organiz$4 ,!y seem to act z a swit*bo>d = ! regulation ( ! fl[ ( ! curr5t ( life ?r\gh ! body4 ,n only d !y come m ne>ly to an adequate expression ( ! physiologic function ( life1 b1 z _! en]gization means an enl>gem5t ( ! scope ( p]ception by giv+ ! ,?9k]'s active consci\sness access to hi!rto unapproa*able realities & by p5etrat+ ! out] mask :i* life ens\ls & also lay+ b>e a doma9 ( unlimit$ k ! manife/ation ( :i* is f> m real ?an any?+ ! s5ses c disclose1 x is evid5t t !y con/itute1 9 _! collaborative functions1 a m highly adaptable m$ium = ! expression ( ! ,?9k]'s consci\sness4 ,& if s1 = ! kosmic consci\sness :i* is ! s\rce ( all =ms ( consci\sness1 !y furni% a specializ+ & adaptiz+ ag5cy4 ,n[1 9 all ^? cases ( inspirations1 revelations1 telepa?ic communications1 clairaudi5ce1 clairvoyance1 dreams1 visions1 etc41 :]e9 ! ,?9k] is enabl$ to p]ceive facts & v]ities :i* are !n pres5t$ to 8 consci\sness 9 a mann] cle>ly )\t ! prov9ce ( ! common s5se-organs1 x mu/ be app>5t t ^! manife/ations are appreh5d$ by a p]ceptual me*anism :i* is entirely indep5d5t ( ext]nal s5se pres5tations b :i* is an int]ior & subtl] =m ( psy*ic activity4 ,s\nds :i* are he>d by s-call$ s5sitives & objects :i* are p]ceiv$ by eyes t are ke5] ?an ^? organs said to h be5 evolv$ f ! m$usa _c be he>d by o!r p]sons nor p]ceiv$ by !m 9 any way4 ,?us x w\ld seem t !re are inn] organs ( p]ception :i* respond to ^! f9] vibrations & :i* enable ! p]son s gift$ to appreh5d !m4 ,!re are ^? :o1 presumably bas+ _! ass]tions ^u actual obs]vation & k1 unqualifi$ly ass]t t 9 ord] to ga9 contact ) ! inn] worlds all t rema9s to be done is ! awak5+ ( ! pituit>y body & ! p9eal gl&4 ,:5 ?is is accompli%$ man w aga9 possess ! faculty ( p]ception 9 ! high] worlds1 b on a gr&] scale ?an =m]ly 7:5 humanity 0 9 its infancy & ex]cis$ a l[] =m ( psy*ic p[] only72 because x w be 9 connection ) ! volunt>y n]v\s sy/em1 & !re=e1 "u ! control ( ! w4 ,?r\gh ?is inn] p]ceptive faculty all av5ues ( k w be op5$ to him & he w h at 8 s]vice a means ( acquir+ in=mation comp>$ ) :i* all o!r me?ods ( inve/igation are b *ild's play4#ca ,x is ! lack ( ?is ability to see1 ) our physical eyes1 z x 71 by ! ,ro5tg5 rays1 to p5etrate ! inw>dness ( ?+s t has baffl$ & conf\nd$ m5 = s long a "t & :i* has ev5tually l$ c]ta9 ma!maticians & o!rs to conjecture su* /range1 & 9 _m cases1 illogical possibilities = ! d5iz5s ( f\r-space4 ,?is inability toge!r ) ! desire to fa?om ! inn]mo/ complexities ( solids & to h&le1 albeit ) unholy h&s1 ! sup]s5su\s1 ! my/]i\s & ! unapproa*able id5tity ( ?+s-9-!mselves h induc$ ! m zeal\s among !m to contrive "s k9d ( hypo!sis :i* w\ld1 at lea/1 (f] an explanation ( ^! ph5om5a4 ,x has driv5 !m to wre/le ) metaphysical possibilities 9 a va9 endeavor to grasp t :i*1 ignis-fatuus l1 ev] evades _! slighte/ intellectual approa*4 ,b :y ?is prolong$ /ruggle1 :y ?is intellectual maneuv]+ & sophi/ry8 ,we c calculate1 compute1 excogitate1 says ,,paul ,,c>us1#cb & describe all ! *>act]i/ics ( f\r-dim5sional space1 s long z we rema9 9 ! realm ( ab/ract ?\ght & d n v5ture to make use ( our motility & execute our plans 9 an actualiz$ con/ruction ( motion2 b z soon z we make an a priori con/ruction ( ! scope ( our motility1 we f9d out ! incompatibility ( ! :ole s*eme4 ,?us ma!maticians are =c$ to rel9qui% all hopes ( trans=m+ ! _w ( life into a sort ( f\r-space dwell+ place :]e ev]y?+ is done accord+ to ! laws ( ma!matics4 ,b :e!r !y %all accept x or n !re is a wid]1 tru] & m rational view :i* recognizes all metageometrical inve/igations1 z well z all k9dr$ ph5om5a1 z univ]sal evid5ces inde$1 z ! v causes :i*1 9 ! future humanity1 w actually awak5 & cause to be accel]at$ 9 _! developm5t ^! little inn] s5se-organs1 ! p9eal gl& & ! pituit>y body1 ^: p]fect developm5t promises to provide = ! ,?9k]'s consci\sness an av5ue ( expression su* z humanity has possess$ nev] be=e4 ,& too1 x is n )\t full k ( ! fact t x has be5 cu/om>y1 among c]ta9 sci5ti/s or p]haps all ( !m1 to reg>d ^! bodies1 at lea/ ! p9eal gl&1 z ve/igal organs belong+ to ! pa/ ( human evolution1 t we make ^! ass]tions4 ,yet1 z man proce$s 9 ! p]fection ( me*anical sci5ce1 9 ! developm5t ( in/rum5ts ( precision t aid 8 ext]nal s5ses1 responds m & m to ! subtle vibrations teem+ ev]y:]e 9 ! atmosph]e ab\t him1 & comes1 9 ! c\rse ( "t1 naturally to possess a m s5sitively key$ n]v\s me*anism1 a f9] body & high] spiritual aspirations1 !re w be a correspond+ wid5+ ( 8 scope ( vision & ! atta9m5t ( l>g] p[]s ( p]ception :i* mu/ inevitably1 9 ! v nature ( ?+s1 t5d t[>ds a deep] & tru] k4 #ca ,rosicrucian ,cosmo-,conception1 p4 #dgg1 ,,max ,,he9del4 #cb ,,f\ndations ,,( ,,ma!matics1 p4 #ij4 ,9 view ( ! =ego+1 x is believ$ t ! g5]al results ( ?is pituit>ial awak5+ :i* may be expect$ z humanity cont9ues to evolve %\ld be se5 9 ! m>k$ effects :i* w be wr\ght 9 ! entire metaboli/ic area ( ! human body :]eby a gradual int5sification & s5sitization ( ! :ole neural me*anism w raise ! peculi> effici5cy ( all ! s5ses :e!r purely physiologic or psy*ic4 ,= !re are und\bt$ly notes s delicate 9 _! int5sity t !y transc5d ! grasp ( ! audital n]ves2 sc5ts & fragrances s subtle 9 _! excell+ purity t x is beyond ! p[]s ( our pres5t olfactorial contrivances to detect !m2 colors & o!r ext]nal /imuli s sublimely sup]s5su\s t a n]v\s me*anism p]haps t5-fold m delicate & responsive ?an ours is requir$ to appreh5d !m4 ,all ^!1 & m ?an at pres5t is conceivable1 w come1 ) ! aid ( pituit>ial /imulation1 )9 ! purview ( a m highly develop$ humanity ( ! future4 ,& because ma!matics h l$ a movem5t into ! v camp ( ! intellectuals--logic-b\nd & te!r$ by ! sev]e/ rigors ( ma!sis--:]eby ! intol]ant intellect has be5 compell$1 by rules ( its own mak+1 to recognize ! exi/5ce ( ! sup]s5su\s1 & by look+ into ! gl>+ light ( ! sun ( ! intuitable to ga9 /r5g? ( vision & boldness to press =w>d1 a great & f>-rea*+ s]vice has be5 wr\ght = humanity4 ,& 9 ! t[] ( hyp]space ma!matics h erect$ a monum5t to ! intellect :i*1 z long z ! human race rema9s1 w m>k ! great turn+ po9t 9 man's pa? to ! highe/ life4 ,:at if x 7 possible t ! sci5ti/1 :5 he _h c>ri$ in/rum5ts to _! utmo/ precision & p5etration1 %\ld sudd5ly1 or o!rwise1 be end[$ ) a cle>-p]ceptivity ( sight1 he>+ & smell1 s t he c\ld ) 8 own p[]s ( vision1 feel+ & he>+ take up ! task :]e ! microscope1 ! microphone & ! micromet] left (f & delve into dep?s f> too unfa?omable = 8 appliances1 p]ceiv+ ! inn]mo/ realities ( ?+s & processes8 ,:at if x 7 possible = him1 ) ^! add$ p[]s1 to see & exam9e )\t ! aid ( ! magnify+ l5s ! electron1 ! atom & ! molecule8 ,:at if ! cell1 ! bact]ium1 & o!r invisible =ms ( life w\ld !n deliv] up _! secrets to 8 kn[+ m9d8 ,:at if he c\ld s5se ) 8 own inn] vision1 ! ultra-violet & ! infra-r$ rays2 :at inde$1 if _s itself1 ! inn]mo/ %ea? ( life1 %\ld be visible & palpable to him & he c\ld note ! int]nal processes1 ! action & movem5ts ( ! inf9itesimals ( life8 ,?9k y n t su* direct contact1 su* imm$iate & incontrov]tible k w\ld be f> sup]ior to any advantage :i* 8 manufactur$ devices n[ be/[8 ,x is ev5 s4 ,?us w react ^u man's p]ceptive app>atus ! flood ( light :i* ! awak5$ intuition w %$ ^u !m & ?us w man rise high]1 driv5 on by ! curr5t ( life ) ! mass ( mat]iality1 to a po9t ( complete spiritualization & take additional /eps 9 t direction :i* leads to ,raja ,yoga or ! ,royal ,union ) ! div9e life ( ! univ]se4 ,be=e ?is /ep is tak51 h[ev]1 & be=e ! passage f me*anics to biog5etics is made1 z made x mu/ be1 man mu/ w9 a complete ma/]y ov] matt]4 ,b ?is he w d2 = m & m he is le>n+ to put all ^? =ms ( labor :i* are s exact+ z to leave him no "t = ! developm5t ( 8 high] p[]s into ! h&s ( ma*9]y4 ,he w n be free until he has done ?is well-nigh completely4 ,?is is ! task ( ! intellect & ) x man mu/ w9 8 way to ^! high] faculties :i* are de/9$ to succe$ ! intellect :]eupon he w be u%]$ out ( a life b\nd & re/rict$ by me*anics to a life ( unimag9able fre$om1 ! intuitive life4 ,! outcome ( ^! new faculties ( p]ception & ! developm5t ( ! intuition w be ! spr++ up ( a new species ( art t1 turn+ away f appe>ances & s9k+ b5ea? or ris+ above1 sup]ficialities1 w seek to portray 9 newly f\nd colors1 ! pla/ic ess5ce ( ?+s s t we %all h an art :i* p]ta9s to ! real1 sup]s$+ t :i* p]ta9s to ! ph5om5al4 ,language & ! ne$ ( x w pass away2 = man w h outgr[n ! use ( signs & symbols 9 8 communion ) 8 fell[s & w use ! language ( ! intuition--direct & in/antane\s cognition4 ,philosophy w be reg5]at$1 re-creat$4 ,speculation w give way to tru? & !re %all be b "o philosophy & t %all be ! k ( ! real4 ,ma!matics1 ! royal insignia ( ! intellectual life1 because x c deal only ) immobilities1 ) segm5ts & p>ts & has no aptitude = ! cont9u\s fl[1 w yield its k+dom to a high] =m ( k9etics :i* w s]ve ! intuitive faculty z ma!matics n[ s]ve ! intellect4 ,sci5ce w !n be no long] empirical 9 its me?od2 b a sy/em ( direct & incontrov]tible tru?s4 ,religion w rise to meet ^! *anges :i* w come 9 ! pa? ( human evolution2 & fai? w surr5d] its place to k4 ,e?ics1 reca/ 9 a new mold1 w deal ) ! new aspect ( man's relation to 8 fell[m54 ,man1 = ^: highe/ good ^! ultimate *anges w come1 w be a new creature1 a high] & bett] man2 & humanity %all evolve a new race4 ,!re %all1 inde$1 be a new heav5 & a new e>?4 ,,! ,,end4 ,,bibliography ,,am]ican ,,ma!matical ,,mon?ly3 ,vol4 ,,viii1 p4 #afa1 ,p4 ,,b>b>91 = ,le ,ma!mati*e1 ,trans1 by ,,geo4 ,b4 ,,hal/$4 ,see also pp4 #ca-ce4 ,vol4 ,,viii1 #aija1 p4 #bag1 ,suppl4 ,report on ,non-,euclidean ,geometry1 ,,geo4 ,,bruce ,,hal/$4 ,vol4 ,,ix1 p4 #ei1 ,,geo4 ,b4 ,,hal/$4 ,idem1 pp4 #aec-aei4 ,vol4 ,,xi1 pp4 #he-hf1 ,simon's ,claim = ,gauss4 ,,am]ican ,,ma!matical ,,society ,,bullet91 ,lanca/]1 ,pa43 ,vol4 ,,ii1 s]ies #ahie4 ,vol4 ,,xx1 #aiad1 pp4 #dji-dab1 ,r4 ,c4 ,,ar*ibald4 ,,annals ,,( ,,ma!matics1 #b;d s]ies1 #aijb3 ,vol4 ,,xii1 ,f4 ,s4 ,,wood4 ,,a/ronomical ,,society ,,notices3 ,vol4 ,,xvi1 p4 #hj1 #ahef4 ,,ball',s ,,%ort ,,acc\nt ,,( ,,! ,,hi/ory ,,( ,,ma!matics4 ,,bo/on ,,colloquium1 = #aijc1 ,n4 ,y4 #aije1 ,=ms ( ,non-,euclidean ,spaces1 ,vols4 ,i-,,iii1 pp4 #ca1 et seq41 #ahia4 ,,bullet9 ,,new ,,york ,,ma!matical ,,society3 ,vol4 ,,ii1 pp4 #a-add4 ,vol4 ,,iii1 pp4 #a1 et seq41 #ahia1 ,g4 ,b4 ,,mccl9tock4 ,,cambridge ,,ma!matical ,,j\rnal3 ,vol4 ,,iv1 #ahde1 ,,cayley1 on ,analytical ,geometry ( n-,dim5sions4 ,,canadian ,,in/itute ,,transactions3 ,vol4 ,,viii1 pp4 #cae-cci1 #aiji1 ,,augu/ ,,kirs*baum4 ,,cayley1 ,a41 vide ,sci5ce1 ,vol4 ,,ix1 pp4 #ei-fc3 ,am]4 ,ma?4 ,mo41 ,vol4 ,,ii1 pp4 #ajb-ajf4 ,am]4 ,ma?4 ,mo41 ,vol4 ,,vi1 pp4 #ei-fe4 ,review ( ,reviews1 ,june1 #ahie1 pp4 #fic-fid4 ,,class ,,book ,,( ,,non-,,euclidean ,,geometry3 ,vide ,sci5ce1 ,,xiii1 pp4 #dfb-dfe4 ,,cornhill ,,magaz9e 7n4s473 ,vol4 ,,xxxvii1 pp4 #fdg-ffe1 ,c4 ,h4 ,,bryan1 on ! ,f\r? ,dim5sion4 ,,easy ,,non-,,euclid3 ,moni/1 ,,xix1 pp4 #cii-djb4 ,,educational ,,review3 ,novemb]1 #aijb1 issue1 pp4 #cdf1 et seq4 ,,euclid',s ,,p>allel-,,po/ulate1 by ,,john ,w4 ,,)]s4 ,,flatl&1 by ,a4 ,,squ>e4 ,,f\ndations ,,( ,,geometry3 ,sci5ce1 ,vol4 ,,vi1 pp4 #dhg-dia4 ,,f\ndations ,,( ,,ma!matics1 by ,,paul ,,c>us4 ,,f\r? ,,dim5sion3 ,by ,,h]man ,,s*ub]t1 ,c4 ,h4 ,,h9ton1 ,,claude ,,bragdon4 ,,f\r? ,,dim5sion1 ,,simply ,,expla9$3 ,edit$ by ,h4 ,p4 ,,mann+4 ,,f\r? ,,dim5sion3 ,cornhill ,magaz9e1 n4s41 ,vol4 ,,xxxvii1 pp4 #fdg-ffe1 by ,c4 ,h4 ,,bryan4 ,,f\r? ,,dim5sion1 ,,! ,,riddle ,,(3 ,h4 ,a4 ,,bruce1 9 ,sci5tific ,am]ican ,supplem5t1 ,vol4 ,,lxvi1 p4 #adf4 ,,geometry1 ,,f\ndations ,,(1 by ,o4 ,,vebl53 ,popul> ,sci5ce ,mon?ly1 ,vol4 ,,lxviii1 pp4 #ba1 et seq4 ,,geometry1 ,,loba*evski',s3 ,!ory ( ,p>allels1 trans4 by ,,geo4 ,,bruce ,,hal/$4 ,,geometry1 ,,non-,,euclidean3 ,am]ican ,ma!matical ,mon?ly1 ,vol4 ,,vii1 pp4 #abc-acc4 ,,geometry1 ,,non-,,euclidean1 ,,report ,,on ,,progress ,,93 ,repr9t$ f ,sci5ce1 n4 s41 ,vol4 ,x1 ,no4 #bea1 pp4 #ede1 et seq41 by ,,geo4 ,,bruce ,,hal/$4 ,,geometry1 ,,non-,,euclidean1 ,,!sis ,,on3 ,by ,m4 ,l4 ,,g]>d4 ,,geometry1 ,,non-,,euclidean3 ,by ,,rob]to ,,bonola1 trans4 by ,h4 ,s4 ,,c>slaw1 ,univ]sity ( ,sydney1 ,n4,s4,w4 ,,geometry1 ,,non-,,euclidean3 ,,julian ,,l[ell ,,coolidge1 pp4 #df1 et seq4 ,,geometry1 ,,non-,,euclidean3 ,by ,h4 ,p4 ,,mann+4 ,,geometry1 ,space &1 9 ,light ( ,physiologic1 ,psy*ologic & ,physical ,inquiry1 vide ,op5 ,c\rt1 #aijf1 by ,e4 ,,ma*4 ,,hal/$1 ,,george ,,bruce3 ,cayley1 ,a41 ,biog4 (1 vide ,am]4 ,ma?4 ,mo41 ,vol4 ,,ii1 p4 #ajb4 ,f\r-fold ,space 9 ,two-fold ,"t1 vide ,sci5ce1 ,vol4 ,,xix1 p4 #cai4 ,hoel1 ,biog4 (1 ,am]ican ,ma?4 ,mo41 ,vol4 ,,ix1 pp4 #ii-aja4 ,lamb]t's ,non-,euclidean ,geometry1 vide ,n4 ,y4 ,ma?4 ,soc4 ,bull41 ,vol4 ,,iii1 p4 #gi4 ,loba*evski1 ,n41 ,biog4 (1 vide ,am]4 ,ma?4 ,mo41 ,vol4 ,,ii1 pp4 #acg-aci2 ,op5 ,c\rt1 ,vol4 ,,xiii1 pp4 #daa-dae4 ,message ( ,ma!matics to ,natural & ,rational ,!ology1 vide ,hibb]t's ,j\rnal1 ,vol4 ,,vii1 #ahji4 ,non-,euclidean ,geometry1 ,inevitable1 vide ,moni/1 ,vol4 ,,iv1 p4 #dhc4 ,non-,euclidean ,geometry1 ,hi/orical & ,expository1 ,am]ican ,ma!matical ,mon?ly3 ,vol4 ,i1 pp4 #gj-gb2 #aab-aae2 #adi-aeb2 #ahh-aie2 #bbb-bbc2 #bei-bfj2 #cja-cjc2 #cde-cdf2 #cgh-cgi2 #dba-dbc 7#ahid74 ,vol4 ,,ii1 pp4 #aj2 #db-dc2 #fg-fi2 #ajh-aji2 #add-ade2 #aha-bad2 #bef-beg2 #cji-cac2 #cdf-cdh 7#ahie74 ,vol4 ,,iii1 pp4 #ac-ad2 #ce-cf2 #fg-fi2 #aji2 #acb-acc 7#ahif74 ,vol4 ,,iv1 pp4 #aj2 #gg-gi2 #aja-ajb2 #agj-aga2 #bjj2 #bdg-bdi2 #bfi-bgj2 #cjg-cjh 7#ahig74 ,vol4 ,v1 pp4 #a-b2 #fg-fi2 #abg2 #bah2 #bij-bia 7#ahih74 ,review ( ,reviews1 ,vol4 ,,ii1 #ahie1 pp4 #fic-fid4 ,space1 ,new ,ideas ,ab\t1 ,popul> ,sci5ce ,mon?ly1 ,vol4 ,,xi1 p4 #cfd4 ,,helmholtz1 ,h41 ,on ,orig9 & ,mean+ ( ,geometric ,axioms3 ,vide ,m9d1 ,"p ,i1 ,no4 #c1 ,july1 #ahgf4 ,= replies & discussions ( ! above1 vide ,nature1 ,,jevons1 ,vol4 ,,iv1 p4 #dha2 ,j4 ,l4 ,,tupp]1 ,nature1 ,vol4 ,v1 p4 #bjb2 ,,helmholtz1 9 ,academy1 ,vol4 ,,iii1 p4 #eb2 ,m9d1 ,"p ,,ii1 ,april1 #ahgh4 ,,h]ma!na1 ,vol4 ,,xiii1 pp4 #dia1 et seq41 #aijf4 ,,high] ,,space1 ,a ,,prim] ,,(1 by ,,claude ,,bragdon4 ,,+leby1 ,c4 ,m43 ,a ,non-,ma!matical ,criticism ( a ,"p ( ,pr(essor ,clif=d's ,lecture on ,curv$ ,space1 ,macmillan's ,magaz9e1 ,octob]1 #ahgb2 also ,nature1 ,vol4 ,,vii1 #ahgc4 ,,j\rnal ,,( ,,ma!matics1 ,,am]ican3 ,vol4 ,i1 pp4 #bfb1 #bgf1 #chd1 #chf2 ,,hal/$ 7#ahgh74 ,,j\r4 ,,philos41 ,,psy*ol4 ,,& ,,sci5tific ,,me?ods3 ,vol4 ,,vi1 pp4 #fag1 et seq4 ,,kant1 ,,emmanuel1 trans4 by ,,fr$4 ,,pauls54 ,,kant1 ,,emmanuel1 ,prolegom5a1 trans4 by ,j4 ,p4 ,,mahaffy & ,j4 ,h4 ,,b]n>d1 pp4 #ce-ci4 ,,lamb]t1 ,,biography ,,(3 ,am]ican ,ma?4 ,mo41 ,vol4 ,,ii1 pp4 #bji-baa4 ,,lie1 ,,sophus3 ,sci5ce1 ,vol4 ,,ix1 pp4 #ddg-ddh4 ,,loba*evski1 ,n43 ,op5 ,c\rt1 ,vol4 ,,xii1 pp4 #daa-dae1 ,am]4 ,ma?4 ,mo41 ,vol4 ,,ii1 pp4 #acg-aci4 ,,london1 ,,ed9burgh ,,& ,,dubl9 ,,philosophical ,,magaz9e3 ,vol4 ,v1 s]ies #f1 p4 #eei4 ,,ma!matics1 ,,f\ndations ,,(3 ,,paul ,,c>us4 ,,ma!matical ,,pap]s ,,( ,,*icago ,,congress1 p4 #ib4 ,,ma!matical ,,pap]s1 pp4 #ee-ga4 ,,ma!matics 7a bro*ure73 ,by ,c4 ,j4 ,,keys]1 ,adrian ,pr(essor ( ,ma!matics1 ,columbia ,univ4 ,,ma!matics1 ,,high]3 ,edit$ by ,,mansfield ,,m]riam & ,,rob]t ,s4 ,,wood1 #aijb1 pp4 #ejh1 et seq4 ,,ma!matics1 ,,spiritual ,,significance ,,(3 ,c4 ,j4 ,,keys]1 repr9t$ f ,columbia ,univ4 ,qu>41 ,decemb]1 #aiaa4 ,,memorial ,,volume ,,( ,,sci5tific ,,pap]s3 ,pub4 by ,univ4 ( ,/4 ,&rews1 pp4 #c-de1 ,d4 ,m4 ,y4 ,,som]ville4 ,,m9d 7,magaz9e73 ,vol4 ,i1 #ahgf1 pp4 #cjc1 et seq4 ,j4 ,n4 ,p4 ,,l&4 ,vol4 ,,ii1 #ahgg1 p4 #dj1 ,j4 ,n4 ,p4 ,,l&4 ,vol4 ,,ix1 pp4 #ebb1 et seq4 #aijj4 ,,moni/ 7,magaz9e73 ,vol4 ,,ii1 pp4 #ej1 #cba1 ,,paul ,,c>us4 ,vol4 ,,iv1 #ahid1 ,articles by ,g4 ,b4 ,,hal/$ & ,j4 ,,delboeuf4 ,vol4 ,,vi1 #ahie1 ,,h]man ,,s*ub]t4 ,vol4 ,,vii1 ,g4 ,b4 ,,hal/$1 on ,sac*]i4 ,vol4 ,,xiii1 pp4 #hj-ajb2 #bah-bcd4 ,vol4 ,,xiv1 ,article by ,e4 ,,ma*4 ,vol4 ,,xv1 p4 #abg1 ,,paul ,,c>us4 ,vol4 ,,xvi1 #aijf1 p4 #dcc1 ,,david ,p4 ,,abbott4 ,idem1 #aijf1 p4 #fe1 ,c4 ,j4 ,,keys]1 on ,ma!matical ,emancipations4 ,,nature 7,magaz9e73 ,vol4 ,,viii1 pp4 #h1 #ad-ag1 #cf-cg 7#ahgc74 ,vol4 ,,xv1 pp4 #ecc-ecg 7#ahgg74 ,vol4 ,,xlv1 ,p4 #djd 7#ahia74 ,,newcomb',s ,,philosophy ,,( ,,hyp]space3 ,sci5ce1 ,vol4 ,,vii1 p4 #bab4 ,,new ,,york ,,ma?4 ,,soc4 ,,bullet93 ,vol4 ,,iii1 p4 #gi 7#ahic71 ,f4 ,s4 ,,wood on ,=ms ( ,non-,euclidean ,space4 ,,op5 ,,c\rt 7,magaz9e73 ,vol4 ,,xvi1 pp4 #eac-eba4 ,vide ,decemb]1 #aiac edition1 p4 #geg4 ,,philosophy ,,( ,,ma!matics1 by ,,paul ,,c>us4 ,,philosophical ,,review3 ,vol4 ,v1 #ahif1 p4 #age1 ,f4 ,c4 ,s4 ,,s*ill]4 ,idem1 p4 #ceg1 ,j4 ,h4 ,,hyslop4 ,vol4 ,,vii1 p4 #fae4 ,vol4 ,x1 pp4 #aac1 #bbi1 #cad1 #cge1 #dhh1 #egi1 #ehc4 ,vol4 ,,xii1 p4 #dic4 ,,popul> ,,sci5ce ,,mon?ly3 ,no4 #ff 7#aije71 pp4 #fci-fdf4 ,vol4 ,,lxvii1 pp4 #fci1 et seq4 ,vol4 ,,lxviii1 pp4 #ba1 et seq4 ,vol4 ,,lxxviii4 p4 #eed 7#aiaa71 ,,samuel ,,m(fat ,,wey]4 ,,popul> ,,a/ronomy3 ,vols4 ,,vii & ,,viii 7#aijj71 ,g4 ,b4 ,,hal/$4 ,vol4 ,,xviii1 pp4 #db1 et seq4 7#aiaj71 ,w4 ,h4 ,,pick]+4 ,vol4 ,,lxxv1 p4 #agi1 ,w4 ,w4 ,,payne1 on ,attraction & ,figure ( ! 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exi/5ce ( ?+s1 #afa-bjb -- degrees (1 #afe -- hyp]space1 a symbol ( a m ext5sive1 #ahj -- progress 91 #aga -- ,?9k]'s sph]e (1 #bgd1 #bhc ,b ,baltz]1 #ff ,b>ri]1 !1 to ! ,?9k]'s c]titude1 #ahf-h ,b>ri]s1 fre$om det]m9$ by abs5ce (1 #bhj ,becom+1 endless labyr9? (1 #bbj -- ! kosmos1 9 a /ate (1 #bfe -- ! ord] (1 #cje ,becom+s1 inf9ity (1 #bcd ,becqu]el rays1 #ccf ,be+1 id5tification ( consci\sness )1 #bje -- ka!kotic1 #baj ,be+1 ! int]iority (1 #bij -- ! num]icity (1 #cji -- ! range (1 co-ext5sive ) reality1 #afh ,be+s1 disc>nate1 #aed ,beltrami1 ,eug5io1 #a-b1 #fc-e1 #ff-g -- -- & ! manifold1 #cag -- -- & ! pseudosph]e1 #fd-e ,besiegem5t ( matt] by life1 #cbi-cj ,bessel1 on geometry z incomplete1 #eh ,bewild]m5t1 new realities cause1 #afi-gj -- ( ! m9d1 #ahb ,biog5etics1 passage f me*anics to1 #ceg -- turn+ to1 f me*anics1 #cbb ,bir?1 z a f\r? dim5sional process1 #aei ,bl9d m5 & ! elephant1 #beg ,bolyai1 ,janos1 #b-c1 #df1 #fj1 #ff1 #hc1 #hg ,b\nd>ies ( a hyp]cube1 #acf-h ,bra91 ! physics (1 #bib ,bra9-consci\sness1 #ahd1 #ahf -- /&>ds (1 #aij ,bro!rhood1 & ! t5d5cies ( ! ,?9k]'s consci\sness1 #cja -- ! keynote ( ! intuition1 #beb ,bulw>ks1 ! =mal1 ( geometry1 #gg-i ,c ,c>pet1 ! s5sible _w z a1 #aif ,c>us1 ,paul1 on f\r-dim5sional space1 #bed -- -- on metageometricians1 #ajb -- -- on space1 #aaj -- -- on ! repres5tation ( ! tess]act1 #acf-g ,cayley1 #c-d1 #ed-e1 #ff-g ,cell-activity z a p]=mance a priori1 #aad ,cell-colony1 #bej1 #cja ,cell-consci\sness z an apo/]iori/ic ph5om5on1 #ahe ,c5t]s1 pyknotic1 #bcb ,c]ta9ty1 geometric1 ! basis (1 #gg-h -- ( ma!tic conclusions1 provisional1 #cg ,*aog5ic p]iod ( involution1 #bjh1 ff ,*aog5y1 #bca1 #bcc -- ! evolution ( *aos into ord]1 #d -- ! laboratory (1 #aic ,*aomorphog5y1 def9$1 #d1 #bca-b ,*aos1 z egg-plasm1 #bfe -- duration (1 #bfh -- movem5t ( life 91 #cjg -- %ores (1 #cjg ,*aos-geometricity1 #cjg -- -intellectuality1 #cjg -- -mat]iality1 #cjg -- -spatiality1 #cjg -- -,!os-,kosmos1 #bae1 #bcc-d1 #bcg -- -- -- a triglyph symboliz+ ka!kos1 #aa-b ,"* ( ! univ]se1 fix$ by consci\sness1 #afb ,*>act]i/ics1 *anges 9 !1 ( reality1 #afi -- f\r? dim5sional1 ( ! e!r1 #aeg -- m9ds ( simil>1 fall into zones ( aff9ity1 #abd -- ( non-,euclidean space1 #gb-c ,*asm1 kosmic1 betwe5 ! real & ! ideal1 #ajg ,*emi/s1 speculative1 & ! our? dim5sion1 #aee ,*rism1 sacr$1 ( creative m5tality1 #ia ,circle1 significance ( process ( squ>+1 #aji ,circle1 ! symbology (1 #cji ,circuits1 clos$1 our int]e/s z1 #afg ,clairaudi5ce1 #ceb ,clairvoyance1 #ceb ,clairvoyant p]ception1 #cdi ,clause1 enabl+1 ( metageometry1 #gf-g ,clavius1 ,*ri/oph1 #df1 #eb1 #hc ,clif=d1 #ff ,code1 psy*ic1 = sy/ematiz+ cognitions1 #aij-a ,cognition1 in/antane\s1 organ (1 #beh -- intimacies ( direct1 #bje -- ! me?od (1 #ahf-h ,cognitions1 intuitive1 #ade1 #aib-c -- psy*ic code = sy/ematiz+1 #aij-a ,comm5surable quality1 dim5sion z1 #adj ,communal consci\sness1 #bgj1 ff ,communalization & ! intuition1 #cja ,con>ium1 !1 #cde ,conceivability & evolution ( m9d1 #bd -- ultimate range (1 #bgh ,conceiv+1 p[] (1 d]iv$ f s5se-exp]i5ce1 #bf ,concept1 z a %ad[1 #aai -- ! hyp]space1 gradual rise (1 #bg-h ,conception & aw>5ess1 #abj -- e1 bas$ ^u prior exp]i5ce1 #be -- fre$om1 !1 ( ! m9d f1 #bh ,conceptions1 symbolic1 dep5d5ce plac$ ^u1 #adg ,concepts1 & ! ,?9k]1 #bdd -- intuitograms z1 #bdh -- quality (1 dep5d5t ^u s5se-exp]i5ce1 #bf ,concepts1 ! p]ception (1 #bee ,conceptual1 relat$ to ! objective1 #bia -- !1 & ma!maticians1 #ga ,conceptualization1 ! act (1 #d -- ! p[] (1 dep5d5t ^u evolution ( m9d1 #be ,conclusions1 ma!tic1 complex dep5d5ce (1 #cg ,concrete hewn into %ape by ! intellect1 #bie ,congru5cy1 !1 betwe5 intellect & ! univ]se1 #cai1 ff ,congruity1 !1 betwe5 concepts & objects1 #abj ,connection1 !1 trac$ out betwe5 reality & object1 #abf ,co-orig9ality ( ?+s1 #cjc ,consci\sness & kosmos1 graph repres5t+1 #bga -- -- ! "* ( ! s5sible _w1 #aff -- -- -- wake ( life1 #bje -- -- "t1 #bbd -- angul>ity (1 #abj -- a priori1 #ahe -- a replica (1 & judgm5ts1 #bje -- z a scale1 #afe -- -- b>ri] to ultimate k1 #bjg -- -- det]m9ant ( dim5sion1 #ade -- -- life1 #bie -- -- v>iable quantity1 #aga -- atta*m5t (1 to ! ord] ( becom+1 #cje -- dawn (1 & dim5sion1 #agi -- degrees (1 #afb -- depriv$ ( ! validity ( notions1 #cad -- evolution (1 #bej -- expansion (1 #afd1 #bgb -- ext5d$1 #hi-ij -- focus (1 #bij ,consci\sness & ! planes ( ! kosmos1 #afc -- fragm5t>y view (1 #bfj -- fre$om (1 9 ! g5us homo1 #ccb -- habitation (1 #bgh -- high]1 & art1 #aha -- -- planes (1 #agh -- hi/ory (1 #bih-i -- id5tification (1 ) objects1 #ahi-ij -- intuitional1 #bee -- key$ to ! entire range ( reality1 #afg-h -- k9ds (1 #bgj1 ff -- kosmic1 ,elysian fields (1 #bce -- ( ! primitive man1 #bec -- organ (1 #ahd1 ff2 #ij -- psy*ics (1 #bib -- rais$ f ! s5su\s to ! conceptual1 #gb -- recipi5t ( tru?s f dual s\rces1 #bf -- s5sible _w z in/rum5t (1 #aii -- triple pres5tation ( notions ( space to1 #gb -- turn$ inw>d1 #bhc -- unification ( ! /ates (1 #aib -- y\?ful1 ( mank9d1 #abb ,consequ5ces1 ! sci5ce (1 #he ,consid]ations1 ma!matical1 & reality1 #abh ,consi/5cy1 kosmic1 #agd -- self1 ( hyp]spatial hypo!ses1 #fg -- ! crit]ion ( geometry1 #hf -- -- inconsi/5ce (1 #agc -- -- metageometrician curtail$ by1 #he ,con/ruction1 idealiz$1 _c be objectifi$1 #add1 #bgf -- ideal1 ! mean+ (1 #d -- m5tal1 traffick+ 91 #aed ,consub/antiality ( intellectuality & spatiality1 #cca1 ff ,cont9uity ( ! psy*ic plasm1 #bfj ,contrivances1 ma!tic1 ! pass+ (1 #bda ,conv]g5ce ( p>allel l9es1 #cae ,convolutions1 duplex1 #adf ,cord9ates1 z spatial det]m9ants1 #bjc -- ( hyp]space1 #id1 #ig1 #ii1 #aae-f -- sy/ems (1 #cja1 ff -- ?ree1 #acb1 #bcb ,copol>ity ( ideas & objects1 #abg ,corpora quadrigem9a1 #cde ,corpuscul> orbits ( p>ticles1 #aeb ,cosmos1 significance (1 #d ,creation1 impregnat$ scre5 (1 #bcb ,creations1 !1 ( ! intellect1 #agc ,crit]ion ( geometry z consi/5cy & conv5i5ce1 #hf -- -- tru?1 #cbc-d ,crookes1 #cdd ,cube1 z succession ( planes1 #adh -- g5]ation ( !1 #add -- illu/rat$1 #acc -- ! g5]at+1 #acd ,curiosities1 analytic1 en]gy sp5t 9 elaborat+ misappropriat$1 #ci ,curr5t1 electric1 z compon5t 9 ! f\r? dim5sion1 #aec ,curvature ( space1 ! doctr9e (1 =mulat$ by ,riemann1 #e -- -- -- valid elem5t 9 ! notion (1 #cje -- ! measure (1 #fa ,curv$ space & metageometricians1 #caf ,d ,d',alemb]t1 note1 #ea ,dante1 #aha ,d>w91 #aha ,day1 ! ,great ,kosmic1 #bac ,de ,tilly1 #ff ,dea?1 z f\r? dim5sional unity1 #aei -- ( ! intellect1 #aie ,decrem5t ( ! diametrical ratio to ! circumf]5ce ( circle1 #cab ,deeps1 fe>ful1 ( kosmic m9d1 #ga1 #ia ,def9ition1 apo!osis (1 #gg-h -- z an arbitr>y det]m9ation1 #ajj -- ! deification (1 #cg ,degrees ( realism1 #afd-e ,dei=m1 basic idea ( !1 #e ,dem>kation betwe5 reality & phantasy1 ! l9e (1 #agc ,deposits ( life1 #agc ,desc>tes1 #cbb ,designs1 cut out 9 mat]iality by life1 #bfd ,details1 ! p[] to dispose ( innum]able1 #cjc ,det]m9ations1 geometrical1 ! necessity (1 inh]es 9 logical d$uctions1 #gh -- ! factors ( consci\s1 #afb ,det]m9ative p]iod ( m5tal developm5t1 #ca ,developm5t ( ! intuitive faculty1 future1 #ahh ,diacritics ( life1 #bhf ,diamet]1 ! ratio (1 to ! circumf]5ce1 #caa-b ,diff]5ce betwe5 concept & ?+1 #aba-b -- betwe5 ma!matical & p]ceptual space1 #abj -- betwe5 ! ideal & ! actual is dynamic1 #ajh ,diff]5tial1 among m9ds1 #abd ,difficulty ( imag9+ ! f\r? dim5sion1 #ij -- ( propagat+ an intuition1 #cae ,difficulties 9 ! acquisition ( real k1 #cbe -- ( hyp]space1 ! logical1 #aci-da ,dilemma ( metageometricians1 #ig-h ,dim5sion1 a di/9ct /age 9 psy*og5esis1 #bg -- -- sy/em ( space measurem5t1 #e -- & analysis1 #afc -- -- ,d',alemb]t1 note1 #ea -- -- ! action ( a t>trate 91 #aef -- z an arbitr>y contrivance1 #bfb -- -- -- assemblage ( elem5ts1 #ic -- -- direction1 #adj -- -- ext5t1 #ih -- -- ly+ ne> ! surface ( ?+s1 #aei-fj -- -- space1 #if -- curr5t def9itions (1 #ih-ajj -- d5i$ legitimate an*orage1 #bfe -- det]m9$ by consci\sness1 #ade -- does n expla9 spiritualism1 #aee -- evolution ( ! f\r?1 #dd -- f\r?1 direction (1 #acd -- z jack ( all trades1 #aef -- impossible to actualize1 #abd -- key1 to non-,euclidean geometry1 #ij -- movem5t ( a plane into1 #adg-h -- no motion ( mat]ial masses into1 #abe -- n a priori1 #aaf -- pro( ( ! exi/5ce ( ! f\r?1 #acf ,dim5sionality1 & ! intellect1 #bjj -- z dep5d5t ^u ! w ( ! inve/igator1 #ie ,dim5sionality1 conception (1 purely conv5tional1 #ib -- logical difficulties :i* beset1 #ig -- ( p]ceptual space1 #gb -- -- space1 ! f\r1 #adb-c ,dim5sions1 f\r1 no basis 9 consci\sness =1 #agb -- pil$ ^u "o ano!r1 #cjj -- vanity1 !1 ( segm5t+ space into _m1 #bii ,direction z dim5sion1 #ii ,disappo9tm5t ) ! s5sible _w1 #abj-a ,discov]ies1 metageometrical1 z excresc5ces ( m5tal unfoldm5t1 #aca -- nev] ! result ( me?odic reflection1 #bi-cj ,disord]1 ! edict (1 & space1 #bcj ,disord]l9ess1 ! fr+e (1 #bgg ,dispossessal ( ! intellect by ! intuition1 #aie ,dissimil>ities1 besetm5t (1 #bia ,di/9ctions1 betwe5 conceptual & p]ceptual space1 fundam5tal1 #gc-e ,div]sity1 a result ( ! fragm5tative t5d5cy ( life1 #f -- z transf9ite quantity1 #db ,div9ity1 prize (1 won by ! intellect1 #dc ,duadic phase ( evolution1 #baj-a ,duodim1 def9$1 #f2 #abh1 #abi1 #acd1 #agg -- consci\sness1 #afc ,duopyknon1 #bab1 #bac -- ! mean+ (1 #f ,duopyknosis1 #bjh-aj1 #bah -- z a /age 9 ! evolution ( space1 #f ,duration & space1 #bbd -- et]nal1 #bcd ,dynamic appe>ance1 space z1 #ajd1 #ajg ,dynamism1 ( ! intellect1 functional1 #cjc ,e ,e>?1 ! nebul\s y\? (1 #cce -- a new1 #ceh ,ea/ effloresces z ,we/1 #cjf ,ego1 !1 #bgj -- & p]cepts1 #bdd -- z sov]eign1 #bdd -- ,?9k]'s dep5d5ce ^u1 #bde -- -- treatm5t (1 #bdf ,egopsy*e1 #bfe -- z an ag5cy ( self-consci\sness1 #beh -- def9$1 #g ,egos1 comp>$ to *oppy sea1 #bef-g ,egypt1 bir?-place ( geometry1 #dd ,eis5lohr1 #dd ,elaborative p]iod ( ! non-,euclidean geometry1 #ff-gj -- -- ( m5tal developm5t1 #ca-cb ,elem5t ( evolution1 basal1 #bei ,elem5ts ( ! non-,euclidean geometry1 #gi-hj ,elephant & bl9d m51 #beg ,ellis1 ,wilmot ,e41 on e!r z f\r-dim5sional1 #aeg-i ,embrace ( direct cognition1 #bje ,eng5d]m5t ( space1 #bfj ,ens\lm5t ( ! _w-plasm1 #cbi ,entities1 hyp]space1 & ! ph5om5al _w1 #abh-acj ,enum]ation1 re=mation ( ! sy/em (1 #ch ,enveilm5t ( consci\sness1 #bgc-d ,environm5t1 artificial & natural1 #afb ,epiphysis1 !1 #cde ,equidi/antial1 describ$ by hyp]spatial p]p5dicul>1 #hj ,ess5ce1 elem5tal1 z _w-plasm1 #cbi ,e!r z possess+ f\r? dim5sional *>act]i/ics1 #aeg ,e?ics reca/ 9 a new mold1 #ceh ,euclid1 #df1 #gj1 #hc1 #bfc -- & ! p>allel-po/ulate1 #de -- nev]-dy+ elem5ts (1 #ec ,evid5ces1 ma!matical1 exemplifies intellectual evolution1 x -- ! vanity ( fragm5t>y1 #bjd ,evolution1 a cont9u\s process1 #cbg -- & ! norms ( reality1 #age -- basal elem5t (1 #bei -- comm5cem5t (1 #bcb-c -- intellectual1 =w>d movem5t (1 #ahd -- kosmic1 vicissitudes (1 #bae -- laws (1 gov]n m9d1 #bh -- m5tal1 results (1 #abb -- ( faculties1 syn*ron\s ) evolution ( matt]1 #ccb -- -- mat]ial *>act]i/ics ( ! e>?1 #cce -- -- organs1 "t requir$ =1 #ahh -- prep>ation ( ! field (1 #bah ,exaltation ( matt] into _s1 #cbi ,examples ( new p]ceptive evid5ces1 #cda-c ,exi/5ce on a high] plane1 /ates (1 #afb ,exp]i5ce1 corroborative te/imony (1 d5i$ hyp]space1 #bfc -- prior1 & conception1 #be ,exp]i5ces1 spatial1 sy/ematization (1 #gh ,ext5sion1 space z an unb\nd$1 #fa ,extra-spatiality1 degrad$ into spatiality1 #bfa ,extravaganza1 ma!matical1 & ! f\r? dim5sion1 #aef ,eyes1 z ,ro5tg5 rays1 #cec ,f ,fact-mass1 #bhi ,factors ( consci\s det]m9ations1 #afb -- f\r1 ( ! crit]ion ( tru?1 #cbd-e ,facts z facets ( tru?1 #bhd -- attempts to re=m1 #cjd -- logic z symbolism (1 #bhg -- -- ! model] (1 #bhh ,faculties1 dual d]ivation (1 #afb -- evolution (1 syn*ron\s ) evolution ( mat]ial qualities1 #ccb1 ff -- ext5d$1 #bci -- =e%ad[$ by ! hyp]dim5sional1 #aca -- high]1 man mu/ w9 8 way to1 #ceg -- new faculties evid5c$ by f\r-space1 #bd-bi -- rudim5t>y nature (1 #cda1 ff -- ! s\rce (1 #cdi ,faculty & ! intellect1 #bdg1 ff -- z transmissible "*1 #bea -- det]m9$ by function1 #ccf -- greatly ext5d$1 #aag -- high] ?an ! intellect1 #abf -- ,i-mak+1 self-consci\sness z1 #bdc -- intuitive1 #ahe -- ( p]ception 9 high] worlds1 #cec -- -- aw>5ess1 ! awak5+ (1 #hi-ia -- ov]%ad[$ by ! intellect1 #ahh -- ( p]ception 9 high] worlds1 #cec -- rudim5t>y condition (1 #aib1 ff ,faculty1 outcropp+ (1 #bdi-ea ,failure ( ef=ts to ju/ify ! objective exi/5ce ( f\r-space1 #abe-f ,failures at solv+ ! p>allel-po/ulate1 outcome (1 #dh1 #hc ,fai?1 dispossess$ by k1 #ceh ,fay1 ma!tic1 #afj ,fe*n]1 #ci ,f9ity & unb\nd$ness ( space1 #gf ,flamm>ion1 ,camille1 #cda-b1 #cdd ,flexity1 z prop]ty ( hyp]space1 #fc ,flexure1 space z a1 #cje ,fluxional1 betwe5 s5se objects & ideal repres5tations1 #abb-c ,fluxion1 psy*ic1 z diff]5ce betwe5 memory image & object1 #g-h2 #abb ,focus ( consci\sness1 #afc1 #bij -- -- ! intellect1 #caj ,fohat1 & ! creation ( morphons1 #bai -- z creative en]gy1 #bac -- ,creator1 #h ,fohatic en]gy1 #bbf ,=m1 z vehicle ( life1 #ccj -- def9ition (1 #h -- driv5 back ov] ! pa? ( its g5esis1 #cbg -- pure1 _c exi/ 9 nature1 #bid -- ! idealty (1 #aaj -- ! univ]se n a pure1 #ajh ,=mative p]iod ( m5tal developm5t1 #ca -- -- ( non-,euclidean geometry1 #ee ,=mula1 eight diff]5t alcohols f "o1 #aee ,f\r-dim5sionality1 ju/ification (1 #agf ,f\r-space1 a curiosity ( analytics1 #dj -- & ,riemann1 #bg -- z a div]tisem5t1 #age -- consci\sness does n act 9 !1 #agb -- exi/5ce (1 d5i$1 #aga-b -- movem5t ( matt] 91 #aeg -- reality (1 glibly proclaim$1 #aed -- !1 #h1 #bdj -- -- d5iz5s (1 #cec -- -- doma9 (1 #aed -- -- /udy (1 #abd -- use ( analogies to popul>ize1 #abh ,f\r? dim5sion1 analogical reason+ (1 #agg-i -- z a transc5d5tal problem1 #adj -- -- an attitude ( ! intellect1 #bjj -- electric curr5t z a compon5t 91 #aec -- imag9ability (1 #ajf-g -- ,simon ,newcomb on1 #abe ,fragm5t>9ess ( ! intellectual me?od1 #afd ,fragm5t>y view ( ! univ]se1 #bfj ,fragm5tation1 t5d5cy to1 #bif -- h>ks back to cell-division1 #cja ,fre$om1 a new1 #cch -- det]m9$ by abs5ce ( bonds1 #bhj -- ma!matical1 #fj -- m5tal1 #ff-g -- n[ dawn+ = ! m9d1 #cb -- ( consci\sness 9 g5us homo1 #ccb -- regal fre$om ( ! m9d1 #aah -- ?ree degrees (1 #abe -- unrealizable1 = ! ,?9k]1 #bee ,fr+e1 *aog5etic1 #cjh1 #cji -- ( disord]l9ess1 #beg -- -- ka!kosity1 #bbi ,fris*auf1 #ff ,full1 ! univ]se z a1 #caj ,function det]m9es faculty1 #ccf ,functions back ( lat5t faculties1 indef9ite1 #cdc -- cellul> & hi/ologic1 #bec ,function+1 in/9ctive1 ( ! intellect1 #bhi ,fundam5tals1 totality (1 kosmic1 #bfe ,g ,gamut ( realism1 #afi ,gauge1 aw>5ess z a1 #afa-bjb ,gauss1 ,*>les ,fr$]ick1 #h-i1 #ef-h1 #ei1 #agd -- -- -- z =mulator ( ! non-,euclidean geometry1 #eg ,gem9os ( ,rhodes1 #de1 #eb ,g5]ability1 z prop]ty ( space1 #fb -- ( hyp]space1 ,keys] on1 #add -- -- space by l9es1 #adc ,g5]ation1 !1 ( ! hyp]cube1 #acd -- ( ! hyp]tetrah$ron1 #ace-f ,g5esis1 ( space1 #baa1 #bbg1 ff -- -- ! e>?1 its nebul\s y\?1 #cce -- -- -- =m1 #cbg -- -- -- s5sible _w1 #afg ,g5us homo1 fre$om ( consci\sness 91 #ccb ,geometricity1 #bff ,geometries1 non-,euclidean1 bas$ ^u a negation ( ! lat5t geometrism1 #bfb-c -- ?ree possible1 #ed ,geometrism1 eng5d]m5t (1 #bfb -- e/abli%$ by life1 #bfd -- kosmic geometrism1 e/abli%m5t (1 #bca -- lat5t1 #beg -- native geometrism ( space1 #bfb -- r$iscov]$ by ! intellect1 #i-aj ,geometrism1 ! basis (1 #bcg1 #bfa ,geometry1 anti-,euclidean1 #fi -- & ! /udy ( magnitudes 9 space1 #bjc -- artificial1 #bfb-d -- a two-fold1 #ei -- breakd[n (1 #bff -- det]m9ative p]iod ( ! non-,euclidean1 #fa-d -- div]se sy/ems (1 #cbc -- ,euclid's ,elem5ts (1 #ec-d -- =mal bulw>ks (1 #gg-i -- ,imag9>y ,geometry1 ,!1 #fj -- natural geometry1 #bfa -- ,plato & ! div9e geometry1 #aic -- possible sy/ems (1 #agd -- radical ess5ce ( pure1 #he ,geometry1 non-,euclidean1 at v>iance ) ! p>allel-po/ulate1 #hc-e -- -- bas$ ^u a misconception1 #ia -- -- det]m9$ by qualitative diff]5ces1 #adj -- -- elaborative p]iod (1 #ff-gj -- -- fir/ publi%$ treatise on1 #fj -- -- =mative p]iod (1 #ee -- -- ! f9al issue (1 #hh-i -- -- gr[? & developm5t (1 #ib -- -- invalidation (1 #agd -- -- key to1 #ij -- ,lamb]t's ,non-,euclidean geometry1 note1 #ea -- -- popul>ization (1 #ff-g -- -- ,s*weik>t's treatise on1 #ei -- -- self-consi/5ce (1 #eg -- -- "s elem5ts (1 #gi-hj -- -- sup]p]ceptual k (1 #gb ,geometry1 non-,leg5drean1 #gj -- symbolic1 & comm5surable quality1 #ade ,g]l+1 z correspond5t ( ,gauss1 #eh ,g]m-plasm1 cont9uity (1 #bfj ,giantism1 #cdg ,glimpse1 a1 ( ! reality ( space1 #cad ,glorification ( ! fle%1 #bbg ,gr\ps1 trans=mation1 discov]y (1 #cj ,guide-po/s to a new doma91 #bgc1 #bgg ,gulf1 int]pos$ betwe5 manife/ation & non-manife/ation1 #bjf ,h ,halley1 memoir (1 ma/]$ by ,la ,grange1 #ej ,hal/ead1 ,g4 ,b41 note1 #di1 #ff2 note1 #gi ,he9del1 ,max1 note1 #cec ,helmholtz1 #ci1 #ff ,hew]1 !1 ( ! concrete1 ! intellect z1 #bie ,h9ton1 ,c4 ,h41 #aed -- on ! f\r? dim5sion1 #aec ,hi/ory1 !1 ( m9d1 ?ree great epo*s (1 #ca-cb ,homog5eity1 !1 ( realism1 #afe ,hoel1 ,j41 #fj1 #ff ,hudson1 #cdd ,humanity & ! exalt+ p[] ( life1 #cca1 ff ,hyp]cube1 b\nd>ies (1 & mirrors1 #acf-i -- ! g5]ation (1 #acd1 #ade ,hyp]dim5sional1 z a prophecy ( new faculties1 #aca ,hyp]space1 #age -- a monum5t to ! intellect1 #cef -- & ! involv$ proc$ure ( arriv+ at a recognition ( its relations1 #gc -- & ! passage ?i!r1 #bic1 ff ,hyp]space z a figurative m\nta9-peak1 #bjj -- -- -- movem5t1 #dd-fh -- -- an all-p[]ful some?+1 #afj -- -- -- idealiz$ con/ruction1 #aj -- -- evid5ce ( new faculties1 #bd -- -- ignes fatuii1 #aed -- -- illusion1 #bjb -- a symbol ( high] consci\sness1 #ahj-d -- concept (1 z an evolution>y quantity1 #dd-e -- conf\nd$ ) real space1 #ia -- creation (1 #cce -- d5i$ ! corroborative te/imony ( exp]i5ce1 #bfc -- direction (1 baffl+ to ma!maticians1 #adf -- discov]y (1 a sign ( m5tal evolution1 #ahj -- doma9 (1 a fairy-l&1 #bci -- magnitudes (1 ! non-s5su\s1 #gb -- my/]i\s hid+ place 91 #abi -- ! logical difficulties (1 #aci-ada -- ! six pill>s (1 #fb-c ,hyp]spatiality z ! toys ( *ildhood1 #bda ,hyp]tetrah$ron1 !1 #ace ,hyp]trophy ( ! pituit>y body1 #cdg ,hyp]volume1 !1 #acd ,hypo!sis1 a sup]foetat$1 #ada -- f\r-space1 utility (1 #abi2 #aed ,hypo!ses1 admissibility (1 #aah -- incompatibility ( ! non-,euclidean1 #fg2 #ga -- ,riemannian1 #hj -- solution (1 ,bolyai1 #ca ,hyslop1 ,james ,h41 on ! logical difficulties ( hyp]space1 #aci-ada ,i ,icosah$ron1 exam9ation ( !1 #bhe ,ideal1 & ! real1 kosmic *asm betwe51 #ajg -- p]ceptual value (1 #bge1 ff ,ideas & words z symbols1 #abf-g -- ,malebran*e on1 #bbb -- realism (1 #bd-ce -- ! symbolism (1 #bje ,id5tification ( consci\sness ) be+1 #bje-f -- ) ! objects ( /udy1 #ahi-ij ,id5tity ( ?+s-9-!mselves1 #cec ,ignes fatuii & hyp]spaces1 #aed ,illu/ration ( plane-rotation1 #adh-aej -- -- ! tess]act1 #acc ,images1 totality (1 recoils ^u u1 #afg ,imag9ability ( ! f\r? dim5sion1 #ij1 #ajf-g ,imag9ation1 premises (1 ! ma!matical1 #adf ,impossibility ( plane-rotation1 ! /ructural1 #aea-c ,impressions1 ! symbolism (1 neurographic1 #ahf ,impulse1 ! satisfaction ( ! orig9al creative1 #caj-a ,incompreh5sibility ( reality to ! intellect1 #abf ,incongruity1 life e/rang$ by a radical1 #cbe ,individual z space1 #bbc ,ineptitude ( intellectual det]m9ations = vitality1 #cad ,inf9ite1 int]pret$ 9 ! t]ms ( ! f9ite1 #hb ,inf9itesimals ( unity1 numb]s z1 #da ,inf9ity z a process1 #aji -- ( becom+s1 #bcd ,inf9ity ( p>allels ?r\gh a giv5 po9t1 #gj -- -- space1 a capital illusion1 #aie -- ! concept (1 #bgg -- -- innate dread (1 #ajc -- -- relativity (1 #aid ,influ5ce ( ab/ract ?\ght1 #cc -- -- ,kant on ! non-,euclidean geometry1 #di-ej -- -- ,la ,grange1 #ea-b -- -- ! intellect1 #cae ,infundibulum1 !1 #cde ,inn] organs ( p]ception1 #ceb ,inn]mo/1 !1 realities ( ?+s1 #cef ,ins\ciance ( ! geomet]1 #if1 #bid ,in/ant-exposure & intellect1 #caa ,in/rum5t1 intellect lik5$ to a color-be>+1 #cac -- = ! measurem5t ( ! passage ( space1 #big -- ( consci\sness1 ! s5sible _w z1 #aii -- -- life1 =m z an1 #cbh ,integ]s1 z fractional p>ts ( unity1 #da ,intellect & its dom9ation ( ! intuition1 #ccc -- -- -- f9al union ) ! space-m9d1 #aid -- -- -- topography1 #cab -- -- spatiality1 #bfc -- -- ! deposits ( life1 #agc -- -- -- designs cut by life 9 mat]iality1 #bfd -- -- -- dictum ( ,s5sationali/s1 #bf -- -- -- in/ant-exposure1 #caa -- -- -- intuitive faculty1 #bdg1 ff -- -- -- prize ( div9ity1 #dc -- z a color-be>+ in/rum5t1 #cac-d -- -- -- se>*light1 #afh ,intellect z a fa%ion] ( ph5om5a1 #aii1 ff -- -- hew] ( ! concrete1 #bie -- -- sole int]pretative ag5cy1 #aff-g -- automatism (1 #bec1 #cch -- _c seize life1 #bhb -- cr[n$ by a diadem ( gold1 #cch -- dom9at$ by ! intuition1 #bej -- fa%ion$ = matt] only1 #bca -- foll[s 9 ! grooves ( logic1 #bid -- hyp]space z a monum5t to1 #cef -- 9 ! field ( vitality1 ix -- its aptitude = />ts & /ops1 #bib1 #cjb -- -- in/9ctive t5d5cy to fragm5tate1 #bif -- quality1 det]m9$ by ma!matics1 #ccg -- makes = individuality1 #beb -- misses ! ceaselessness ( life1 #bja -- modus viv5di (1 its influ5ce ^u k1 #ahd -- ! con/itution (1 #bia -- -- cut & mode (1 #afg -- -- focus (1 #caj -- -- illusion (1 #bdf -- -- illusion>y "* (1 #cbc -- -- incompreh5sibility ( reality to1 #abf -- -- in/9ctive function+ (1 #bhi -- -- judgm5ts (1 #cjb -- -- moods (1 #bjb -- -- pr$om9at+ t5d5cy 91 #cbj-a -- -- sci5tific t5d5ce (1 #afe-f -- -- /ruggle (1 aga9/ dispossessal1 #aie -- unsuit$ to deal ) reality1 #cbb1 ff ,intellectuality & reality1 #cjd -- -- spatiality1 consub/antial1 #cca ,intellectuality z co-ext5sive ) spatiality & mat]iality1 #bcf -- ! s\rce (1 #bfj -- -- ,?9k] makes 8 own1 #bdb ,intellig5ce & automatism1 #bec1 ff -- ! ,?9k] z a pure1 #bdc -- transf9ite intellig5ce & ! degrees ( realism1 #afd ,int5t1 ! kosmic1 ( ! intellect1 #cbf ,int]e/s1 ! sph]e ( our1 z clos$ circuits1 #afg ,int]ior1 ! great1 #bij ,int]iority ( be+1 #bij ,int]pretation1 ! /&>ds (1 v>y z consci\sness v>ies1 #aga ,int]/ices ( mat]iality1 #bfd ,intuition & bro!rhood1 #beb -- -- communalization1 #cja -- -- ! riddle ( spatiality1 #cbe -- z dispossessor ( ! intellect1 #aie -- _c be s]v$ by ma!matics1 #ccg -- dom9at$ by ! intellect1 #ccc -- held 9 abeyance1 #cch1 ff -- its dom9ation ( ! intellect1 #bej -- ! developm5t ( a spatial1 n absurd1 #ade -- -- ne$ ( a sympa!tic attitude t[>ds1 #bdi -- -- results ( ! developm5t (1 #ceg ,intuitional consci\sness1 #bee -- ! sup]iority (1 ov] ! rational1 #ahg ,intuitions & ! lead ( life1 #aia -- -- -- ,?9k]1 #bg -- free1 mobile & =mless1 #aff -- ! conceptualization (1 #bdh -- -- humility (1 #afe -- -- nature (1 #ahe ,intuitograms1 z concepts1 #bdh ,intuitograph z means ( contact+ ! egopsy*ic consci\sness by ! ,?9k]1 #aj -- z sup]-concepts1 #bee -- ! difficulty ( transmitt+1 #cae ,inv>iability1 ! vaunt$1 ( ! laws ( ma!sis1 #cg ,inv>iants1 psy*ological1 #bd ,inve/igations1 metageometrical1 & ! new s5se-organs1 #ced ,involution1 z anti!sis ( evolution1 #aj-aa -- kosmic involution1 #bbf -- ( matt]1 #cbh -- ! movem5t (1 #bai -- -- sev5 /ages (1 #bjh-ab ,ions1 creation (1 #bai -- magnitude ( a hydrog5 ion1 #bbe ,j ,judgm5ts a priori1 ,kant on1 #he-f -- & ! faculty a priori1 #aij-a -- -- zones ( aff9ity1 #abd -- bas$ ^u a replica ( consci\sness1 #bje -- no tru/wor?y1 c be pr$icat$ ^u fragm5t>y k1 #bhb -- ( ! intellect1 #cjb -- ! less5+ ( error 91 #bef -- -- m complex ! m at v>iance ) ! nature ( ?+s1 #ge -- -- syn!sis (1 #beg-h -- valid judgm5ts long delay$1 #agj-a ,judicative p[] ( ma!matics1 #ahj ,ju/ification = a multi-dim5sional quality 9 space1 #bfb -- ( f\r-dim5sionality1 #agf ,ju/ification ( s5se-deliv]ies by "o ano!r1 #gf -- -- ! exi/5ce ( ! f\r? dim5sion1 #abe ,k ,kant1 #he1 #aha1 #ahb1 #cbb -- & ! faculty ( ?9k+1 #bfa -- -- -- idea ( space1 #cbb-c -- influ5ce (1 on ! hyp]space movem5t1 #di-ej -- on ! nature ( ?+s1 #aai -- -- space z an intuition1 #aae ,ka!kos1 #bcc-d -- z *aos1 #bff -- -- symbol ( ,*aos-,!os-,kosmos1 #aa-ab -- symbology (1 #bcd ,ka!kosis1 note1 #bbg ,ka!kosity1 fr+e (1 #bbi -- rock-b\nd coa/ (1 #bfg -- significance (1 #ab ,ka!kotic consci\sness1 #bgb -- p]iod1 #bji ,key to ! my/]ies ( nature1 ! f\r? dim5sion z1 #aca ,keys]1 ,cassius ,jackson1 & fre$om ( ! m9d1 #cc -- -- -- on attitude ( metageometricians1 #ga -- -- -- -- dim5sionality1 #id-e -- -- -- -- f\r-dim5sionality ( space1 #adb-c -- -- -- -- g5]ability ( hyp]space1 #add ,kle91 ,felix1 #ab1 #ed-e1 #ff-g ,k1 all1 relative1 #aja -- b>ri] to ! c]titude ( ! ,?9k]'s1 #ahf-g -- fabric (1 #aif -- hypo!tical nature (1 #ahi1 ff -- immeasurable realm (1 laid b>e by ! telescope1 #bih ,k1 ma!matical1 apriority (1 que/ion$1 #cg -- nature ( ! non-,euclidean1 sup]p]ceptual1 #gb -- real1 difficulties ( acquir+1 #cbe -- relat$ to ! /ream ( life & to ! %ore ( mat]iality1 #cbc -- relative1 degrees exi/ =1 #afd -- sph]e (1 #ahd -- sy/ematization (1 #abf -- ultimate1 consci\sness z a b>ri] to1 #bjg -- unification (1 #bef ,kosmog5esis1 ! lat5t geometrism (1 #bfd -- -- scope (1 #bcg ,kosmomet]1 !1 #big ,kosmos1 & consci\sness1 graph repres5t+1 #bga -- arrangem5ts ( ! cont5ts (1 #cag-h -- 9 a /ate ( becom+1 #bfe -- magnitude (1 #cjh -- moods (1 #caa -- space z ! consi/5ce (1 #bci -- see ,cosmos1 #ab ,l ,labor1 division (1 betwe5 ! tuitional & ! intuitional faculties1 #aic-d -- ma!matical labors1 significance (1 #agf ,la ,grange1 ,joseph ,l\is1 #ab1 #ci1 #ej-c1 #cba1 #cbb -- -- -- -- & ! p>allel-po/ulate1 #ea-b ,lamb]t1 ,john1 #eh -- -- & ! !ory ( p>allels1 #dh-i ,language1 ! pass+ (1 #ceg ,leg5dre1 #gj ,leibnitz' dictum1 #bf ,leon>d rays1 #ccf ,lic5se1 ma!matic1 p]missibility (1 #ch ,lie1 ,sophus1 #ab1 #fg -- -- & trans=mation gr\ps1 #cj ,life1 analysis incapable ( deal+ )1 #cai -- & consci\sness z "o1 #bbd -- -- =m root$ 9 pyknosis1 #bad1 #cbh -- -- ! f\r? dim5sion1 #agb -- -- -- inaptitude ( ma!matics =1 #agi -- -- -- p[] to create1 #big -- z ag5t ( creation1 #cdc -- -- creative ag5t1 #bfd -- -- expression1 #cjc -- -- vassal ( mat]iality1 #cbi-cj -- causative ag5cies 9 prolong+1 #abc -- curr5t (1 z eng5d]+ elem5t1 #cca -- deposits (1 & ! intellect1 #agc -- e/rang$ by a radical incongruity1 #cbe -- exalt+ p[] (1 & humanity1 #cca1 ff2 #cdb -- exhibition ( its rema9s1 #bhb -- fl[ (1 #bfe1 #big -- =m z an in/rum5t (1 #cbh -- indescribable signs (1 #bai -- inf9itive action (1 #cbg -- intellect has no aptitude =1 #bca -- intuitive1 values (1 x -- l>g] life ( ! ,?9k]1 #aif -- lead (1 foll[$ by intuition1 #aia -- limits (1 fix$ by consci\sness1 #aih1 ff -- mo/ solid facts (1 z %ad[s1 #aie -- motility (1 admits ( endless v>iations1 #ce ,life1 movem5t ( *aos 91 #cjg -- passage (1 #bja -- passage ?r\gh spatiality1 #bhh -- p[] to manipulate1 #cjc -- recurr5t movem5t (1 #cjg -- totality ( egoic1 #bdc -- undulations 9 ! curr5t (1 #cbi -- uniqu5ess (1 #da -- wake (1 & consci\sness1 #bje1 #bhh ,life-cycle1 evolution>y results ( !1 #bei ,life-/ream1 !1 #bgh ,light1 pol>iz$1 & ! f\r? dim5sion1 #aef -- consci\sness z a spread+1 #afh ,light-ye>s & space1 #bgh ,limits1 ! sph]e (1 consci\sness z1 #afc ,l9e1 z g5]at+ elem5t1 #add -- ! /raight1 a curv$1 #gf ,l9eage ( e pr9ciple runs back to monopyknosis1 #bac ,l9es1 p]p5dicul>ity (1 9 f\r space1 #acj ,loba*evski1 #ee1 #fj1 #ff1 #hg ,lodge1 ,sir ,oliv]1 #cdj-a2 #cdd ,logic z ar*itect1 #aah -- conv5tional =ms (1 #bfb -- data (1 #bhf -- intellect foll[s 9 ! grooves laid out by1 #bid -- miracle p[] (1 ov] facts1 #bhh-i -- rules (1 all[ability "u1 #afc -- -- -- ! game (1 #afd -- z symbolism ( facts1 #bhg ,logos & ! limits ( space1 #aic -- be+ (1 #bah -- body ( be+ (1 #bad -- consci\sness (1 #bjd -- creative1 #ab1 #bac -- !1 #baf-g ,lor5z1 #hc ,lu!r1 ,m>t91 #aha ,m ,magnitudes1 geometry1 a /udy (1 #bjc -- non-s5su\s1 ( hyp]space1 #gb ,makrokosmic consci\sness1 #bgj ,malebran*e1 ,n41 #bbb2 see note ,manife/ation & non-manife/ation1 #bjf ,manifold1 f9ite1 ?\gh unb\nd$1 #gj -- manufactur$ by ! analy/1 #gg -- !1 #fa-b1 #agb ,manifoldness1 analytical manifoldnesses1 z m5tal excitants1 #hi-ij -- z a conv5tional con/ruction1 #bfb -- -- an intuition1 #cah -- ( space1 z a ne>-tru?1 #cag ,mann+1 #hb1 #aeg -- & maneuv]s 9 ! f\r? dim5sion1 #aeb ,manvant>a1 #bac1 #bbh-i1 #bcb -- z evolution & involution comb9$1 #ac ,mask1 logic z a1 #bhh-i ,mass-t]m9i1 ( l9es1 #bcf ,ma/]y ( life ov] matt]1 #ccj -- ( ! s5sible _w1 #aif-g ,mat]iality z a deposit ( life1 #bie -- -- consub/antial ) spatiality1 #cca1 ff -- becom+ spatializ$1 #bfa -- *>act]i/ics (1 #bfj -- eng5d]$ by kosmic m9d1 #bfa -- eng5d]m5t (1 #bid -- int]p5etrative ) spirituality1 #bcf -- int]/ices (1 #bfd -- neglect (1 #cbj ,mat]iality1 %ore (1 #cbc -- transmut$ into spirituality1 #cbh ,ma!maticians & ! def9ition1 #cg -- -- -- limitations ( consci\sness1 #agh -- -- -- ph5om5al _w1 #aah-i -- z prophets1 #ccf -- respect$ by humanity1 #ccg -- ! gods ( ma!sis1 #hd ,ma!matics1 a det]m9ant ( ! quality ( ! intellect1 vii -- & ! crit]ion ( tru?1 #cbc -- -- -- kosmic int5t ( ! intellect1 #cbf -- z symbology1 #ahd -- ,euclidean1 #adj -- fails :5 x enc\nt]s life1 #ccg -- its inaptitude = life1 #agi -- -- k+dom yield$ to k9etics1 #ceh -- possesses no judicative p[] ov] life1 #ahj -- ! or?odoxy (1 #cd ,ma!sis1 & conceptional space1 #bjc -- conduct ( ! intellect 9 ! field (1 vii -- def9ition (1 #ac -- doma9 (1 z orig9 ( f\r? dim5sion1 #acj -- gods (1 #hd -- m>vel\s doma9 (1 #aah -- realm (1 n submissive to laws ( s5sible space1 #cd -- ?+s (1 z emblems ( kosmic =ces1 #bci -- _w (1 #fg1 #abg ,matt] & m9d1 syncretization (1 #bii -- appulses ( life aga9/1 #cbh -- z a deposit ( life1 #ccj -- honeycombs (1 #cci ,matt] metamorphos$ by life1 #cbh -- m9d z w$d$ to1 #bdi -- movem5t (1 9 f\r-space1 #aeg -- qualities (1 & faculties1 #ccb -- sev5 planes (1 #bab -- spiritualization (1 z end ( evolution1 #cbg -- totality (1 act$ ^u by totality ( life1 #cbh -- unity (1 ) space1 #bfj -- univ]sum (1 #bfa ,matut9al c]emonials ( creation1 #bba ,measurability1 z prop]ty ( space1 #fb-c ,measurem5t ( hyp]spaces1 ! sci5ce (1 #gc ,measurem5ts1 space det]m9$ by ! numb] (1 #fa -- sy/ems ( space1 #ia ,measur] ( space1 n-dim5sionality z a1 #bif-g ,mecanique ,analytique1 #ej-a1 #cba ,me*anics ( matt]1 ! passage f1 to ! dynamics ( life1 #cbf -- to biog5etics1 ! passage f #ceg -- ! turn+ f1 to biog5etics1 #cbb1 ff ,me*anism1 ! doctr9e (1 due to analytics1 #dj ,memories1 /or$ 9 ! omnipsy*e1 #beh ,m5 z gods1 #bhi ,m5tal evolution1 det]m9ative p]iod (1 #ca -- -- elaborative p]iod (1 #ca-cb -- -- =mative p]iod (1 #ca ,m5tality1 inn] my/]ies ( creative1 #ia -- infantile out-feel+s ( !1 #ccf -- ! pr9ciple (1 #baj1 ff ,m5talities1 ! adaptation ( ph5om5a to1 #ahd ,m5tograph1 !1 #aba -- ! basis ( intellectual consci\sness1 #ac ,mesozoic man & 8 environm5ts1 #cdg-h ,metageometrical inve/igations & ! new s5se-organs1 #ced ,metageometricians & hyp]space1 #bch -- -- pro( ( rotation ab\t a plane1 #adi-aea -- -- ! curv$ space1 #caf -- -- -- f\r? dim5sion1 #ade -- -- -- key to ! my/]ies ( nature1 #aca -- baffl$ by ! direction ( hyp]space1 #adf -- dilemma (1 #ig-h -- es*ew s5se-data1 #gc-d -- ,keys] on ! attitude (1 #ga -- p]ceptual obliquity (1 #ajb -- -- se$ ?\ght (1 #ahb -- turn$ to idealiz$ con/ructions1 #bfc ,metageometry1 z a /epp+ /one1 #bch -- def9$1 #ac -- ,riemann1 ! fa!r (1 #fc -- ! fabric (1 #ff ,metamorphosis ( matt] by life1 #cbh -- ( ! monopyknon1 #bad ,metamorphotic /age ( space-g5esis1 #bbh ,metaphysician1 ! pres]ves (1 usurp$ by ma!maticians1 #ada ,meta-self z m$ium ( kosmic consci\sness1 #ac1 #bag ,me?ods ( ! ego1 #cdd -- sci5tific1 & ! ample explication ( ph5om5a1 #aed ,mikrokosmic consci\sness1 #bgj ,m9d1 am5ability (1 to ! evolution>y movem5t1 #bh-cb -- & fre$om f conception1 #bh -- -- -- -- problems ( physical exi/5ce1 #cb -- -- ! new fre$om1 #cc -- z vehicle ( life1 #bhe-f -- -- w$d$ to matt]1 #bdi -- coevalism (1 & space1 #bdj -- consub/antial ) space1 #bci-dj -- div9e1 ( ! kosmos1 #agf -- evolution (1 & conceivability1 #bd -- ( ! duodim1 #abh -- p[]s (1 n atta9$ simultane\sly1 #ccd -- pr(\nd influ5ce ( hyp]space on !1 #ia -- space z prog5itor (1 #bbd -- ?ree great epo*s ( ! hi/ory (1 #cj-ca -- tuitional1 ! limitations (1 #aib-c -- ! unity (1 ) space1 #bbd ,m9d-pr9ciple1 ! qu9topyknon z ! basis (1 #bba1 ff ,mirrors1 ?ree1 & ! hyp]cube1 #acf-h ,mobility1 life z1 #bfd ,molecule1 ! f\r-dim5sional1 ,newcomb on1 #aei ,monadic phase ( evolution1 #baj-a ,mon]on & man1 ! gulf betwe51 #bh ,monopyknon1 !1 #bac1 #baf ,monopyknosis1 def9$1 #ag1 #bjh-aj1 #bah ,mon/rosities1 ma!tic1 #bjb ,moods ( ! kosmos1 #caa ,morphog5y1 #ac1 #bcc-d ,morphons1 ! creation (1 #bai ,motility1 ! scope (1 #aca ,movem5t1 =w>d1 9 k1 #ccf -- hyp]space z an evolution>y1 #dd-fh -- -- influ5ce ( ,kant on1 #di-ej -- ( life 9 *aos1 #cjg ,multi-dim5sional quality ( space1 ju/ification =1 #bfb ,multiplication ( hypo!ses1 #aah ,mutuality1 intuition z promot] (1 #cja1 ff ,my/]ies1 inn]1 ( creative m5tality1 #ia -- kosmic1 l[-ly+ pla9s (1 #bci --- ( life & m9d1 #cbf -- -- ! sci5ces & ! f\r-space op]ator1 #aca ,my/]y1 kosmic1 ! revelation (1 =e%ad[$ 9 manifold1 #gg -- ( reaction1 #afg-h -- -- space decreases z copes ( consci\sness increases1 #bgc1 ff ,n n-,cord9ates1 #bjc n-,dim5sionality1 z a phase ( geometry1 #cjj -- -- prop]ty ( intellectuality1 #bfi -- -- quality ( conceptual space1 #ad -- irreconcilable ) p]ceptual space1 #aef -- no ju/ification =1 #bce -- n surpris+ t ! intellect fell ^u1 #bif1 ff -- pr$icates conc]n+1 #aeh n-,space1 imp]ceptibility (1 #id ,nasir-,edd91 #df1 #ec ,natural symbols1 ideas z1 #abf ,nature1 repres5tative1 ( ?+s1 #aai -- ! vacuum-/illness (1 #cci ,naught to unity1 consci\sness regi/]s f1 #afe ,ne>-tru?1 #cjj1 ff -- z v>iation f crit]ion ( tru?1 #cbd -- bas$ ^u p>tial k1 #ad -- space-curvature z a1 #cjf -- space-manifold z a1 #cah ,nebulosity1 #bfg ,necessity1 z a bulw>k ( geometry1 #gg-h ,n]ve-body1 !1 #cdi ,neurogram1 #ad ,neurograph1 ! ,?9k]'s scrut9y (1 #aij ,neurographical communications1 #bdd ,newcomb1 ,simon1 #ad-e1 #ff -- -- & ! f\r-dim5sional molecule1 #aei -- -- on ! f\r? dim5sion1 #abe ,non-,euclideans & ! mean+ ( dim5sion1 #ig -- -- ?+s z !y actually are1 #ga -- dilemma (1 #hf -- mean+ ( ! t]m1 #fi -- results obta9$ by1 #hh ,non-manife/ation1 z anti!sis ( manife/ation1 #ajf -- & manife/ation1 #bjf ,non-me?odic advancem5t ( human consci\sness1 #bii ,non-spatiality1 cut (f f spatiality1 #bff ,norm1 z a value assign$ by ! intellect1 #afg -- consci\sness z a1 #ae2 #afa-bjb -- ( life1 f\nd by syn!sis1 #cjj -- -- ! natural geometry1 #bfc ,note1 ! dom9ant1 ( communality1 #cja ,notions ( space1 triple pres5tations to ! consci\sness1 #gb ,numb]1 z a phase ( kosmog5esis1 #cji -- numb]s z inf9itesimals ( unity1 #da ,num]icity ( be+1 #cji ,o ,objects & ideas1 #abf-g -- passage (1 into ! f\r? dim5sion1 #acj -- ( /udy1 id5tification ( consci\sness )1 #ahi ,obliquity1 p]ceptual1 ( metageometricians1 #ajb ,obscurantism1 ma!tic1 #aed ,occulti/ & ! sci5ti/1 #cej ,omnipsy*e1 #bfe -- z ag5cy ( kosmic consci\sness1 #beh -- -- neglect$ factor ( evolution1 #bei -- def9$1 #ae ,"o-space repres5t$ by a l9e1 #acd ,ontog5y recapitulates phylog5y1 #bg1 #ccd ,ord]1 kosmic1 ! diff]5ce betwe51 & hyp]space1 #adc -- ma!matical1 discov]$ by ! intellect1 #bfa -- ! fiat (1 #bjh -- ! totality (1 #bfe ,ord]l9ess1 #bff ,organ1 det]m9$ by function to be p]=m$1 #ccf ,organs brok5 up by life into special p>ts1 #cdc -- ! evolution (1 #ahh ,or?odoxy ( ma!matics1 #cd ,outcome ( new adju/m5ts1 #bef ,out-feel+s ( ! ,?9k]1 infantile1 #ccf ,outlook1 ! spiritualization ( our m5tal1 #dj ,p ,papyrus1 a hi]atic1 #dd ,p>allel-po/ulate & ! surface ( a sph]e1 #gj -- z basis ( non-,euclidean geometry1 #ed -- -- /at$ by ,euclid1 #ee -- -- -- -- ,loba*evski1 #ee -- -- -- -- ,mann+1 #hb -- failures to demon/rate1 #dh1 #hb-c -- 9 ! ,elem5ts ( ,euclid1 #af -- ,sac*]i's pro( (1 #dg ,p>allels1 conv]g5ce (1 #hj -- inf9ity (1 ?r\gh a giv5 po9t1 #gj -- meet at inf9ity1 #hh -- !ory (1 #dg-i ,passage f me*anics to biog5etics1 #ceg -- f me*anics to dynamics1 #cbf -- f ?ree-space to f\r-space1 #bib-c -- ( ma!tic contrivances1 #bda -- ( space1 #af1 #big ,pa?way ( life1 s9uosities 91 #ccj ,patt]ns ( ! intellect1 ready-made1 #aff ,p5tagrammaton ( space1 #bcg ,p]ceptibility 9 ! ,?9k]1 ! faculty (1 #ahh ,p]ception1 doma9 (1 & ! s5sible _w1 #ai -- inn] organs (1 #ceb -- replac$ by conception1 #bee ,p]cepts1 & ! ego1 #bdd ,p]iod1 *aomorphog5ic1 #bjh1 ff -- det]m9ative1 #fa-e -- ka!kotic1 #baj ,p]isophical nature ( analytics1 #cbj1 ff ,p]isophism1 a1 #cjj ,p]missibility ( ma!tic lic5se1 unlimit$1 #ch ,p]p5dicul>ity1 #acb1 #agg -- ( l9es 9 ! f\r-space1 #acj ,phantasy & reality1 l9e ( dem>kation betwe51 #agc -- ! _w (1 #adf ,phantom-ideal1 !1 #bgg ,phase ( ! _w age1 evolution>y1 #bji ,ph5om5a1 ef=ts to expla91 on ! basis ( ! f\r? dim5sion1 #abi -- fa%ion$ by ! intellect1 #aii -- fragm5t>y int]pretation (1 #cjb -- m9d's me?od ( appreh5d+1 #ahf -- physical ph5om5a amply expla9$ by sci5tific me?ods1 #aed ,ph5om5al1 ! inv]se ( realism1 #bgh ,philosophy & ! crit]ion ( tru?1 #cbc-d -- reg5]ation (1 #ceh -- sy/ems (1 & zones ( aff9ity1 #abd ,phosphoresc5ce1 dim1 add$ to ! unillum9at$ pool ( s5se-consci\sness by ! intuition1 #bf ,phylog5y & ontog5y1 #ccd -- repres5t$ 9 ontog5y1 #bg ,physical z embodim5t ( all possibilities1 #bbg -- ph5om5a z space-activities1 #bbi ,physicality1 ! pr9ciple (1 #baj1 ff ,physics ( ! bra91 #bib ,pi proportion1 significance (1 #caa-b ,pick]+ on space-curvature1 #bgi ,p9eal gl&1 en]giz$ by ! pituit>y body1 #cdh-i -- -- !1 #cdd1 ff -- -- n a ve/igal organ1 #ced ,pituit>ial awak5+1 g5]al results (1 #cee-h ,pituit>y body & ! ,?9k]1 #cea -- -- z an organ1 #cdd-ceb -- -- ,c4 ,de ,m4 ,saj\s on1 #cde -- -- hyp]trophy (1 #cdg -- -- location (1 #bdf -- -- !1 #cdd1 ff ,plane1 z g5]at+ elem5t1 #add -- movem5t (1 into ! f\r? dim5sion1 #adg -- realism appe>s to be divid$ into1 #afd -- rotation ab\t a1 #acj1 #adf-aea -- ! sev5 planes ( matt]1 #bab ,planes1 a cube z a succession (1 #adh-i ,plasm1 kosmic1 /riv+s (1 #bae -- psy*ic1 #bfj -- ! diff]5tiation (1 #bad ,plato1 #cbb -- & ! div9e geometry1 #aic1 #bcg -- -- -- %ad[ consci\sness1 #bha -- on ,god z geometriz]1 #aha -- -- ideas1 #cd ,play1 s5su\s1 ( ! intellect1 #bie ,pl5um1 space z a1 #bcj -- ! univ]se z a1 #ajg ,po9cair1 #ij ,po9t1 an inf9ity ( p>allels ?r\gh a giv51 #gj -- z g5]at+ elem5t1 #add -- position (1 #acb -- succession ( po9ts1 a l9e z1 #adh ,pol>ity betwe5 concrete & ab/ract1 #bid-e ,pond]ability1 z prop]ty ( hyp]space1 #fc ,popul>ization ( ! f\r? dim5sion1 #abh -- ( ! non-,euclidean geometry1 #ff-g ,possibilities 9 ! _w ( hyp]space1 #abi -- ( f\r-space1 ! m>vel\s1 #acj ,po/ulate-sy/ems1 ! multiplication (1 #he ,p[]s ( m9d1 n atta9$ at "o & ! same "t1 #ccd ,pralaya1 #bac -- z kosmic quietude1 #ag ,pr$icates1 all ma!matical1 n ju/ifi$ by ! ph5om5al1 #abh ,pr9ciple1 ens\l+1 #bad-e ,pr9t+ press1 ! inv5tion (1 & ! laws ( psy*og5esis1 #cj ,problem1 ! f\r? dim5sion z a transc5d5tal1 #adj ,proc$ure1 ! involv$1 ( arriv+ at hyp]space notions1 #gc ,process1 evolution a cont9u\s1 #cbg -- space z a dynamic1 #cjg ,proclus1 #hc ,pr(undities1 kosmic1 & hyp]space1 #aef ,progression ea/w>d t]m9ates at ! we/1 #cjf ,pro( ( rotation ab\t a plane1 #adf-aea ,propagation ( intuitographs1 difficulty (1 #cae ,propositions1 geometric1 subjunctive quality (1 #ch ,pseudosph]e & ! %ape ( space1 #gj -- z basis ( ,beltrami's calculations1 #ag -- ! nature (1 #fd-e ,psy*ics ( consci\sness1 #bib -- transmut$1 #bfj ,psy*og5esis1 al*emy (1 #bbe -- kosmic1 #bgb -- laws (1 & ! pr9t+ press1 #cj1 #aaf ,psy*og5esis1 m9d's place 91 #abc -- outgr[n phase (1 #cjb -- out/&+ facts (1 #aca ,psy*og5y1 def9$1 #ag ,ptolemy1 #de1 #eb1 #hc ,publici/1 ! ma!matical1 & ! duodim1 #abh -- ! non-,euclidean1 #adf ,pyknon z a kosmic pr9ciple1 #bab -- -- basis ( space-g5esis1 #ag ,pyknosis1 #bab -- & involution1 #baj1 #bca -- z a metamorphotic process1 #bad -- ! sev5 processes (1 #ag1 #bid ,q ,quality1 dim5sion z comm5surable1 #adj ,quantities1 algebraic1 _c repres5t space1 #abe-g ,quantity1 consci\sness z a tri-space1 #agb ,qu>todim1 #ah1 #acd ,qu>todim5sionality1 #bib ,qu>topyknosis1 #ag1 #bjh-aj ,qu>topyknotic1 pr9ciple z basis ( spirituality1 #bbh ,qu9topyknon1 #bbj ,qu9topyknosis & ! a priori1 #bbc -- mean+ (1 #ag1 #bjh-aj ,qu9topyknotic pr9ciple z basis ( m5tality1 #bbh ,r ,race1 humanity to evolve a new1 #ceh -- respl5d5t1 #cch ,rajah-,tamas1 #bbj ,rajah ,yoga1 #ceg ,rational1 valueless :5 unsanction$ by ! intuition1 #ahg ,reaction1 z a my/]y1 #afg-h ,real1 ,?9k] z a "p ( !1 #bja ,realism & its degrees1 #afd-e1 #bgi -- -- ! ,?9k]1 #cae -- z life1 #bhf -- consci\sness z t\*-/one (1 #afh -- f\nd 9 ! direction inv]se to ! ph5om5al _w1 #bgh -- homog5eity (1 #afe -- illusion>y nature (1 #cf -- inf9ite gamut (1 #cf -- its degrees & ! /ates ( consci\sness1 #aig -- new scope (1 bewild]s ! m9d1 #agj-a -- n ( ma!matical import1 #bij -- ( concepts & ! s5sible _w1 #dj -- -- ! doma9 ( ma!sis1 #cc-d -- psy*ological quality (1 #bhe -- ! ?read (1 #afi -- ?ree dim5sional scope (1 #agb ,realities1 ab/ractioniz+1 #add1 #bid -- incompreh5sible to ! intellect1 #abf -- inn]mo/1 ( ?+s1 #cef -- less] give way to great]1 #aie -- natural symbolism (1 #abh -- our1 non-exi/5t to be+s on _s-levels1 #ce -- %ap$ ^u conv5tional models1 #bid -- sup]s5su\s1 #ahj ,reality1 z life & consci\sness1 #agc -- b>ri] to ! cognition (1 #ahi1 ff1 #bgc -- compreh5sion (1 #afe1 #cjc -- curr5t (1 #cbb -- def9$ z life1 #ah -- fl[ (1 #cai -- fl[+ /ream (1 #abd -- myriad ways ( pres5t+ itself1 #bhg -- nak$ contact )1 #aic -- n an inscrutable quantity1 #aid -- obscur$1 #cjb -- ( ! f\r-space glibly ass]t$1 #aed -- ?read (1 #bjj -- univ]sum (1 #abg ,realms1 sup]s5su\s1 #cch ,re-becom+1 life & consci\sness z a1 #beg ,reciprocity ( consci\sness & realism1 #aig-h -- ( ! manife/ & ! unmanife/1 #bag ,recoil ( images ^u u1 #afg-h ,reflexive developm5t ( ! intellect1 #bed ,relativity ( all k1 #aja ,religion & realism1 #agj -- ! *anges 91 #ceh ,rema9s ( life exhibit$ to ! intellect1 #bhc ,remak+ ( moods by ! intellect1 #bja ,replica ( consci\sness z basis ( judgm5ts1 #bje ,repres5tation1 s5su\s1 comp>$ ) a %ad[1 #aai-abj ,rese>*1 improvem5t 9 ! me?ods (1 #abe ,res]voir1 psy*ic1 ( evolution1 #bfj ,residuum1 ! unexpla9$1 #aeg-h ,revelational impressions1 #bi ,riddle ( spatiality & ! intuition1 #cbe ,riemann1 ,g4 ,f4 ,b41 #ah1 #ai1 #ed1 #ff-g1 #hg -- & a limit$ space1 #ajh-i -- -- ! curvature ( space1 #e -- -- -- det]m9ative p]iod1 #fe -- -- f9ite space1 #ajc -- -- -- f\r-space1 #bg -- -- -- manifold1 #cag -- -- -- z inv5tor ( ! manifold1 #hf -- on ! bases ( geometry1 #fa-d ,ro5tg5 rays1 #ccf ,rotation ab\t a l9e1 #adg-h -- ab\t a plane1 #adf-aea -- -- -- -- illu/rat$1 #adh-ej -- intra-corpuscul>1 #aeb ,rudim5t>y organs1 vague functions ly+ back (1 #cdc ,rule 9 ! evolution ( faculties1 #ccc ,s ,sac*]i1 ,girolamo1 #dg-h1 #eb1 #hc ,saj\s1 ,c4 ,de ,m41 on ! pituit>y body1 #cde ,s*ematism1 ! suitability ( ! pres5t1 #cbj-a ,s*weik>t1 ,f]d9& ,k>l1 #ai1 #ff1 #fi -- on ! non-,euclidean geometry1 #eh-fj ,sci5ce ,absolute ( ,space1 #fj ,sci5ce & reality1 #agj-a -- no long] empirical1 #ceh -- skeptical attitude (1 #cdi ,sci5ti/1 me?od ( !1 oppos$ to ! analy/1 #hd-e ,scopographic impressions1 #ai1 #aij ,scre51 ! impregnat$1 ( creation1 #bcb ,sea1 *oppy1 & egos1 #bef-g ,se>*1 ! pa? (1 = spatial und]/&+1 #bgh ,seb1 ! god1 #bae ,sects1 coplan>1 #gi ,self & ! imm5sity ( space1 #bbc -- ( ! univ]se1 #bag -- ! kosmic1 #bgh ,self-consci\sness1 #bgj -- & space1 #bbc -- z ,i-mak+ faculty1 #bdc -- det]m9ation (1 #cjb ,self-consi/5cy1 #agc ,sella turcica1 !1 #cde ,semi-,euclidean geometry1 !1 #gj ,s5sationali/s on ! intellect1 #bf ,s5se-data1 spurn$ by ! metageometrician1 #gc ,s5se-deliv]y1 "o1 ju/ifi$ by ! o!r1 #gf -- symbolism (1 #bjc-d ,s5se-k1 ! sph]e (1 ext5d$1 #cci-dj ,s5ses1 ! answ] (1 to new ne$s1 #ccb ,s5sible _w1 z doma9 ( p]ception1 #ai ,s5sographic impressions1 z p]ceptions1 #ai ,s5so-me*anisms ( ! intellect1 #afe ,s5ti5ce1 ! pr9ciple (1 #baj1 ff ,septopyknon1 !1 #bbg ,septopyknosis1 z kosmic mat]iality1 #ah1 #bjh-aj ,septopyknotic1 !1 pr9ciple1 #bbh ,sev5 planes ( matt]1 #bab ,sextopyknon1 !1 #bji ,sextopyknosis1 def9$ z kosmic s5sibility1 #ah1 #bjh-aj ,sextopyknotic1 z emotional pr9ciple1 #bbh ,%ad[ lik5$ to a s5se pres5tation1 #aai ,%ad[graphs1 #bha ,sil5ces1 nature's great1 #cci ,similitude ( ag5t & pr9ciple1 #bdc-f ,s9uosities 9 ! pa?way ( life1 #ccj ,socrates1 #cbb ,solit>9ess ( intellectual te/imony1 #gf ,space & edict ( disord]1 #bcj -- -- f\r-dim5sional entities1 #abh-acj ,space & qu>topyknons1 #bai-bj -- -- self-consci\sness1 #bbc -- -- ! idealiz$ con/ruction1 #add -- z a dynamic process1 #baf -- -- all-"m1 #bbi-cj -- -- an assemblage ( sph]es1 #adc -- -- becom+1 #aie -- -- b\nd>y ( ano!r space1 #di-ej -- -- consi/5ce ( ! kosmos1 #bci -- -- curv$1 #afd -- -- dynamic appe>ance1 #bbh1 #cjg -- -- elde/ born ( ka!kosis1 #bae -- -- eng5d]$ product ( life1 #cjh1 ff -- -- evolution1 #bbf1 ff -- -- f9ite ext5sion1 #fb1 #ajf -- -- g5]able quantity1 #ajc -- -- inf9ite cont9uum1 #gj -- -- intuitional concept1 #bbe -- -- kosmic ord]1 #bfe1 #bfg -- -- ne!r pole ( non-manife/ation1 #bjg-h -- -- pa? ( life1 #bic-d -- -- pseudosph]e1 #gj -- -- %e] room9ess1 #aae -- -- sy/em ( cord9ates1 #ii -- -- unb\nd$ ext5sion1 #fa -- be/ /udy (1 ! consci\sness1 #bfi -- conceptual1 z basis ( non-,euclidean geometry1 #gb -- -- fundam5tally di/9ct f p]ceptual1 #gb-ge -- elliptical1 #fg -- eng5d]m5t (1 #bfj -- ess5tial nature (1 #bab -- fabric (1 !1 l5ds itself to measurem5t1 #ii-ajj -- f\r-1 #h -- fractionaliz$ space1 #bif -- f\ndations (1 #bba -- f\r-dim5sional1 #da -- ,paul ,c>us on1 #ced -- f\r? dim5sion (1 ef=ts at mak+ x ?9kable1 #abe -- g5]ability (1 by l9es1 #adc -- g5esis (1 #bbg1 ff -- geometric1 purely =mal con/ruction1 #ge-f -- limits ( & ! ,creative ,logos1 #aic -- manifoldness (1 #gg -- m9d &1 ! coevalism (1 #bdj -- my/]y (1 #bgh1 ff -- nature (1 answ]$ to by m9d1 #aih-i -- ne!r pole ( non-manife/ation1 #bjg-h -- non-,euclidean1 ! *>act]i/ics (1 #gb-c -- n a pure =m1 #aaj -- passage (1 #af -- pa? ( se>* =1 mu/ be ,?9k]-w>d1 #bgh -- p]ceptual1 irreconcilable ) ! f\r? dim5sion1 #aef -- possible curvature (1 & ! non-,euclidean geometry1 #gf-g -- primeval1 & tridim5sionality1 #bcf -- problem ( devis+ a1 #hg-h -- psy*ological nature (1 #cje -- real1 conf\nd$ ) hyp]space1 #ia -- ,riemann on ! curvature (1 #e -- ! unity (1 #bbd -- -- -- -- ) matt]1 #bfj ,space-activities1 z *emism & physicism1 #bbi-cj ,space-c5t]1 !1 #cjf-g ,space-consci\sness1 #bbe -- z a direct process1 #bbd -- m]g5ce (1 ) ! individual consci\sness1 #aie ,space-curvature1 z an arbitr>y con/ruction1 #bfb -- z ne>-tru?1 #cjf -- nature (1 #bgi -- no ne$ =1 #bcg -- translation (1 9 t]ms ( ! intellect1 #cae ,space-=ms1 ! con/ruction (1 #gd ,space-g5esis1 #bj1 #bcb1 #bcc -- alphabet (1 #bcg -- completion (1 #bbf -- norm (1 #agd -- pyknon z a basis (1 #ag -- symbolism (1 #bjh1 ff1 #bce ,space-manifold1 !1 #bgi ,space-measurem5t1 & reality1 ,euclid's sy/em (1 #if -- sy/ems (1 #bja ,space-m9d & ar*eological evid5ces1 #aic -- -- k1 #ahg -- -- ! ,?9k]1 #bec1 #bgb -- atta9m5t (1 #bbe1 #bca -- gran>ies (1 #bce -- ! realization (1 #bch ,space-process1 !1 #cje ,space-realities1 hyp]space z a /epp+ /one to1 #bch ,sp>k1 ! omnipsy*e z a1 #beh ,spatiality & ! intellect1 #bfc-d -- consub/antial ) mat]iality1 #bj1 #cca1 ff -- cut-(f f non-spatiality1 #bff -- int]p5etrative ) mat]iality1 #bcf -- noncon=mity (1 ) logic1 #afd -- riddle (1 & ! intuition1 #cbe --1 rise (1 #ahj -- ,?9k]'s outlook 91 #caf -- _w ( nasc5t1 #bcb ,sp5c]1 ,h]b]t1 #cbb ,sp9oza1 #cbb ,spiritism1 ! ph5om5a (1 #aed ,spirituali/s1 ! claim (1 reg>d+ ! f\r? dim5sion1 #aed-e ,spirituality1 mat]iality transmut$ into1 #cbh -- pr9ciple (1 #baj1 ff -- se$s (1 #bba ,spiritualization ( ! fle%1 #bbg -- -- man's m5tal outlook1 #dj -- -- matt]1 ! end ( evolution1 #cbg ,squ>es1 ! =m (1 9 ! non-,euclidean geometry1 #ei ,/4 ,m>ie1 ,flye1 #ff ,/age ( pyknosis1 #bjh1 ff --1 qu>topyknotic1 #bai1 ff ,/anley1 ,hiram ,m41 on space z dynamism1 #ajd-g ,/ates1 ! two1 ( consci\sness2 "o unaw>e ( ! o!r1 #aib ,/raight1 a1 det]m9$ by two po9ts1 #gi ,/uff1 e!realiz$ f\r-dim5sional1 #afj ,sum1 angul>1 #gi -- triangul>1 less ?an two "r angles1 #ei ,sup]concepts1 z intuitographs1 #bee ,sup]conceptual1 z ! intuitional1 #bj ,sup]p]ception & automatism ( ! intellect1 #bj ,sup]p]ceptual1 !1 #gd ,sup]unodim1 !1 #agg ,sw$5borg1 #ahj1 #ahd ,symbol1 psy*ic1 & ! bra91 #aij -- words z symbols ( ideas1 #abf-g ,symbolism ( life1 #bhf -- -- neurographical impressions1 #ahf -- -- realities1 #abh -- -- s5se-deliv]ies1 #bjd -- -- space-g5esis1 #bjh1 ff ,symbology1 depict+ planes ( consci\sness1 #bgj -- ( ma!matical k1 #bjc1 ff ,syn*ron\s evolution ( faculties & prop]ties ( matt]1 #ccb ,syncretization ( m9d & matt]1 #bii ,syn!sis & ! norm ( reality1 #cjj ,syn!tic s*ool ( geometry1 #ef ,t ,tactographic impressions1 #aij ,t>trate & a compon5t 9 ! f\r? dim5sion1 #aef-g ,task ( m5tal evolution1 ! supreme1 #afi ,taur9us1 #ef-g1 #fi ,telescope1 its effect ^u consci\sness1 #bih ,t5d5ce1 intellect z sci5tific1 #afe-f ,t5d5cies1 de/9$ to fl[] z faculties1 #hi-ia1 #ccb ,t5d5cy to fragm5tate1 ! intellect &1 #bif ,tess]act z repres5t$ by ,c>us1 #acf-h -- illu/rat$1 #acc -- !1 #bj1 #ade -- ! elem5ts (1 #ace -- ! f\r cord9ates (1 #acb ,te/imony ( ! intellect1 incapable ( comp>ison1 #gf ,tetragrammaton1 !1 #cjh ,tetrah$ron1 !1 #ace ,?alam5cephalon1 !1 #cde ,?ales1 #dd ,!ory ( k1 #bij ,?+ness ( objects & ! impossibility ( compreh5d+1 #abb ,?+s1 ! dual nature (1 #aai -- -- value (1 #afa ,?+s-9-!mselves1 ! id5tity (1 #cec ,?9kability ( ! f\r? dim5sion1 #abe ,?9k] z a pure intellig5ce1 #ahd1 #bdh -- -- eng5d]] ( ! intellect1 #bia -- -- pr9cipal to ! ego1 #bdc1 ff -- -- six times remov$ f ! s5sible _w1 #bja -- -- ! s\rce ( ! intuition1 #bf -- & concepts1 #bdd -- -- 8 approa* to ! kosmic m9d1 #bjb1 #bbc -- -- -- l>g] life1 #aif -- -- -- treatm5t ( ! ego1 #bdf -- -- -- ( s5se-impressions1 #gd-e -- -- realism1 #cae -- -- space1 #aic -- -- a segm5t ( reality1 #aga -- !1 & ! amplitude ( ! degrees ( realism1 #aih1 #bgj -- & ! b>ri]s ( consci\sness1 #bjg -- -- -- bro!rhood ( man1 #cja -- -- -- degrees ( realism1 #age -- -- -- manipulation ( concepts1 #bee -- -- -- nature ( space1 #bfh -- -- -- neurograph1 #aij -- -- -- new faculty1 #cce -- -- -- p]ceptive faculty1 #ahh -- -- -- pituit>y body1 #cea -- def9$ z ! spiritual man1 #ba -- 8 consci\sness & ! e!r1 #bhj -- -- dep5d5ce ^u ! ego1 #bde -- -- me?od ( contact+ ! ext]nal _w1 #ahi-aia -- -- outlook ^u ! univ]se ( spatiality1 #bdb ,?9k]1 8 s*ematism ( cognitive p[]s1 #bjf -- -- sph]e ( aw>5ess1 #bhc -- ! diff]5ce betwe51 & ! intellectuality1 #bef -- -- evolution>y ne$s (1 #ccf -- -- uprea*+ ye>n+s (1 #ccf ,?9k]-w>d1 space mu/ be s\ght 9 a direction1 #bgh ,?9k+1 ab/ract1 elevat+ influ5ce (1 #cc ,?\ght1 prolong$ ab/ract1 b5efits (1 #bdi ,"t1 z an aspect ( consci\sness1 #bbd -- dive/$ ( timel9ess1 #bgi ,todhunt]1 #df ,tool1 fa%ion+1 life z a1 #bfd ,topography ( ! intellect1 #cab ,t\*/one1 consci\sness z a1 #afh ,trac]y ( connection betwe5 ideas & objects1 #abf ,traffick+ 9 m5tal con/ructions1 #aed ,transc5d5tal1 ! realm (1 & ma!maticians1 #adb ,transf9ite z a limit1 #abb1 #baf ,transf9ity1 #ba-b ,tree-reality1 #abf ,triadic phase ( evolution1 #baj-a ,triangles1 angul> sum (1 #gh1 #hh ,tridim1 !1 #bb1 #abi1 #acd1 #adg1 #agg ,tridim5sion1 !1 #adg ,tridim5sionality & primeval space1 #bcf -- & ! space-m9d1 #aic -- a quality ( p]ceptual space1 #bb -- ma/]y ( ! ph5om5a (1 #agb -- ! suffici5cy (1 #aih ,tripyknon1 !1 #bab1 #bac ,tripyknosis1 #ag1 #bjh-aj1 #bai ,tru? comp>$ ) facts1 #bhh -- crit]ion (1 #e1 #cbc-d -- facets (1 #bhd -- k9ds (1 #cbd -- logic does n illum9ate1 #bhg-h ,tuitive1 !1 & ! intuitive faculties1 #aib-c ,u ,ultima ,?ule1 !1 #bjg ,unb\nd$1 !1 z a f9ite ext5sion1 #gj ,undulations1 ?ree1 9 ! curr5t ( life1 #cbi ,unfoldm5t1 m5tal1 & metageometrical discov]ies1 #aca ,uni-circle1 !1 #cjh ,unification ( all k1 #bef ,uniqu5ess ( real space1 #ie ,unit>9ess ( all exi/5ces1 #bda ,unity1 z end ( analysis1 #db -- dea? z a f\r? dim5sional1 #aei -- kosmic1 integ]s z fractional p>ts (1 #da -- ( m9d & space1 #bbd1 #bcj -- ! new realization (1 #bbe ,univ]sality1 geometric1 bas$ ^u ! =mal "* ( assumptions1 #gg-h ,univ]se1 a glorifi$1 #bbf1 #bfh -- z a full1 #cjh -- -- -- pl5um1 #ajg -- & ! sev5 planes ( matt]1 #bab -- "* (1 fix$ by consci\sness1 #afb -- limit$ & condition$1 #abg -- n a pure =m1 #ajh -- ! p]fect$1 & ! circle1 #caj -- -- !ory ( ! me*anical orig9 (1 due to analytics1 #dj -- unity 9 !1 #cja-b ,univ]sum ( appe>ance1 #ahg -- ( life & consci\sness1 #beg ,univ]sum ( reality1 #abg -- -- space1 #bfi ,unkn[able z a symbol1 #aid -- ! d>kness :i* %uts out !1 #bjg ,unodim1 !1 #abi1 #acd1 #agf-g -- -- consci\sness1 #afc -- def9$1 #bb ,up-raisem5t ( matt]1 #cbi ,upspr++ ( a new faculty1 #ccc ,v ,vacuum-/illness ( nature1 #cci ,validity ( ma!matical conclusions1 #aja ,value assign$ by ! intellect to ! s5sible _w1 #afg -- assumptional1 vitiat+ influ5ce (1 #afc -- -- ( ! ideal1 #bge ,vanity ( fragm5t>y evid5ces1 #bjd -- ( intellectual me?od1 #cbe1 ff -- -- segm5t+ space into _m dim5sions1 #bii ,vassal1 life z !1 ( mat]iality1 #cbi ,vehicle ( life1 =m z1 #ccj -- -- -- m9d z1 #bhf ,vicissitudes ( kosmic evolution1 #bae ,vision1 ! inn]1 #cef ,w ,wa*t]1 #fi ,wallis1 ,john1 #df1 #hc ,weissman1 note1 #bfj ,words1 z symbols ( ideas1 #abf-g1 #bjd ,_w & ! *ild m9d1 #aba -- z in/rum5t ( consci\sness1 #aii1 #bih -- fabric (1 & geometrism1 #bfa -- impossibility ( objectify+ ! f\r? dim5sion 9 ! p]ceptual1 #abd -- ( phantasy1 conditions (1 id5tifi$ ) s5sible realm1 #adf -- ph5om5al1 & hyp]space entities1 #abh-acj -- s5sible1 z a c>pet1 #aif -- ! doma9 ( a p]ception1 #ai -- -- g5esis (1 #afg ,_w-plasm1 ka!kotic1 #bfg -- z elem5tal ess5ce1 #cbi ,y ,yoga1 ,rajah1 #ceg ,y\? ( ! e>?1 ! nebul\s1 #cce ,z ,zolln]1 & ! claims ( ! spirituali/s1 #aed ,zones ( ,aff9ity1 #bb1 #abd ,zoomet]1 !1 #big ,transcrib]'s ,notes ,v>iations 9 spell+1 punctuation & hyph5ation h be5 reta9$ except 9 obvi\s cases ( typographical errors4 ,inconsi/5cies betwe5 ! text & index h be5 resolv$ 9 fav\r ( ! text4 ,duplication ( ! sub title 7,! ,my/]y ( ,space7 on consecutive pages has be5 remov$4 ,italics are %[n ?us italic4 ,9 ! five cases :]e illu/rations c\ld be reali/ically r5d]$ us+ only text symbols ?is has be5 done4