,transcriber's ,notes3 ,underscores 80 before and after a word or phrase indicate italics in the original text4 ,a single underscore after a symbol indicates a subscript4 ,small capitals have been converted to ,,solid capitals4 ,illustrations have been moved so they do not break up paragraphs4 ,typographical and punctuation errors have been silently corrected4 ,,giant ,,brains ,,or ,,machines ,,that ,,think ,,edmund ,,callis ,,berkeley ,consultant in ,modern ,technology ,president1 ,e4 ,c4 ,berkeley and ,associates ,,john ,,wiley ,,sons1 ,,inc41 ,,new ,,york ,,chapman ,,hall1 ,,limited1 ,,london ,copyright1 #aidi by ,,edmund ,,callis ,,berkeley ,all ,rights ,reserved ,this book or any part thereof must not be reproduced in any form without the written permission of the publisher4 ,second ,printing1 ,february1 #aiej ,printed in the ,united ,states of ,america ,to my friends1 whose help and instruction made this book possible ,,preface ,the ,subject1 ,purpose1 and ,method of this ,book ,the subject of this book is a type of machine that comes closer to being a brain that thinks than any machine ever did before #aidj4 ,these new machines are called sometimes mechanical brains and sometimes sequence-controlled calculators and sometimes by other names4 ,essentially1 though1 they are machines that can handle information with great skill and great speed4 ,and that power is very similar to the power of a brain4 ,these new machines are important4 ,they do the work of hundreds of human beings for the wages of a dozen4 ,they are powerful instruments for obtaining new knowledge4 ,they apply in science1 business1 government1 and other activities4 ,they apply in reasoning and computing1 and1 the harder the problem1 the more useful they are4 ,along with the release of atomic energy1 they are one of the great achievements of the present century4 ,no one can afford to be unaware of their significance4 ,in this book ,i have sought to tell a part of the story of these new machines that think4 ,perhaps you1 as you start this book1 may not agree with me that a machine can think3 the first chapter of this book is devoted to the discussion of this question4 ,my purpose has been to tell enough about these machines so that we can see in general how they work4 ,i have sought to explain some giant brains that have been built and to show how they do thinking operations4 ,i have sought also to talk about what these machines can do in the future and to judge their significance for us4 ,it seems to me that they will take a load off men's as great as the load that printing took off men's writing3 a tremendous burden lifted4 ,we need to examine several of the new mechanical brains3 ,massachusetts ,institute of ,technology's differential analyzer1 ,harvard's ,,ibm automatic sequence-controlled calculator1 ,moore ,school's ,,eniac 7,electronic ,numerical ,integrator and ,calculator71 and ,bell ,laboratories' general-purpose relay calculator4 ,these are described in the sequence in which they were finished between the years #aidb and #aidf4 ,we also have to go on some excursions--for instance1 the nature of language and of symbols1 the meaning of thinking1 the human brain and nervous system1 the future design of machinery that can think1 and a little algebra and logic4 ,i have also sought to discuss the relations between machines that think and human society--what we can foresee as likely to happen or be needed as a result of the remarkable invention of machines that can think4 ,,reading ,,this ,,book ,this book is intended for everyone4 ,i have sought to put it together in such a way that any reader can select from it what he wants4 ,perhaps at first reading you want only the main thread of the story4 ,then read only what seems interesting1 and skip whatever seems uninteresting4 ,the subheadings should help to tell you what to read and what to skip4 ,nearly all the chapters can be read with little reference to what goes before1 although some reference to the supplements in the back may at times be useful4 ,perhaps your memory of physics is dim1 like mine4 ,the little knowledge of physics needed is explained here and there throughout the book1 and the index should tell where to find any explanation you may want4 ,perhaps it is a long time since you did any algebra4 ,then ,supplement #b on mathematics may hold something of use to you4 ,two sections 7one in ,chapter #e and one in ,chapter #f7 labeled as containing some rather mathematical details may be skipped with no great loss4 ,perhaps you are unacquainted with logic that uses symbols--the branch of logic called mathematical logic4 ,in fact1 very few people are familiar with it4 ,no discussion in the book hinges on understanding this subject1 except for ,chapter #i where a machine that calculates logical truth is described4 ,in all other chapters you may freely skip all references to mathematical logic4 ,but1 if you are curious about the subject and how it can be usefully applied in the field of mechanical brains1 then begin with the introduction to the subject in ,chapter #i1 and note the suggestions in the section entitled 8,algebra of ,logic0 in ,supplement #b4 ,in any case1 glance at the table of contents1 the chapter headings and subheadings1 and the supplements at the back4 ,these should give an idea of how the book is put together and how you may select what may be interesting to you4 ,please do not read this book straight from beginning to end unless that way proves to be congenial to you4 ,if you are not interested in technical details1 skip most of the middle chapters1 which describe existing mechanical brains4 ,if1 on the other hand1 you want more details than this book contains1 look up references in ,supplement #c4 ,here are listed1 with a few comments1 over #bej books1 articles1 and pamphlets related to the subject of machinery for computing and reasoning4 ,these cover many parts of the field2 some parts1 however1 are not yet covered by any published information4 ,there are no photographs in this book1 although there are over #hj drawings4 ,photographs of these complicated machines can really show very little3 panels1 lights1 switches1 wires1 and other kinds of hardware4 ,what is important is the way the machine works inside4 ,this cannot be shown by a photograph but may be shown by schematic drawings4 ,in the same way1 a photograph of a human being shows almost nothing about how he thinks4 ,,understanding ,,this ,,book ,i have tried to write this book so that it could be understood4 ,i have attempted to explain machinery for computing and reasoning without using technical words any more than necessary4 ,to do this seemed to be easy in some places1 much harder in others4 ,as a test of this attempt1 a count has been made of all the different words in the book that have two syllables or more1 that are used for explaining1 and that are not themselves defined4 ,there are fewer than #ahjj of these words4 ,in ,supplement #a1 entitled 8,words and ,ideas10 ,i have digressed to discuss further the problem of explanation and understanding4 ,every now and then in the book1 along comes a word or a phrase that has a special meaning1 for example1 the name of something new4 ,when it first appears1 it is put in italics and is explained or defined4 ,in addition1 all the words and phrases having special meaning appear again in the index1 and next to each is the page number of its explanation or definition4 ,in many places1 ,i have talked of mechanical brains as if they were living4 ,for example1 instead of 8capacity to store information0 ,i have spoken of 8memory40 ,of course1 the machines are not living2 but they do have individuality1 responsiveness1 and other traits of living beings1 just as a political party pictured as a living elephant does4 ,besides1 to treat things as persons is a help in making any subject vivid and understandable1 as every song writer and cartoonist illustrates4 ,we speak of 8,old ,man ,river0 and 8,father ,time02 we may speak of a ship or a locomotive as 8she02 and the crew on the first ,harvard sequence-controlled calculator has often called her 8,bessy1 the ,bessel engine40 ,let us pause a little longer on the subject of understanding4 ,what is the understanding of something new8 ,it is a state of knowing1 a process of knowing more and more4 ,the more we know about something new1 the better we understand it4 ,it is possible for almost anybody to understand almost anything1 ,i believe4 ,what is mainly needed in order to grasp an idea is a good collection of true statements about it and some practice in using those statements in situations4 ,for example1 no one has ever seen or touched the separate scraps of electricity called electrons4 ,but electrons have been described and measured2 hundreds of thousands of people work with electrons2 they know and use true statements about electrons4 ,in effect1 these people understand electrons4 ,probably the hardest task of an author is to make his statements understandable yet accurate4 ,it is too much to hope for complete success4 ,i shall be very grateful to any reader who points out to me the statements that he has not understood or that are in error4 ,as to the views ,i have expressed1 ,i do not expect every reader to agree with me4 ,in fact1 ,i shall be glad if many a reader disagrees with me4 ,for then someone else may say to both of us1 8,you're both right and both wrong--the truth lies atwixt and atween you40 ,thoughtful and tolerant disagreement is the finest climate for scientific progress4 ,,basic ,,facts ,many of the mechanical brains described in this book will do good work for years2 but their design is already out of date4 ,many organizations are hard at work finding new tricks in electronics1 materials1 and engineering and making new mechanical brains that are better and faster4 ,in spite of future developments1 though1 the basic facts about mechanical brains will endure4 ,these basic facts are drawn from the principles of thinking1 of mathematics1 of science1 of engineering1 etc4 ,these facts govern all handling of information4 ,they do not depend very much on human or mechanical energy4 ,they do not depend very much on signs4 ,they do not depend very much on the century1 or the language1 or the country4 ,for example1 8,,ii et ,,iii ,v sunt10 the ,romans may have said2 8deux et trois font cinq10 say the ,french2 8#b #c #e10 say the mathematicians2 and we say1 8two and three make five40 ,the main effort in this book has been to make clear the basic facts about mechanical brains1 for they are now a masterly instrument for obtaining new knowledge4 ,,edmund ,,callis ,,berkeley ,new ,york #aa1 ,n4 ,y4 ,june #cj1 #aidi ,,acknowledgments ,this book has been over seven years in the making and has evolved through many different plans for its contents4 ,it springs essentially from the desire to see human beings use their knowledge better3 we know enough1 but how are we to use what we know8 ,machines that handle information1 that make knowledge accessible1 are a long step in the direction of using what we know4 ,for help in causing this desire to come to fruition1 ,i should like to express my indebtedness especially to ,professor 7then ,commander1 ,u4,s4,n4,r47 ,howard ,h4 ,aiken of ,harvard ,university1 whose stimulus1 while ,i was stationed for ten months in #aide-df in his laboratory1 was very great4 ,i should also like to express my appreciation to ,mr4 ,harry ,j4 ,volk1 whose vision and enthusiasm greatly encouraged me in the writing of this book4 ,for careful reviews and helpful comments on the chapters dealing with existing mechanical brains1 ,i am especially grateful to ,dr4 ,franz ,l4 ,alt1 ,mr4 ,e4 ,g4 ,andrews1 ,professor ,samuel ,h4 ,caldwell1 ,dr4 ,grace ,m4 ,hopper1 ,mr4 ,theodore ,a4 ,kalin1 and ,dr4 ,john ,w4 ,mauchly1 who are experts in their fields4 ,dr4 ,ruth ,p4 ,berkeley1 ,dr4 ,rudolf ,flesch1 ,mr4 ,j4 ,ross ,macdonald1 ,dr4 ,z4 ,i4 ,mosesson1 ,mr4 ,irving ,rosenthal1 ,mr4 ,max ,s4 ,weinstein1 and many others have been true friends in reading and commenting upon many parts of the manuscript4 ,mr4 ,frank ,w4 ,keller devoted much time and skill to converting my rough sketches into illustrations4 ,mr4 ,murray ,b4 ,ritterman has been of invaluable help in preparing and checking much of the bibliography4 ,miss ,marjorie ,l4 ,black has helped very greatly in turning scraps of paper bearing sentences into an excellent manuscript for the printer4 ,for permission to use the quotations on various pages in ,chapters #aa and #ab1 ,i am indebted to the kindness of3 ,e4 ,p4 ,dutton ,co41 for quotations from ,frankenstein1 by ,mary ,w4 ,shelley1 ,everyman's ,library1 ,no4 #faf4 ,samuel ,french1 for quotations from ,r4 ,u4 ,r41 by ,karel apek4#a ,modern ,industry1 for a quotation from the issue of ,february #ae1 #aidg4 #a ,copyright #aibc by ,doubleday1 ,page and ,co42 all rights reserved2 quotations reprinted by permission of ,karel apek and ,samuel ,french4 ,responsibility for the statements and opinions expressed in this book is solely my own4 ,these statements and opinions do not necessarily represent the views of any organization with which ,i may be or have been associated4 ,to the best of my knowledge and belief no information contained in this book is classified by the ,department of ,defense of the ,united ,states4 ,,edmund ,,callis ,,berkeley ,,contents #a4 ,,can ,,machines ,,think8 ,what ,is a ,mechanical ,brain8 #a #b4 ,,languages3 ,systems for ,handling ,information #aj #c4 ,a ,,machine ,,that ,,will ,,think3 ,the ,design of a ,very ,simple ,mechanical ,brain #bb #d4 ,,counting ,,holes3 ,punch-,card ,calculating ,machines #db #e4 ,,measuring3 ,massachusetts ,institute of ,technology's ,differential ,analyzer ,no4 #b #fe #f4 ,,accuracy ,,to #bc ,,digits3 ,harvard's ,,ibm ,automatic ,sequence-,controlled ,calculator #hi #g4 ,,speed--#ejjj ,,additions ,a ,,second3 ,moore ,school's ,,eniac 7,electronic ,numerical ,integrator and ,calculator7 #aac #h4 ,,reliability--,,no ,,wrong ,,results3 ,bell ,laboratories' ,general-,purpose ,relay ,calculator #abh #i4 ,,reasoning3 ,the ,kalin-,burkhart ,logical-,truth ,calculator #add #aj4 ,,an ,,excursion3 ,the ,future ,design of ,machines ,that ,think #afg #aa4 ,,the ,,future3 ,machines ,that ,think1 and ,what ,they ,might ,do for ,men #ahj #ab4 ,,social ,,control3 ,machines ,that ,think1 and ,how ,society ,may ,control ,them #aif ,,supplements #a4 ,words and ,ideas #bji #b4 ,mathematics #bad #c4 ,references #bbh ,,index #beg ,chapter #a ,,can ,,machines ,,think8 ,,what ,,is ,a ,,mechanical ,,brain8 ,recently there has been a good deal of news about strange giant machines that can handle information with vast speed and skill4 ,they calculate and they reason4 ,some of them are cleverer than others--able to do more kinds of problems4 ,some are extremely fast3 one of them does #ejjj additions a second for hours or days1 as may be needed4 ,where they apply1 they find answers to problems much faster and more accurately than human beings can2 and so they can solve problems that a man's life is far too short to permit him to do4 ,that is why they were built4 ,these machines are similar to what a brain would be if it were made of hardware and wire instead of flesh and nerves4 ,it is therefore natural to call these machines mechanical brains4 ,also1 since their powers are like those of a giant1 we may call them giant brains4 ,several giant mechanical brains are now at work finding out answers never before known4 ,two are in ,cambridge1 ,mass42 one is at ,massachusetts ,institute of ,technology1 and one at ,harvard ,university4 ,two are in ,aberdeen1 ,md41 at the ,army's ,ballistic ,research ,laboratories4 ,these four machines were finished in the period #aidb to #aidf and are described in later chapters of this book4 ,more giant brains are being constructed4 ,can we say that these machines really think8 ,what do we mean by thinking1 and how does the human brain think8 ,,human ,,thinking ,we do not know very much about the physical process of thinking in the human brain4 ,if you ask a scientist how flesh and blood in a human brain can think1 he will talk to you a little about nerves and about electrical and chemical changes1 but he will not be able to tell you very much about how we add #b and #c and make #e4 ,what men know about the way in which a human brain thinks can be put down in a few pages1 and what men do not know would fill many libraries4 ,injuries to brains have shown some things of importance2 for example1 they have shown that certain parts of the brain have certain duties4 ,there is a part of the brain1 for instance1 where sights are recorded and compared4 ,if an accident damages the part of the brain where certain information is stored1 the human being has to relearn--haltingly and badly--the information destroyed4 ,we know also that thinking in the human brain is done essentially by a process of storing information and then referring to it1 by a process of learning and remembering4 ,we know that there are no little wheels in the brain so that a wheel standing at #b can be turned #c more steps and the result of #e read4 ,instead1 you and ,i store the information that #b and #c are #e1 and store it in such a way that we can give the answer when questioned4 ,but we do not know the register in our brain where this particular piece of information is stored4 ,nor do we know how1 when we are questioned1 we are able automatically to pick up the nerve channels that lead into this register1 get the answer1 and report it4 ,since there are many nerves in the brain1 about #aj billion of them1 in fact1 we are certain that the network of connecting nerves is a main part of the puzzle4 ,we are therefore much interested in nerves and their properties4 ,,nerves ,,and ,,their ,,properties ,a single nerve1 or nerve cell1 consists of a cell nucleus and a fiber4 ,this fiber may have a length of anything from a small fraction of an inch up to several feet4 ,in the laboratory1 successive impulses can be sent along a nerve fiber as often as #ajjj a second4 ,impulses can travel along a nerve fiber in either direction at a rate from #c feet to #cjj feet a second4 ,because the speed of the impulse is far less than #ahf1jjj miles a second--the speed of an electric current--the impulse in the nerve is thought by some investigators to be more chemical than electrical4 ,we know that a nerve cell has what is called an all-or-none response1 like the trigger of a gun4 ,if you stimulate the nerve up to a certain point1 nothing will happen2 if you reach that point1 or cross it1--bang6--the nerve responds and sends out an impulse4 ,the strength of the impulse1 like the shot of the gun1 has no relation whatever to the amount of the stimulation4 ,illustration3 ,,fig4 #a4 ,scheme of a nerve cell4 ,the structure between the end of one nerve and the beginning of the next is called a synapse 7see ,fig4 #a74 ,no one really knows very much about synapses1 for they are extremely small and it is not easy to tell where a synapse stops and other stuff begins4 ,impulses travel through synapses in from to #c thousandths of a second4 ,an impulse travels through a synapse only in one direction1 from the head 7or axon7 of one nerve fiber to the foot 7or dendrite7 of another4 ,it seems clear that the activity in a synapse is chemical4 ,when the head of a nerve fiber brings in an impulse to a synapse1 apparently a chemical called acetylcholine is released and may affect the foot of another fiber1 thus transmitting the impulse2 but the process and the conditions for it are still not well understood4 ,it is thought that nearly all information is handled in the brain by groups of nerves in parallel paths4 ,for example1 the eye is estimated to have about #ajj million nerves sensitive to light1 and the information that they gather is reported by about #a million nerves to the part of the brain that stores sights4 ,not much more is yet known1 however1 about the operation of handling information in a human brain4 ,we do not yet know how the nerves are connected so that we can do what we do4 ,probably the greatest obstacle to knowledge is that so far we cannot observe the detailed structure of a living human brain while it performs1 without hurting or killing it4 ,,behavior ,,that ,,is ,,thinking ,therefore1 we cannot yet tell what thinking is by observing precisely how a human brain does it4 ,instead1 we have to define thinking by describing the kind of behavior that we call thinking4 ,let us consider some examples4 ,when you and ,i add #ab and #h and make #bj1 we are thinking4 ,we use our minds and our understanding to count #h places forward from #ab1 for example1 and finish with #bj4 ,if we could find a dog or a horse that could add numbers and tell answers1 we would certainly say that the animal could think4 ,with no trouble a machine can do this4 ,an ordinary #aj-;column adding machine can be given two numbers like #a1cgh1iag1gff and #b1cee1gii1hfg and the instruction to add them4 ,the machine will then give the answer1 #c1gcd1gag1fcc1 much faster than a man4 ,in fact1 the mechanical brain at ,harvard can add a number of #bc digits to another number of #bc digits and get the right answer in _/ of a second4 ,or1 suppose that you are walking along a road and come to a fork4 ,if you stop1 read the signpost1 and then choose left or right1 you are thinking4 ,you know beforehand where you want to go1 you compare your destination with what the signpost says1 and you decide on your route4 ,this is an operation of logical choice4 ,a machine can do this4 ,the mechanical brain now at ,aberdeen which was built at ,bell ,laboratories can examine any number that comes up in the process of a calculation and tell whether it is bigger than #c 7or any stated number7 or smaller4 ,if the number is bigger than #c1 the machine will choose one process2 if the number is smaller than #c1 the machine will choose another process4 ,now suppose that we consider the basic operation of all thinking3 in the human brain it is called learning and remembering1 and in a machine it is called storing information and then referring to it4 ,for example1 suppose you want to find #cje ,main ,street in ,kalamazoo4 ,you look up a map of ,kalamazoo2 the map is information kindly stored by other people for your use4 ,when you study the map1 notice the streets and the numbering1 and then find where the house should be1 you are thinking4 ,a machine can do this4 ,in the ,bell ,laboratories' mechanical brain1 for example1 the map could be stored as a long list of the blocks of the city and the streets and numbers that apply to each block4 ,the machine will then hunt for the city block that contains #cje ,main ,street and report it when found4 ,a machine can handle information2 it can calculate1 conclude1 and choose2 it can perform reasonable operations with information4 ,a machine1 therefore1 can think4 ,,the ,,definition ,,of ,a ,,mechanical ,,brain ,now when we speak of a machine that thinks1 or a mechanical brain1 what do we mean8 ,essentially1 a mechanical brain is a machine that handles information1 transfers information automatically from one part of the machine to another1 and has a flexible control over the sequence of its operations4 ,no human being is needed around such a machine to pick up a physical piece of information produced in one part of the machine1 personally move it to another part of the machine1 and there put it in again4 ,nor is any human being needed to give the machine instructions from minute to minute4 ,instead1 we can write out the whole program to solve a problem1 translate the program into machine language1 and put the program into the machine4 ,then we press the 8start0 button2 the machine starts whirring2 and it prints out the answers as it obtains them4 ,machines that handle information have existed for more than #bjjj years4 ,these two properties are new1 however1 and make a deep break with the past4 ,how should we imagine a mechanical brain8 ,one way to think of a mechanical brain is shown in ,fig4 #b4 ,we see here a railroad line with four stations1 marked input1 storage1 computer1 and output4 ,these stations are joined by little gates or switches to the main railroad line4 ,we can imagine that numbers and other information move along this railroad line1 loaded in freight cars4 ,input and output are stations where numbers or other information go in and come out1 respectively4 ,storage is a station where there are many platforms and where information can be stored4 ,the computer is a special station somewhat like a factory2 when two numbers are loaded on platforms #a and #b of this station and an order is loaded on platform #c1 then another number is produced on platform #d4 ,illustration3 ,,fig4 #b4 ,scheme of a mechanical brain4 ,we see also a tower1 marked control4 ,this tower runs a telegraph line to each of its little watchmen standing by the gates4 ,the tower tells them when to open and when to shut which gates4 ,now we can see that1 just as soon as the right gates are shut1 freight cars of information can move between stations4 ,actually the freight cars move at the speed of electric current1 thousands of miles a second4 ,so1 by closing the right gates each fraction of a second1 we can flash numbers and information through the system and perform operations of reasoning4 ,thus we obtain a mechanical brain4 ,in general1 a mechanical brain is made up of3 #a4 ,a quantity of registers where information 7numbers and instructions7 can be stored4 #b4 ,channels along which information can be sent4 #c4 ,mechanisms that can carry out arithmetical and logical operations4 #d4 ,a control1 which guides the machine to perform a sequence of operations4 #e4 ,input and output devices1 whereby information can go into the machine and come out of it4 #f4 ,motors or electricity1 which provide energy4 ,,the ,,kinds ,,of ,,thinking ,a ,,mechanical ,,brain ,,can ,,do ,there are many kinds of thinking that mechanical brains can do4 ,among other things1 they can3 #a4 ,learn what you tell them4 #b4 ,apply the instructions when needed4 #c4 ,read and remember numbers4 #d4 ,add1 subtract1 multiply1 divide1 and round off4 #e4 ,look up numbers in tables4 #f4 ,look at a result1 and make a choice4 #g4 ,do long chains of these operations one after another4 #h4 ,write out an answer4 #i4 ,make sure the answer is right4 #aj4 ,know that one problem is finished1 and turn to another4 #aa4 ,determine most of their own instructions4 #ab4 ,work unattended4 ,they do these things much better than you or ,i4 ,they are fast4 ,the mechanical brain built at the ,moore ,school of ,electrical ,engineering at the ,university of ,pennsylvania does #ejjj additions a second4 ,they are reliable4 ,even with hundreds of thousands of parts1 the existing giant brains have worked successfully4 ,they have remarkably few mechanical troubles2 in fact1 for one of the giant brains1 a mechanical failure is of the order of once a month4 ,they are powerful4 ,the big machine at ,harvard can remember #gb numbers each of #bc digits at one time and can do #c operations with these numbers every second4 ,the mechanical brains that have been finished are able to solve problems that have baffled men for many1 many years1 and they think in ways never open to men before4 ,mechanical brains have removed the limits on complexity of routine3 the machine can carry out a complicated routine as easily as a simple one4 ,already1 processes for solving problems are being worked out so that the mechanical brain will itself determine more than #ii per cent of all the routine orders that it is to carry out4 ,but1 you may ask1 can they do any kind of thinking8 ,the answer is no4 ,no mechanical brain so far built can3 #a4 ,do intuitive thinking4 #b4 ,make bright guesses1 and leap to conclusions4 #c4 ,determine all its own instructions4 #d4 ,perceive complex situations outside itself and interpret them4 ,a clever wild animal1 for example1 a fox1 can do all these things2 a mechanical brain1 not yet4 ,there is1 however1 good reason to believe that most1 if not all1 of these operations will in the future be performed not only by animals but also by machines4 ,men have only just begun to construct mechanical brains4 ,all those finished are children2 they have all been born since #aidj4 ,soon there will be much more remarkable giant brains4 ,,why ,,are ,,these ,,giant ,,brains ,,important8 ,most of the thinking so far done by these machines is with numbers4 ,they have already solved problems in airplane design1 astronomy1 physics1 mathematics1 engineering1 and many other sciences1 that previously could not be solved4 ,to find the solutions of these problems1 mathematicians would have had to work for years and years1 using the best known methods and large staffs of human computers4 ,these mechanical brains not only calculate1 however4 ,they also remember and reason1 and thus they promise to solve some very important human problems4 ,for example1 one of these problems is the application of what mankind knows4 ,it takes too long to find understandable information on a subject4 ,the libraries are full of books3 most of them we can never hope to read in our lifetime4 ,the technical journals are full of condensed scientific information3 they can hardly be understood by you and me4 ,there is a big gap between somebody's knowing something and employment of that knowledge by you or me when we need it4 ,but these new mechanical brains handle information very swiftly4 ,in a few years machines will probably be made that will know what is in libraries and that will tell very swiftly where to find certain information4 ,thus we can see that mechanical brains are one of the great new tools for finding out what we do not know and applying what we do know4 ,chapter #b ,,languages3 ,,systems ,,for ,,handling ,,information ,as everyone knows1 it is not always easy to think4 ,by thinking1 we mean computing1 reasoning1 and other handling of information4 ,by information we mean collections of ideas--physically1 collections of marks that have meaning4 ,by handling information1 we mean proceeding logically from some ideas to other ideas--physically1 changing from some marks to other marks in ways that have meaning4 ,for example1 one of your hands can express an idea3 it can store the number #c for a short while by turning #c fingers up and #b down4 ,in the same way1 a machine can express an idea3 it can store information by arranging some equipment4 ,the ,harvard mechanical brain can store #acb numbers between #j and #ii1iii1iii1iii1iii1iii1iii1iii for days4 ,when you want to change the number stored by your fingers1 you move them3 perhaps you need a half second to change the number stored by your fingers from #c to #b1 for example4 ,in the same way1 a machine can change a stored number by changing the arrangement of some equipment3 the electronic brain ,eniac can change a stored number in _/ of a second4 ,,languages ,since it is not always easy to think1 men have given much attention to devices for making thinking easier4 ,they have worked out many systems for handling information1 which we often call languages4 ,some languages are very complete and versatile and of great importance4 ,others cover only a narrow field--such as numbers alone--but in this field they may be remarkably efficient4 ,just what is a language8 ,every language is both a scheme for expressing meanings and physical equipment that can be handled4 ,for example1 let us take spoken ,english4 ,the scheme of spoken ,english consists of more than #aej1jjj words expressing meanings1 and some rules for putting words together meaningfully4 ,the physical equipment of spoken ,english consists of 7#a7 sounds in the air1 and 7#b7 the ears of millions of people1 and their mouths and voices1 by which they can hear and speak the sounds of ,english4 ,for another example1 let us take numbers expressed in the ,arabic numerals and the rules of arithmetic4 ,the scheme of this language contains only ten digits #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i or their equivalents1 and some rules for combining them4 ,sufficient physical equipment for this language might very well be a ten-column desk calculating machine with its counter wheels1 gears1 keys1 etc4 ,if we tried to exchange the physical equipment of these two languages1 we would be blocked3 the desk calculating machine cannot possibly express the meaningful combinations of #aej1jjj words1 and sounds in the air are not permanent enough to express the steps of division of one large number by another4 ,,schemes ,,for ,,expressing ,,meanings ,if we examine languages that have existed1 we can observe a number of schemes for expressing meanings4 ,in the table on pp4 #ab-ac is a rough list of a dozen of them4 ,from among these we can choose the schemes that are likely to be useful in mechanical brains4 ,schemes #aa and #ab are the schemes that have been predominantly used in machinery for computing4 ,scheme #ab consisting of combinations of just two marks1 1 1 provides one of the best codes for mechanical handling of information4 ,this scheme1 called binary coding 7see ,supplement #b71 is also useful for measuring the quantity of information4 ,,quantity ,,of ,,information ,how should we measure the quantity of information8 ,the smallest unit of information is a 8yes0 or a 8no10 a check mark 77 or a cross 771 an impulse in a nerve or no impulse1 a #a or a #j1 black or white1 good or bad1 etc4 ,this twofold difference is called a binary digit of information 7see ,supplement #b74 ,it is the convenient unit of information4 ,,schemes ,,for ,,expressing ,,meanings ,,example3 _/-------------------------------------- ---------------------------- ,,principle ,,sign ,,used ,,in ,,significance ,,name ,,of ,,no4 ,,of ,,scheme ,,scheme 7#a7 7#b7 7#c7 7#d7 7#e7 7#f7 ,sounds #a4 ,sound of new ,bobwhite#b ,spoken kind of quail1 ,imitative2 word is like ,english so called bowwow sound of from its note theory referent #b4 ,an utterance ,pooh6#b ,spoken ,the speaker ,pooh-pooh becomes a ,english expresses theory new word disdain #c4 ,new word is ,chortle#b ,spoken 8,chuckle0 ,analogical like another ,english2 and word invented by 8snort0 ,lewis ,carroll1 blended #ahif #d4 ,word has ,mother#b ,spoken ,female ,historical been used ,english parent through the ages ,sights #e4 ,picture picture ,egyptian2 ,picture of ,imitative2 is like of eye ,ojibwa eye and pictographic referent 7,american tears1 to ,indian7 mean grief #f4 ,pattern is #e ,english2 ,five2 ,ideographic2 symbol of ,french2 cinq2 mathematical2 an idea ,german2 fnf2 symbolic2 etc4 etc4 numeric ,mapping of ,sounds #g4 ,object picture ,possible ,picture of ,rebus- pictured of knot ,english a knot to writing2 has the mean 8not0 phonographic wanted sound #h4 ,pattern is picture ,ancient ,sign for ,syllable- symbol for of star ,cypriote the writing a large 7island of syllable sound unit ,cyprus7 mu #i4 ,pattern is ,international ,the sound ,phonetic symbol for ,phonetic zh1 as writing a small ,alphabet of s in alphabetic sound unit #hg characters 8measure0 writing2 ,mapping of ,sights or ,symbols #aj4 ,systematic ,,eniac ,abbreviations1 ,initial ,alphabetic combinations etc4 letters coding of #bf of a letters #e-word title #aa4 ,systematic #ace-jc-abbh ,abbreviations1 ,social ,numeric combinations nomenclature1 ,security coding of #aj digits etc4 ,no4 of a person #ab4 ,systematic 1111 ,checking 8yes10 ,binary combinations lists1 8no10 coding of #b marks etc4 8no10 8yes10 8yes10 respectively #b ,the preceding word is the spoken word1 not the written one4 ,with #b units of information or #b binary digits 7#a or #j7 we can represent #d pieces of information3 #jj1 #ja1 #aj1 #aa ,with #c units of information we can represent #h pieces of information3 #jjj1 #jja1 #jaj1 #jaa1 #ajj1 #aja1 #aaj1 #aaa ,with #d units of information we can represent #af pieces of information3 #jjjj #jjja #jjaj #jjaa #jajj #jaja #jaaj #jaaa #ajjj #ajja #ajaj #ajaa #aajj #aaja #aaaj #aaaa ,now #d units of information are sufficient to represent a decimal digit #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i and allow #f possibilities to be left over2 #c units of information are not sufficient4 ,for example1 we may have3 #j #jjjj #e #jaja #a #jjja #f #jaaj #b #jjaj #g #jaaa #c #jjaa #h #ajjj #d #jajj #i #ajja ,we say1 therefore1 that a decimal digit #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i is equivalent to #d units of information4 ,thus a table containing #aj1jjj numbers1 each of #aj decimal digits1 is equivalent to #djj1jjj units of information4 ,one of the #bf letters of the alphabet is equivalent to #e units of information1 for1 #e binary digits 7#a or #j7 have #cb possible arrangements1 and these are enough to provide for the #bf letters4 ,any printed information in ,english can be expressed in about #hj characters consisting of #aj numerals1 #eb capital and small letters1 and some #ah punctuation marks and other types of marks2 #f binary digits 7#a or #j7 have #fd possible arrangements1 and #g binary digits 7#a or #j7 have #abh possible arrangements4 ,each character in a printed book1 therefore1 is roughly equivalent to #g units of information4 ,it can be determined that a big telephone book or a big reference dictionary stores printed information at the rate of about #a billion units of information per cubic foot4 ,if the #aj billion nerves in the human brain could independently be impulsed or not impulsed1 then the human brain could conceivably store #aj billion units of information4 ,the largest library in the world is the ,library of ,congress1 containing #g million volumes including pamphlets4 ,it stores about #ajj trillion units of information4 ,we can thus see the significance of a quantity of information from #a unit to #ajj trillion units4 ,no distinction is here made between information that reports facts and information that does not4 ,for example1 a book of fiction about persons who never existed is still counted as information1 and1 of course1 much instruction and entertainment may be found in such a source4 ,,physical ,,equipment ,,for ,,handling ,,information ,the first thing we want to do with information is store it4 ,the second thing we want to do is combine it4 ,we want equipment that makes these two processes easy and efficient4 ,we want equipment for handling information that3 #a4 ,costs little4 #b4 ,holds much information in little space4 #c4 ,is permanent1 when we want to keep the information4 #d4 ,is erasable1 when we want to remove information4 #e4 ,is versatile1 holds easily any kind of information1 and allows operations to be done easily4 ,the amount of human effort needed to handle information correctly depends very much on the properties of the physical equipment expressing the information1 although the laws of correct reasoning are independent of the equipment4 ,for example1 the great difficulty with spoken sounds as physical equipment for handling information is the trouble of storing them4 ,the technique for doing so was mastered only about #ahgg when ,thomas ,a4 ,edison made the first phonograph4 ,even with this advance1 no one can glance at a soundtrack and tell quickly what sounds are stored there2 only by turning back the machine and listening to a groove can we determine this4 ,it was not possible for the men of #bjjj ,b4,c4 to wait thousands of years for the storing of spoken sounds4 ,the problem of storing information was accordingly taken to other types of physical equipment4 ,,physical ,,equipment ,,for ,,handling ,,information ,,physical ,,arranged ,,operated ,,or ,,low ,,little ,,perm- ,,eras- ,,vers- ,,no4 ,,objects ,,in ,,or ,,on ,,produced ,,by ,,cost8 ,,space8 ,,anent8 ,,able8 ,,atile8 7#a7 7#b7 7#c7 7#d7 7#e7 7#f7 7#g7 7#h7 7#i7 ,mind #a4 ,nerve ,human ,body cells brain ,sounds #b4 ,sounds ,air ,voice #c4 ,sound- ,wax ,machines tracks cylinders1 and phonograph motors records ,sights #d4 ,marks ,sand ,stick #e4 ,colored ,cave ,paintbrush painting walls1 and paints canvases1 etc4 #f4 ,marks1 ,clay1 ,stylus1 inscript- stone chisel ions #g4 ,marks ,slate ,chalk #h4 ,marks ,paper1 ,pen parchment1 and ink1 etc4 pencil #i4 ,letters1 ,paper1 ,printing etc4 books1 press1 etc4 movable type1 motor1 and hands #aj4 ,photo- ,film1 ,camera graphs prints1 etc4 #aa4 ,letters1 ,paper1 ,typewriter etc4 mimeograph and stencil1 fingers etc4 ,body #ab4 ,gestures ,space ,body #ac4 ,fingers ,hands ,body ,objects #ad4 ,pebbles ,slab ,hands #ae4 ,knots ,string ,hands #af4 ,tallies1 ,stick ,knife notches #ag4 ,beads ,rods in ,hands a frame1 abacus #ah4 ,ruled ,rulers1 ,hands1 lines1 scales1 pressure1 pointers dials etc4 ,machines #ai4 ,counter ,desk ,motor wheels1 calculating and gears1 machines1 hands keys1 fire-control lights1 instruments1 etc4 etc4 #bj4 ,punched ,punch card ,motor cards machinery1 and and teletype1 input paper etc4 instructions tape #ba4 ,relays ,dial ,motor telephone1 and other input machinery instructions #bb4 ,elect- ,machinery ,motor ronic and tubes input instructions #bc4 ,magnetic ,machinery ,motor surfaces3 and wire1 input tape1 instructions discs #bd4 ,delay ,machinery ,motor lines3 and electric1 input acoustic instructions #be4 ,electro- ,machinery ,motor static and storage input tubes instructions yes1 very4 yes1 adequately4 not generally4 not at all4 ,what are the types of physical equipment for handling information1 and which are the good ones8 ,in the table on pp4 #af-ag is a rough list of #be types of physical equipment for handling information4 means 8yes1 very20 means 8yes1 adequately20 means 8not generally20 means 8not at all40 ,for example1 our fingers 7see ,no4 #ac7 as a device for handling information are very expensive for most cases4 ,they take up a good deal of space4 ,certainly they are very temporary storage2 any information they may express is very erasable2 and what we can express with them alone is very limited4 ,yet1 with a typewriter 7see ,no4 #aa71 our fingers become versatile and efficient4 ,in fact1 our fingers can make #d strokes a second2 we can select any one of about #ch keys2 and1 since each key is equivalent to #e or #f units of information1 the effective speed of our fingers may be about #hjj units of information a second4 ,,languages ,,of ,,physical ,,objects ,the use of pebbles 7see ,no4 #ad7 for keeping track of numerical information is shown in the history of the words containing the root calc-of the word calculate4 ,the ,latin word calcis meant pertaining to lime or limestone1 and the ,latin word calculus derived from it meant first a small piece of limestone1 and later any small stone1 particularly a pebble used in counting4 ,all three of these meanings have left descendants3 8chalk10 8calcite10 8calcium10 relating in one way or another to lime2 in medicine1 8calculus10 referring to stones in the kidneys or elsewhere in the body2 and in mathematics1 8calculate10 8calculus10 referring to computations1 once done with pebbles4 ,the pebbles1 and the slab 7for which the ancient ,greek word is abax7 on which they were arranged and counted1 were later replaced1 for ease in handling1 by groups of beads strung on rods and placed in a frame 7see ,no4 #ag74 ,these constituted the abacus 7see ,supplement #b and the figure there74 ,this was the first calculating machine4 ,it is still used all over ,asia2 in fact1 even today more people use the abacus for accounting than use pencil and paper4 ,the skill with which the abacus can be used was shown in ,november #aidf in a well-publicized contest in ,japan4 ,kiyoshi ,mastuzaki1 a clerk in the ,japanese communications department1 using the abacus1 challenged ,private ,thomas ,wood of the ,u4 ,s4 ,army1 using a modern desk calculating machine1 and defeated him in a speed contest involving additions1 subtractions1 multiplications1 and divisions4 ,the heaps of small pebbles1 the notches in sticks1 and the abacus had the advantage of being visible and comparatively permanent4 ,storing and reading were relatively easy4 ,they were rather compact and easy to manipulate1 certainly much easier than spoken words4 ,but they were subject to disadvantages also4 ,moving correctly from one arrangement to another was difficult1 since there was no good way for storing intermediate steps so that the process could be easily verified4 ,furthermore1 these devices applied to specified numbers only4 ,also1 there was no natural provision for recording what the several numbers belonged to4 ,this had to be recorded with the help of another language1 writing4 ,the language of physical objects was picked up from obscurity by the invention of motors and the demands of commerce and business4 ,commencing in the late #ahjj's1 desk calculating machines 7see ,no4 #ai7 were constructed to meet mass calculation requirements4 ,they would add1 subtract1 multiply1 and divide specific numbers with great accuracy and speed4 ,but until recently they still were adjuncts to the other languages1 for they provided figures one at a time for insertion in the spaces on the ledger pages or calculation sheets where figures were called for4 ,beginning in the #aibj's1 a remarkable change has taken place4 ,instead of performing single operations1 machines have been developed to perform chains of operations with many kinds of information4 ,one of these machines is the dial telephone3 it can select one of #g million telephones by successive sorting according to the letters and digits of a telephone number4 ,another of these machines is a fire-control instrument1 a mechanism for controlling the firing of a gun4 ,for example1 in a modern anti-aircraft gun the mechanism will observe an enemy plane flying at several hundred miles an hour1 convert the observations into gun-aiming directions1 and determine the aiming directions fast enough to shoot down the plane4 ,punch-card machinery1 machines handling information expressed as punched holes in cards1 enable the fulfillment of social security legislation1 the production of the census1 and countless operations of banks1 insurance companies1 department stores1 and factories4 ,and1 finally1 in #aidb the first mechanical brain was finished at ,massachusetts ,institute of ,technology4 ,,the ,,crucial ,,devices ,,for ,,mechanical ,,brains ,let us consider the two modern physical devices for handling information which make mechanical brains possible4 ,these are relays and electronic tubes 7,nos4 #ba and #bb74 ,the last three kinds of equipment listed in the table 7magnetic surfaces1 ,no4 #bc2 delay lines1 ,no4 #bd2 and electrostatic storage tubes1 ,no4 #be7 were not included in any mechanical brains functioning by the middle of #aidh4 ,the discussion of them is therefore put off to ,chapter #aj1 where we talk about the future design of mechanical brains4 ,illustration3 ,,fig4 #a4 ,relay ,figure #a shows a simple relay4 ,there are two electrical circuits here4 ,one has two terminals--,pickup and ,ground4 ,the other has three terminals--,common1 ,normally ,open1 and ,normally ,closed4 ,when current flows through the coil of wire around the iron1 it makes the iron a magnet2 the magnet pulls down the flap of iron above1 overcoming the force of the spring4 ,when there is no current through the coil1 the iron is not a magnet1 and the flap is held up by the spring4 ,now suppose that there is current in ,common4 ,when there is no current in ,pickup1 the current from ,common will flow through the upper contact1 to the terminal marked ,normally ,closed4 ,when there is current in ,pickup1 the current from ,common will flow through the lower contact1 to the terminal marked ,normally ,open4 ,thus we see that a relay expresses a 8yes0 or a 8no10 a #a or #j1 a binary digit1 a unit of information4 ,a relay costs #e to #aj4 ,it is rather expensive for storing a single unit of information4 ,the fastest it can be changed from #a to #j1 or vice versa1 is about _/ of a second4 ,illustration3 ,,fig4 #b4 ,electronic tube4 ,figure #b shows a simple electronic tube4 ,it has three parts--the ,cathode1 the ,grid1 and the ,plate4 ,the ,grid actually is a coarse net of metal wires4 ,electrons can flow from the ,cathode to the ,plate1 provided the voltage on the ,grid is such as to permit them to flow4 ,so we can see that an electronic tube is a very simple on-off device and expresses a 8yes0 or a 8no10 a #a or #j1 a binary digit1 a unit of information4 ,a simple electronic tube suitable for calculating purposes costs #ej cents to a #a1 only the cost of a relay4 ,it can be changed from #a to #j1 or back again1 in #a millionth of a second4 ,relays have been widely used in the mechanical brains so far built1 and electronic tubes are the essence of ,eniac4 ,in the next chapter1 we shall see how physical equipment for handling information can be put together to make a simple mechanical brain4 ,chapter #c ,a ,,machine ,,that ,,will ,,think3 ,,the ,,design ,,of ,a ,,very ,,simple ,,mechanical ,,brain ,we shall now consider how we can design a very simple machine that will think4 ,let us call it ,simon1 because of its predecessor1 ,simple ,simon4 ,,simon1 ,,the ,,very ,,simple ,,mechanical ,,brain ,by designing ,simon1 we shall see how we can put together physical equipment for handling information in such a way as to get a very simple mechanical brain4 ,at every point in the design of ,simon1 we shall make the simplest possible choice that will still give us a machine that3 handles information1 transfers information automatically from one part of the machine to another1 and has control over the sequence of operations4 ,simon is so simple and so small1 in fact1 that it could be built to fill up less space than a grocery-store box1 about #d cubic feet4 ,if we know a little about electrical work1 we will find it rather easy to make ,simon4 ,what do we do first to design the very simple mechanical brain1 ,simon8 ,,simon',s ,,flesh ,,and ,,nerves--,,representing ,,information ,the first thing we have to decide about ,simon is how information will be represented3 as we put it into ,simon1 as it is moved around inside of ,simon1 and as it comes out of ,simon4 ,we need to decide what physical equipment we shall use to make ,simon's flesh and nerves4 ,since we are taking the simplest convenient solution to each problem1 let us decide to use3 punched paper tape for putting information in1 relays 7see ,chapter #b7 and wires for storing and transferring information1 and lights for putting information out4 ,illustration3 ,,two-,,holed ,,tape ,,reader3 ,simon's left ear that listens to numbers and operations4 ,,four-,,holed ,,tape ,,reader3 ,simon's right ear that listens to instructions4 ,,light ,,bulbs3 ,simon's eyes that wink answers4 ,,fig4 #a4 ,simon1 the very simple mechanical brain4 ,for the equipment inside ,simon1 we could choose either electronic tubes or relays4 ,we choose relays1 although they are slower1 because it is easier to explain circuits using relays4 ,we can look at a relay circuit laid out on paper and tell how it works1 just by seeing whether or not current will flow4 ,examples will be given below4 ,when we look at a circuit using electronic tubes laid out on paper1 we still need to know a good deal in order to calculate just how it will work4 ,how will ,simon perceive a number or other information by means of punched tape1 or relays1 or lights8 ,with punched paper tape having1 for example1 #b spaces where holes may be1 ,simon can be told #d numbers--#jj1 #ja1 #aj1 #aa4 ,here the binary digit #a means a hole punched2 the binary digit #j means no hole punched4 ,with #b relays together in a register1 ,simon can remember any one of the #d numbers #jj1 #ja1 #aj1 and #aa4 ,here the binary digit #a means the relay picked up or energized or closed2 #j means the relay not picked up or not energized or open4 ,with #b lights1 ,simon can give as an answer any one of the #d numbers #jj1 #ja1 #aj1 #aa4 ,in this case the binary digit #a means the light glowing2 #j means the light off4 7,see ,fig4 #a47 ,we can say that the two lights by which ,simon puts out the answer are his eyes and say that he tells his answer by winking4 ,we can say also that the two mechanisms for reading punched paper tape are ,simon's ears4 ,one tape1 called the input tape1 takes in numbers or operations4 ,the other tape takes in instructions and is called the program tape4 ,,simon',s ,,mentality--,,possible ,,range ,,of ,,information ,we can say that ,simon has a mentality of #d4 ,we mean not age #d but just the simple fact that ,simon knows only #d numbers and can do only #d operations with them4 ,but ,simon can keep on doing these operations in all sorts of routines as long as ,simon has instructions4 ,we decide that ,simon will know just #d numbers1 #j1 #a1 #b1 #c1 in order to keep our model mechanical brain very simple4 ,then1 for any register1 we need only #b relays2 for any answer1 we need only #b lights4 ,any calculating machine has a mentality1 consisting of the whole collection of different ideas that the machine can ever actually express in one way or another4 ,for example1 a #aj-place desk calculating machine can handle numbers up to #aj decimal digits without additional capacity4 ,it cannot handle bigger numbers4 ,illustration3 ,,fig4 #b4 ,four directions4 ,what are the #d operations with numbers which ,simon can carry out8 ,let us consider some simple operations that we can perform with just #d numbers4 ,suppose that they stood for #d directions in the order east1 north1 west1 south 7see ,fig4 #b74 ,or suppose that they stood for a turn counterclockwise through some right angles as follows3 #j3 ,turn through #j1 or no right angles4 #a3 ,turn through #ij1 or #a right angle4 #b3 ,turn through #ahj1 or #b right angles4 #c3 ,turn through #bgj1 or #c right angles4 ,then we could have the operations of addition and negation1 defined as follows3 ,,addition ,,negation c a b c -a b3 #j #a #b #c ac a ------------------ ---------------- #j #j #a #b #c #j #j #a #a #b #c #j #a #c #b #b #c #j #a #b #b #c #c #j #a #b #c #a ,for example1 the first table says1 8#a plus #c equals #j40 ,this means that1 if we turn #a right angle and then turn in the same direction #c more right angles1 we face in exactly the same way as we did at the start4 ,this statement is clearly true4 ,for another example1 the second table says1 8#b is the negative of #b40 ,this means that1 if we turn to the left #b right angles1 we face in exactly the same way as if we turn to the right #b right angles1 and this statement also is1 of course1 true4 ,with only these two operations in ,simon1 we should probably find him a little too dull to tell us much4 ,let us1 therefore1 put into ,simon two more operations4 ,let us choose two operations involving both numbers and logic3 in particular1 7#a7 finding which of two numbers is greater and 7#b7 selecting4 ,in this way we shall make ,simon a little cleverer4 ,it is easy to teach ,simon how to find which of two numbers is the greater when all the numbers that ,simon has to know are #j1 #a1 #b1 #c4 ,we put all possible cases of two numbers a and b into a table3 b3 #j #a #b #c a------------------ #j #a #b #c ,then we tell ,simon that we shall mark with #a the cases where a is greater than b and mark with #j the cases where a is not greater than b3 ,,greater ,,than b3 #j #a #b #c a------------------ #j #j #j #j #j #a #a #j #j #j #b #a #a #j #j #c #a #a #a #j ,for example1 8#b is greater than #c0 is false1 so we put #j in the table on the #b line in the #c column4 ,we see that1 for the #af possible cases1 a is greater than b in #f cases and a is not greater than b in #aj cases4 ,there is a neat way of saying what we have just said1 using the language of mathematical logic 7see ,chapter #i and ,supplement #b74 ,suppose that we consider the statement 8a is greater than b0 where a and b may be any of the numbers #j1 #a1 #b1 #c4 ,we can say that the truth value p of a statement ,p is #a if the statement is true and that it is #j if the statement is false3 p #a if ,p is true1 #j if ,p is false ,the truth value of a statement ,p is conveniently denoted as ,t7,p7 7see ,supplement #b73 p ,t7,p7 ,now we can say that the table for the operation greater than shows the truth value of the statement 8a is greater than b03 p ,t7a b7 ,let us turn now to the operation selection4 ,by selecting we mean choosing one number a if some statement ,p is true and choosing another number b if that statement is not true4 ,as before1 let p be the truth value of that statement ,p1 and let it be equal to #a if ,p is true and to #j if ,p is false4 ,then the operation of selection is fully expressed in the following table and logical formula 7see ,supplement #b73 ,,selection c ap b7#a - p7 p3 #j #j #j #j #a #a #a #a b3 #j #a #b #c #j #a #b #c a------------------------------------ #j #j #a #b #c #j #j #j #j #a #j #a #b #c #a #a #a #a #b #j #a #b #c #b #b #b #b #c #j #a #b #c #c #c #c #c ,for example1 suppose that a is #b and b is #c and the statement ,p is the statement 8#b is greater than #j40 ,since this statement is true1 p is #a1 and ap b7#a - p7 #b7a7 #c7j7 #b ,this result is the same as selecting #b if #b is greater than #j and selecting #c if #b is not greater than #j4 ,thus we have four operations for ,simon that do not overstrain his mentality2 that is1 they do not require him to go to any numbers other than #j1 #a1 #b1 and #c4 ,these four operations are3 addition1 negation1 greater than1 selection4 ,we label these operations also with the numbers #jj to #aa as follows3 addition1 #jj2 negation1 #ja2 greater than1 #aj2 selection1 #aa4 ,,simon',s ,,memory--,,storing ,,information ,the memory of a mechanical brain consists of physical equipment in which information can be stored4 ,usually1 each section of the physical equipment which can store one piece of information is called a register4 ,each register in ,simon will consist of #b relays4 ,each register will hold any of #jj1 #ja1 #aj1 #aa4 ,the information stored in a register #jj1 #ja1 #aj1 #aa may express a number or may express an operation4 ,illustration3 ,s#a-b ,relay energized ,illustration3 ,s#a-a ,relay not energized ,,fig4 #c4 ,register ,s#a storing #aj4 ,how many registers will we need to put into ,simon to store information8 ,we shall need one register to read the input tape and to store the number or operation recorded on it4 ,we shall call this register the input register ,i4 ,we shall need another register to store the number or operation that ,simon says is the answer and to give it to the output lights4 ,we shall call this register the output register ,o4 ,we shall need #e registers for the part of ,simon which does the computing1 which we shall call the computer3 we shall need #c to store numbers put into the computer 7,c#a1 ,c#b1 ,c#c71 #a to store the operation governing the computer 7,c#d71 and #a to store the result 7,c#e74 ,suppose that we decide to have #h registers for storing information1 so as to provide some flexibility for doing problems4 ,we shall call these registers storage registers and name them ,s#a1 ,s#b1 ,s#c1 ,s#h4 ,then ,simon will have #ae registers3 a memory that at one time can hold #ae pieces of information4 ,how will one of these registers hold information8 ,for example1 how will register ,s#a hold the number #b 7see ,fig4 #c78 ,the number #b in machine language is #aj4 ,register ,s#a consists of two relays1 ,s#a-b and ,s#a-a4 #aj stored in register ,s#a means that relay ,s#a-b will be energized and that relay ,s#a-a will not be energized4 ,,the ,,control ,,of ,,simon ,so far we have said nothing about the control of ,simon4 ,is he docile8 ,is he stubborn8 ,we know what his capacity is1 but we do not know how to tell him to do anything4 ,how do we connect our desires to his behavior8 ,how do we tell him a problem8 ,how do we get him to solve it and tell us the answer8 ,how do we arrange control over the sequence of his operations8 ,for example1 how do we get ,simon to add #a and #b and tell us the answer #c8 ,on the outside of ,simon1 we have said1 there are two ears3 little mechanisms for reading punched paper tape4 ,also there are two eyes that can wink3 light bulbs that by shining or not shining can put out information 7see ,fig4 #a74 ,one of the ears--let us call it the left ear--takes in information about a particular problem3 numbers and operations4 ,here the problem tape or input tape is listened to4 ,each line on the input tape contains space for #b punched holes4 ,so1 the information on the input tape may be #jj1 #ja1 #aj1 or #aa--;either a number or an operation4 ,the other ear--let us call it the right ear--takes in information about the sequence of operations1 the program or routine to be followed4 ,here the program tape or routine tape or control tape is listened to4 ,each line on the program tape contains space for #d punched holes4 ,we tell ,simon by instructions on the program tape what he is to do with the information that we give him on the input tape4 ,the information on the program tape1 therefore1 may be #jjjj1 #jjja1 #jjaj1 1 #aaaa1 or any number from #j to #ae expressed in binary notation 7see ,supplement #b74 ,how is this accomplished8 ,in the first place1 ,simon is a machine1 and he behaves during time4 ,he does different things from time to time4 ,his behavior is organized in cycles4 ,he repeats a cycle of behavior every second or so4 ,in each cycle of ,simon1 he listens to or reads the input tape once and he listens to or reads the program tape twice4 ,every complete instruction that goes on the program tape tells ,simon a register from which information is to be sent and a register in which information is to be received4 ,the first time that he reads the program tape he gets the name of the register that is to receive certain information1 the receiving register4 ,the second time he reads the program tape he gets the name of the register from which information is to be sent1 the sending register4 ,he finishes each cycle of behavior by transferring information from the sending register to the receiving register4 ,for example1 suppose that we want to get an answer out of ,simon's computer into ,simon's output lights4 ,we put down the instruction ,send information from ,c#e into ,o or1 more briefly1 ,c#e ,o ,but he does not understand this language4 ,we must translate into machine language1 in this case punched holes in the program tape4 ,naturally1 the punched holes in the program tape must be able to specify any sending register and any receiving register4 ,there are #ae registers1 and so we give them punched hole codes as follows3 ,,register ,,code ,,register ,,code ,i #jjja ,c#a #ajaj ,s#a #jjaj ,c#b #ajaa ,s#b #jjaa ,c#c #aajj ,s#c #jajj ,c#d #aaja ,s#d #jaja ,c#e #aaaj ,s#e #jaaj ,o #aaaa ,s#f #jaaa ,s#g #ajjj ,s#h #ajja ,to translate the direction of transfer of information1 which we showed as an arrow1 we put on the program tape the code for the receiving register first--in this case1 output1 ,o1 #aaaa--;and the code for the sending register second--in this case1 ,c#e1 #aaaj4 ,the instruction becomes #aaaa1 #aaaj4 ,the first time in any cycle that ,simon listens with his right ear1 he knows that what he hears is the name of the receiving register2 and the second time that he listens1 he knows that what he hears is the name of the sending register4 ,one reason for this sequence is that any person or machine has to be prepared beforehand to absorb or take in any information4 ,now how do we tell ,simon to add #a and #b8 ,on the input tape1 we put3 ,add #jj #a #ja #b #aj ,on the program tape1 we need to put3 ,i ,c#d ,i ,c#a ,i ,c#b ,c#e ,o which becomes3 #aaja1 #jjja2 #ajaj1 #jjja2 #ajaa1 #jjja2 #aaaa1 #aaaj ,,the ,,usefulness ,,of ,,simon ,thus we can see that ,simon can do such a problem as3 ,add #j and #c4 ,add #b and the negative of #a4 ,find which result is greater4 ,select #c if this result equals #b2 otherwise select #b4 ,to work out the coding for this and like problems would be a good exercise4 ,simon1 in fact1 is a rather clever little mechanical brain1 even if he has only a mentality of #d4 ,it may seem that a simple model of a mechanical brain like ,simon is of no great practical use4 ,on the contrary1 ,simon has the same use in instruction as a set of simple chemical experiments has3 to stimulate thinking and understanding and to produce training and skill4 ,a training course on mechanical brains could very well include the construction of a simple model mechanical brain as an exercise4 ,in this book1 the properties of ,simon may be a good introduction to the various types of more complicated mechanical brains described in later chapters4 ,the rest of this chapter is devoted to such questions as3 ,how do transfers of information actually take place in ,simon8 ,how does the computer in ,simon work so that calculation actually occurs8 ,how could ,simon actually be constructed8 ,what follows should be skipped unless you are interested in these questions and the burdensome details needed for answering them4 ,,simon',s ,,thinking--,,transferring ,,information ,the first basic thinking operation for any mechanical brain is transferring information automatically4 ,let us see how this is done in ,simon4 ,illustration3 ,,fig4 #d4 ,scheme of ,simon4 ,let us first take a look at the scheme of ,simon as a mechanical brain 7see ,fig4 #d74 ,we have #a input1 #h storage1 #e computer1 and #a output registers1 which are connected by means of transfer wires or a transfer line along which numbers or operations can travel as electrical impulses4 ,this transfer line is often called the bus1 perhaps because it is always busy carrying something4 ,in ,simon the bus will consist of #b wires1 one for carrying the right-hand digit and one for carrying the left-hand digit of any number #jj1 #ja1 #aj1 #aa4 ,simon also has a number of neat little devices that will do the following3 ,when any number goes into a register1 the coils of the relays of the register will be connected with the bus4 ,when any number goes out of a register1 the contacts of the relays of the register will be connected with the bus4 ,for example1 suppose that in register ,c#e the number #b is stored4 ,in machine language this is #aj4 ,that means the left-hand relay 7,c#e-b7 is energized and the right-hand relay 7,c#e-a7 is not energized4 ,suppose that we want to transfer this number #b into the output register ,o1 which has been cleared4 ,what do we do8 ,let us take a look at a circuit that will transfer the number 7see ,fig4 #e74 ,first we see two relays in this circuit4 ,they belong to the ,c#e register4 ,the ,c#e-b relay is energized since it holds #a2 current is flowing through its coil1 the iron core becomes a magnet1 and the contact above it is pulled down4 ,the ,c#e-a relay is not energized since it holds #j2 its contact is not pulled down4 ,the next thing we see is two rectifiers4 ,the sign for these is a triangle4 ,these are some modern electrical equipment that allow electrical current to flow in only one direction4 ,in the diagram1 the direction is shown by the pointing of the triangle along the wire4 ,rectifiers are needed to prevent undesired circuits4 ,next1 we see the bus1 consisting of two wires4 ,one carries the impulses for left-hand or #b relays1 and the other carries impulses for the right-hand or #a relays4 ,next1 we see two relays1 called the entrance relays for the ,o register4 ,current from ,source #a may flow to these relays1 energize them1 and close their contacts4 ,when the first line of the program tape is read1 specifying the receiving register1 the code #aaaa causes ,source #a to be energized4 ,this fact is shown schematically by the arrow running from the program tape code #aaaa to ,source #a4 ,finally1 we see the coils of the two relays for the ,output or ,o register4 ,we thus see that we have a circuit from the contacts of the ,c#e register through the bus to the coils of the ,o register4 ,illustration3 ,,fig4 #e4 ,transfer circuit4 ,we are now ready to transfer information when the second line of the program tape is read4 ,this line holds #aaaj and designates ,c#e as the sending register and causes ,source #b to be energized4 ,this fact is shown schematically by the arrow running from the second line of the program tape to ,source #b4 ,when the second line is read1 current flows3 #a4 ,from ,source #b4 #b4 ,through the contacts of the ,c#e register if closed4 #c4 ,through the rectifiers4 #d4 ,through the bus4 #e4 ,through the entrance relay contacts of the ,o register4 #f4 ,through the coils of the ,o register relays1 energizing such of them as match with the ,c#e closed contacts2 and finally #g4 ,into the ground4 ,thus relay ,o-#b is energized2 it receives current because contact ,c#e-b is closed4 ,and relay ,o-#a is not energized2 it receives no current since contact ,c#e-a is open4 ,so we have actually transferred information from the ,c#e register to the ,o register4 ,the same process in principle applies to all transfers3 ,the pattern of electrical impulses1 formed by the positioning of one register1 is produced in the positioning of another register4 ,,simon',s ,,computing ,,and ,,reasoning ,now so far the computing registers in ,simon are a mystery4 ,we have said that ,c#a1 ,c#b1 and ,c#c take in numbers #jj1 #ja1 #aj1 #aa1 that ,c#d takes in an operation #jj1 #ja1 #aj1 #aa1 and that ,c#e holds the result4 ,what process does ,simon use so that he has the correct result in register ,c#e8 ,let us take the simplest computing operation first and see what sort of a circuit using relays will give us the result4 ,the simplest computing operation is negation4 ,in negation1 a number #jj1 #ja1 #aj1 #aa goes into the ,c#a register1 and the operation #ja meaning negation goes into the ,c#d register1 and the correct result must be in the ,c#e register4 ,so1 first1 we note the fact that the ,c#d-b relay must not be energized1 since it contains #j1 and that the ,c#d-a relay must be energized1 since it contains #a4 ,now the table for negation1 with c -a1 is3 a c ---------------- #j #j #a #c #b #b #c #a ,negation in machine language will be3 a c ---------------- #jj #jj #ja #aa #aj #aj #aa #ja ,now if a is in the ,c#a register and if c is in the ,c#e register1 then negation will be3 ,c#a ,c#e -------------------- #jj #jj #ja #aa #aj #aj #aa #ja ,but each of these registers ,c#a1 ,c#e will be made up of two relays1 the left-hand or #b relay and the right-hand or #a relay4 ,so1 in terms of these relays1 negation will be3 ,c#a-b ,c#a-a ,c#e-b ,c#e-a ---------------------------------------- ---------------- #j #j #j #j #j #a #a #a #a #j #a #j #a #a #j #a ,now1 on examining the table1 we see that the ,c#e-a relay is energized if and only if the ,c#a-a relay is energized4 ,so1 in order to energize the ,c#e-a relay1 all we have to do is transfer the information from ,c#a-a to ,c#e-a4 ,this we can do by the circuit shown in ,fig4 #f4 7,in this and later diagrams1 we have taken one more step in streamlining the drawing of relay contacts3 the contacts are drawn1 but the coils that energize them are represented only by their names47 ,illustration3 ,,fig4 #f4 ,negation--right-hand digit4 ,illustration3 ,,fig4 #g4 ,negation--left-hand digit4 ,taking another look at the table1 we see also that the ,c#e-b relay must be energized if and only if3 ,c#a-b ,,and ,c#a-a ,,holds3 ,,holds3 #j #a #a #j ,a circuit that will do this is the one shown in ,fig4 #g4 ,in ,fig4 #h is a circuit that will do all the desired things together3 give the right information to the ,c#e relay coils if and only if the ,c#d relays hold #ja4 ,illustration3 ,,fig4 #h4 ,negation circuit4 ,let us check this circuit4 ,first1 if there is any operation other than #ja stored in the ,c#d relays1 then no current will be able to get through the ,c#d contacts shown and into the ,c#e relay coils1 and the result is blank4 ,second1 if we have the operation #ja stored in the ,c#d relays1 then the ,c#d-b contacts will not be energized--a condition which passes current--and the ,c#d-a contacts will be energized--another condition which passes current--and3 ,,if ,,the ,,number ,,and ,,the ,c#e ,,relays ,,in ,c#a ,,is3 ,,then ,c#a-a3 ,,and ,c#a-b3 ,,energized ,,are3 #j does not close does not close neither #a closes does not close ,c#e-b1 ,c#e-a #b does not close closes ,c#e-b only #c closes closes ,c#e-a only ,thus we have shown that this circuit is correct4 ,we see that this circuit uses more than one set of contacts for several relays 7,c#a-b1 ,c#d-a1 ,c#d-b72 relays are regularly made with #d1 #f1 or #ab sets of contacts arranged side by side1 all controlled by the same pickup coil4 ,these are called #d-1 #f-1 or #ab-pole relays4 ,illustration3 ,,fig4 #i4 ,addition circuit4 ,illustration3 ,,fig4 #aj4 ,greater-than circuit4 ,circuits for addition1 greater than1 and selection can also be determined rather easily 7see ,figs4 #i1 #aj1 #aa74 7,note3 ,by means of the algebra of logic1 referred to in ,chapter #i and ,supplement #b1 the conditions for many relay circuits1 as well as the circuit itself1 may be expressed algebraically1 and the two expressions may be checked by a mathematical process47 ,for example1 let us check that the addition circuit in ,fig4 #i will enable us to add #a and #b and obtain #c4 ,we take a colored pencil and draw closed the contacts for ,c#a-a 7since ,c#a holds #ja7 and for ,c#b-b 7since ,c#b holds #aj74 ,then1 when we trace through the circuit1 remembering that addition is stored as #jj in the ,c#d relays1 we find that both the ,c#e relays are energized4 ,hence ,c#e holds #aa1 which is #c4 ,thus ,simon can add #a and #b and make #c6 ,illustration3 ,,fig4 #aa4 ,selection ,circuit4 ,,putting ,,simon ,,together ,in order to put ,simon together and make him work1 not very much is needed4 ,on the outside of ,simon we shall need two small mechanisms for reading punched paper tape4 ,inside ,simon1 there will be about #ej relays and perhaps #ajj feet of wire for connecting them4 ,in addition to the #ae registers 7,i1 ,s#a to ,s#h1 ,c#a to ,c#e1 and ,o71 we shall need a register of #d relays1 which we shall call the program register4 ,this register will store the successive instructions read off the program tape4 ,we can call the #d relays of this register ,p#h1 ,p#d1 ,p#b1 ,p#a4 ,for example1 if the ,p#h and ,p#b relays are energized1 the register holds #ajaj1 and this is the program instruction that calls for the #hth plus #bnd1 or #ajth1 register1 which is ,c#a4 ,for connecting receiving registers to the bus1 we shall need a relay with #b poles1 one for the #b-line and one for the #a-line1 for each register that can receive a number from the bus4 ,for example1 for entering the output register1 we actually need only one #b-pole relay instead of the two #a-pole relays drawn for simplicity in ,fig4 #e4 ,there will be #ac #b-pole relays for this purpose1 since only #ac registers receive numbers from the bus2 registers ,i and ,c#e do not receive numbers from the bus4 ,we call these #ac relays the entrance relays or ,e relays1 since ,e is the initial letter of the word entrance4 ,illustration3 ,,fig4 #ab4 ,select-,receiving-,register circuit4 ,the circuit for selecting and energizing the ,e relays is shown in ,fig4 #ab4 ,we call this circuit the ,select-,receiving-,register circuit4 ,for example1 suppose that the ,p#h and ,p#b relays are energized4 ,then this circuit energizes the ,e#aj relay4 ,the ,e#aj relay closes the contacts between the ,c#a relay coils and the bus2 and so it connects the ,c#a register to receive the next number that is sent into the bus4 ,this kind of circuit expresses a classification and is sometimes called a pyramid circuit since it spreads out like a pyramid4 ,a similar pyramid circuit is used to select the sending register4 ,we shall need a relay for moving the input tape a step at a time4 ,we shall call this relay the ,,mi relay1 for moving input tape4 ,we also need a relay for moving the program tape a step at a time4 ,we shall call this relay the ,,mp relay for moving program tape4 ,here then is approximately the total number of relays required3 ,,relays ,,name ,,number ,i1 ,s1 ,c1 ,o ,input1 ,storage1 ,computer1 ,output #cj ,p ,program #d ,e ,entrance #ac ,,mi ,move ,input ,tape #a ,,mp ,move ,program ,tape #a -------- ,total #di ,a few more relays may be needed to provide more contacts or poles4 ,for example1 a single ,p#a relay will probably not have enough poles to meet all the need for its contacts4 ,illustration3 ,,fig4 #ac4 ,latch relay4 ,each cycle of the machine will be divided into #e equal time intervals or times #a to #e4 ,the timing of the machine will be about as follows3 ,,time ,,action #a ,move program tape4 ,move input tape if read out of in last cycle4 #b ,read program tape1 determining the receiving register4 ,read through the computing circuit setting up the ,c#e register4 #c ,move program tape4 ,energize the ,e relay belonging to the receiving register4 #d ,read program tape again1 determining the sending register4 #e ,transfer information by reading through the ,select-,sending-,register circuit and the ,select-,receiving-,register circuit4 ,in order that information may remain in storage until wanted1 register relays should hold their information until just before the next information is received4 ,this can be accomplished by keeping current in their coils or in other ways4 ,there is a type of relay called a latch relay1 which is made with two coils and a latch4 ,this type of relay has the property of staying or latching in either position until the opposite coil is impulsed 7see ,fig4 #ac74 ,this type of relay would be especially good for the registers of ,simon4 ,if any reader sets to work to construct ,simon1 and if questions arise1 the author will be glad to try to answer them4 ,chapter #d ,,counting ,,holes3 ,,punch-,,card ,,calculating ,,machines ,when we think of counting1 we usually think of saying softly to ourselves 8one1 two1 three1 four1 40 ,this is a good way to find the total of a small group of objects4 ,but when we have a large group of objects or a great many groups of objects to be counted1 a much faster way of counting is needed4 ,a very fast way of sorting and counting is punch-card calculating machinery4 ,this is machinery which handles information expressed as holes in cards4 ,punch-card machines can3 ,sort1 count1 file1 select1 and copy information1 ,make comparisons1 and choose according to instructions1 ,add1 subtract1 multiply1 and divide1 ,list information1 and print totals4 ,for example1 in a life insurance company1 much routine handling of information about insurance policies is necessary3 ,writing information on newly issued policies4 ,setting up policy-history cards4 ,making out notices of premiums due4 ,making registers of policies in force1 lapsed1 died1 etc41 for purposes of valuation as required by law or good management4 ,calculating and tabulating premium rates1 dividend rates1 reserve factors1 etc4 ,computing and tabulating expected and actual death rates2 and much more4 ,all these operations can be done almost automatically by punch-card machines4 ,,origin ,,and ,,development ,when a census of the people of a country is taken1 a great quantity of sorting and counting is needed3 by village1 county1 city1 and state2 by sex2 by age2 by occupation2 etc4 ,in #ahhf1 the census of the people of the ,united ,states which had been taken in #ahhj was still being sorted and counted4 ,among the men then studying census problems was a statistician and inventor1 ,herman ,hollerith4 ,he saw that existing methods were so slow that the next census 7#ahij7 would not be finished before the following census 7#aijj7 would have to be begun4 ,he knew that cards with patterns of holes had been used in weaving patterns in cloth4 ,he realized that the presence or absence of a property1 for example employed or unemployed1 could be represented by the presence or absence of a hole in a piece of paper4 ,an electrical device could detect the hole1 he believed1 since it would allow current to flow through1 whereas the absence of the hole would stop the current4 ,he experimented with sorting and counting1 using punched holes in cards1 and with electrical devices to detect the holes and count them4 ,a definite meaning was given to each place in the card where a hole might be punched4 ,then electrical devices handled the particular information that the punches represented4 ,these devices either counted or added1 singly or in various combinations1 as might be desired4 ,more than #ej years of development of punch-card calculating machinery have since then taken place4 ,several large companies have made quantities of punch-card machines4 ,a great degree of development has taken place in the punch-card machines of ,international ,business ,machines ,corporation 7,,ibm71 and for this reason these machines will be the ones described in this chapter4 ,what is said here1 however1 may also in many ways apply to punch-card machines made by other manufacturers--,remington-,rand1 ,powers1 ,control ,instrument1 etc4 ,,general ,,principles ,to use punch-card machines1 we first convert the original information into patterns of holes in cards4 ,then we feed the cards into the machines4 ,electrical impulses read the pattern of holes and convert them into a pattern of timed electrical currents4 ,actually1 the reading of a hole in a column of a punch card is done by a brush of several strands of copper wire pressed against a metal roller 7,fig4 #a74 ,the machine feeds the card 7the bottom edge first1 where the #i's are printed7 with very careful timing over the roller2 and1 when the punched hole is between the brush and the roller1 an electrical circuit belonging to that column of the card is completed4 ,the machine responds according to its general design and its wiring for the particular problem3 it punches new cards1 or it prints new marks1 or it puts information into new storage places4 ,clerks1 however1 move the cards from one machine to another4 ,they wait on the machines1 keep the card feeds full1 and empty the card hoppers as they fill up4 ,a human error of putting the wrong block of cards into a machine may from time to time cause a little trouble1 especially in sorting4 ,actually1 in a year1 billions of punch cards are handled precisely4 ,illustration3 ,,fig4 #a4 ,reading of punch cards4 ,the punch card is a masterpiece of engineering and standardization4 ,its exact thickness matches the knife-blade edges that feed the cards into slots in the machines1 and matches the channels whereby these cards travel through the machines4 ,the standard card is #g inches long and #c inches wide1 and it has a standard thickness of #j4jjfe inch and other standard properties with respect to stiffness1 finish1 etc4 ,illustration3 ,,fig4 #b4 ,scheme of standard punch card4 7,note3 ,positions #aa and #ab are not usually marked by printed numbers or letters47 ,the standard ,,ibm punch card of today has #hj columns and #ab positions for punching in each column 7,fig4 #b74 ,a single punched hole in each of the positions known as #j to #i stands for each of the digits #j to #i respectively4 ,the remaining #b single punch positions available in any column are usually called the #aa position and #ab position 7though sometimes called the numerical ,x position and ,y position74 ,these two positions do not behave arithmetically as #aa and #ab4 ,actually1 in the space between one card and the next card as they are fed through the machines1 more positions occur4 ,for example1 there may be #d more3 a #aj position preceding the #i1 and a #ac1 a #ad1 and a #ae position following the #ab4 ,the #af positions in total correspond to a full turn1 #cfj1 of the roller under the brush1 and to a complete cycle in the machine2 and a single position corresponds to _/ of #cfj1 or #bb4 ,in some machines1 the total number of positions may be #bj4 ,a pair of punches stands for each of the letters of the alphabet1 according to the scheme shown4 ,a #ab-a ,j #aa-a ,unused #j-a ,b #ab-b ,k #aa-b ,s #j-b ,c #ab-c ,l #aa-c ,t #j-c ,d #ab-d ,m #aa-d ,u #j-d ,e #ab-e ,n #aa-e ,v #j-e ,f #ab-f ,o #aa-f ,w #j-f ,g #ab-g ,p #aa-g ,x #j-g ,h #ab-h ,q #aa-h ,y #j-h ,i #ab-i ,r #aa-i ,z #j-i ,for example1 the word ,,mason is shown punched in ,fig4 #c4 ,illustration3 ,,fig4 #c4 ,alphabetic punching4 ,illustration3 ,,fig4 #d4 ,single-panel plugboard4 ,to increase the versatility of the machines and provide them with instructions1 many of them have plugboards 7,fig4 #d74 ,these are standard interchangeable boards filled with prongs on one side and holes or terminals called hubs on the other side4 ,the side with the prongs connects to the ends of electrical circuits in the punch-card machine1 which are brought together in one place for the purpose4 ,on the other side of the board1 using plugwires1 we can connect the hubs to each other in different ways to produce different results4 ,the single-panel plugboard is #aj inches long and #e inches wide4 ,it contains #ffj hubs in front and #ffj corresponding prongs in the back4 ,a double-panel plugboard or a triple-panel plugboard applies to some machines4 ,in less time than it takes to describe it1 we can take one wired-up plugboard out of a machine and put in a new wired-up plugboard and thus change completely the instructions under which the machine operates4 ,many of the machines have a number of different switches that we must also change1 when going from one kind of problem to another4 ,the numbers that are stored or sorted in punch-card machines may be of any size up to #hj digits1 one in each column of the punch card4 ,in doing arithmetic 7adding1 subtracting1 multiplying1 and dividing71 however1 the largest number of digits is usually #aj4 ,beyond #aj digits1 we can work out tricks in many cases4 ,,types ,,of ,,punch-,,card ,,machines ,the chief ,,ibm punch-card machines are3 the key punch1 the verifier1 the sorter1 the interpreter1 the reproducer1 the collator1 the multiplying punch1 the calculating punch1 and the tabulator4 ,of these #i machines1 the last #f have plugboards and can do many different operations as a result4 ,there is a flow of punch cards through each of these machines4 ,the machines differ from each other in the number and relation of the paths of flow1 or card channels1 and in the number and relation of the momentary stopping places1 or card stations1 at which cards are read1 punched1 or otherwise acted on4 ,we can get a good idea of what a machine is from a picture of these card channels4 ,key ,punch ,we use a key punch 7,fig4 #e7 to punch original information into blank cards4 ,in the key punch there is one card channel2 it has one entrance1 one station1 and one exit4 ,at the card station1 there are #ab punching dies1 one for each position in the card column1 and each card column is presented one by one for punching4 ,the numeric keyboard 7,fig4 #f7 for the key punch has #ad keys3 ,one key for each of the punches #j to #i1 #aa1 and #ab1 ,a space key1 which allows a column of the punch card to go by with no punch in it1 ,a release key1 which ejects the card and feeds another card4 ,illustration3 ,,fig4 #e4 ,key punch4 ,illustration3 ,,fig4 #f4 ,keyboard of key punch4 ,of course1 in using a key punch1 we must punch the same kind of information in the same group of columns4 ,for example1 if these cards are to contain employees' social security numbers1 we must punch that number always in the same card columns1 numbered1 say1 #ae to #bc1 or #gj to #gh1 etc4 ,verifier ,the verifier is really the same machine as the key punch1 but it has dull punching dies moving gently instead of sharp ones moving with force4 ,it turns on a red light and stops when there is no punched hole in the right spot to match with a pressed key4 ,sorter ,the sorter is a machine for sorting cards1 one column at a time 7,fig4 #g74 ,the sorter has a card channel that forks2 it has one entrance1 one station1 and #ac exits4 ,each exit corresponds to3 one of the #ab punch positions #j to #i1 #aa1 and #ab2 or reject1 which applies when the column is nowhere punched4 ,it has one card station where a brush reads a single column of the card4 ,we can turn a handle and move the brush to any column4 ,illustration3 ,,fig4 #g4 ,sorter4 ,interpreter ,the interpreter takes in a card1 reads its punches1 prints on the card the marks indicated by the punches1 and stacks the card4 ,we call this process interpreting the card1 since it translates the punched holes into printed marks4 ,the interpreter 7,fig4 #h7 has one card channel1 with one entrance1 #b card stations1 and one exit4 ,what the machine does at the second card station depends on what the machine reads at the first card station and on what we have told the machine by switches and plugboard wiring to do4 ,illustration3 ,,fig4 #h4 ,interpreter4 ,reproducer ,the reproducer or reproducing punch can3 ,reproduce1 or copy the punches in one group of cards into another group of cards 7in the same or different columns74 ,compare1 or make sure that the punches in two groups of cards agree 7and shine a red light if they do not74 ,gang punch1 or copy the punches in a master card into a group of detail cards4 ,summary punch1 or copy totals or summaries obtained in the tabulator into blank cards in the reproducer4 ,illustration3 ,,fig4 #i4 ,reproducer4 ,the reproducer 7,fig4 #i7 has #b independent card channels1 the cards not mingling in any way1 called the reading channel and the punching channel4 ,we can run the machine with only the punching channel working2 in fact1 ,,ibm equips some models only with the punching channel1 particularly for 8summary punch0 operation4 ,the machine is timed so that1 when any card is at the middle station in either channel1 then the next preceding card is at the latest station1 and the next following card is at the earliest station4 ,at #e stations1 the machine reads a card4 ,at the middle station of the punching channel1 the machine punches a card4 ,using a many-wire cable1 we can connect the tabulator to the reproducer and so cause the tabulator to give information electrically to the reproducer4 ,this connection makes possible the 8summary punch0 operation4 ,here is an instance with punch-card machines where1 in order to transfer information from one machine to another1 we are not required to move cards physically from one machine to another4 ,collator ,the collator is a machine that arranges or collates cards4 ,it is particularly useful in selecting1 matching1 and merging cards4 ,the collator 7,fig4 #aj7 has #b card channels which join and then fork into #d channels ending in pockets called ,hoppers #a1 #b1 #c1 and #d4 ,the #b card feeds are called the ,primary ,feed and the ,secondary ,feed4 ,cards from the ,primary ,feed may fall only into the first and second hoppers4 ,cards from the ,secondary ,feed may fall only into the second1 third1 and fourth hoppers4 ,the collator has #c stations at which cards may be read4 ,illustration3 ,no4#a--,selected primaries ,no4#b--,merged cards and unselected primaries ,no4#c--,separate secondaries not selected ,no4#d--,selected secondaries ,,fig4 #aj4 ,collator4 ,,ibm can supply additional wiring called the collator counting device4 ,with this we can make the collator count cards as well as compare them4 ,for example1 we could put #ab blank cards from the ,secondary ,feed behind each punched-card from the ,primary ,feed in order to prepare for some other operation4 ,calculating ,punch ,the calculating punch was introduced in #aidf4 ,it is a versatile machine of considerable capacity4 ,it adds1 subtracts1 multiplies1 and divides4 ,it also has a control over a sequence of operations1 in some cases up to half a dozen steps4 ,this machine 7,fig4 #aa7 has one card channel with #d stations called1 respectively1 control brushes1 reading brushes1 punch feed1 and punching dies4 ,at station #a1 there are #bj brushes2 we can set these by hand to read any #bj of the #hj card columns4 ,at station #b there are #hj regular reading brushes4 ,at station #c the card waits for a part of a second while the machine calculates1 and1 when that is done1 the card is fed into station #d1 where it is punched or verified4 ,the multiplying punch is an earlier model of the calculating punch1 without the capacity for division4 ,illustration3 ,,fig4 #aa4 ,calculating punch4 ,tabulator ,the tabulator can select and list information from cards4 ,also1 it can total information from groups of cards in counters of the tabulator and can print the totals4 ,illustration3 ,,fig4 #ab4 ,tabulator4 ,the tabulator 7,fig4 #ab7 has one card channel with two stations where cards may be read1 called the ,upper ,brushes and ,lower ,brushes4 ,when the ,lower ,brush station is reading one card1 the ,upper ,brush station is reading the next card4 ,the tabulator also has another channel1 which is for endless paper 7and sometimes separate sheets or cards74 ,this channel has one station2 here printing takes place4 ,unlike the typewriter1 the tabulator prints a whole row at a time4 ,it can print up to #hh numerals or letters across the sheet in one stroke4 ,the cards flowing through the card channel and the paper flowing through the paper channel do not have to move in step2 in fact1 we need many different time relations between them1 and the number of rows printed on the paper may have almost any relation to the number of punch cards flowing through the card channel4 ,at the station where paper is printed1 we can put on the machine a mechanism called the automatic carriage4 ,this is like a typewriter carriage1 which holds the paper for a typewriter1 but we can control the movement of paper through the automatic carriage by plugboard wiring1 switch settings1 and holes in punch cards4 ,thus we can arrange for headings1 spacing1 and feeding of new sheets to be controlled by the information and the instructions1 with a great deal of versatility4 ,,handling ,,information ,we have now described briefly the chief available punch-card machines as of the middle of #aidh4 ,the next question is3 ,how do we actually get something done by means of punch cards8 ,let us go back to the census example1 even though it may not be a very typical example1 and see what would be done if we wished to compile a census by punch cards4 ,the first thing we do is plan which columns of the punch card will contain what information about the people being counted4 ,for example1 the following might be part of the plan3 ,,no4 ,,of ,,information ,,possibilities ,,columns ,state #fj #a- #b ,county #a1jjj #c- #e ,township #aj1jjj #f- #i ,city or village #aj1jjj #aj-ac ,sex #b #ad ,age last birthday #ajj #ae-af ,occupation #ajj1jjj #ag-ba 444 444 444 ,under the heading state1 we know that there are #dh states1 the ,district of ,columbia1 and several territories and possessions--all told1 perhaps #fj possibilities4 ,so1 #b punch-card columns are enough3 they will allow #ajj different sets of punches from #jj to #ii to be put in them4 ,we then assign the code #jj to ,maine1 #ja to ,new ,hampshire1 #jb to ,vermont1 etc41 or we might assign the code #jj to ,alabama1 #ja to ,arizona1 #jb to ,arkansas1 etc4--whichever would be more useful4 ,under the other headings1 we do the same thing3 count the possibilities2 assign codes4 ,in this case1 it will be reasonable to use numeric codes #j to #i in each column in all places because we shall have millions of cards to deal with and numeric codes can be sorted faster than alphabetic codes4 ,alphabetic codes require #b punched holes in each column1 and sorting any column takes #b operations4 ,the punch cards are printed with the chosen headings4 ,we set up the codes in charts and give them to clerks4 ,using key punches and verifiers1 they punch up the cards and check them4 ,they work from the original information collected by the census-taker in the field4 ,since the original information will come in geographically1 probably only one geographic code at a time will be needed1 and it will be simple to keep track of4 ,as to occupation1 however1 it may be useful to assign other clerks full-time to examining the original information and specifying the right code for the occupation4 ,then the clerks who do the punching will have only copying to do4 ,the great bulk of the work with the census will be sorting1 counting1 and totaling4 ,the original punch cards will be summarized into larger and larger groups4 ,for example1 the cards for all males age #bc last birthday living in the state of ,massachusetts are sorted together4 ,this group of cards may be put into a tabulator wired to a summary punch4 ,when the tabulator has counted the last card of this group1 the summary punch punches one card1 showing the total number in this group4 ,some time later a card like this will be ready for every state4 ,then the whole group of state cards may be fed into the tabulator wired to the reproducer acting as summary punch4 ,when totaled1 the number of males age #bc last birthday in the ,united ,states will be punched into a single card4 ,after more compiling1 a card like this will be ready for all males in the ,united ,states at each age4 ,then this group of cards may be fed into the tabulator wired to the summary punch4 ,each card may be listed by the tabulator on the paper flowing through it1 showing the age and the number of males living at that age4 ,at the end of the listing1 the tabulator will print the total number of all males in the list1 and the summary punch will punch a card containing this total4 ,,arithmetical ,,operations ,punch-card machines can perform the arithmetical operations of counting1 adding1 subtracting1 multiplying1 dividing1 and rounding off4 ,counting ,counting can be done by the sorter1 the tabulator1 and the collator4 ,the tabulator can print the total count4 ,the tabulator and summary punch wired together can put the total count automatically into another punch card4 ,the sorter shows the count in dials4 ,adding and ,subtracting ,adding and subtracting can be done by the tabulator1 the calculating punch1 and the multiplying punch4 ,in the calculating and multiplying punches1 the sum or difference is usually punched into the same card from which the numbers were first obtained4 ,the tabulator1 however1 obtains the result first in a counter2 from the counter1 it can be printed on paper or punched into a blank card with the aid of the summary punch4 ,numbers are handled as groups of decimal digits1 and the machines mirror the properties of digits in the decimal system4 ,negative numbers are usually handled as complements 7see ,supplement #b74 ,for example1 if we have in the tabulator a counter with a capacity of six digits1 the number-#jjjjac is stored in the counter as the complement #iiiihg4 ,we cannot store in the counter the number #iiiihg1 since we cannot distinguish it from-#jjjjac4 ,in other words1 if a counter is to be used for both positive and negative numbers1 its capacity is actually one digit less1 since in the last decimal place on the left #j will mean positive and #i will mean negative4 ,multiplying and ,dividing ,multiplying is done in the calculating and multiplying punches4 ,in both cases1 the multiplication table is built into the circuits of the machine1 and the system of left-hand components and right-hand components is used 7see ,supplement #b74 ,dividing is done in the calculating punch and is carried out in that machine much as in ordinary arithmetic4 ,by means of an estimating circuit the calculating punch guesses what multiple of the divisor will go into the dividend4 ,then it determines that multiple and tries it4 ,rounding ,off ,rounding off may be done in #c punch-card machines1 the calculating and multiplying punches1 and the tabulator4 ,for example1 suppose we have the numbers #di4adgf1 #fh4ecbg1 and we wish to round them off to #b decimal places4 ,the results will be #di4ae and #fh4ec4 ,for the first number1 we raise the 4#jjgf1 turning 4#adgf into 4#ae1 since 4#jjgf is more than 4#jje4 ,for the second number1 we drop the 4#jjbg since it is less than 4#jje4 ,each of these punch-card machines provides what is called a #e impulse in each machine cycle4 ,when the number is to be rounded off1 the #e impulse is plugged into the first decimal place that is to be dropped1 and it is there added4 ,if the figure in the decimal place to be dropped is #j to #d1 the added #e makes no difference in the last decimal place that is to be kept4 ,but1 if the figure in the decimal place to be dropped is #e to #i1 then the added #e makes a carry into the last decimal place that is to be kept1 increasing it by #a1 and this is just what is wanted for rounding off4 ,,logical ,,operations ,punch-card machines do many operations of reasoning or logic that do not involve addition1 subtraction1 multiplication1 or division4 ,just as we can write equations for arithmetical operations1 so we can write equations for these logical operations using mathematical logic 7see ,chapter #i and ,supplement #b74 ,if any reader1 however1 is not interested in these logical equations1 he should skip each paragraph that begins with 8in the language of logic10 or a similar phrase4 ,translating ,reading and writing are operations perhaps not strictly of reasoning but of translating from one language to another4 ,basically these operations take in a mark in one language and give out a mark with the same meaning in another language4 ,for example1 the interpreter takes in punched holes and gives out printed marks1 but the holes and the marks have the same meaning4 ,the major part of sorting is done by a punch-card sorting machine and can be considered an operation of translating4 ,in sorting a card1 the machine takes in a mark in the form of a punched hole on a punch card and specifies a place bearing the same mark where the card is put4 ,the remaining part of sorting is done by human beings4 ,this part consists of picking up blocks of cards from the pockets of the sorter and putting the blocks together in the right sequence4 ,comparing ,illustration3 ,,fig4 #ac4 ,comparer4 ,the first operation of reasoning done by punch-card machines is comparing4 ,for an example of comparing in the operation of the tabulator1 let us take instructing the machine when to pick up a total and print it4 ,as an illustration1 suppose that we are making a table by state1 county1 and township of the number of persons counted in a census4 ,suppose that for each township we have one punch card telling the total number of persons4 ,if all the cards are in sequence1 then1 whenever the county changes1 we want a minor total1 and1 whenever the state changes1 we want a major total4 ,what does the machine do8 ,the tabulator has a mechanism that we shall call a comparer 7,fig4 #ac74 ,a comparer has #b inputs that may be called ,previous and ,current and one output that may be called ,unequal4 ,the comparer has the property of giving out an impulse if and only if there is a difference between the #b inputs4 ,in the language of the algebra of logic 7see ,supplement #b and ,chapter #i71 let the pieces of information coming into the comparer be a and b1 and let the information coming out of the comparer be p4 ,then the equation of the comparer is3 p ,t7a b7 where 8,t 770 is 8the truth value of 0 and 80 is a statement1 and where the truth value is #a if true and #j if false4 ,in wiring the tabulator so that it can tell when to total1 we use the comparer4 ,we feed into it the county from the current card and the county from the previous card4 ,out of the comparer we get an impulse if and only if these two pieces of information are different4 ,this is just what happens when the county changes4 ,the impulse from the comparer is then used in further wiring of the tabulator3 it makes the counter that is busy totaling the number of persons in the county print its total and then clear4 ,in the same way1 another comparer1 which watches state instead of county1 takes care of major totals when the state changes4 ,selecting ,the next operation of reasoning which punch-card machines can do is selecting4 ,the tabulator1 collator1 interpreter1 reproducer1 and calculating punch all may contain mechanisms that can select information4 ,these mechanisms are called selectors4 ,for example1 suppose that we are using the tabulator to make a table showing for each city the number of males and the number of females4 ,in the table we shall have three columns3 first1 city2 second1 males2 third1 females4 ,suppose that each punch card in columns #cj to #cf shows the total of males or females in a city4 ,suppose that1 if and only if the card is for females1 it has an ,x punch 7or #aa punch7 in column #gi4 ,what do we want to have happen8 ,we want the number in columns #cj to #cf to go into the second column of the table if there is no ,x in column #gi1 and we want it to go into the third column of the table if there is an ,x in column #gi4 ,this is just another way of saying that we want the number to go into the males column if it is a number of males1 and into the females column if it is a number of females4 ,we make this happen by using a selector4 ,a selector 7,fig4 #ad7 is a mechanism with #b inputs and #b outputs4 ,the #b inputs are called ,x ,pickup and ,common4 ,the #b outputs are called ,x and ,no ,x4 ,the ,x ,pickup1 as its name implies1 watches for ,x's4 ,the ,common takes in information4 ,what comes out of ,x is what goes into ,common if and only if an ,x punch is picked up2 otherwise nothing comes out4 ,what comes out of ,no ,x is what goes into ,common if and only if an ,x punch is not picked up2 otherwise nothing comes out4 ,from the point of view of ordering punch-card equipment1 we should note that there are two types of selectors3 ,x selectors or ,x distributors1 which have a selecting capacity of one column--that is1 one decimal digit--and class selectors1 which ordinarily have a selecting capacity of #aj columns or #aj decimal digits4 ,but we shall disregard this difference here1 as we have disregarded most other questions of capacity in multiplication1 division1 etc4 ,illustration3 ,,fig4 #ad4 ,selector4 ,in the language of logic 7see ,chapter #i and ,supplement #b71 if p1 a1 b1 c are the information in ,x ,pickup1 ,common1 ,x1 and ,no ,x1 respectively1 then the equations for a selector are3 b ap c a7#a - p7 ,returning now to the table we wish to make1 we connect columns #cj to #cf of the punch card to ,common4 ,we connect column #gi of the punch card to the ,x ,pickup4 ,we connect the output ,no ,x to the males column of the table4 ,we connect the output ,x to the females column of the table4 ,in this way we make the number in the punch card appear in either one of two places in the table according to whether the number counts males or females4 ,we might mention several more properties of selectors4 ,a selector can be used in the reverse way1 with ,x ,pickup1 ,x1 and ,no ,x as inputs and ,common as output 7,fig4 #ae74 ,what will come out of ,common is 7#a7 what goes into input ,no ,x if there is no ,x punch in the column to which input ,x ,pickup is wired1 and 7#b7 what goes into input ,x if there is an ,x punch in the column to which input ,x ,pickup is wired4 ,in this case the logical equation for the selector is3 a bp c7#a - p7 ,also1 selectors can be used one after another1 so that selecting based on #b or #c ,x punches can be made4 ,illustration3 ,,fig4 #ae4 ,selector4 ,in the language of logic1 if p1 q1 r are the truth values of 8there is an ,x punch in column i1 j1 k10 respectively1 then by means of selectors we can get such a function as3 c apq b7#a - q77#a - r7 ,also1 a selector may often be energized not only by an ,x punch but also by a punch #j1 #a1 #b1 1 #i and #ab4 ,in this case1 the selector is equipped with an additional input that can respond to any digit4 ,this input is called the ,digit ,pickup4 ,digit ,selector ,something like an ordinary selector is another mechanism called a digit selector 7,fig4 #af74 ,this has one input1 ,common1 and #ab outputs1 #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i1 #aa1 #ab4 ,this mechanism is often included in the tabulator and may be included in other punch-card machines4 ,for example1 suppose that we want to do something if and only if column #fb of a punch card contains a #c or a #d or a #i4 ,then we connect a brush that reads column #fb of the punch card to the ,common input of the digit selector4 ,and we connect out from the digit selector jointly from outputs #c1 #d1 and #i4 ,illustration3 ,,fig4 #af4 ,digit selector4 ,in the language of logic1 if a is the digit going into ,common1 and if p is the impulse coming out of the digit selector1 then the equation of the mechanism in this case is3 p ,t7a #c1 #d1 #i7 ,sequencer ,a fourth operation of reasoning done by punch-card machines is finding that one number is greater than1 or equal to1 or less than another4 ,this operation is done in the collator and may be called sequencing4 ,for example1 suppose that we have a file of punch cards for cities1 showing in columns #da to #dh the number of people4 ,suppose that we wish to pick out the cards for cities over #abe1jjj in population4 ,now the collator has a mechanism that has #b inputs and #c outputs 7,fig4 #ag74 ,we may call this mechanism a sequencer1 since it can tell the sequence of two numbers4 ,what goes into the ,primary input is a number3 let us call it a4 ,what goes into ,secondary is another number3 let us call it b4 ,an impulse comes out of ,low ,primary if a is less than b4 ,an impulse comes out of ,equal if a equals b4 ,an impulse comes out of ,low ,secondary if a is greater than b4 ,illustration3 ,,fig4 #ag4 ,sequencer4 ,in the language of logic1 if p1 q1 r are the three indications in ,low ,primary1 ,equal1 and ,low ,secondary1 then3 p ,t7a b7 q ,t7a b7 r ,t7a b7 ,returning to our example1 we punch up a card with #abe1jjj in columns #dc to #dh1 and we put this card into the ,secondary ,feed4 ,we take the punch cards for cities and put them into the ,primary ,feed4 ,in the plugboard1 we connect the hubs of the ,secondary ,brushes 7that read the card in the ,secondary ,feed71 columns #dc to #dh1 to the ,secondary input of the ,sequencer4 ,we connect the hubs of the ,primary ,brushes 7that read the card in the ,primary ,feed71 columns #da to #dh1 to the ,primary input of the ,sequencer4 ,then we connect the ,low ,primary output of the ,sequencer to a device that causes the city card being examined to fall into pocket #a4 ,we connect ,equal output and ,low ,secondary output to a device that causes the city card being examined to fall into pocket #b4 ,then1 when the card for any city comes along1 the machine compares the number of people in the city with #abe1jjj4 ,if the number is greater than #abe1jjj1 the card will fall into pocket #a2 otherwise the card will fall into pocket #b4 ,at the end of the run1 we shall find in pocket #a all the cards we want4 ,,new ,,developments ,we may expect to see over the next few years major developments in punch-card machinery4 ,it would seem likely that types of punch-card machines like the following might be constructed3 ,a punch-card machine that performs any arithmetical or logical operation at high speed and may perform a dozen such operations in sequence during the time that a punch card passes through the machine4 ,a punch-card machine that uses loops of punched paper tape1 which express either a sequence of values in a table that the machine can consult or a sequence of instructions that govern the operations of the machine4 ,punch-card machinery that uses a larger card than the #hj-;column card4 ,a punch-card machine that may have a fairly large amount of internal memory1 perhaps #cj or #dj registers where numbers or words may be stored and referred to4 ,,speed ,the speed of various operations with present ,,ibm punch-card machines is about as shown in the table4 ,,machine ,,operation ,,time ,,in ,,seconds ,key punch ,punch #hj columns ,about #bj to #dj ,verifier ,check #hj columns ,about #bj to #dj ,sorter ,sort #a card on #a column #j4ae ,interpreter ,print #a line #j4h ,reproducer ,reproduce a card1 all #hj columns #j4f ,collator ,merge #b cards #j4be ,multiplying punch ,multiply by #h digits #e4f ,calculating punch ,add #j4c ,calculating punch ,multiply by #h digits #c4f ,calculating punch ,divide1 obtaining #h quotient digits #i4j ,tabulator ,print #a line1 numbers only #j4d ,tabulator ,print #a line1 letters included #j4ge ,tabulator ,add numbers from #a card #j4d ,,cost ,punch-card machines may be either rented or purchased from some manufacturers but only rented from others4 ,if we take the cost of a clerk as #abj to #aej a month1 the monthly rent of most punch-card machines ranges from of the cost of a clerk for the simplest type of machine1 such as a key punch1 to #c times the cost of a clerk for a complicated and versatile type of machine1 such as a tabulator with many attachments4 ,the rental basis is naturally convenient for many kinds of jobs4 ,,reliability ,the reliability of work with punch cards and punch-card machines is often much better than #ii per cent3 in #aj1jjj operations1 failures should be less than #b or #c4 ,this is1 of course1 much better than with clerical operations4 ,there are a number of causes for machine or card failures4 ,sometimes cards may be warped and may not feed into the machines properly4 ,or1 the air in the room may be very dry1 and static electricity may make the cards stick together4 ,or1 the air may be too humid2 the cards may swell slightly and may jam in the machine4 ,a punch may get slightly out of true alignment1 and punches in the cards may be slightly off4 ,a relay may get dust on its contact points and1 from time to time1 fail to perform in the right way4 ,considerable engineering effort has been put into remedying these and other troubles1 with much success4 ,to make sure that we have correct results from human beings working with punch-card machines1 we may verify each process4 ,information that is punched on the key punch may be verified on the verifier4 ,multiplications done with multiplicand a and multiplier b may be repeated and compared with multiplications done with multiplicand b and multiplier a4 ,cards that are sorted on the sorter may be put through the collator to make sure that their sequence is correct4 ,it is often good to plan every operation so that we have a proof that the result is right4 ,it is standard practice to have the machines inspected regularly in order to keep them operating properly4 ,on the average1 for every #ej to #ge machines1 there will be one full-time service man maintaining them and taking care of calls for repairs4 ,of course1 as with any machinery1 some service calls will be a result of the human element2 for example1 a problem may have been set up wrongly on a machine4 ,,general ,,usefulness ,punch-card calculations are much faster and more accurate than hand calculations4 ,with punch cards1 work is organized so that all cases are handled at the same time in the same way4 ,this process is very different from handling each case separately from start to finish4 ,as soon as the number of cases to be handled is more than a hundred and each item of information is to be used five or more times1 punch cards are likely to be advantageous1 provided other factors are favorable4 ,vast quantities of information have been handled very successfully by punch-card machines4 ,over #cj scientific and engineering laboratories in the ,united ,states are doing computation by punch cards4 ,over a billion punch cards1 in fact1 are used annually in this country4 ,chapter #e ,,measuring3 ,,massachusetts ,,institute ,,of ,,technology',s ,,differential ,,analyzer ,,no4 #b ,in the previous chapter we talked about machines that move information expressed as holes in cards4 ,in this chapter we shall talk about machines that move information expressed as measurements4 ,,analogue ,,machines ,a simple example of a device that uses a measurement to handle information is a doorpost4 ,here the height of a child may be marked from year to year as he grows 7,fig4 #a74 ,or1 suppose that we have a globe of the world and wish to find the shortest path between ,chicago and ,moscow4 ,we may lay a piece of string on the globe1 pull it tight between those points1 and then measure the string on a scale to see about what distance it shows 7,fig4 #b74 ,machines that handle information as measurements of physical quantities are called analogue machines1 because the measurement is analogous to1 or like1 the information4 ,a common example of analogue machine is the slide rule4 ,with this we calculate by noting the positions of ruled lines on strips that slide by each other4 ,these strips are made of fine wood1 or of plastic1 or of steel1 in such fashion that the ruled lines will hold true positions and not warp4 ,if we space the rulings so that #a1 #b1 #c1 #d1 #e1 #f are equally spaced1 then the slide rule is useful for addition 7,fig4 #c74 ,but if we space the rulings so that powers 7for example1 powers of two--#a1 #b1 #d1 #h1 #af1 #cb 7 7,fig4 #d7 are equally spaced1 we can do multiplication4 ,the spacings are then according to the logarithms of numbers 7see ,supplement #b74 ,multiplication is more troublesome than addition1 and so more slide rules are made for multiplication than for addition4 ,illustration3 ,,fig4 #a4 ,measurement by doorpost4 ,illustration3 ,,fig4 #b4 ,measurement by string4 ,illustration3 ,,fig4 #c4 ,slide ,rule for adding4 ,illustration3 ,,fig4 #d4 ,slide ,rule for multiplying4 ,during ,world ,war ,,ii1 the aiming and firing of guns against hostile planes was done by machine4 ,after sighting a plane1 these machines automatically calculated how to direct fire against it4 ,they were much better and faster than any man4 ,these fire-control instruments were analogue machines with steel and electrical parts built to fine tolerances4 ,with care we can get accuracy of #a part in #aj1jjj with analogue machines1 but greater accuracy is very hard to get4 ,,physical ,,quantities ,suppose that we wish to make an analogue machine4 ,we need to represent information by a measurement of something4 ,what should we select8 ,what physical thing to be measured should we choose to put into the machine8 ,different amounts of this physical quantity will match with different amounts of the measurement being expressed4 ,in the case of the doorpost1 the string1 and the slide rule1 the physical quantity is distance4 ,in many fire-control instruments1 the physical quantity is the amount of turning of a shaft 7,fig4 #e74 ,many other physical quantities have from time to time been used in analogue machines1 such as electrical measurements4 ,the speedometer of an automobile tells distance traveled and speed4 ,it is an analogue machine4 ,it uses the amount of turning of a wheel1 and some electrical properties4 ,it handles information by means of measurements4 ,the basic physical quantity that it measures is the amount of turning of a shaft4 ,illustration3 ,,fig4 #e4 ,measurement by amount of turning of a shaft4 ,,differential ,,analyzer ,the biggest and cleverest mechanical brain of the analogue type which has yet been built is the differential analyzer finished in #aidb at ,massachusetts ,institute of ,technology in ,cambridge1 ,mass4 ,the fundamental physical quantity used in this machine is the amount of turning of a shaft4 ,the name analyzer means an apparatus or machine for analyzing or solving problems4 ,it happens that the word 8analyzer0 has been used rather more often in connection with analogue machines1 and so in many cases the word 8analyzer0 carries the meaning 8analogue0 as well4 ,the word 8differential0 in the phrase 8differential analyzer0 refers to the main purpose of the machine3 it is specially adapted for solving problems involving differential equations4 ,now what is a differential equation8 ,,differential ,,equations ,in order to explain what a differential equation is1 we need to use certain ideas4 ,these ideas are3 equation2 formula2 function2 rate of change2 interval2 derivative2 and integral4 ,in the next few paragraphs1 we shall introduce these ideas briefly1 with some explanation and examples4 ,it is entirely possible for anyone to understand these ideas rather easily1 by collecting true statements about them2 no one should feel that because these ideas may be new they cannot be understood readily4 ,,physical ,,problems ,in physics1 chemistry1 mechanics1 and other sciences there are many problems in which the behavior of distance1 of time1 of speed1 heat1 volume1 electrical current1 weight1 acceleration1 pressure1 and many other physical quantities are related to each other4 ,examples of such problems are3 ,illustration3 ,,fig4 #f4 ,paths of a shot from a gun1 trajectories4 ,what are the various angles to which a gun should be raised in order that it may shoot various distances8 7,see ,fig4 #f47 7,the paths of a shot from a gun are called trajectories47 ,if a plane flies in a direction always at the same angle from the north1 how much farther will it travel than if it flew along the shortest path8 7,see ,fig4 #g47 7,a path always at the same angle from the north is called a loxodrome1 and a shortest path on a globe is called a great circle47 ,how should an engine be designed so that it will have the least vibration when it moves fast8 ,in physical problems like these1 the answer is not a single number but a formula4 ,what we want to do in any one of these problems is find a formula so that any one of the quantities may be calculated1 given the behavior of the others4 ,for example1 here is a familiar problem in which the answer is a formula and not a number3 ,illustration3 ,,fig4 #g4 ,paths of a flight4 ,illustration3 ,,fig4 #h4 ,room formulas4 ,how are the floor area of a room1 its length1 and its width related to each other8 7,see ,fig4 #h47 ,the answer is told in any one of three equations3 7floor area7 ,,equals 7length7 ,,times 7width7 7length7 ,,equals 7floor area7 ,,divided ,,by 7width7 7width7 ,,equals 7floor area7 ,,divided ,,by 7length7 ,the first equation shows that the floor area depends on the length of the room and also on the width of the room4 ,so we say floor area is a function of length and width4 ,this particular function happens to be product1 the result of multiplication4 ,in other words1 floor area is equal to the product of length and width4 ,now there is another kind of function called a differential function or derivative4 ,a differential function or derivative is an instantaneous rate of change4 ,an instantaneous rate of change is the result of two steps3 7#a7 finding a rate of change over an interval and then 7#b7 letting the interval become smaller and smaller indefinitely4 ,for example1 suppose that we have the problem3 ,how are speed1 distance1 and time related to each other8 ,one of the answers is3 7speed7 ,,equals ,,the ,,instantaneous ,,rate ,,of ,,change ,,of 7distance7 ,,with ,,respect ,,to 7time7 ,or we can say1 and it is just the same thing in other words3 7speed7 ,,equals ,,the ,,derivative ,,of 7distance7 ,,with ,,respect ,,to 7time7 ,now we can tell what a differential equation is4 ,it is simply an equation in which a derivative occurs1 such as the last example4 ,perhaps the commonest kind of equation in physical problems is the differential equation4 ,,solving ,,physical ,,problems ,now we were able to change the equation about floor area into other forms1 if we wanted to find length or width instead of floor area4 ,when we did this1 we ran into the inverse or opposite of multiplication3 division4 ,in the same way1 we can change the equation about speed into other forms1 if we want to find distance or time instead of speed4 ,if we do this1 we run into a new idea1 the inverse or opposite of the derivative1 called integral4 ,the two new equations are3 7distance7 ,,equals ,,the ,,integral ,,of 7speed7 ,,with ,,respect ,,to 7time7 7time7 ,,equals ,,the ,,integral ,,of ,,one ,,divided ,,by 7speed7 ,,with ,,respect ,,to 7distance7 ,these equations may also be called differential equations4 ,an integral is the result of a process called integrating4 ,to integrate speed and get distance is the result of three steps3 7#a7 breaking up an interval of time into a large number of small bits1 7#b7 adding up all the small distances that we get by taking each bit of time and multiplying by the speed which applied in that bit of time1 and 7#c7 letting the bits of time get smaller and smaller1 and letting the number of them get larger and larger1 indefinitely4 ,in other words1 7total distance7 ,,equals ,,the ,,sum ,,of ,,all ,,the ,,small 7distances71 ,,each ,,equal ,,to3 ,a ,,bit ,,of 7time7 ,,multiplied ,,by ,,the 7speed7 ,,applying ,,to ,,that ,,bit ,this is another way of saying as before1 7distance7 ,,equals ,,the ,,integral ,,of 7speed7 ,,with ,,respect ,,to 7time7 ,to solve a differential equation1 we almost always need to integrate one or more quantities4 ,,origin ,,and ,,development ,,of ,,the ,,differential ,,analyzer ,for at least two centuries1 solving differential equations to answer physical problems has been a main job for mathematicians4 ,mathematics is supposed to be logical1 and perhaps you would think this would be easy4 ,but mathematicians have been unable to solve a great many differential equations2 only here and there1 as if by accident1 could they solve one4 ,so they often wished for better methods in order to make the job easier4 ,a ,british mathematician and physicist1 ,william ,thomson 7,lord ,kelvin71 in #ahgi suggested solving differential equations by a machine4 ,he went further3 he described mechanisms for integrating and other mathematical processes1 and how these mechanisms could be connected together in a machine4 ,no such machine was then built2 engineering in those years was not equal to it4 ,in #aibc1 a machine of this type for solving the differential equations of trajectories was proposed by ,l4 ,wainwright4 ,in #aibe1 at ,massachusetts ,institute of ,technology1 the problem of a machine to solve differential equations was again being studied by ,dr4 ,vannevar ,bush and his associates4 ,dr4 ,bush experimented with mechanisms that would integrate1 add1 multiply1 etc41 and methods of connecting them together in a machine4 ,a major part of the success of the machine depended on a device whereby a very small turning force would do a rather large amount of work4 ,he developed a way in which the small turning force1 about as small as a puff of breath1 could be used to tighten a string around a drum already turning with a considerable force1 and thus clutch the drum1 bring in that force1 and do the work that needed to be done4 ,you may have watched a ship being loaded1 seen a man coil a rope around a winch1 and watched him swing a heavy load into the air by a slight pull on the rope 7,fig4 #i74 ,if so1 you have seen this same principle at work4 ,the turning force 7or torque7 that pulls on the rope is greatly increased 7or amplified7 by such a mechanism1 and so we call it a torque amplifier4 ,illustration3 ,,fig4 #i4 ,increasing turning force2 winch1 or torque amplifier4 ,by #aicj1 ,dr4 ,bush and his group had finished the first differential analyzer4 ,it was entirely mechanical1 having no electrical parts except the motors4 ,it was so successful that a number of engineering schools and manufacturing businesses have since then built other machines of the ,bush type4 ,each time1 some improvements were made in accuracy and capacity for solving problems4 ,but1 if you changed from one problem to another on this type of machine1 you had to do a lot of work with screwdrivers and wrenches4 ,you had to undo old mechanical connections between shafts and set up new ones4 ,accordingly1 in #aice1 the men at ,,mit started designing a second differential analyzer4 ,in this one you could make all the connections electrically4 ,,mit finished its second differential analyzer in #aidb1 but the fact was not published during ,world ,war ,,ii1 for the machine was put to work on important military problems4 ,in fact1 a rumor spread and was never denied that the machine was a white elephant and would not work4 ,the machine was officially announced in ,october #aide4 ,it was the most advanced and efficient differential analyzer ever built4 ,we shall talk chiefly about it for the rest of this chapter4 ,a good technical description of this machine is in a paper1 8,a ,new ,type of ,differential ,analyzer10 by ,vannevar ,bush and ,samuel ,h4 ,caldwell1 published in the ,journal of the ,franklin ,institute for ,october #aide4 ,,general ,,organization ,,of ,,mit ,,differential ,,analyzer ,,no4 #b ,a differential analyzer is basically made up of shafts that turn4 ,when we set up the machine to solve a differential equation1 we assign one shaft in the machine to each quantity referred to in the equation4 ,it is the job of that shaft to keep track of that quantity4 ,the total amount of turning of that shaft at any time while the problem is running measures the size of that quantity at that time4 ,if the quantity decreases1 the shaft turns in the opposite direction4 ,for example1 if we have speed1 time1 and distance in a differential equation1 we label one shaft 8speed10 another shaft 8time10 and another shaft 8distance40 ,if we wish1 we may assign #aj turns of the 8time0 shaft to mean 8one second10 #b turns of the 8distance0 shaft to mean 8one foot10 and #d turns of the 8speed0 shaft to mean 8one foot per second40 ,these are called scale factors4 ,we could1 however1 use any other convenient units that we wished4 ,by just looking at a shaft or a wheel1 we can tell what part of a full turn it has made--a half1 or a quarter1 or some other part--but we cannot tell by looking how many full turns it has made4 ,in the machine1 therefore1 there are mechanisms that record not only full turns but also tenths of turns4 ,these are called counters4 ,we can connect a counter to any shaft4 ,when we want to know some quantity that a shaft and counter are keeping track of1 we read the counting mechanism4 ,the second differential analyzer1 which ,,mit finished in #aidb1 went a step further than any previous one4 ,in this machine1 a varying number can be expressed either 7#a7 mechanically as the amount of turning of a shaft1 or 7#b7 electrically as the amount of two voltages in a pair of wires4 ,the ,,mit men did this by means of a mechanism called an angle-indicator4 ,angle indicators have essentially three parts3 a transmitter1 a receiver1 and switches4 ,the transmitter 7,fig4 #aj7 can sense the exact amount that a shaft has turned and give out a voltage in each of two wires which tells exactly how much the shaft has turned 7,fig4 #aa74 ,the receiving device 7,fig4 #ab71 which has a motor1 can take in the voltages in the two wires and drive a second shaft1 making it turn in step with the first shaft4 ,by means of the switchboard 7,fig4 #ac71 the two wires from the transmitter of any angle-indicator can lead anywhere in the machine and be connected to the receiver of any other angle indicator4 ,illustration3 ,,fig4 #aj4 ,scheme of angle-indicator transmitter4 ,illustration3 ,,fig4 #aa4 ,indication of angle4 ,illustration3 ,,fig4 #ab4 ,scheme of angle-indicator receiver4 ,in a differential analyzer1 we can connect the shafts together in many different ways4 ,for example1 suppose that we want one shaft b to turn twice as much as another shaft a4 ,for this to happen we must have a mechanism that will connect shaft a to shaft b and make shaft b turn twice as much as shaft a4 ,we can draw the scheme of this mechanism in ,fig4 #ad3 a box1 standing for any kind of simple or complicated mechanism2 a line going into it1 standing for input of the quantity a2 a line going out of it1 standing for output of the quantity b2 and a statement saying that b equals #b;a4 ,illustration3 ,,fig4 #ac4 ,switchboard4 ,one mechanism that will make shaft b turn twice as much as shaft a is a pair of gears such that3 7#a7 they mesh together and 7#b7 the gear on shaft a has twice as many teeth as the gear on shaft b 7,fig4 #ae74 ,on the mechanical differential analyzer that ,,mit finished in #aicj1 a pair of gears was the mechanism actually used for doubling4 ,to make one shaft turn twice as much as another by this device1 we would3 go over to the machine with a screwdriver2 pick out from a box two gears1 one with twice as many teeth as the other2 slide them onto the shafts that are to be connected2 make the gears mesh together2 and screw them tight on their shafts4 ,illustration3 ,,fig4 #ad4 ,scheme of a doubling mechanism4 ,illustration3 ,,fig4 #ae4 ,example of a doubling mechanism4 ,on the ,,mit differential analyzer ,no4 #b1 however1 we are better off4 ,a much more convenient device for doubling is used4 ,we make use of3 a gearbox in whichthere are two shafts that may be geared so that one turns twice as much as the other1 and two angle-indicator transmitters and receivers4 ,looking at the drawing 7,fig4 #af71 we can see that3 shaft a drives shaft c to turn in step1 shaft c drives shaft d to turn twice as much1 and shaft d drives shaft b to turn in step4 ,here we can accomplish doubling by closing the pairs of switches that connect to the gearbox shafts4 ,illustration3 ,angle indicators3 ,t1 transmitters1 and ,r1 receivers ,,fig4 #af4 ,another example of a doubling mechanism4 ,above1 we have talked about a mechanism with gears that would multiply the amount of turning by the constant ratio #b4 ,but1 of course1 in a calculation1 any ratio1 say #g4fe1 #c4adb1 1 might be needed1 not only #b4 ,in order to handle various constant ratios1 gearboxes of two kinds are in differential analyzer ,no4 #b4 ,the first kind is a one-digit gearbox4 ,it can be set to give any of #aj ratios1 #j4a1 #j4b1 #j4c1 1 #a4j4 ,the second kind is a four-digit gearbox4 ,it can be set to give any one of more than #aa thousand ratios1 #j4jjjj1 #j4jjja1 #j4jjjb1 1 #a4aaji1 #a4aaaj4 ,we can thus multiply by constant ratios4 ,adders ,we come now to a new mechanism1 whose purpose is to add or subtract the amount of turning of two shafts4 ,it is called an adder4 ,the scheme of it is shown in ,fig4 #ag3 an input shaft with amount of turning a1 another input shaft with amount of turning b1 and an output shaft with amount of turning a b4 ,the adder essentially is another kind of gearbox1 called a differential gear assembly4 ,this name is confusing3 the word 8differential0 here has nothing to do with the word 8differential0 in 8differential analyzer40 ,this mechanism is very closely related to the 8differential0 in the rear axle of a motor car1 which distributes a driving thrust from the motor to the two rear wheels of the car4 ,illustration3 ,,fig4 #ag4 ,scheme of an adder mechanism4 ,illustration3 ,,fig4 #ah4 ,example of an adding mechanism 7differential gear assembly74 ,a type of differential gear assembly that will add is shown in ,fig4 #ah4 ,this is a set of #e gears ,a to ,e4 ,the #b gears ,a and ,b are input gears4 ,the amount of their turning is a and b1 respectively4 ,they both mesh with a third gear1 ,c1 free to turn1 but the axis of ,c is fastened to the inside rim of a fourth1 larger gear1 ,d4 ,thus ,d is driven1 and the amount of its turning is 7a b7_/#b4 ,this gear meshes with a gear ,e with half the number of teeth1 and so the amount of turning of ,e is a b4 ,we can subtract the turning of one shaft from the turning of another simply by turning one of the input shafts in the opposite direction4 ,integrators ,another mechanism in a differential analyzer1 and the one that makes it worth while to build the machine1 is called an integrator4 ,this mechanism carries out the process of integrating1 of adding up a very large number of small changing quantities4 ,figure #ai shows what an integrator is4 ,it has three chief parts3 a disc1 a little wheel1 and a screw4 ,the round disc turns horizontally on its vertical shaft4 ,the wheel rests on the disc and turns vertically on its horizontal shaft4 ,the screw goes through the support of the disc2 when the screw turns1 it changes the distance between the edge of the wheel and the center of the disc4 ,illustration3 ,,fig4 #ai4 ,mechanism of integrator4 ,now let us watch this mechanism move4 ,if the disc turns a little bit1 the wheel pressing on it must turn a little bit4 ,if the screw turns a small amount1 the distance between the edge of the wheel and the center of the disc changes4 ,the amount that the wheel turns is doubled if its distance from the center of the disc is doubled1 and halved if that distance is halved4 ,so we see that3 7the total amount that the wheel turns7 ,,equals ,,the ,,sum ,,of ,,all ,,the ,,small 7amounts of turning71 ,,each ,,equal ,,to3 ,a ,,bit ,,of 7disc turning7 ,,multiplied ,,by ,,the 7distance from the center of the disc to the edge of the wheel7 ,,applying ,,to ,,that ,,bit ,if we look back at our discussion of integrating 7p4 #gb71 we see that the capital words here are just the same as those used there4 ,thus we have a mechanism that expresses integration3 7the total amount that the wheel turns7 ,,equals ,,the ,,integral ,,of 7the distance from the center of the disc to the wheel7 ,,with ,,respect ,,to 7the amount that the disc turns7 ,the scheme of this mechanism is shown in ,fig4 #bj4 ,for example1 suppose that the screw measures the speed at which a car travels and that the disc measures time4 ,the wheel1 consequently1 will measure distance traveled by the car4 ,the mechanism ,,integrates speed with respect to time and gives distance4 ,illustration3 ,,fig4 #bj4 ,scheme of integrator4 ,this mechanism is the device that ,lord ,kelvin talked about in #ahgi and that ,dr4 ,bush made practical in #aibe4 ,the mechanical difficulty is to make the friction between the disc and the wheel turn the wheel with enough force to do other work4 ,in the second differential analyzer1 the angle indicator set on the shaft of the wheel solves the problem very neatly4 ,illustration3 ,,fig4 #ba4 ,graph of air resistance coefficient4 ,function ,tables ,the behavior of some physical quantities can be described only by a series of numbers or a graphic curve4 ,for example1 the resistance or drag of the air against a passing object is related to the speed of the object in a rather complicated way4 ,part of the relation is called the drag coefficient or resistance coefficient2 a rough graph of this is shown in ,fig4 #ba4 ,this graph shows several interesting facts3 7#a7 when the object is still1 there is no air resistance2 7#b7 as it travels faster and faster1 air resistance rapidly increases2 7#c7 when the object travels with the speed of sound1 resistance is very great and increases enormously2 7#d7 but1 when the object starts traveling with a speed about #bj per cent faster than sound1 the drag coefficient begins to decrease4 ,this drawing or graph shows in part how air resistance depends on speed of object2 in other words1 it shows the drag coefficient as a function of speed 7see ,supplement #b74 ,illustration3 ,,fig4 #bb4 ,pointer following graph4 ,now we need a way of putting any function we wish into a differential analyzer4 ,to do this1 we use a mechanism called a function table4 ,we draw a careful graph of the function according to the scale we wish to use1 and we set the graph on the outside of a large drum 7,fig4 #bb74 ,for example1 we can put the resistance coefficient graph on the drum2 the speed 7or independent variable7 goes around the drum1 and the resistance coefficient 7or dependent variable7 goes along the drum4 ,the machine slowly turns the drum1 as may be called for by the problem4 ,a girl sits at the function table and watches1 turning a handwheel that keeps the sighting circle of a pointer right over the graph4 ,the turning of the handwheel puts the graphed function into the machine4 ,instead of employing a person1 we can make one side of the graph black1 leaving the other side white1 and put in a phototube 7an electronic tube sensitive to amount of light7 that will steer from pure black or pure white to half and half 7see ,fig4 #bc74 ,we do not need many function tables to put in information1 because we can often use integrators in neat combinations to avoid them4 ,we shall say more about this possibility later4 ,we can also use a function table to put out information and to draw a graph4 ,to do so1 we disconnect the handwheel2 we connect the shaft of the handwheel to the shaft that records the function we are interested in2 we take out the pointer and put in a pen2 and we put a blank sheet of graph paper around the drum4 ,illustration3 ,,fig4 #bc4 ,phototube following graph4 ,we have now described the main parts of the second ,,mit differential analyzer4 ,they are the parts that handle numbers4 ,we can now tell the capacity of the differential analyzer by telling the number of main parts that it holds3 ,shafts ,about #acj ,one-digit gearboxes #ab ,four-digit gearboxes #af ,adders ,about #af ,integrators #ah ,function tables #c ,on a simpler level1 we can say that the machine holds these physical parts3 ,miles of wire ,about #bjj ,relays ,about #cjjj ,motors ,about #aej ,electronic tubes ,about #bjjj ,,instructing ,,the ,,mit ,,differential ,,analyzer ,,no4 #b ,besides the function tables for putting information into the machine1 there are three mechanisms that read punched paper tape4 ,the three tapes are called the ,a tape1 the ,b tape1 and the ,c tape4 ,from these tapes the machine is set up to solve a problem4 ,suppose that we have decided how the machine is to solve a problem4 ,suppose that we know the number of integrators1 adders1 gearboxes1 etc41 that must be used1 and know how their inputs and outputs are to be connected4 ,to carry out the solution1 we now have to put the instructions and numbers into the machine4 ,the ,a tape contains instructions for connecting shafts in the machine4 ,each instruction connects a certain output of one type of mechanism 7adder1 etc47 to a certain input of another type of mechanism4 ,when the machine reads an instruction on this tape1 it connects electrically the transmitting angle-indicator of an output shaft to the receiving angle-indicator of another input shaft4 ,now the connecting part of the differential analyzer behaves as if it were very intelligent3 it assigns an adder or an integrator or a gearbox1 etc41 to a new problem only if that mechanism is not busy4 ,for example1 if a problem tape calls for adder #c 7in the list belonging to the problem71 the machine will assign the first adder that is not busy1 perhaps adder #ad 7in the machine71 to do the work4 ,each time that adder #c 7in the problem list7 is called for in the ,a tape1 the machine remembers that adder #ad was chosen and assigns it over again4 ,this ability1 of course1 is very useful4 ,the ,b tape contains the ratios at which the gearboxes are to be set4 ,for example1 suppose that we want gearbox #d 7in the problem list7 to change its input by the ratio of #j4begc4 ,the machine1 after reading the ,a tape1 has assigned gearbox #aa 7in the machine list74 ,then1 when the machine reads the ,b tape1 it sets the ratio in gearbox #aa to #j4begc4 ,the answer to a differential equation is different for different starting conditions4 ,for example1 when we know speed and time and wish to find distance traveled and where we have arrived1 we must know the point at which we started4 ,we therefore need to arrange the machine so that we can put in different starting conditions 7or different initial conditions1 as the mathematician calls them74 ,the ,c tape puts the initial conditions into the machine4 ,for example1 reading the ,c tape for the problem1 the machine finds that #cjjj should1 at the start of the problem1 stand in counter #d4 ,the machine then reads the number at which counter #d actually stands1 say #fgbh4c4 ,it subtracts the two numbers and remembers the difference1 -#cgbh4c4 ,and whenever the machine reads that counter later1 finding1 say1 #idfh4d in it1 first the #cgbh4c is subtracted1 and then the answer #egdj4a is printed4 ,,answers ,information may come out of the machine in either one of two ways3 in printed numbers or in a graph4 ,in fact1 the same quantity may come out of the machine in both ways at the same time4 ,to obtain a graph1 we change a function table from input to output1 put a pen on it1 and have it draw the graph4 ,the machine has #c electric typewriters4 ,the machine will take numerical information out of the counters at high speed even while they are turning1 and it will put the information into relays4 ,then it will read from the relays into the typewriter keys one by one while they type from left to right across the page4 ,,how ,,the ,,differential ,,analyzer ,,calculates ,up to this point in this chapter1 the author has tried to tell the story of the differential analyzer in plain words4 ,but for reading this section1 a little knowledge of calculus is necessary4 7,see also ,supplement #b47 ,if you wish1 skip this section1 and go on to the next one4 ,we have described how varying quantities1 or variables1 are operated on in the machine in one way or another3 adding1 subtracting1 multiplying by a constant1 referring to a table1 and integrating4 ,what do we do if we wish to multiply #b variables together8 ,a neat trick is to use the formula3 xy x dy y dx ,to multiply in this way requires #b integrators and #a adder4 ,the connections that are made between them are as follows3 ,shaft x ,to ,integrator #a1 ,screw ,shaft x ,to ,integrator #b1 ,disc ,shaft y ,to ,integrator #a1 ,disc ,shaft y ,to ,integrator #b1 ,screw ,integrator #a1 ,wheel ,to ,adder #a1 ,input #a ,integrator #b1 ,wheel ,to ,adder #a1 ,input #b ,adder #a1 ,output ,to ,shaft expressing xy ,a product of #b variables under the integral sign can be obtained a little more easily1 because of the curious powers of the differential analyzer4 ,thus1 if it is desired to obtain xy dt1 we can use the formula3 xy dt x d y dt and this operation does not require an adder4 ,the connections are as follows3 ,shaft t ,to ,integrator #a1 ,disc ,shaft y ,to ,integrator #a1 ,screw ,integrator #a1 ,wheel ,to ,integrator #b1 ,disc ,shaft x ,to ,integrator #b1 ,screw ,integrator #b1 ,wheel ,to ,shaft expressing xy dt ,in order to get the quotient of #b variables1 x_/y1 we can use some more tricks4 ,first1 the reciprocal #a_/y can be obtained by using the two simultaneous equations3 #a #a -------- dy log y1 - -------- d7log y7 y y y ,the connections are as follows3 ,shaft y ,to ,integrator #a1 ,disc ,,and ,,to ,integrator #b1 ,wheel ,shaft log y ,to ,integrator #a1 ,wheel ,,and ,,to ,integrator #b1 ,disc ,shaft #a_/y ,to ,integrator #a1 ,screw1 ,,and ,,negatively ,,to ,integrator #b1 ,screw ,in order to get x_/y1 we can then multiply x by #a_/y4 ,we see that this setup gives us log y for nothing1 that is1 without needing more integrators or other equipment4 ,clearly1 other tricks like this will give sin x1 cos x1 e1 x1 and other functions that satisfy simple differential equations4 ,an integral of a reciprocal can be obtained even more directly4 ,suppose that #a y ---------- dt x #a ,then ,dy ----------1 ,dy t x1 x and t x dy ,the connections therefore are3 ,shaft t ,to ,integrator1 ,wheel ,shaft x ,to ,integrator1 ,screw ,shaft y ,to ,integrator1 ,disc ,the light wheel then drives the heavy disc4 ,clearly only the angle-indicator device makes this possible at all4 ,naturally1 the closer the wheel gets to the center of the disc1 that is1 x approaching zero1 the greater the strain on the mechanism1 and the more likely the result is to be off4 ,mathematically1 of course1 the limit of #a_/x as x approaches zero equals infinity1 and this gives trouble in the machine4 ,there is no standard mathematical method for solving any differential equation4 ,but the machine provides a standard direct method for solving all differential equations with only one independent variable4 ,first3 assign a shaft for each term that appears in the equation4 ,for example1 the highest derivative that appears and the independent variable are both assigned shafts4 ,the integral of the highest derivative is easily obtained1 and the integral of that integral1 etc4 ,second3 connect the shafts so that all the mathematical relations are expressed4 ,both explicit and implicit equations may be expressed4 ,third3 for any shaft there must be just one drive1 or source of torque4 ,a shaft may1 however1 drive more than one other shaft4 ,fourth3 choose scale factors so that the limits of the machine are not exceeded yet at the same time are well used4 ,for example1 the most that an integrator or a function table can move is #a or #b feet4 ,also1 the number of full turns made by a shaft in representing its variable should be large1 often between #ajjj and #aj1jjj4 ,of course1 as with all these large machines1 anyone would need some months of actual practice before he could put on a problem and get an answer efficiently4 ,,an ,,appraisal ,,of ,,the ,,machine ,the second ,,mit differential analyzer is probably the best machine ever built for solving most differential equations4 ,it regularly has an accuracy of #a part in #aj1jjj4 ,this is enough for most engineering problems4 ,if greater accuracy is needed1 the second differential analyzer cannot provide it4 ,once in a while the machine can reach an accuracy of #a part in #ej1jjj2 but1 to balance this1 it is sometimes less accurate than #a part in #aj1jjj4 ,the ,,mit differential analyzer ,no4 #b can find answers to problems very quickly4 ,the time for setting up a problem to be run on the machine ranges from #e to #ae minutes4 ,the time for preparing the tapes that set up the problem is1 of course1 longer2 but the punch for preparing the tape is a separate machine and does not delay the differential analyzer4 ,the time for the machine to produce a single solution to a problem ranges usually from #c minutes to a half-hour4 ,it is easy to put on a problem1 run a few solutions1 take the problem off1 study the results1 change a few numbers1 and then put the problem back on again4 ,this virtue is a great help in a search in a new field4 ,while the study is going on1 time is not wasted1 for the machine can be busy with a different problem4 ,running a problem a second time is a good check on the reliability of an answer4 ,for1 when the problem is run the second time1 we can arrange that the machine will route the problem to other mechanisms4 ,the machine has a control panel4 ,here the operator watching the machine can tell what units are doing what parts of what problems4 ,if a unit gives trouble or needs to be inspected1 the clerk can throw a 8busy0 switch4 ,then the machine cannot choose that unit for work to be done4 ,the machine contains many protecting signals and alarms4 ,it is idle for repairs less than #e per cent of the time4 ,it is not easy to determine the total cost of the machine1 for it was partially financed by several large gifts4 ,also1 much of the labor was done by graduate students in return for the instruction that they gained4 ,the actual out-of-pocket cost was about #abe1jjj4 ,if the machine were to be built by industry1 the cost would likely be more than #d times as much4 ,a simple differential analyzer1 however1 can be cheap4 ,small scale differential analyzers have been built for less than #ajjj2 their accuracy has been about #a part in #ajj4 ,there are many things that this machine cannot do2 it was not built to do them4 7#a7 ,it cannot choose methods of solution4 7#b7 ,it cannot perform steps in solving a problem that depend on results as they are found4 7#c7 ,it cannot solve differential equations containing two or more independent variables4 ,such equations are called partial differential equations2 they appear in connection with the flow of heat or air or electricity in #b or #c dimensions1 and elsewhere4 7#d7 ,it cannot solve problems requiring #f or more digits of accuracy4 7#e7 ,the machine1 while running1 can store numbers only for an instant1 since it operates on the principle of smoothly changing quantities2 however1 when the machine stops1 the number last held by each device is permanently stored4 ,none of these comments1 however1 are criticisms of the machine4 ,instead they show avenues of development for future machines4 ,as was said before1 for solving most differential equations1 this machine has no equal to date4 ,the range of problems which any differential analyzer can do depends mostly on the number of its integrators4 ,the second differential analyzer has #ah and provides for expansion to #cj4 ,the machine is constructed1 also1 so that it can be operated in #c independent sections1 each working to solve a different problem4 ,the differential analyzer can operate unattended4 ,after it has been set up and the first few results examined1 it can be left alone to grind out large blocks of answers4 ,an interesting example of the experimental use of a differential analyzer in a commercial business is the following3 ,in ,great ,britain1 ,r4 ,e4 ,beard of the ,pearl ,assurance ,company built a differential analyzer with #f integrators4 ,he applied this machine to compute to #c figures certain insurance values known as continuous annuities and continuous contingent insurances4 ,he has described the machine and the application he made in a paper published in the ,journal of the ,institute of ,actuaries1 ,vol4 #ga1 #aidb1 pp4 #aic-bbg4 ,chapter #f ,,accuracy ,,to #bc ,,digits3 ,,harvard',s ,,ibm ,,automatic ,,sequence-,,controlled ,,calculator ,one of the first giant brains to be finished was the machine in the ,computation ,laboratory at ,harvard ,university called the ,,ibm ,automatic ,sequence-,controlled ,calculator4 ,this great mechanical brain started work in ,april #aidd and has been running #bd hours a day almost all the time ever since4 ,it has produced quantities of information for the ,united ,states ,navy4 ,although many problems that have been placed on it have been classified by the ,navy as confidential1 the machine itself is fully public4 ,the way it was working on ,sept4 #a1 #aide1 has been thoroughly described in a #edj-page book published in #aidf1 ,volume ,i of the ,annals of the ,harvard ,computation ,laboratory1 entitled ,manual of ,operation of the ,automatic ,sequence-,controlled ,calculator4 ,since then the machine has been improved in many ways4 ,this machine does thousands of calculating steps1 one after another1 according to a scheme fixed ahead of time4 ,this property is what gives the machine its name3 automatic1 since the individual operations are automatic1 once the punched tape fixing the chain of operations has been put on the machine1 and sequence-controlled1 since control over the sequence of its operations has been built into the machine4 ,,origin ,,and ,,development ,more than a hundred years ago1 an ,english mathematician and actuary1 ,charles ,babbage 7#agib-ahga71 designed a machine--or engine as he called it--that would carry out the sequences of mathematical operations4 ,in the #ahcj's he received a government grant to build an analytical engine whereby long chains of calculations could be performed4 ,but he was unsuccessful1 because the refined physical devices necessary for quantities of digital calculation were not yet developed4 ,only in the #aicj's did these physical devices become sufficiently versatile and reliable for a calculator of hundreds of thousands of parts to be successful4 ,the ,automatic ,sequence-,controlled ,calculator at ,harvard was largely the concept of ,professor ,howard ,h4 ,aiken of ,harvard4 ,it was built through a partnership of efforts1 ideas1 and engineering between him and the ,international ,business ,machines ,corporation1 in the years #aicg to #aidd4 ,the calculator was a gift from ,,ibm to ,harvard ,university4 ,some very useful additional control units1 named the ,subsidiary ,sequence ,mechanism1 were built at the ,harvard ,computation ,laboratory in #aidg and joined to the machine4 ,illustration3 ,,fig4 #a4 ,scheme of ,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator4 ,,general ,,organization ,the machine 7see ,fig4 #a7 is about #ej feet long1 #h feet high1 and about #b feet wide4 ,it consists of #bb panels2 #ag of them are set in a straight line1 and the last #e are at the rear of the machine4 ,in the scheme of the machine shown in ,fig4 #a1 the details you would see in a photograph have been left out4 ,instead you see the sections of the machine that are important because of what they do3 input1 memory1 control1 and output4 ,why do we not see a section labeled 8computer08 ,because in this mechanical brain the computing part of the machine is closely joined to the memory3 every storage register can add and subtract4 ,we shall soon discuss these sections of the machine more fully4 ,,physical ,,devices ,now in order for any brain to work1 physical devices must be used4 ,for example1 in the human body1 a nerve is the physical device that carries information from one part of the body to another4 ,in the ,harvard machine1 an insulated wire is the physical device that carries information from one part of the machine to another4 ,one side of every panel in the ,harvard machine is heavily laden with a great network of wires4 ,between the panels1 you can see in many places cables as thick as your arm and containing hundreds of wires4 ,more than #ejj miles of wire are used4 ,the physical devices in the ,harvard machine are numerous1 as we would expect4 ,it is perhaps not surprising that this machine has more than #gfj1jjj parts4 ,but1 curiously enough1 there are only #g main kinds of physical devices in the major part of the machine4 ,they are3 wire1 two-position switches1 two-position relays 7see ,chapter #b71 ten-position switches1 ten-position relays1 buttons1 and cam contacts 7see below74 ,these are the devices that handle information in the form of electrical impulses4 ,they can be combined by electrical circuits in a great variety of ways4 ,there are1 of course1 other kinds of physical devices that are important1 but they are not numerous1 and they have rather simple duties4 ,looking at the machine1 you can see three examples easily4 ,physical devices of the first kind convert punched holes into electrical impulses3 #b card feeds1 #d tape feeds4 ,those of the second kind convert electrical impulses into punched holes3 #a card punch1 #a tape punch4 ,those of the third kind convert electrical impulses into printed characters3 #b electric typewriters4 ,we can think of a fourth kind of physical device that would be a help1 but1 at present writing1 it does not yet exist3 a device that converts printed characters into electrical impulses4 ,the ,harvard machine1 of course1 is complicated4 ,but it is complicated because of the variety of ways in which relatively simple devices have been connected together to make a machine that thinks4 ,switches ,a two-position switch 7see ,fig4 #b7 turned by hand connects a wire to either one of #b others4 ,these #b positions may stand for 8yes0 and 8no10 #j and #a1 etc4 ,there are many two-position switches in the machine4 ,a ten-position switch or dial switch 7see ,fig4 #c7 turned by hand connects the wire running into the center of the switch with a wire at any one of ten positions #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i around the edge4 ,there are over #adjj dial switches in the machine4 ,how does turning the pointer on the top of the dial make connection between the center wire and the edge wire8 ,under the face of the dial is the part that works1 a short rod of metal fastened to the pointer 7shown with dashes in ,fig4 #c74 ,when the pointer turns1 this rod also turns1 making the desired connection4 ,illustration3 ,,fig4 #b4 ,two-position switch4 ,illustration3 ,,fig4 #c4 ,dial switch4 ,relays ,two-position relays--more often called just relays 7see ,chapter #b7--;do the automatic routing of the electrical impulses that cause computing to take place4 ,each relay may take #b positions1 open or closed1 and these positions may stand for #j and #a4 ,there are more than #cjjj relays in the ,harvard machine4 ,a magnet pulling one way and a spring pulling the other way are sufficient in an ordinary relay to give #b positions1 8on0 and 8off10 8yes0 and 8no10 #j and #a4 ,but how do we make a relay that can hold any one of #aj positions8 ,figure #d shows one scheme for a ten-position relay4 ,the arm can take any one of #aj positions1 connecting the contact ,common to any one of the contacts ,o1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 and #i so that current can flow4 ,the gear turns all the time4 ,when an impulse comes in on the ,pickup line1 the clutch connects the arm to the gear4 ,when an impulse comes in on the ,drop-out line1 the clutch disconnects the arm from the gear4 ,for example1 suppose that the ten-position relay is stopped at contact #b1 as shown4 ,suppose that we now pick up the relay1 hold it just long enough to turn #c steps1 and then drop it out4 ,the relay will now rest at contact #e4 ,illustration3 ,,fig4 #d4 ,scheme of a ten-position relay1 or counter position4 ,illustration3 ,,fig4 #e4 ,scheme of a counter wheel4 ,in the ,harvard machine1 the ten-position relays1 much like the scheme shown1 do the same work as counter wheels 7,fig4 #e7 in an ordinary desk calculating machine1 and so they are often spoken of as counter positions in the ,harvard machine4 ,they are very useful in the machine not only because they express the #aj decimal digits #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i but also because adding and subtracting numbers is accomplished by turning them through the proper number of steps4 ,in fact1 an additional impulse is provided when the counter position turns from #i to #j1 for purposes of carry4 ,a group of #bd counter positions makes up each storage counter--or storage register--in the machine4 ,there are #bbjj of these counter positions4 ,each is connected to a continuously running gear on a small shaft 7,fig4 #f74 ,all these shafts are connected by other gears and shafts to a main drive shaft1 and they are driven by a #e-;horsepower motor at the back of the machine4 ,when a counter position is supposed to step1 a clutch connects the drive to the running gear1 and the counter position steps4 ,when the counter position is supposed to stay unchanged1 the clutch is disconnected and the driving gear runs free4 ,in fact1 when you first approach the ,harvard machine1 about the first thing you are aware of is the running of these gears and the intermittent whirring and clicking of the counter positions as they step4 ,the machine gives a fine impression of being busy6 ,illustration3 ,,fig4 #f4 ,scheme of counter #af4 ,timing ,contacts ,a button 7see ,fig4 #g7 is a device for closing an electric circuit when and only when you push it4 ,a simple example is the button for ringing a bell3 you push the button1 a circuit is closed1 and something happens4 ,when you let go1 the circuit is opened4 ,the ,harvard machine has a button for starting1 a button for stopping1 and many others4 ,illustration3 ,,fig4 #g4 ,button4 ,illustration3 ,,fig4 #h4 ,cam1 with #e lobes and contact4 ,a cam contact 7see ,fig4 #h7 is an automatic device for closing an electric circuit for just a short interval of time4 ,when the lobes on the cam strike the contact1 it closes and current flows4 ,when the lobes have gone by1 the spring pushes open the contact1 and no current flows4 ,just as a two-position relay is the automatic equivalent of a two-position switch1 and a ten-position relay is the automatic equivalent of a ten-position switch1 so a cam contact is the automatic equivalent of a button4 ,all the cams in the machine have #bj pockets where small round metal lobes may or may not be inserted4 ,each cam makes a full turn once in _/ of a second and is in time with all the others4 ,thus we can time all the electrical circuits in the machine in units of _/ of a second4 ,,numbers ,numbers in the machine regularly consist of #bc decimal digits4 ,the #bdth numerical position at the left in any register contains only #j for a positive number and only #i for a negative number4 ,nines complements 7see ,supplement #b7 are used for negative numbers4 ,for example1-#jjbhd is represented as #iiigae1 supposing that we had #e-;digit numbers instead of #bc-;digit numbers4 ,the sum of two nines complements is automatically corrected so that it is still a correct nines complement4 ,the device that accomplishes this is called end-around-carry 7see ,supplement #b74 ,the decimal point is fixed for each problem2 in other words1 in any problem1 the decimal point is consistently kept in one place1 usually between the #aeth and #afth decimal columns from the right4 ,,how ,,information ,,goes ,,into ,,the ,,machine ,numerical information may go into the machine in any one of #c ways3 7#a7 by regular ,,ibm punch cards1 using standard ,,ibm card feeds 7panel #af72 7#b7 by hand-set dial switches 7panels #a1 #b72 and 7#c7 by long loops of punched tape placed on the value tape feeds 7panels #ab to #ad74 ,three sets of #bd columns each punched on a regular ,,ibm punch card can be used to send #c numbers and their signs into the machine in one machine cycle4 ,this is the fastest way for giving numbers to the machine1 but the most limited2 for the cards must be referred to in order and can be referred to automatically only once4 ,also1 there is the risk that they may be out of order4 ,a card may be passed through the machine without reading2 this saves some sorting in preparing cards for the machine4 ,machines for preparing the cards are regular ,,ibm key punches1 and machines for sorting them after preparation are regular ,,ibm card sorters4 ,in panels #a and #b there are #fj registers by which unchanging numbers like #a1 or #c4adaeibfe1 or #g4fe may be put into the machine4 ,these are called the constant registers4 ,each constant register consists of #bd dial switches and contains #bc digits and a sign1 #j if positive and #i if negative4 ,whenever the mathematician says a certain constant is needed for a problem1 the operator of the machine walks over to these panels1 and1 while the machine is turned off1 sets the dial switches for the number1 one by one1 by hand4 ,if we need #dj constants of #aj digits each for a problem1 then the operator sets #djj dial switches by hand and makes certain that the remaining #ad switches in each of the #dj constant registers used are either at #j or #i1 depending on the sign of the number4 ,only then can he return to start the machine4 ,illustration3 ,,fig4 #i4 ,value tape code4 ,the third means by which numerical information can be put into the machine is the value tape feeds1 in panels #ab1 #ac1 and #ad4 ,here the machine can consult tables of numbers4 ,the numbers are punched on paper tape #bd holes wide1 made of punch-card stock4 ,tapes for the value tape feeds may be prepared by hand or by the machine itself using punch cards or machine calculation4 ,the tapes use equally spaced arguments 7see ,supplement #b74 ,the tape punch changes the decimal digits in its keyboard into the following punching code 7see ,fig4 #i73 #j #jjjj #e #aajj #a #ajjj #f #ajaj #b #jajj #g #ajja #c #jjaj #h #jaaj #d #jjja #i #jaja ,here the #a denotes a punched hole and #j no punched hole1 and the #d columns from left to right of the code correspond to #d rows of the paper tape from bottom to top4 ,to make sure the value tape is correct1 the machine itself can read the value tape and check it mathematically or compare it with punch-card values4 ,,how ,,information ,,comes ,,out ,,of ,,the ,,machine ,information comes out of the machine in any one of three ways3 7#a7 by punching on ,,ibm cards with a regular ,,ibm card punch that is built into the machine 7panel #ag71 7#b7 by typing on paper sheets with electric typewriters 7panels #af and #ag71 and 7#c7 by punching paper tape #bd holes wide of the same kind as is fed into the machine4 ,usually1 one of the electric typewriters is used to print a result for a visual check and to print it before the machine makes a specified check of the value4 ,then1 about #aj seconds later1 after the result has been checked as specified in the machine1 the checked result is printed by the second typewriter4 ,in the second typewriter1 a special one-use carbon ribbon of paper is used to produce copy for publication by a photographic process4 ,the card punch writes a number more rapidly than an electric typewriter4 ,this extra speed is sometimes very useful4 ,however1 the punch's chief purpose is to record intermediate results on punch cards4 ,then1 if there is a machine failure1 and if the problem has been well organized1 the problem may be run over from these intermediate results1 instead of requiring a return to the original starting information4 ,the tape punch used for preparing tape by hand can also be operated by cable from the machine4 ,,how ,,information ,,is ,,handled ,,in ,,the ,,machine ,the machine is a mechanical brain4 ,so1 between taking in information and putting out information1 the machine does some 8thinking40 ,it does this thinking according to instructions4 ,the instructions go into the machine as3 7#a7 the setting of switches1 or 7#b7 the pressing of buttons1 or 7#c7 the wiring of plugboards1 or 7#d7 feeding in tape punched with holes4 ,the instructions are remembered in the machine in these #d ways1 and we can call these sets of devices the control of the machine4 ,to illustrate3 ,one of the buttons pressed for every problem is the ,start ,key3 when you press it1 the machine starts to work on the problem4 ,one of the switches with which you give instructions is a switch that turns electric typewriter #a on or off4 ,one of the plugboards contains some hubs by which you can tell the machine how many figures to choose in the quotient when dividing1 for clearly you do not need a quotient of #bc figures every time the machine divides4 ,you can have #e choices in any one problem2 you can specify them by plugging1 and you can call for any one of #e choices of quotient size from time to time during the problem4 ,in many cases1 when we wish the machine to do the same thing for all of a single problem and do it whenever the occasion arises1 we can put the instruction into the wiring of a plugboard4 ,we use plugboard wiring1 for example1 in fixing the decimal point in multiplication1 so that the product will read out properly1 and in guiding the operation of the typewriters1 so that printing will take place in the columns where we want it4 ,sequence of ,steps ,the most important part of the control of the machine is the sequence-tape feed and its sequence-control tape4 ,these tell the machine a great part of what operations are to be performed4 ,illustration3 ,,fig4 #aj4 ,sequence-control tape code4 ,at the end of the room where the machine is1 there is the special tape punch mentioned above4 ,it holds a big spool of card stock that is thin1 flexible1 smooth1 and tough4 ,with one keyboard we may prepare value tape4 ,with another keyboard we prepare the sequence-control tape4 ,the tape 7see ,fig4 #aj7 contains places for #bd round punched holes in each row4 ,some and only some of these holes are punched4 ,each row of punched holes is equivalent to an instruction to the machine and is called a line of coding or coding line4 ,in general1 the instruction has the form3 ,take a number out of ,register ,a2 put the number into ,register ,b2 and perform operation ,c4 ,the first group of #h holes at the left is called the ,a field or the out-field4 ,here we tell the machine where a number is to be taken from4 ,the middle group of #h holes is called the ,b field or the in-field4 ,here we tell the machine where a number is to be put4 ,the last group of #h holes is called the ,c field or the miscellaneous field4 ,here we tell the machine part or all of the operation that is to be performed4 ,to illustrate 7see ,fig4 #aj71 we have holes #c1 #b1 #a punched in the ,a field1 holes #c1 #b punched in the ,b field1 and hole #g punched in the ,c field4 ,now #cba is the code--or machine language1 or machine call number--for storage counter #g2 #cb is the code for storage counter #f2 and #g in the ,c field is the code 7in this case1 and generally7 for 8,add1 and read the next line of coding40 ,so1 if we punch out this line of coding and put the tape on the machine1 we tell the machine to read the number in counter #g1 add it into counter #f1 and proceed to the next line of coding and read that4 ,the holes in each group of #h holes from left to right are numbered3 #h1 #g1 #f1 #e1 #d1 #c1 #b1 #a4 ,the code #fca1 for example1 means that holes #f1 #c1 #a are punched and that no holes are punched at #h1 #g1 #e1 #d1 #b4 ,since it is more natural1 the code is read from left to right1 or #fca1 instead of from right to left in the sequence #acf4 ,the devices in the machine have in-codes1 used in the in-field1 and out-codes1 used in the out-field4 ,for each of the #gb regular storage counters1 the in-code and the out-code are the same4 ,the first #h storage counters have the codes #a1 #b1 #ba1 #c1 #ca1 #cb1 #cba1 #d1 #da2 the last #b storage counters1 the #gast and the #gbnd1 have the codes #gcba1 #gd4 ,the constant registers--often called constant switches1 or just switches--naturally have only out-codes1 since numbers can be entered into the constant registers only by setting dial switches by hand4 ,the first #h constant registers have the out-codes #gda1 #gdb1 #gdba1 #gdc1 #gdca1 #gdcb1 #gdcba1 #ge1 and the #eith and #fjth constant registers have the out-codes #hba1 #hc4 ,transferring1 ,adding1 and ,clearing ,each storage counter has the property that any number transferred into it is added into it4 ,for example1 the instruction ,take the number in switch #gda2 transfer it into storage register #cba is coded3 #gda1 #cba1 #g ,the #g in the third column is an instruction to the sequence-tape feed to turn up to the next coding line and read it4 ,if any number is already stored in register #cba1 the content of #gda will be added to it1 and the total will then be stored in #cba4 ,resetting or clearing a regular storage register is accomplished by a coding that is a departure from the usual scheme of 8out0 and 8in40 ,the instruction ,clear register #cba2 read the next coding line is coded3 #cba1 #cba1 #g ,similarly1 you can clear any other regular storage register if you repeat its code in the out-and in-fields4 ,however1 a few of the storage registers in the machine have special reset codes1 and these may occur in any of the three fields ,a1 ,b1 ,c4 ,as the result of a recent modification of the machine1 you can easily double the number in any storage register4 ,for example1 the instruction ,double the number in register #cba2 read the next coding line is coded3 #cba1 #cba1 #gdc ,subtracting ,if the number in switch #gda is to be subtracted from the number in storage counter #cba1 the instruction is changed into3 ,take the negative of the number in switch #gda2 transfer it into storage register #cba2 read the next line of coding ,the coding line becomes3 #gda1 #cba1 #gcb ,by putting #cb in the ,c field1 we cause the number in switch #gda to be subtracted from whatever number is in register #cba4 ,we have #b more choices in adding and subtracting4 ,the value of the number without regard to sign--in other words1 its absolute value 7see ,supplement #b7--may be added or subtracted4 ,the instruction ,add the absolute value of is expressed by a ,c field code #b1 and the instruction ,add the negative of the absolute value of is expressed by a ,c field code #a4 ,multiplying ,when we wish to multiply one number by another and get a product1 we have #c numbers4 ,we tell the machine about each of these numbers on a separate line of coding4 ,multiplication is signaled by sending a number into the multiplicand counter4 ,the multiplicand counter has an in-code #gfa4 ,if the multiplicand is in #cba1 the instruction is3 ,take the number in #cba2 enter it as multiplicand2 read the next coding line ,the coding is3 #cba1 #gfa1 #g ,on the third following coding line1 the multiplier is sent into the multiplier counter4 ,if the multiplier is in switch #gda1 the instruction is3 ,take the number in #gda2 enter it as multiplier2 read the next coding line ,the coding is3 #gda1 ----1 #g ,we do not punch anything in the middle field3 the machine is 8educated0 and 8knows0 that it has started a multiplication and needs a multiplier1 and it expects this multiplier in the third coding line4 ,to have no code for the multiplier counter is1 of course1 a departure from the general rule1 but it saves some punching and permits the use of this space for certain other codes1 thus saving some operating time4 ,we need not confuse the #gfa in-code for the multiplicand counter with the #gfa out-code1 which happens to be the out-code of the #beth constant register1 because neither can occur in the other's field4 ,we may1 of course1 use other registers besides #cba and #gda for supplying the multiplicand and multiplier4 ,to get the product and put it into any storage counter ,d1 we use two lines of coding one right after the other3 ---- ---- #fdba #hgfa ,d ---- ,the product counter has the out-code #hgfa4 ,when the product is desired1 it is called for1 transferred into counter ,d1 and the multiplication unit is automatically cleared4 ,it takes time1 however1 for the machine to perform a multiplication4 ,that is the reason for the preceding coding line and the #fdba in the ,c field4 ,while the multiplication is going on1 we can instruct the machine to do other things that we want done4 ,we can insert or interpose coding lines in between the multiplier line and the product line4 ,for example1 if we have a multiplier of #aj digits1 we can insert #h coding lines and maybe more4 ,the #fdba code essentially tells the machine to finish both the multiplication and the interposed instructions1 and1 as soon as the later one of these two tasks is finished1 to transfer out the product to counter ,d4 ,up to the middle of #aidf1 the wiring of the machine was a little different and less convenient4 ,when the product was obtained by the multiplication unit1 it had to be accepted and transferred at once into one of the #gb storage registers4 ,dividing ,division is called for by first sending the divisor into the divisor counter1 and this has a code #gf in the ,b field4 ,if the divisor is in counter #cba1 the instruction may be3 ,take the number in #cba2 enter it as divisor2 read the next coding line ,the coding will then be3 #cba1 #gf1 #g ,three coding lines later1 the dividend is called for1 and the coding1 if the dividend is in switch #gdca1 is3 #gdca1 ----1 #g ,we can send the quotient1 when ready1 into any desired counter ,q by the following two lines of coding3 ---- ---- #fdb #hgf ,q ---- ,in the same way as with multiplication1 we can insert a number of coding lines in between the dividend line and the first quotient line4 ,both multiplication and division are carried out in the same unit of the machine1 the multiply-divide unit4 ,the machine first constructs a table of the multiples of the multiplicand or divisor3 #a times1 #b times1 #c times1 1 #i times4 ,in multiplication this table is then used by selecting multiples according to the digits of the multiplier one after another4 ,in division the table is used by comparing multiples of the divisor against the dividend and successive remainders1 finding which will go and which will not4 ,since the numbers in the machine are normally of #ae to #bc digits1 any particular multiple will be used1 on the average1 several times1 and so this process is relatively efficient4 ,actually the multiplicand and the divisor go into the same counter4 ,division1 however1 has the code #gf and multiplication the code #gfa1 and so the difference is essentially an operation code not in the third or ,c field4 ,consulting a ,table ,when we desire the machine to consult a table of values 7i4e41 a function--see ,supplement #b71 we punch the table with its arguments and function values on a tape1 and we put the tape on a value tape feed mechanism4 ,the instruction to the machine may be3 ,take the number in register ,a2 find the value of the function for this number1 and enter it in register ,b4 ,the coding is3 ---- ---- #gc ,a #gfed #fa ---- ---- #gfb ---- ---- #edc ---- ---- #gedca #hda #gfed ---- ,a #gfc #fdba #hgfb ,b #gc ---- #hgfc #g ,without explaining this coding line by line1 we can say that this is what happens3 ,the machine reads the argument in register ,a4 ,the machine reads the argument in the table at which the value tape feed is resting4 ,it subtracts them1 and thereby determines how far away the desired argument is4 ,the machine then turns the tape that required distance4 ,it checks that the new argument is the wanted argument4 ,it reads the value of the function entered at that point on the function tape4 ,selecting ,there is a storage counter in the machine that is called the selection counter4 ,the selection counter is counter #gj and has the code #gcb4 ,it has all the properties of an ordinary storage counter and1 in addition1 one extra property3 depending on the sign of the number stored in the selection counter1 it is possible to select whether some other number shall be treated positively or negatively4 ,in other words1 addition of a number anywhere in the machine may take place either positively or negatively1 if the number stored in the selection counter is positive or negative1 respectively4 ,for example1 suppose that x is the number in the selection counter4 ,suppose that y is the number in some other counter ,a4 ,suppose that z is the number in counter ,b4 ,suppose that we use the coding3 ,a1 ,b1 #gdcb ,what we get in ,b1 because of the #gdcb in the third or ,c field1 is z plus y if x is positive or zero1 and z minus y if x is negative4 ,in the language of the algebra of logic 7see ,chapter #i and ,supplement #b71 where ,t7 4447 is 8the truth value of 44410 the number in b equals3 z y,t7x #j7 - y,t7x #j7 7,the nines complement of #j1 namely #iiii to #bd digits1 is treated by the machine as negative47 ,why do we need an operation like this in a mechanical brain8 ,among other reasons1 what we want to do with a number1 in mathematics1 often depends on its sign4 ,it may happen that a table is1 for negative arguments1 the negative of what it is for positive arguments2 in other words1 ,f7-x7 -,f7x74 ,this is true1 for instance1 for a table of cubes ,f7x7 x or for a table of trigonometric tangents 7see ,supplement #b74 ,if so1 we certainly do not want to take the time and trouble to list the whole table4 ,we put down only half the table and then1 if x is negative1 use the negative of the value in the table4 ,in order to apply such a time-saving rule when using the machine1 we need the selection counter or its equivalent4 ,checking ,there is another special counter in the machine that is called the check counter4 ,it also has all the properties of an ordinary storage counter and1 in addition1 one extra property3 ,if the sign of the number stored in the check counter on a certain coding line is negative1 then on the next coding line the machine may be stopped4 ,in other words1 suppose that the check counter stores a certain tolerance t4 ,suppose1 under the instructions we give the machine1 that it calculates a positive number x that ought to be less than this tolerance4 ,suppose that something may go wrong and that x actually may be greater than t4 ,then we put a check into our instructions4 ,we tell the machine3 ,when you have found x1 subtract it from t4 ,if the result is positive1 go ahead4 ,if the result is negative or zero1 stop6 ,here is the coding4 ,suppose that the tolerance t is in switch #gea4 ,suppose that the number x to be checked is in counter #dcba4 ,then the instructions and coding are3 ,clear the check counter -- -- #g ,put in the tolerance1 from switch #gea #gea #gd #g ,subtract the absolute value of the number to be checked #dcba #gd #ga ,stop1 ,o ,mechanical ,brain1 if your result be negative6 -- -- #fd ,an operation like this is very useful in a mechanical brain4 ,it enables the calculation to be interrupted if something has gone wrong4 ,of course1 other operations of checking besides this one are used--for example1 inspecting for reasonableness the results printed on typewriter #a4 ,other ,operations ,there are other operations in the machine4 ,there are two pairs of storage registers that can be coupled together so that we can handle problems requiring numbers of #df digits instead of #bc4 ,registers #fd and #fe can be coupled1 and registers #fh and #fi can be coupled4 ,there is another storage counter1 ,no4 #ga1 that has an extra property4 ,we can read out the number it holds times #a1 or times #aj1 or times #aj1 as may be called for4 ,as a result of this counter1 we can do problems requiring #add registers storing numbers of #aa digits each1 instead of #gb registers storing #bc digits each4 ,bigger statistical problems can be handled1 for example4 ,there are some minor sequences of operations1 or subroutines1 that can be called for by a single code4 ,the subroutine may be a whole set of additions1 subtractions1 multiplications1 divisions1 and choices1 having a single purpose3 to compute some number by a process of rapid approximation 7see ,supplement #b74 ,there are built-in subroutines for some special mathematical functions3 the logarithm of a number to the base #aj1 the exponential of a number to the base #aj1 and the sine of a number4 7,see ,supplement #b47 ,there are also #aj changeable subroutines1 each of #bb coding lines1 which can be called in1 when wanted1 by the main sequence-control tape or by each other4 ,these subroutines constitute the ,subsidiary ,sequence ,mechanism1 and are extremely useful4 ,they have ,a1 ,b1 and ,c fields just like the main sequence-control1 but they are given information by plugging with short lengths of wire instead of by feeding punched paper tape4 ,,rapid ,,approximation ,,for ,a ,,logarithm ,up to this point in this chapter the author has tried to tell the facts about the ,harvard machine in plain words4 ,but for reading this section1 a little knowledge of calculus is necessary4 7,see also ,supplement #b47 ,if you wish1 skip this section and go on to the next one4 ,what is the process that the machine uses to compute any desired logarithm to #bc digits8 ,suppose that we take for an example the process by which the machine computes log#aj #di4cgbd4 ,we choose a #f-;digit number for simplicity2 the machine would handle a #bc-;digit number in the same way4 ,the process uses #b fundamental equations involving the logarithm3 the sum relation log 7abc7 log a log b log c and the series relation h h h log7#a h7 h - -------- -------- - -------- 1 h #a #b #c #d ,the error in this series is less than the first neglected term4 ,now1 the machine stores the base #aj logarithms 7to #bc decimal places7 of the following #cf numbers3 #a #a4a #a4ja #a4jja #b #a4b #a4jb #a4jjb 444 444 444 444 #i #a4i #a4ji #a4jji ,first1 the number #di4cgbd is examined in a counter called the ,logarithm-,in-,out counter1 and the position of the decimal point is determined1 giving the characteristic of the logarithm4 ,the number #di4cgbd has the characteristic #a4 ,next1 #d successive divisions are performed1 in which the #d divisors are 7#a7 the first digit of the number1 7#b7 the first #b digits of the quotient1 7#c7 the first #c digits of the next quotient1 and 7#d7 the first #d digits of the subsequent quotient2 thus1 #d4icgbd_/d #a4bcdca #a4bcdca_/a4b #a4jbhfj #a4jbhfj_/a4jb #a4jjhdc #a4jjhdc_/a4jjh #a4jjjdc ,for simplicity we have kept only #f digits1 although the machine1 of course1 would keep #bc4 ,it is interesting to note that the machine is able to sense digits and thus determine the #d divisors2 this is an arithmetical and numerical process and one that cannot be done in ordinary algebra4 ,we now have3 log #di4cgbd #a log #d log #a4b log #a4jb log #a4jjh log #a4jjjdc ,to compute log #a4jjjdc to #ba decimals we use 7 h h h h h 7 loge 7h - ---------- ---------- - -------- ---------- - ----------7 7 #b #c #d #e #f 7 with h #j4jjjdc4 ,only #f terms of the series relation are needed4 ,for1 the error is less than h_/#g1 which is less than #aj_/g1 since h _/4 ,the machine uses the series relation in the form log 7#a h7 77ch c7h ch ch c7h ch where c ,m1 c -,m_/#b1 c ,m_/#c1 1 and ,m loge #j4dcdbid4 ,the #f values of the c's are also stored in the machine4 ,when any logarithm is to be computed1 the sum of the characteristic1 of the #d logarithms of the successive divisors1 and of the first #f terms of the series relation gives the logarithm4 ,the maximum time required is #ij seconds4 ,,an ,,appraisal ,,of ,,the ,,calculator ,the ,,ibm ,automatic ,sequence-,controlled ,calculator at ,harvard is a landmark in the development of machines that think4 ,its capacity for many problems for which it is suited is far beyond the capacity of a hundred human computers4 ,speed ,the time required in the machine for adding1 subtracting1 transferring1 or clearing numbers is _/ of a second4 ,this is the time of one machine cycle or of reading one coding line4 ,multiplication takes at the most #f seconds1 and an average of #d seconds4 ,division takes at the most #af seconds1 and an average of #aa seconds4 ,each1 however1 requires only #c lines of coding1 or _/ of a second's attention from the sequence mechanism2 interposed operations fill the rest of the time4 ,to calculate a logarithm1 an exponential1 or a sine to the full number of digits obtainable by means of the automatic subroutine takes at the most #ij1 #ff1 and #fj seconds1 respectively4 ,to get three #bd-;digit numbers from feeding a punch card takes second4 ,to punch a number takes from second up to #c seconds4 ,to print a number takes from #a seconds up to #g seconds4 ,cost and ,value ,the cost of the machine was somewhere near #c or #d hundred thousand dollars1 if we leave out some of the cost of research and development1 which would have been done whether or not this particular machine had ever been built4 ,a staff of #aj men1 consisting of #d mathematicians1 #d operators1 and #b maintenance men1 are needed to keep the machine running #bd hours a day4 ,this might represent1 if capitalized1 another #a or #b hundred thousand dollars4 ,if a capital value of #ejj1jjj is taken as equivalent to #ej1jjj a year1 then the cost of the machine in operation #bd hours a day is in the neighborhood of #aej a day or #f an hour4 ,the value of the machine1 however1 is very much greater4 ,if #ajj human beings with desk calculators were set to work #h hours a day at #a4ej an hour1 the cost would be #abjj a day1 or #h times as much4 ,yet it is very doubtful that the work they could produce would equal that turned out by the machine1 either in quality or quantity1 when the machine is well suited to the problem4 ,reliability ,by reliability we mean the extent to which the results produced by the machine can be relied on to be right4 ,the machine contains no built-in device for making its operations reliable4 ,so1 if we wish to check a multiplication1 for example1 we can do the multiplication a second time1 interchanging the multiplier and the multiplicand4 ,but if1 say1 digit #af of the product were not transferring correctly1 we would get the same wrong result both ways and we would not have a sufficient check4 ,thus1 when we set up a problem for the machine to do1 one of the big tasks we have is checking4 ,we have to work out ways of making sure that the result1 when we get it1 is right and ways of instructing the machine to make the tests we want4 ,this is not a new task4 ,whenever you or ,i set out to solve a problem1 we have to make sure--usually by doing the problem twice1 and preferably by doing it a different way the second time--that our answer1 when we get it1 is correct4 ,one of the chief tasks for the mathematician1 in making a sequence-control tape for the machine1 is to put into it sufficient checks to make sure that the results are correct4 ,we can use a number of different kinds of partial checks3 the check counter2 differences1 and smoothness 7see ,supplement #b72 watching the results printed on typewriter #a2 mathematical checks2 comparison with known specific values2 etc4 ,in actual experience on the machine1 human failures1 such as failure to state the problem exactly or failure to put it on the machine correctly1 have given about as much trouble as mechanical failures4 ,the machine operates without mechanical failure about #ij to #ie per cent of the time4 ,the balance of the time the machine is idle while being serviced or repaired4 ,the machine is serviced by mechanics trained and supervised at ,harvard4 ,often when we change the machine from one problem to another problem1 we find some kind of trouble4 ,consequently1 we need to work out in detail the first part of any calculation placed on the machine4 ,we then compare the results step by step with the results produced by the machine4 ,any mathematician working with the machine needs considerable training in order to diagnose trouble quickly and guide the maintenance men to the place where repair or replacement is needed4 ,once you find the trouble1 you can fix it easily4 ,without disturbing the soldered connections1 you can easily pull out from its socket a relay that is misbehaving and plug in a new relay4 ,with a screwdriver you can change a counter position--detach it from its socket and replace it by another one that is working correctly4 ,one 8bug0 that will long be remembered around the ,laboratory was a case involving a #e that would incorrectly come in to a number every now and then4 ,it did not happen often--only once in a while4 ,after a week of search the bug was finally located3 the insulation on a wire that carried a #e had worn through in one spot1 and once in a while this wire would shake against a post that could carry current and took in the #e6 ,efficiency ,in many respects1 this machine is efficient and well-balanced4 ,its reading and writing speed is close to its calculating speed4 ,we can punch or print a result on the average for every #aj additions or #a multiplications4 ,the memory of #gb numbers in the machine is extremely useful2 a smaller memory is a serious limitation on the achievements of a computing machine4 ,the machine can do many kinds of arithmetic and logic4 ,it is well educated and can compute automatically some rather complicated mathematical functions1 like logarithm or sine4 ,it has done difficult and important problems4 ,it has computed and tabulated 7see ,supplement #b7 ,bessel functions1 definite integrals1 etc4 ,it can solve differential equations 7see ,chapter #e7 and many other problems in mathematics1 physics1 and engineering4 ,on the other hand1 no calculator will ever again be built just like this one1 useful though it is4 ,electronic computing is easily #ajj times as fast as relay computing2 nearly every future calculator will do its computing electronically4 ,many other improvements will be made4 ,for example1 in this calculator1 there are #gb addition-subtraction mechanisms1 yet only one of these can be used at a time4 ,also1 the machine has only one combined multiply-divide unit4 ,so we have to organize any computation with few multiplications1 and with still fewer divisions1 for they take longer still4 ,until #aidg1 we had to organize any computation in this calculator into one single fixed sequence of operations4 ,in other words1 there was no way to move from one subroutine to another subroutine depending on some indication that turned up in our computation4 ,recently1 the ,harvard ,computation ,laboratory decided to remedy this condition and provided the ,subsidiary ,sequence ,mechanism equivalent to #aj subroutines of #bb lines of coding each4 ,these are on relays and plug wires and may be called for by the sequence-control tape or by each other4 ,this provision has added greatly to the efficiency of the calculator4 ,whatever else can be said about the ,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator1 it must be said that this was the first general-purpose mechanical brain using numbers in digit form and able to do arithmetic and logic in hundreds of thousands of steps one after another4 ,and great credit must go to ,professor ,howard ,h4 ,aiken of ,harvard and the men of ,international ,business ,machines ,corporation who made this great mechanical brain come into existence4 ,chapter #g ,,speed--#ejjj ,,additions ,a ,,second3 ,,moore ,,school',s ,,eniac 7,,electronic ,,numerical ,,integrator ,,and ,,calculator7 ,another of the giant brains that has begun to work is named ,,eniac4 ,this name comes from the initial letters of the full name1 ,electronic ,numerical ,integrator and ,calculator4 ,eniac was born in #aidb at the ,moore ,school of ,electrical ,engineering1 of the ,university of ,pennsylvania1 in ,philadelphia4 ,eniac's father was the ,ordnance ,department of the ,u4 ,s4 ,army1 which provided the funds to feed and rear the prodigy4 ,in the short space of four years1 ,eniac grew to maturity1 and in ,february #aidf he began to earn his own living by electronic thinking4 ,eniac promptly set several world's records4 ,he was the first giant brain to use electronic tubes for calculating4 ,he was the first one to reach the speed of #ejjj additions a second4 ,he was the first piece of electronic apparatus containing as many as #ah1jjj electronic tubes all functioning together successfully4 ,as soon as ,eniac started thinking1 he promptly made relay calculators obsolete from the scientific point of view1 for they have a top speed of perhaps #aj additions a second4 ,at the age of #e1 he moved to ,maryland at a cost of about #ij1jjj1 and his permanent home is now the ,ballistic ,research ,laboratories at the ,u4 ,s4 ,army's ,proving ,ground at ,aberdeen1 ,md4 ,,origin ,,and ,,development ,in the ,department of ,terrestrial ,magnetism in the ,carnegie ,institution of ,washington1 a great deal of information about the earth is studied4 ,many kinds of physical observations are there gathered and analyzed3 electricity in the atmosphere1 magnetism in the earth1 and the weather1 for example4 ,in #aida1 a physicist1 ,dr4 ,john ,w4 ,mauchly1 was thinking about the great mass of numerical information they had to handle4 ,he became convinced that much swifter ways of handling these numbers were needed4 ,he was certain electronic devices could be used for computing at very high speeds1 yet he found no one busy applying electronics in this field4 ,with hopes of finding some way of developing electronic computing1 he joined the staff of the ,moore ,school of ,electrical ,engineering in the autumn of #aida4 ,the ,moore ,school in #aicd and #aice had built a differential analyzer2 and1 from that time on1 the school had made a number of improvements in it4 ,in #aida1 with war imminent1 the differential analyzer was put hard at work calculating tables for the ,army's ,ballistic ,research ,laboratories4 ,these tables were mostly firing tables1 tables of the paths along which projectiles travel when fired--trajectories2 obviously1 you cannot fire a gun usefully1 unless you know how to aim it4 ,the amount of calculation of trajectories was so huge that ,dr4 ,mauchly suggested that a machine using electronic tubes be constructed to calculate them4 ,a good deal of discussion took place between men at the ,moore ,school1 men at the ,ballistic ,research ,laboratories1 and men from the ,ordnance ,department in ,washington4 ,a contract for research into an electronic trajectory computer was concluded with the ,ordnance ,department of the ,u4 ,s4 ,army4 ,mauchly and one of the young electronics engineers studying at ,moore ,school1 ,j4 ,presper ,eckert1 ,jr41 set to work on the design4 ,gradually the design of a machine took form1 and the crucial experiments on equipment were completed4 ,in #aidc1 the design was settled as a special-purpose machine to calculate trajectories4 ,later on1 the group modified the plans here and there to enable the machine to calculate a very wide class of problems4 ,a group of ,moore ,school electronics engineers and technicians during #aidd and #aide built the machine1 using as much as possible standard radio tubes and parts4 ,here1 again1 in spite of the successful progress of the electronic machine1 the rumor that it was a 8white elephant0 was allowed to spread in order to protect the work from prying enemy ears4 ,,general ,,organization ,the main part of ,eniac consists of #db panels1 which are placed along the sides of a square ,u4 ,each of these panels is #i feet high1 #b feet wide1 and #a foot thick4 ,they are of sheet steel1 painted black1 with switches1 lights1 etc41 mounted on them4 ,at the tops of all the panels are air ducts for drawing off the hot air around the tubes4 ,large motors and fans above the machine suck the heated air away through the ducts4 ,there are also #e pieces of equipment which can be rolled from place to place and are called portable1 but there is no choice as to where they can be plugged in4 ,we shall call this equipment panels #dc to #dg4 ,panels ,now what are these panels1 and what do they do8 ,each panel is an assembly of some equipment4 ,the names of the panels are shown in the accompanying table4 ,the arrangement of ,eniac at the ,ballistic ,research ,laboratories as shown in the table is slightly different from the arrangement of ,eniac at ,moore ,school4 ,,names ,,of ,,panels ,,of ,,eniac ,,panel ,,no4 ,,name 7,,and ,,additional ,,names ,,in ,,some ,,cases7 #a ,initiating ,unit #b ,cycling ,unit #c1 #d ,master ,programmer1 panels #a1 #b #e ,accumulator #a #f ,accumulator #b #g ,accumulator #c #h ,accumulator #d 7,quotient7 #i ,divider-,square-,rooter #aj ,accumulator #e 7,numerator ,i7 #aa ,accumulator #f 7,numerator ,,ii7 #ab ,accumulator #g 7,denominator--,square ,root ,i7 #ac ,accumulator #h 7,denominator--,square ,root ,,ii7 #ad ,accumulator #i 7,shift ,i7 #ae ,accumulator #aj 7,shift ,,ii7 #af ,blank panel for new unit 7,converter7 #ag ,accumulator #aa 7,multiplier7 #ah ,accumulator #ab 7,multiplicand7 #ai-ba ,multiplier1 panels #a1 #b1 #c #bb ,accumulator #ac 7,left-,hand ,partial ,products ,i7 #bc ,accumulator #ad 7,left-,hand ,partial ,products ,,ii7 #bd ,accumulator #ae 7,right-,hand ,products ,i7 #be ,accumulator #af 7,right-,hand ,products ,,ii7 #bf ,blank panel for new unit 7#ajj ,registers7 #bg ,accumulator #ag #bh ,accumulator #ah #bi ,accumulator #ai #cj ,accumulator #bj #ca1 #cb ,function ,table #a1 panels #a1 #b #cc1 #cd ,function ,table #b1 panels #a1 #b #ce1 #cf ,function ,table #c1 panels #a1 #b #cg-ci ,constant ,transmitter1 panels #a1 #b1 #c #dj-db ,printer1 panels #a1 #b1 #c #dc-de ,portable ,function ,tables ,a1 ,b1 and ,c #df ,,ibm ,card ,reader #dg ,,ibm ,summary ,punch ,note3 ,the accumulators from which a number can be sent to the printer are now accumulators #a1 #b1 and #ae to #bj4 ,in reading over the table1 we find a number of words that need explaining4 ,some of the explanation we can give in the summary of the units of ,eniac3 ,,summary ,,of ,,units ,,of ,,eniac ,,quantity ,,device ,,significance #bj ,accumulators ,store1 add1 and subtract numbers #a ,multiplier ,multiplies #a ,divider-,square-,rooter ,divides1 and obtains twice the square root of a number 7see ,supplement #b7 #c ,function ,tables ,part of the memory1 for referring to tables of numbers #a ,constant ,transmitter ,stores numbers from the card reader and from hand-set switches #a ,printer ,punches machine results into cards #a ,cycling ,unit ,controls the timing of the various parts of the machine #a ,initiating ,unit ,has controls for starting a calculation1 for clearing1 etc4 #a ,master ,programmer ,holds the chief controls for coordinating the various parts of the machine ,an accumulator is a storage counter4 ,it can hold a number2 it can clear a number2 it can transmit a number either positively or negatively2 and it can receive a number by adding the number in and thus holding the sum of what it held before and the number received4 ,eniac when first built had only #bj accumulators1 and so it could remember only #bj numbers at one time 7except for constant numbers set in switches74 ,this small memory was the most serious drawback of ,eniac2 panel #bf was designed1 therefore1 to provide a great additional memory capacity4 ,the divider-square-rooter1 as its name tells1 is a mechanism that can divide and that can find twice the square root of a number4 ,eniac is one of the several giant brains that have had square root capacity built into them1 particularly since square root is needed for solving trajectories4 ,many panels of ,eniac have double duty and some have triple duty4 ,for example1 panel #bd is an accumulator1 but it also 7#a7 stores the right-hand partial products 7see ,supplement #b7 of the multiplier and 7#b7 was a register1 when ,eniac was at ,moore ,school1 from which information to be punched in the printer could be obtained4 ,clearly1 if we have a multiplication to do1 we cannot also use this accumulator for storing a number that is to remain unchanged during the multiplication4 ,parts ,the total number of parts in ,eniac is near half a million1 even if we count electronic tubes as single parts4 ,there are over #ah1hjj electronic tubes in the machine4 ,it is interesting to note that only #aj kinds of electronic tubes are used in the calculating circuits and only about #fj kinds of resistors and #cj kinds of capacitors4 ,a resistor is a device that opposes the steady flow of electric current through it to a certain extent 7called resistance and measured in ohms74 ,a capacitor is a device that can store electrical energy up to a certain extent 7called capacitance and measured in farads74 ,all these tubes and parts are standard parts in radios4 ,all types are identified by the color labels established in standard radio manufacturing4 ,it is the combinations of these parts1 like the combinations of pieces in a chess game1 that give rise to the marvelous powers of ,eniac4 ,the combinations of parts at the first level are called plug-in units4 ,a plug-in unit is a standard box or tray or chassis made of sheet steel containing a standard assembly of tubes1 wires1 and other parts4 ,it can be pushed in or pulled out of a standard socket with many connections4 ,an example of a plug-in unit is a decade1 or1 more exactly1 an accumulator decade4 ,this is just a counter wheel or decimal position expressed in ,eniac language3 it can express successively all the digits from #j to #i and then pass from #i to #j1 giving rise to a carry impulse4 ,it is striking that a mechanical counter to hold #aj digits can be made up of #aj little wheels1 inch wide and an inch high4 ,but an accumulator in ,eniac1 to hold #aj digits1 is a set of #aj decades each #b inches wide and #b feet high4 ,there are only about #bj kinds of plug-in units altogether4 ,each plug-in unit is interchangeable with any other of the same kind4 ,so1 if a decade1 for example1 shows trouble1 you can pull it out of its socket and plug in a spare decade instead4 ,numbers ,numbers in ,eniac are of #aj decimal digits with a sign that may be plus or minus4 ,the decimal point is fixed4 ,however1 when you are connecting one accumulator with another1 you can shift the decimal point if you want to4 ,also1 #b accumulators may be coupled together so as to handle numbers of #bj digits4 ,,how ,,information ,,goes ,,into ,,the ,,machine ,there are three ways by which information--numbers or instructions--can go into the ,eniac4 ,numbers can be put into the machine by means of punch cards fed into the ,card ,reader1 panel #df1 or switches on the ,constant ,transmitter1 panels #cg to #ci4 ,numbers or instructions can also go into the machine by means of the ,function ,tables1 panels #dc to #de4 ,here there are dial switches1 which are set by hand4 ,instructions can also go into the machine by setting the switches1 plugging the inputs and outputs1 etc41 of the wires or lines along which numbers and instructions travel4 ,,how ,,information ,,comes ,,out ,,of ,,the ,,machine ,there are two ways by which numerical information can come out of the machine4 ,numbers can come out of the machine punched on cards by the ,summary ,punch1 panel #dg4 ,they are then printed in another room by means of a separate ,,ibm tabulator4 ,also1 numbers can be read out of the machine by means of the lights in the neon bulbs mounted on each accumulator4 ,you can read in the lights of a panel the number held by the accumulator1 if the panel is not computing4 ,,how ,,information ,,is ,,manipulated ,,in ,,the ,,machine ,eniac handles information rather differently from any other of the big brains4 ,instead of having only one bus or 8railroad line0 along which numbers can be sent1 ,eniac has more than #aj such lines4 ,they are called digit trays and labeled ,a1 ,b1 ,c1 4 ,each contains #aa digit trunk lines or digit trunks--#aj to carry the digits of a number1 and the #aath to carry the sign4 ,instead of having only one telegraph line along which instructions can be sent1 ,eniac has more than #ajj such lines4 ,they are called program trunk lines or program trunks and labeled ,a#a1 ,a#b1 1 ,a#aa1 ,b#a1 ,b#b1 1 ,b#aa1 1 etc4 ,they are assembled in groups of #aa to a tray2 the program trays1 in fact1 look just like the digit trays1 except for their connectors and their purpose1 which are different4 ,below1 we shall make clear how the program trays carry control information4 ,now1 actually1 ,eniac has many more trunk lines than we have just stated1 for each of the lines we have mentioned can be divided into numerous separate sections by the removal of plug connections4 ,how we choose to do this depends on the needs of the problem1 the space between the panels1 the time when the line is used1 etc4 ,transferring ,numbers1 ,adding1 and ,subtracting ,basically1 a number is represented in ,eniac by an arrangement of on and off electronic tube elements in pairs1 called flip-flops4 ,there is one flip-flop enclosed in a single tube 7type #f,,sn#g7 for each value #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i for each of the #aj digits stored in an accumulator4 ,so we have at least #ajj flip-flops for each accumulator1 and thus at least #ajj electronic tubes are required to store #aj digits4 ,actually1 an accumulator needs #eej electronic tubes4 ,so we see that there is not very much of a future in this type of arrangement4 ,the newer electronic brains use different devices for storage of numbers4 ,in order to show what number is stored in an accumulator1 there are #ajj little neon bulbs mounted on the face of each accumulator panel4 ,each bulb glows when the flip-flop that belongs to it is on4 ,for example1 suppose that the #dth decade in ,accumulator #aa holds the digit #g4 ,then the #gth flip-flop in that decade will be on1 and all the others will be off4 ,the #gth neon bulb for that decade will glow4 ,now suppose that the number #g is in the #dth decade in ,accumulator #aa and is to be added into1 say1 the #dth decade in ,accumulator #ac4 ,and suppose that it is to be subtracted from the #dth decade in ,accumulator #af4 ,what do we do1 and what will ,eniac do8 ,first1 we pick out #b digit trays1 say ,b and ,d4 ,accumulator #aa has #b outputs1 called the add output and the subtract output4 ,we plug ,b into the add output and ,d into the subtract output4 ,then we go over to ,accumulators #ac and #af4 ,they have #e inputs1 that is1 #e ways of being plugged to receive numbers from digit trunks4 ,these inputs are named with ,greek letters1 1 1 1 1 4 ,we choose one input1 say 1 for ,accumulator #ac1 and we plug ,b into that input4 ,we choose one input1 say 1 for ,accumulator #af1 and we plug ,d into that input4 ,now we have the 8railroad0 switching for numbers accomplished4 ,we have set up a channel whereby the number in ,accumulator #aa will be routed positively into ,accumulator #ac and negatively into ,accumulator #af4 ,now let us suppose that1 at some definite time fixed by the control1 ,accumulator #aa is stimulated to transmit and ,accumulators #ac and #af are conditioned to receive4 ,when this happens1 a group of #aj pulses comes along a direct trunk from the cycling unit1 and a group of #i pulses comes along another trunk4 ,we can think of each pulse as a little surge of electricity lasting about #b millionths of a second4 ,the ten-pulses1 as the first group is called1 are #aj millionths of a second apart4 ,the nine-pulses1 as the second group is called1 are also #aj millionths of a second apart but are sandwiched between the ten-pulses4 ,when the #ast ten-pulse comes along1 the #gth flip-flop in ,accumulator #aa goes off1 the #hth flip-flop goes on1 the following nine-pulse goes through and goes out on the subtract line to ,accumulator #af4 ,then the #bnd ten-pulse comes along1 the #hth flip-flop goes off1 the #ith flip-flop goes on1 and the next nine-pulse goes out on the subtract line to ,accumulator #af4 ,now the decade sits at #i1 and for this reason the next ten-pulse changes an electronic switch 7actually another flip-flop7 so that all later nine-pulses will go out on the add line4 ,this ten-pulse also turns off the #ith flip-flop and turns on the #jth flip-flop without causing any carry4 ,now the #dth of the ten-pulses comes along1 turns the #jth flip-flop off1 and turns the #ast flip-flop on1 and the next nine-pulse goes out on the add line to ,accumulator #ac4 ,the next #f of the ten-pulses then come along and change ,accumulator #aa back to the digit #g as before1 and the next #f of the nine-pulses go out to ,accumulator #ac4 ,thus ,eniac has added #g into ,accumulator #ac1 has added #b1 the nines complement of #g 7see ,supplement #b71 into ,accumulator #af1 and has left ,accumulator #aa holding the same number as before4 ,this is just the result that we wanted4 ,in this way1 the nines complement of any digit in a decade is transferred out along the subtract line1 and the digit unchanged is transmitted out along the add line4 ,as the pulses arrive at any other accumulator1 they add into that accumulator4 ,multiplying and ,dividing ,eniac performs multiplication by a built-in table of the products in the #aj-;by-#aj multiplication table1 using the method of left-hand components and right-hand components 7see ,supplement #b74 ,for example1 suppose that the #crd digit of the multiplier is #g and that the #eth digit of the multiplicand is #f4 ,then1 when ,eniac attends to the #crd digit of the multiplier1 the right-hand digit of the #db #f #g is gathered in one accumulator1 and the left-hand digit #d is gathered in another accumulator4 ,after ,eniac has attended to all the digits of the multiplier1 then ,eniac performs one more addition and transfers the sum of the left-hand digits into the right-hand digits accumulator4 ,eniac does division in rather a novel way4 ,first1 the divisor is subtracted over and over until the result becomes negative or #j4 ,then the machine shifts to the next column and adds the divisor until the result becomes positive or #j4 ,it continues this process1 alternating from column to column4 ,for example1 suppose that we divide #c into #hd in this way4 ,we have3 #c 7 #hd 7 #cb -#c ---- #ed -#c ---- #bd -#c ---- -#f #c ---- -#c #c ---- #j ,after we subtract #c the third time1 the result becomes negative1-#f2 in the next column1 after we add #c twice1 the result becomes #j4 ,the quotient is #cb1 which is the same as #cj - #b1 or #bh2 and #c #bh is #hd4 ,thus the process checks4 ,consulting a ,table ,eniac has three ,function ,tables4 ,here you can store numbers or instructions for the machine to refer to4 ,each ,function ,table has #ajd arguments 7see ,supplement #b74 ,for each argument1 you can store #ab digits and #b signs that may be plus or minus4 ,this capacity can be devoted to one #ab-;digit number with a sign1 or to two #f-;digit numbers each with a sign1 or to six #b-;digit instructions4 ,the three ,function ,tables are panels #dc1 #dd1 and #de4 ,to put in the numbers or instructions1 you have to go over to these panels and set the numbers or instructions1 digit by digit1 turning dial switches by hand4 ,it is slow and hard to do this right1 but once it is done1 ,eniac can refer to any number or instruction in any table in _/ of a second4 ,this is much faster than the table reference time in any other of the giant brains built up to #aidh4 ,programming ,we said above that ,eniac has over #ajj control lines or program trunks along which instructions can be sent4 ,these instructions are expressed as pulses called program pulses4 ,now how do we make these pulses do what we want them to do8 ,for example1 how can we instruct ,accumulator #aa to add what it holds into ,accumulator #ac8 ,on each unit of ,eniac there are plug hubs or sockets 7called program-pulse input terminals7 to which a program trunk may be connected4 ,a program pulse received here can make the unit act in some desired way4 ,on each accumulator of ,eniac1 we find #ab program-pulse input hubs4 ,corresponding to each of these hubs1 there is a nine-way switch1 called a program-control switch4 ,the setting of this switch determines what the accumulator will do when the program-pulse input hub belonging to the switch receives a program pulse4 ,for instance1 there are switch settings for3 receive input on the line1 receive input on the line1 etc42 and transmit output on the add line1 etc4 ,there is even a switch setting that instructs the accumulator to do nothing1 and this instruction may be both useful and important4 ,now1 in order that ,accumulator #aa may transfer a number to ,accumulator #ac1 we need3 7#a7 a digit tray1 say ,b1 for the number to travel along2 7#b7 a program trunk line1 say ,g#c1 to tell ,accumulator #aa when to send the number and ,accumulator #ac when to receive it2 and 7#c7 certain plugging as follows3 #a4 ,we plug from program trunk ,g#c into a program-pulse input hub1 say ,no4 #e1 of ,accumulator #aa2 #b4 ,we plug from the same program trunk ,g#c into a program-pulse input hub1 say ,no4 #g1 of ,accumulator #ac2 #c4 ,we set program-control switch ,no4 #e of ,accumulator #aa to 8add02 #d4 ,we set program-control switch ,no4 #g of ,accumulator #ac to some input1 say 4 #e4 ,we plug from digit tray ,b into the add output of ,accumulator #aa4 #f4 ,we plug from digit tray ,b into the input of ,accumulator #ac4 ,now1 when the program pulse comes along line ,g#c1 it makes ,accumulator #ac transmit additively along digit tray ,b into ,accumulator #ac4 ,and that is the result that we wanted4 ,as each mechanism of ,eniac finishes what it is instructed to do1 it may or may not put out a program pulse4 ,this pulse in turn may be plugged into any other program trunk line and may stimulate another mechanism to act4 ,then1 when this mechanism finishes1 it too may or may not put out a program pulse1 and so on4 ,in general1 there are two different ways to instruct ,eniac to do a problem4 ,one way is to set all the switches1 plug all the connections1 etc41 for the specific problem4 ,this is a long and hard task4 ,very often1 even with great care1 it is done not quite correctly1 and then the settings must be carefully checked all over again4 ,a second method 7called the von ,neumann programming method7 is to store all the instructions for a problem in one or two function tables of ,eniac and then tell ,eniac to read the function tables in sequence and to do what they say4 ,the rest of the machine is then wired up in a standard fashion4 ,this method of instructing ,eniac was proposed by ,dr4 ,john von ,neumann of the ,institute of ,advanced ,study at ,princeton1 ,n4 ,j4 ,eniac has been modified to the slight extent needed so that this method can be used when desired4 ,in this method1 each instruction is a selected one of #fj different standard instructions or orders--one of them1 for example1 being 8multiplication40 ,each standard order is expressed by #b decimal digits4 ,the #fj standard orders are sufficient so that ,eniac can do any mathematical problem that does not overstrain its capacity4 ,since each of the #c ,function ,tables can hold #fjj #b-;digit instructions1 the machine can hold a program of #ahjj instructions under the von ,neumann programming method4 ,,an ,,appraisal ,,of ,,eniac ,,as ,a ,,computer ,as a general-purpose calculating machine1 ,eniac suffers from unbalance4 ,that is to say1 ,eniac operates rapidly and successfully in some respects1 and slowly and troublesomely in other respects4 ,this is altogether to be expected1 however1 in a calculator as novel as ,eniac and made to so large an extent out of standard radio parts4 ,it was certainly better to finish a calculator like this one and then start on a new one1 as the ,moore ,school of ,electrical ,engineering did1 than to prolong design and construction indefinitely in order to make improvements4 ,speed ,eniac adds or subtracts very swiftly at the rate of #ejjj a second4 ,eniac multiplies at the rate of #cfj to #ejj a second4 ,division1 however1 is slow1 relatively2 the rate is about #ej a second4 ,reading numbers from punched cards1 #ab a second for #aj-;digit numbers1 is even slower4 ,as a result of these rates1 you find1 when you put a problem on ,eniac1 that one division delays you as long as #ajj additions or #h multiplications4 ,division might have been speeded somewhat by 7#a7 rapidly convergent approximation 7see ,supplement #b7 to the reciprocal of the divisor and 7#b7 multiplying by the dividend2 this might have taken #e or #f multiplication times instead of #h4 ,also1 the use of a standard ,,ibm punch-card feed and card punch slows the machine greatly4 ,one way to overcome this drawback might be to install one or two additional sets of such equipment1 which might increase input and output speed4 ,ease of ,programming ,eniac has a very rapid and flexible automatic control over the programming of operations4 ,eniac has more than #aj channels along which numbers can be transferred and more than #ajj channels along which program-control pulses can be transferred4 ,there are many ways for providing subroutines4 ,eniac has the additional advantage that there is no delay in giving the machine successive instructions3 all the instructions the machine may need at any time are ready at the start of the problem1 and indications occurring in the calculation can change the routine completely4 ,all these advantages1 however1 are paid for rather heavily by the slow methods for changing programming4 ,you have to plug large numbers of program trunk lines and digit trunk lines1 or you have to set large numbers of switches1 or both4 ,also1 when you wish to return to a previous problem1 you must do all the plugging and switch setting over again4 ,many delays in the operation of the machine are due to human errors in setting the machine for a new problem4 ,here again1 we must remember that ,eniac was originally designed as a special-purpose machine for solving trajectories4 ,to calculate a large family of trajectories very little changing of wires and switches would be needed4 ,memory ,the most severe limitation on the usefulness of ,eniac was1 at the outset1 the fact that it had only #bj registers for storing numbers4 ,there are large numbers of problems that cannot be simply handled with so small an internal memory4 ,even the ,harvard ,,ibm calculator 7see ,chapter #f7 is often strained during a problem because of the number of intermediate results that must be stored for a time before combining4 ,the ,ballistic ,research ,laboratories1 however1 contracted for extensions to ,eniac to provide more memory and easier changing of instructions4 ,reliability ,checking results with ,eniac is not easy4 ,there is no built-in guarantee that ,eniac's results are correct4 ,a large calculator can and does make both constant and intermittent errors4 ,ways for checking with ,eniac are3 ,mathematical1 if and when available1 and this will be seldom4 ,running the problem a second time1 and this will1 at most1 prove consistency4 ,deliberate testing of small parts of the problem1 which is very useful and is standard practice but leads only to a probability that the final result is correct4 ,you can operate ,eniac one addition at a time1 and even one pulse at a time1 and see what the machine shows in its little neon bulbs4 ,this is a very useful partial check4 ,cost ,the cost of ,eniac is higher than that of some of the other large mechanical brains--over half a million dollars4 ,because some of the work was done at the ,moore ,school by students1 the cost was probably less than it otherwise would have been4 ,the largest part of the cost was the designing of the machine and the construction of the panels2 the tubes were only a small portion of the cost4 ,the tubes used in the calculating circuits cost only #bj to #ij cents4 ,however1 no later electronic calculator need cost as much1 for many improvements can now be seen4 ,the power required for ,eniac is about #aej kilowatts or about #bjj horsepower1 most of which is used for the heaters of the electronic tubes4 ,the largest number of electronic tubes mentioned for future electronic calculators is about #cjjj1 so we can see that they are likely to use less than a quarter of the power needed for ,eniac4 ,eniac will doubtless give a number of years of successful operation and be extremely useful for problems that employ its assets and are not excluded by its limitations4 ,in fact1 at the ,ballistic ,research ,laboratories1 for a typical week of actual work1 ,eniac has already proved to be equal to #ejj human computers working #dj hours with desk calculating machines1 and it appears that soon two or three times as much work may be obtained from ,eniac4 ,chapter #h ,,reliability--,,no ,,wrong ,,results3 ,,bell ,,laboratories' ,,general-,,purpose ,,relay ,,calculator ,in #aidf1 ,bell ,telephone ,laboratories in ,new ,york finished two general-purpose relay calculators--mechanical brains4 ,they were twins4 ,one was shipped in ,july #aidf to the ,national ,advisory ,committee for ,aeronautics at ,langley ,field1 ,virginia4 ,the other1 after some months of trial operation1 was shipped in ,february #aidg to the ,ballistic ,research ,laboratories at the ,u4 ,s4 ,army's ,proving ,ground1 ,aberdeen1 ,md4 ,each machine is remarkably reliable and versatile4 ,it can do a wide variety of calculations in a great many different ways4 ,yet the machine never takes a new step without a check that the old step was correctly performed4 ,there is1 therefore1 a chance of better than #ii4iii1iii1iii per cent that the machine will not let a wrong result come out4 ,the automatic checking1 of course1 does not prevent 7#a7 human mistakes--for example1 instructing the machine incorrectly--or 7#b7 mechanical failures1 in which the machine stops dead in its tracks1 letting no result at all come out4 ,,origin ,,and ,,development ,in ,bell ,telephone ,laboratories the telephone system of the country is continually studied4 ,their research produced the common type of dial telephone system3 a masterly machine for selecting information4 ,now when a telephone engineer studies an electric circuit1 he often finds it very convenient to use numbers in pairs3 like #b1 #e or-#d1-a4 ,here the comma is a separation sign to keep the two numbers in the pair separate and in sequence4 ,mathematicians call numbers of this kind1 for no very good reason1 complex numbers2 of course1 they are far less complex than why the sun shines or why plants grow4 ,when ,bell ,laboratories test the design of new circuits1 girl computers do arithmetic with complex numbers4 ,addition and subtraction are easy3 each means two operations of addition or subtraction of ordinary numbers4 ,for example1 #b1 #e1 plus-#d1-a equals #b-d1 #e-a1 which equals-#b1 #d4 ,and #b1 #e minus-#d1-a is the same as #b1 #e plus #d1 #a2 and this equals #b #d1 #e #a1 which equals #f1 #f4 ,multiplication of two complex numbers1 however1 is more work4 ,if a1 b and c1 d are two complex numbers1 then the formula for their product is 7a c7-7b d71 7a d7 7b c74 ,to get the answer1 we need #d multiplications1 #a subtraction1 and #a addition4 ,division of two complex numbers requires even more work4 ,if a1 b and c1 d are two complex numbers1 the formula for the quotient of a1 b divided by c1 d is3 7a c7 7b d7 7c c7 7d d71 7b c7 - 7a d7 7c c7 7d d7 ,for example1 7#b1 #e7 7-#d1 -#a7 7#b -#d -#h7 7#e -#a -#e7 7-#d -#d #af7 7-#a -#a #a71 7#e -#d -#bj7 - 7#b -#a -#b7 #af #a -7_/71 -7_/7 ,thus1 division of one complex number by another needs #f multiplications1 #b additions1 #a subtraction1 and #b divisions of ordinary numbers--and always in the same pattern or sequence4 ,the ,complex ,computer ,about #aici1 an engineer at ,bell ,telephone ,laboratories in ,new ,york1 ,dr4 ,george ,r4 ,stibitz1 noticed the great volume of this pattern arithmetic4 ,he began to wonder why telephone switching equipment could not be used to do the multiplications and divisions automatically4 ,he decided it could4 ,all that was necessary was that the relays 7see ,chapter #b7 used in regular telephone equipment should have a way of remembering and calculating with numbers4 ,regular telephone equipment would take care of the proper sequence of operations4 ,regular equipment known as teletypewriters would print the numbers of the answer when it was obtained4 ,a teletypewriter consists essentially of a typewriter that may be operated by electrical impulses4 ,it has a keyboard that may produce electrical impulses in sets corresponding to letters2 and it can receive or transmit over wires4 ,dr4 ,stibitz coded the numbers3 each decimal digit was matched up with a group of four relays in sequence1 and each of these relays could be open or closed4 ,if #j means open and #a means closed1 here is the pattern or code that he used3 ,,decimal ,,digit ,,relay ,,code #j #j #j #a #a #a #j #a #j #j #b #j #a #j #a #c #j #a #a #j #d #j #a #a #a #e #a #j #j #j #f #a #j #j #a #g #a #j #a #j #h #a #j #a #a #i #a #a #j #j ,with regular telephone relays and regular telephone company techniques1 ,dr4 ,stibitz and ,bell ,telephone ,laboratories designed and constructed the machine4 ,it was called the ,complex ,computer and was built just for multiplying and dividing complex numbers4 ,six or eight panels of relays and wires were in one room4 ,two floors away1 some of the girl computers sat in another room1 where one of the teletypewriters of the machine was located4 ,when they wished1 they could type into the machine's teletypewriter the numbers to be multiplied or divided4 ,in a few seconds back would come the answer4 ,in fact1 there were two more computing rooms where teletypewriters of the machine were stationed4 ,to prevent conflicts between stations1 the machine had a circuit like the busy signal from a telephone4 ,in #aidj1 a demonstration of the ,complex ,computer took place3 the computing panels remained in ,new ,york1 but the teletypewriter input-output station was set up at ,dartmouth ,college in ,hanover1 ,n4 ,h4 ,mathematicians gave problems to the machine in ,dartmouth1 it solved them in ,new ,york1 and it reported the answers in ,dartmouth4 ,special-,purpose ,computers ,with this as a beginning1 ,bell ,laboratories developed another machine for a wide variety of mathematical processes called interpolating 7see ,supplement #b74 ,then1 during ,world ,war ,,ii1 ,bell ,laboratories made more special-purpose computing machines4 ,they were used in military laboratories charged with testing the accuracy of instruments for controlling the fire of guns4 ,these computers took in a set of gun-aiming directions put out by the fire-control instrument in some test4 ,they also took in the set of observations that went into the fire-control instrument on that test4 ,then they computed the differences between the gun-aiming produced by the fire-control instrument and the gun-aiming really required by the observations4 ,using these differences1 the fire-control instrument could be adjusted and corrected4 ,these special-purpose computers were also useful in checking the design of new fire-control instruments and in checking changes due to new types of guns or explosives4 ,regularly1 after each of these special-purpose computers was finished1 people began to put other problems on it4 ,it seemed to be fated that1 as soon as you had made a machine for one purpose1 you wanted to use it for something else4 ,accordingly1 in #aidd1 two agencies of the ,u4 ,s4 ,government together made a contract with ,bell ,telephone ,laboratories for two general-purpose relay computers4 ,these two machines were finished in #aidf and are twins4 ,,organization ,,of ,,the ,,general-,,purpose ,,computer ,when a man sits down at a desk to work on a computation1 he has six things on his desk to work with3 a work sheet2 a desk calculator1 to add1 subtract1 multiply1 and divide2 some rules to be followed2 the tables of numbers he will need2 the data for the problem2 and an answer sheet4 ,in his head1 he has the capacity to make decisions and to do his work in a certain sequence of steps4 ,these seven subdivisions of calculation are all found in the ,bell ,laboratories' general-purpose relay computer4 ,the general-purpose computer is a computing system1 in fact1 more than it is a single machine4 ,the part of the system which does the actual calculating is called1 in the following paragraphs1 the computer1 or else1 since it is in two halves1 ,computer #a and ,computer #b4 ,physical ,units ,the computing system delivered to the ,ballistic ,research ,laboratories fills a room about #cj by #dj feet and consists of the following3 #b computers3 panels of relays1 wiring1 etc41 which add1 subtract1 multiply1 divide1 select1 decide1 control1 etc4 #d problem positions3 tables each holding #ab mechanisms for feeding paper tape1 which read numbers and instructions punched on tape and convert them into electrical impulses4 #b hand perforators3 keyboard devices for punching instructions and numbers on paper tape4 #a processor3 a table holding mechanisms for feeding #b paper tapes and punching a third paper tape1 used for checking numbers and instructions punched on tape4 #b recorders3 each a table holding a teletypewriter1 a tape punch1 and a tape feed1 used for recording answers and1 if necessary1 consulting them again4 ,the #b computers correspond to the work sheet1 the desk calculator1 and the man's capacity to make decisions and to carry out a sequence of steps4 ,the #d problem positions correspond to the problem data1 the rules1 and the tables of numbers4 ,the #b recorders correspond to the answer sheet4 ,the #b hand perforators and the processor are auxiliary machines3 they translate the ordinary language of arithmetic into the machine language of punched holes in paper tape4 ,this is the computing system as organized for the ,ballistic ,research ,laboratories at ,aberdeen4 ,the one for the ,national ,advisory ,committee for ,aeronautics has only #c problem positions4 ,the computer system may1 in fact1 be organized with #a to #aj computers and with #a to #bj problem positions4 ,the great bulk of this computing system1 like the mechanical brains described in previous chapters1 is made up of large numbers of identical parts of only a few kinds4 ,these are3 standard telephone relays2 wire2 and standard teletype transmitters1 mechanisms that read punched paper tape and produce electrical impulses4 ,numbers ,the numbers that the ,bell machine contains range from #j4ajjjjjj to #j4iiiiiii times a power of #aj varying from #aj1jjj1jjj1jjj1jjj1jjj1jjj to #j4jjj1jjj1jjj1jjj1jjj1jjj1a1 or1 in other words1 from #aj to #aj4 ,the machine also contains zero and infinity3 zero arises when the number is smaller than #aj1 and infinity arises when the number is equal to or greater than #i1iii1iii1jjj1jjj1jjj1jjj4 7,see ,supplement #b47 ,the system used in the machine to represent numbers on relays is called biquinary--the bi-1 because it is partly twofold like the hands1 and the -quinary because it is partly fivefold like the fingers4 ,this system is used in the abacus 7see ,chapter #b and ,supplement #b74 ,in the machine1 for each decimal digit1 #g relays are used4 ,these relays are called the #jj and #e relays1 and the #j1 #a1 #b1 #c1 and #d relays4 ,if1 as before1 #j indicates a relay that is not energized and #a indicates a relay that is energized1 then each decimal digit is represented by the positioning of the #g relays as follows3 ,,decimal ,,digit ,,relays #jj #e #j #a #b #c #d #j #a #j #a #j #j #j #j #a #a #j #j #a #j #j #j #b #a #j #j #j #a #j #j #c #a #j #j #j #j #a #j #d #a #j #j #j #j #j #a #e #j #a #a #j #j #j #j #f #j #a #j #a #j #j #j #g #j #a #j #j #a #j #j #h #j #a #j #j #j #a #j #i #j #a #j #j #j #j #a ,then1 for any decimal digit1 one and only one of the #jj and #e relays is energized1 and one and only one of the #j1 #a1 #b1 #c1 and #d relays is energized4 ,if more or less than exactly one relay in each set is energized1 then the machine knows that it has made a mistake1 and it stops dead in its tracks4 ,thus any accidental failure of a relay is at once caught1 and the chance of two compensating failures occurring at the same time is extremely small4 ,,how ,,information ,,goes ,,into ,,the ,,machine ,in order to put a problem into this machine--just as with the other machines--first a mathematician who knows how the problem is to be solved1 and who knows how to organize it for the machine1 lays out the scheme of calculation4 ,then1 a girl goes to one of the hand perforators4 ,sitting at the keyboard1 she presses keys and punches out feet or yards of paper tape expressing the instructions and numbers for the calculation4 ,each character punched--digit1 letter1 or sign--has one or more of a maximum of #f holes across the tape4 ,another girl1 using the other hand perforator1 also punches out the instructions and numbers for the calculation4 ,if she wishes to erase a wrong character1 she can press an erase key that punches all #f holes1 and then the machine will pass by this row as if it were not there4 ,three kinds of tapes are produced for the machine3 ,problem tapes1 which contain information belonging to the particular problem4 ,table tapes1 which contain tables of numbers to be referred to from time to time4 ,routine tapes1 which contain the program1 or routine1 or sequence of steps that the machine is to carry out4 ,in each of these tapes one character takes up of an inch along the tape4 ,in the case of a table tape1 however1 an ordinary #a-;digit number requires #d characters on the tape1 and a #g-;digit number requires #aa characters on the tape4 ,on a table tape there will be on the average about #a inch of tape per number4 ,the ,processor ,the two paper tapes prepared on the perforator should agree4 ,but whether or not they agree1 a girl takes them over to the processor and puts them both in4 ,the processor has two tape feeds1 and she puts one tape on each and starts the machine4 ,the processor compares them row by row1 making sure that they agree1 and punches a new tape row by row4 ,if the two input tapes disagree1 the processor stops4 ,you can look to see which tape is right1 and then you can put the correct punch into the new tape with a keyboard mounted on the processor4 ,as the processor compares the two input tapes1 it also converts any number written in the usual way into machine language4 ,for example1 the processor will automatically translate #bc1ahh into 4#bca #hhjj #aj4 ,the processor also puts in certain safeguards4 ,if you want it to1 the processor will also make a printed record of a tape4 ,also1 when a tape becomes worn from use in the machine1 you can put it into the processor and make a fresh copy4 ,the ,problem ,positions ,next1 the girl takes the punched tape made by the processor over to a problem position that is idle4 ,two of the problem positions are always busy guiding the two computers4 ,the other two problem positions stand by1 ready to be loaded with problems4 ,a problem position looks like a large covered-over table4 ,under the covers are #ab tape feeds1 or tape transmitters4 ,all these transmitters look exactly alike except for their labels and consist of regular teletype transmitters4 ,six-hole paper tape can be fed into any transmitter4 ,six metal fingers sense the holes in the paper tape and give out electrical impulses at proper times4 ,at the front of the problem position is a small group of switches that provide complete control over the problem while it is on the machine4 ,these are switches for starting1 disconnecting1 momentary stop1 etc4 ,one tape transmitter is the problem tape transmitter4 ,it takes in all the data for the problem such as the starting numbers4 ,the first thing it does at the start of a problem is to check 7by comparing tape numbers7 that the right tapes are in the right feeds4 ,five transmitters are routine tape transmitters4 ,each of these takes in the sequence of computing steps4 ,the routine tapes also contain information for referring to table tapes and instructions for printing and punching tape4 ,the machine can choose according to instructions between the five routine tapes and can choose between many different sections on each tape4 ,therefore1 we can use a large number of different routines in a calculation1 and this capacity makes the machine versatile and powerful4 ,six transmitters are table tape transmitters4 ,they read tables of numbers when directed to4 ,a table tape can be as long as #ajj feet and will hold numbers at the rate of #a inch per number1 so that about #abjj numbers of seven decimal digits can be stored on a table tape4 ,when we look up a number in a table1 such as the following1 #b #c #c ---------------------------------------- ---------------- #a #a4jbejj #a4jcjjj #a4jcejj #b #a4jejfc #a4jfjij #a4jgabc #c #a4jgfhi #a4jibgc #d #a4ajcha #e #a4acada #f #a4aeifi #g #h #i #aj we look along the top and down the side until we find the column and row of the number we are looking for4 ,these are called the arguments of the tabular value that we are looking for 7see ,supplement #b74 ,now when we put this table on a tape to go into the ,bell ,laboratories machine1 we write it all on one line1 one figure after another1 and we punch it as follows3 #b- #a-e #a4jbejj #a4jejfc #a4jgfhi #a4ajcha #a4acada #f-aj #a4aeifi #aa-ae #c #a-e #a4jcjjj #a4jfjij #c #a-e #a4jcejj ,you will notice that the column labels #b1 #c1 #c have been put on the tape1 each in front of the group of numbers they apply to4 ,the row labels #a to #e1 #f to #aj1 have also been put on the tape1 each in front of the group of numbers they apply to4 ,the appropriate column and row numbers1 or arguments1 must be put often on every table tape1 so that it is easy for the machine to tell what part of the table tape it is reading4 ,in the ,bell ,laboratories machine1 we do not need to put equal blocks of arguments like #a-e1 #f-aj on the table tape4 ,instead we can put individual arguments like #a1 #b1 #c1 #d 1 or1 if we wish1 we can use blocks of different sizes1 like #a-c1 #d-ae1 #af-cj4 ,for some tables1 such as income tax tables1 it is very useful to have varying-sized blocks of arguments4 ,the machine1 when hunting for a certain value in the table1 makes a comparison at each block of arguments4 ,the machine needs about #f seconds to search a foot of tape4 ,if we want to set up a table economically1 therefore1 we need to consider the average length of time needed for searching4 ,illustration3 ,,fig4 #a4 ,scheme of a recorder4 ,,how ,,information ,,comes ,,out ,,of ,,the ,,machine ,at either one of the two recorders 7,fig4 #a71 information comes out of the machine1 either in the form of printed characters or as punched tape4 ,the recorder consists of a printer1 a reperforator1 and a tape transmitter4 ,one recorder table belongs to each computer and records the results it computes4 ,the printer is a regular teletypewriter connected to the machine4 ,it translates information produced by the machine as electrical impulses and prints the information in letters and digits on paper4 ,the reperforator is an automatic tape punch4 ,it translates information produced by the machine in the form of electrical impulses and punches the information on paper tape4 ,next to the tape punch is a tape transmitter4 ,after the tape comes through the punch1 it is fed into the transmitter4 ,here the machine can hunt for a previous result punched in the tape1 read that result1 and use it again4 ,,how ,,information ,,is ,,manipulated ,,in ,,the ,,machine ,the main part of the computing system consists of #bg large frames loaded with relays and wiring1 called the computer1 or ,computer #a and ,computer #b4 ,in this 8telephone central station10 all the 8phone calls0 from one number to another are attended to4 ,there are #h types of these frames in the computer3 ,,frames ,,number ,storing register frames #f ,printer frames #b ,problem frames #b ,position frames #b ,calculator frames #f ,control frames #b ,routine frames #d ,,btl 7,block-,trig-,log7 frames #b ,permanent table frames #a ---- ,total #bg ,in most but not quite all respects1 the two halves1 ,computer #a and ,computer #b1 can compute independently4 ,the storing register frames hold enough relays to store #cj numbers4 ,the registers for these numbers are named ,a1 ,b1 ,c1 ,d1 1 ,m1 ,n1 ,o in two groups of #ae each4 ,one group belongs to ,computer #a and the other to ,computer #b4 ,in each ,computer1 the calculator frames hold enough relays for storing two numbers 7held in the ,x and ,y registers7 and for performing addition1 subtraction1 multiplication1 division1 and square root4 ,in each ,computer1 the problem frame stores the numbers that are read off the problem tape and the table tapes1 and the printer frame stores the numbers that are read into the printer4 ,the printer frame also stores indications1 for example1 the signs of numbers1 plus or minus1 for purposes of combining them4 ,these frames also hold the relays that control the printer1 the problem tape1 and the table tapes4 ,jointly for both ,computers1 the position frames connect a problem in some problem position to a ,computer that becomes idle4 ,for example1 one problem may finish in the middle of the night2 the machine automatically and unattended switches to another problem position and proceeds with the instructions there contained4 ,a backlog of computing on hand can be stored in two of the problem positions1 while the other two control the two ,computers4 ,in each ,computer1 the routine frames hold the relays that make the ,computer follow the routine instructions4 ,jointly for both ,computers1 the remaining frames--the control frames1 the ,,btl frames1 and the permanent table frames--hold the relays that control3 the alarms and lights for indicating failures2 some circuits called the ,,btl controls2 the tape processor2 and the mathematical tables that are permanently wired into the machine4 ,the permanent table frames hold the following mathematical functions 7see ,supplement #b73 sine1 cosine1 antitangent1 logarithm1 and antilogarithm4 ,storing ,numbers can be stored in the machine in the #cj regular storing registers of both ,computers together4 ,they can also be stored1 at the cost of tying up some machine capacity1 in the other registers3 the #d calculator registers1 the #b problem registers1 the #b table registers1 and the #b printer registers4 ,numbers can also be punched out on tape1 in either of the two printers1 and later read again from the tape4 ,labels identifying the numbers can also be punched and read again from the tape4 ,each register in the machine stores a number in the biquinary notation1 as explained above4 ,in programming the machine1 after mentioning a register it is necessary--as a part of the scheme for checking--to tell the machine specifically whether to hold the number in the register or to clear it4 ,addition and ,subtraction ,the calculator frames can add two numbers together1 if so instructed in the routine tape4 ,suppose that the two numbers are in the registers ,b and ,d and that we wish to put the sum in register ,f4 ,suppose that we wish to clear the ,d number but hold the ,b number after using them4 ,the code on the routine tape is ,b ,h ,d ,c ,f4 ,h and ,c coming right after the names of the registers always designate 8hold0 and 8clear10 respectively4 ,the calculator frames can1 likewise1 subtract a number4 ,the routine instruction ,b ,h-,d ,c ,f means3 ,take the number in register ,b 7hold it72 subtract the number in ,d 7clear it72 put the result in ,f ,multiplication and ,division ,the calculator frames perform multiplication by storing the digits of the multiplier1 adding the multiplicand over and over1 and shifting1 until the product is obtained4 ,however1 if the multiplier is #aihi1 for example1 the calculator treats it as #bjjj-aa4 ,this short-cut applies to digits #f1 #g1 #h1 #i and cuts the time required for multiplying4 ,the routine instruction is ,b ,h ,d ,c ,f4 ,the calculator performs division by repeated subtraction4 ,the routine instruction is ,b ,h ,d ,c ,f4 ,the operation signs 1-1 1 actually appear on the keyboard of the perforator and on the printed tape produced by the printer4 ,discrimination ,discrimination is the term used in the ,bell ,laboratories computer for what we have previously called selection1 or comparison1 or sequencing4 ,the discriminator is a part of the calculator that compares or selects or decides--8discriminates40 ,the discriminator can decide whether a number is zero or not zero4 ,in the language of the algebra of logic 7see ,chapter #i and ,supplement #b71 if a is a number1 the discriminator can find ,t7a #j74 ,the discriminator can also decide whether a number is positive or negative4 ,in the language of logic1 it can find ,t7a #j7 or ,t7a #j74 ,the actions that a discriminator can cause to be taken are3 ,stop the machine4 ,stop the problem1 and proceed to another problem4 ,stop the routine going on1 and proceed with a new routine4 ,permit printing1 or prevent printing2 etc4 ,in this way the discriminator can3 ,distinguish between right and wrong results4 ,tell that a certain result is impossible4 ,recognize a certain result to be the answer4 ,control the number of repetitions of a formula4 ,change from one formula to another formula4 ,check a number against a tolerance2 etc4 ,,problems ,among the problems that have been placed on the machine successfully are3 solving the differential equation of a trajectory 7see ,chapter #e7 and solving #cb linear simultaneous equations in #cb unknowns 7see ,supplement #b74 ,in the second case1 the routine tapes were designed to apply equally well to #aa to #ajj linear equations in #aa to #ajj unknowns4 ,however1 the machine can do a very broad class of problems1 including1 for example1 computing a personal income tax4 ,this calculation with all its complexity of choices cannot be placed on any of the mechanical brains described in previous chapters4 ,the machine can1 of course1 be used to calculate any tables that we may wish to refer to4 ,,an ,,appraisal ,,of ,,the ,,calculator ,the ,bell ,telephone ,laboratories general-purpose relay computer is probably the best mechanical brain made up to the end of #aidg1 in regard to the two important factors of reliability and versatility4 ,reliability ,the machine produces results that are practically #ajj per cent reliable1 for the machine checks each step before taking the next one4 ,the checking principle is that exactly a certain number of relays must be energized4 ,for example1 as we said before1 for each decimal digit there are #g relays4 ,exactly #b of these relays must be energized--no more1 no less4 ,if this does not happen1 the machine stops at once without losing any numbers4 ,lights shine for many circuits in the control panel1 and1 if you compare what they ought to show with what they do show1 you can usually find at once the location of the mistake4 ,the trouble may be a speck of dirt between two contact points on a relay1 and1 when it is brushed away1 the machine can go right ahead from where it stopped4 ,according to a statement by ,franz ,l4 ,alt1 director of the computing laboratory at the ,ballistic ,research ,laboratories1 in ,december #aidg1 8the ,bell machine had not given a single wrong result in eight months of operation1 except when operators interfered with its normal running40 ,to guard against the risk of putting tapes in the wrong transmitters1 the machine will check by the instructions contained in the tapes that the right tapes are in the right places4 ,time ,required ,the time required to do problems on this mechanical brain is perhaps longer than on the others4 ,the numbers are handled digit by digit on the input tapes1 and the typewriter in the recorder moves space by space in order to get to the proper writing point4 ,these are slow procedures4 ,the speeds of numerical operation are3 addition1 _/ second2 multiplication1 #a second on the average2 division1 #b4g seconds on the average2 square root1 #d4e seconds on the average2 logarithm1 about #ae seconds4 ,staff ,in order to operate the machine1 the staff required is3 one maintenance man2 one mathematical engineer2 about six girls for punching tape1 etc41 depending on the number of problems to be handled at the rate of about one problem per week per girl4 ,unlike any of the other mechanical brains built by the end of #aidg1 this machine will run unattended4 ,maintenance ,the relays in the machine will operate for years with no failure2 they have the experience of standard telephone techniques built into them4 ,under laboratory conditions this type of relay had by #aidf operated successfully much more than #ajj million times4 ,the tape feeding and reading equipment in the machine may be maintained by periodic inspection and service4 ,the total number of teletype transmitters in the machine is #ch4 ,if one fails1 it is easy to plug in a spare4 ,the total power required for the machine is about #bh horsepower4 ,batteries are furnished so that1 if the power supply should be interrupted1 the machine can still operate for as long as a half-hour4 ,cost ,the cost of production of this machine in the size of #d problem positions and #b computers has been roughly estimated as half a million dollars4 ,this cost includes material1 manufacture1 installation1 and testing4 ,no development cost is included in this figure4 ,instead1 the cost of development has been reckoned as squaring with patents and other contributions of the work to the telephone switching art4 ,it is unlikely that the general-purpose relay computer will be manufactured generally4 ,the pressure of orders for telephones1 the need to catch up with the backlog of demand1 and the development of electronic computers--all indicate that the ,bell system will hardly go further with this type of computer4 ,in an emergency1 however1 the ,bell system would probably construct such machines for the government1 if requested4 ,in the meantime1 many principles first used in the general-purpose relay computer are likely to find applications in telephone system work4 ,in fact1 a present major development being pursued in the telephone sections of ,bell ,laboratories is the application of the computer principles to the automatic computation of telephone bills4 ,chapter #i ,,reasoning3 ,,the ,,kalin-,,burkhart ,,logical-,,truth ,,calculator ,so far we have talked about mechanical brains that are mathematicians4 ,they are fond of numbers2 their main work is with numbers2 and the other kinds of thinking they do are secondary4 ,we now come to a mechanical brain that is a logician4 ,it is fond of reasoning--logic2 its main work is with what is logically true and what is logically false2 and it does not handle numbers4 ,this mechanical brain was finished in ,june #aidg4 ,it is called the ,kalin-,burkhart ,logical-,truth ,calculator4 ,as its name tells1 it calculates logical truth4 ,now what do we mean by that8 ,,truth ,to be true or false is a property of a statement4 ,usually we say that a statement is true when it expresses a fact4 ,for example1 take the statement 8,salt dissolves in water40 ,we consider this statement to be true because it expresses a fact4 ,actually1 in this case we can roughly prove the fact ourselves4 ,we take a bowl1 put some water in it1 and put in a little salt4 ,after a while we look into the water and notice that no salt whatever is to be seen4 ,of course1 this statement1 like many another1 occurs in a context where certain things are understood4 ,one of the understandings here1 for example1 is 8a small amount of salt in a much larger amount of water40 ,for if we put a whole bag full of salt in just a little water1 not all the salt will dissolve4 ,nearly every statement occurs in a context that we must know if we are to decide whether the statement is true or false4 ,,logical ,,truth ,logical truth is different from ordinary truth4 ,with logical truth we appeal not to facts but to suppositions4 ,usually we say that a statement is logically true when it follows logically from certain suppositions4 ,in other words1 we play a game that has useful1 even wonderful1 results4 ,the game starts with 8if0 or 8suppose0 or 8let us assume40 ,while the game lasts1 any statement is logically true if it follows logically from the suppositions4 ,for example1 let us take five statements3 #a4 8,the earth is flat like a sheet of paper40 #b4 8,the earth is round like a ball40 #c4 8,john ,doe travels as fast as he can1 without turning to left or to right1 for many days40 #d4 8,john ,doe will fall off the earth40 #e4 8,john ,doe will arrive back at his starting point40 ,let us also take a certain context in which3 ,we know what we mean by such words as 8earth10 8flat10 8falling10 etc42 we have other statements and understandings such as 8if ,john ,doe walks off the edge of a cliff1 he will fall10 8a flat sheet of paper has an edge10 etc4 ,in this context1 if statements #a and #c are supposed1 then statement #d is logically true4 ,on the other hand1 if statements #b and #c are supposed1 then statement #e is logically true4 ,of course1 for many centuries1 nearly all men believed statement #a2 and the importance of the years #adib to #aeba 7,columbus to ,magellan7 is linked with the final proof that statement #b expresses a fact4 ,so1 depending on the game1 or the context1 whichever we wish to call it1 almost any statement can be logically true4 ,what we become interested in1 therefore1 is the connections between statements which make them follow logically4 ,,logical ,,patterns ,perhaps the most familiar example of 8following logically0 is a pattern of words like the following3 #a4 ,all igs are ows4 #b4 ,all ows are umphs4 #c4 ,therefore1 all igs are umphs4 ,if statements #a and #b are supposed1 then statement #c is logically true4 ,in other words1 statement #c logically follows from statements #a and #b4 ,this word pattern is logically true1 no matter what substitutions we make for igs1 ows1 and umphs4 ,for example1 we can replace igs by men1 ows by animals1 and umphs by mortals1 and obtain3 #d4 ,all men are animals4 #e4 ,all animals are mortals4 #f4 ,therefore1 all men are mortals4 ,the invented words 8igs10 8ows10 8umphs0 mark places in the logical pattern where we can insert any names we are interested in4 ,the words 8all10 8are10 8therefore0 and the ending s mark the logical pattern4 ,of course1 instead of using invented words like 8igs10 8ows10 8umphs0 we would usually put ,a's1 ,b's1 ,c's4 ,this logical pattern is called a syllogism and is one of the most familiar4 ,but there are even simpler logical patterns that are also familiar4 ,,the ,,simplest ,,logical ,,patterns ,many simple logical patterns are so familiar that we often use them without being conscious of doing so4 ,the simple logical patterns are marked by words like 8and10 8or10 8else10 8not10 8if10 8then10 8only40 ,in the same way1 simple arithmetical patterns are marked by words like 8plus10 8minus10 8times10 8divided by40 ,let us see what some of these simple logical patterns are4 ,suppose that we take two statements about which we have no factual information that might interfere with logical supposing3 #a4 ,john ,doe is eligible for insurance4 #b4 ,john ,doe requires a medical examination4 ,in practice1 we might be concerned with such statements when writing the rules governing a plan of insurance for a group of employees4 ,here1 we shall play a game3 7#a7 ,we shall make up some new statements from statements #a and #b1 using the words 8and10 8or10 8else10 8not10 8if10 8then10 8only40 7#b7 ,we shall examine the logical patterns that we can make4 7#c7 ,we shall see what we can find out about their logical truth4 ,suppose we make up the following statements3 #c4 ,john ,doe is not eligible for insurance4 #d4 ,john ,doe does not require a medical examination4 #e4 ,john ,doe is eligible for insurance and requires a medical examination4 #f4 ,john ,doe is eligible for insurance1 and ,john ,doe is eligible for insurance4 #g4 ,john ,doe is eligible for insurance1 or ,john ,doe requires a medical examination4 #h4 ,if ,john ,doe is eligible for insurance1 then he requires a medical examination4 #i4 ,john ,doe requires a medical examination if and only if he is eligible for insurance4 #aj4 ,john ,doe is eligible for insurance or else he requires a medical examination4 ,now clearly it is troublesome to repeat quantities of words when we are interested only in the way that 8and10 8or10 8else10 8not10 8if10 8then10 8only0 occur4 ,so1 let us use just #a and #b for the two original statements1 remembering that 8#a ,,and #b0 means here 8statement #a ,,and statement #b0 and does not mean #a plus #b4 ,then we have3 #c3 ,,not-#a #d3 ,,not-#b #e3 #a ,,and #b #f3 #a ,,and #a #g3 #a ,,or #b #h3 ,,if #a1 ,,then #b #i3 #a ,,if ,,and ,,only ,,if #b #aj3 #a ,,or ,,else #b ,here then are some simple logical patterns that we can make4 ,,calculation ,,of ,,logical ,,truth ,now what can we find out about the logical truth of statements #c to #aj8 ,if we know something about the truth or falsity of statements #a and #b1 what will logically follow about the truth or falsity of statements #c to #aj8 ,in other words1 how can we calculate the logical truth of statements #c to #aj1 given the truth or falsity of statements #a and #b8 ,for example1 #c is ,,not-#a2 that is1 statement #c is the negative or the denial of statement #a4 ,it follows logically that1 if #a is true1 #c is false2 if #a is false1 #c is true4 ,suppose that we use ,t for logically true and ,f for logically false4 ,then we can show our calculation of the logical truth of statement #c in ,table #a4 ,table #a ,table #b #a ,,not-#a #c #b ,,not-#b #d ,t ,f ,t ,f ,f ,t ,f ,t ,our rule for calculation is3 ,for ,t put ,f2 for ,f put ,t4 ,of course1 exactly the same rule applies to statements #b and #d 7see ,table #b74 ,the ,t and ,f are called truth values4 ,any meaningful statement can have truth values4 ,this type of table is called a truth table4 ,for any logical pattern1 we can make up a truth table4 ,let us take another example1 8,,and40 ,statement #e is the same as statement #a ,,and statement #b4 ,how can we calculate the logical truth of statement #e8 ,we can make up the same sort of a table as before4 ,on the left-hand side of this table1 there will be #d cases3 #a4 ,statement #a true1 statement #b true4 #b4 ,statement #a false1 statement #b true4 #c4 ,statement #a true1 statement #b false4 #d4 ,statement #a false1 statement #b false4 ,on the right-hand side of this table1 we shall put down the truth value of statement #e4 ,statement #e is true if both statements #a and #b are true2 statement #e is false in the other cases4 ,we know this from our common everyday experience with the meaning of 8,,and0 between statements4 ,so we can set up the truth table1 and our rule for calculation of logical truth1 in the case of ,,and1 is shown on ,table #c4 ,table #c #a #b #a ,,and #b #e ,t ,t ,t ,f ,t ,f ,t ,f ,f ,f ,f ,f 8,,and0 and the other words and phrases joining together the original two statements to make new statements are called connectives1 or logical connectives4 ,the connectives that we have illustrated in statements #g to #aj are3 ,,or1 ,,if ,,then1 ,,if ,,and ,,only ,,if1 ,,or ,,else4 ,table #d shows the truth table that applies to statements #g1 #h1 #i1 and #aj4 ,this truth table expresses the calculation of the logical truth or falsity of these statements4 ,table #d #a ,,if ,,and #a ,,or #b ,,if #a1 ,,then #b ,,only ,,if #b #a ,,or ,,else #b #a #b #g #h #i #aj ,t ,t ,t ,t ,t ,f ,f ,t ,t ,t ,f ,t ,t ,f ,t ,f ,f ,t ,f ,f ,f ,t ,t ,f ,the 8,,or0 7as in statement #g7 that is defined in the truth table is often called the inclusive 8or0 and means 8,,and_/,,or40 ,statement #g1 8#a ,,or #b10 is considered to be the same as 8#a ,,or #b ,,or ,,both40 ,there is another 8,,or0 in common use1 often called the exclusive 8or10 meaning 8,,or ,,else0 7as in statement #aj74 ,statement #aj1 8#a ,,or ,,else #b10 is the same as 8#a ,,or #b ,,but ,,not ,,both0 or 8,,either #a ,,or #b40 ,in ordinary ,english1 there is some confusion over these two 8,,or's40 ,usually we rely on the context to tell which one is intended4 ,of course1 such reliance is not safe4 ,sometimes we rely on a necessary conflict between the two statements connected by 8,,or0 which prevents the 8both0 case from being possible4 ,in ,latin the two kinds of 8,,or0 were distinguished by different words1 vel meaning 8,,and_/,,or10 and aut meaning 8,,or ,,else40 ,the 8,,if ,,then0 that is defined in the truth table agrees with our usual understanding that 7#a7 when the 8,,if clause0 is true1 the 8,,then clause0 must be true2 and 7#b7 when the 8,,if clause0 is false1 the 8,,then clause0 may be either true or false4 ,the 8,,if ,,and ,,only ,,if0 that is defined in the truth table agrees with our usual understanding that 7#a7 if either clause is true1 the other is true2 and 7#b7 if either clause is false1 the other is false4 ,in statement #f1 there are only two possible cases1 and the truth table is shown in ,table #e4 ,table #e #a #a ,,and #a #f ,t ,t ,f ,f ,we know that #f is true if and only if #a is true4 ,in other words1 the statement 8#a ,,and #a ,,if ,,and ,,only ,,if #a0 is true1 no matter what statement #a may refer to4 ,it is because of this fact that we never use a statement in the form 8#a and #a03 it can always be replaced by the plain statement 8#a40 ,,logical-,,truth ,,calculation ,,by ,,examining ,,cases ,,and ,,reasoning ,now you may say that this is all very well1 but what good is it8 ,almost anybody can use these connectives correctly and certainly has had a great deal of practice using them4 ,why do we need to go into truth values and truth tables8 ,when we draft a contract or a set of rules1 we often have to consider several conditions that give rise to a number of cases4 ,we must avoid3 #a4 ,all conflicts1 in which two statements that disagree apply to the same case4 #b4 ,all loopholes1 in which there is a case not covered by any statement4 ,if we have one statement or condition only1 we have to consider #b possible cases3 the condition satisfied or the statement true2 the condition not satisfied or the statement false4 ,if we have #b conditions1 we have to consider #d possible cases3 true1 true2 false1 true2 true1 false2 false1 false4 ,if we have #c conditions1 we have to consider #h possible cases one after the other 7see ,table #f74 ,table #f ,,case #a,,st ,,condition #b,,nd ,,condition #c,,rd ,,condition #a ,t ,t ,t #b ,f ,t ,t #c ,t ,f ,t #d ,f ,f ,t #e ,t ,t ,f #f ,f ,t ,f #g ,t ,f ,f #h ,f ,f ,f ,instead of ,t's and ,f's1 we would ordinarily use check-marks 77 and crosses 771 which1 of course1 have the same meaning4 ,we may consider and study each case individually4 ,in any event1 we must make sure that the proposed contract or set of rules covers all the cases without conflicts or loopholes4 ,the number of possible cases that we have to consider doubles whenever one more condition is added4 ,clearly1 it soon becomes too much work to consider each case individually1 and so we must turn to a second method1 thoughtful classifying and reasoning about classes of cases4 ,now suppose that the number of conditions increases3 #d conditions give rise to #af possible cases2 #e1 #f1 #g1 #h1 #i1 #aj1 conditions give rise to #cb1 #fd1 #abh1 #bef1 #eab1 #ajbd1 cases respectively4 ,because of the large number of cases1 we soon begin to make mistakes while reasoning about classes of cases4 ,we need a more efficient way of knowing whether all cases are covered properly4 ,,logical-,,truth ,,calculation ,,by ,,algebra ,one of the more efficient ways of reasoning is often called the algebra of logic4 ,this algebra is a part of a new science called mathematical logic4 ,mathematical logic is a science that has the following characteristics3 ,it studies chiefly nonnumerical reasoning4 ,it seeks accurate meanings and necessary consequences4 ,its chief instruments are efficient symbols4 ,mathematical logic studies especially the logical relations expressed in such words as 8or10 8and10 8not10 8else10 8if10 8then10 8only10 8the10 8of10 8is10 8every10 8all10 8none10 8some10 8same10 8different10 etc4 ,the algebra of logic studies especially only the first seven of these words4 ,the great thinkers of ancient ,greece first studied the problems of logical reasoning as these problems turned up in philosophy1 psychology1 and debate4 ,aristotle originated what was called formal logic4 ,this was devoted mainly to variations of the logical pattern shown above called the syllogism4 ,in the last #aej years1 the fine symbolic techniques developed by mathematicians were applied to the problems of the calculation of logical truth1 and the result was mathematical logic1 much broader and much more powerful than formal logic4 ,a milestone in the development of mathematical logic was ,the ,laws of ,thought1 written by ,george ,boole1 a great ,english mathematician1 and published in #ahed4 ,boole introduced the branch of mathematical logic called the algebra of logic1 also called ,boolean algebra4 ,in late years1 all the branches of mathematical logic have been improved and made easier to use4 ,we can give a simple numerical example of ,boolean algebra and how it can calculate logical truth4 ,suppose that we take the truth value of a statement as #a if it is true and #j if it is false4 ,now we have numbers #a and #j instead of letters ,t and ,f4 ,since they are numbers1 we can add them1 subtract them1 and multiply them4 ,we can also make up simple numerical formulas that will let us calculate logical truth4 ,if ,p and ,q are statements1 and if p and q are their truth values1 respectively1 we have ,table #g4 ,table #g ,,statement ,,truth ,,value ,,not-,p #a - p ,p ,,and ,q pq ,p ,,or ,q p q - pq ,,if ,p1 ,,then ,q #a - p pq ,p ,,if ,,and ,,only ,,if ,q #a - p - q #bpq ,p ,,or ,,else ,q p q - #bpq ,for example1 suppose that we have two statements ,p and ,q3 ,p3 ,john ,doe is eligible for insurance4 ,q3 ,john ,doe requires a medical examination4 ,to test that the truth value of 8,p ,,or ,q0 is p q-pq1 let us put down the four cases1 and calculate the result 7see ,table #h74 ,table #h p q p q - pq #a #a #a #a - #a #a #j #a #j #a - #j #a #a #j #a #j - #j #a #j #j #j #j - #j #j ,now we know that ,p or ,q is true if and only if either one or both of ,p and ,q are true1 and thus we see that the calculation is correct4 ,the algebra of logic 7see also ,supplement #b7 is a more efficient way of calculating logical truth4 ,but it is still a good deal of work to use the algebra4 ,for example1 if we have #aj conditions1 we shall have #aj letters like p1 q to handle in calculations4 ,thus we need a still more efficient way4 ,,calculation ,,of ,,circuits ,,by ,,the ,,algebra ,,of ,,logic ,in #aicg a research assistant at ,massachusetts ,institute of ,technology1 ,claude ,e4 ,shannon1 was studying for his degree of master of science4 ,he was enrolled in the ,department of ,electrical ,engineering4 ,he was interested in automatic switching circuits and wondered why an algebra should not apply to them4 ,he wrote his thesis on the answer to this question and showed that3 7#a7 ,there is an algebra that applies to switching circuits4 7#b7 ,it is the algebra of logic4 ,a paper1 based on his thesis1 was published in #aich in the ,transactions of the ,american ,institute of ,electrical ,engineers with the title 8,a ,symbolic ,analysis of ,relay and ,switching ,circuits40 ,illustration3 ,,fig4 #a4 ,switches in series4 ,for a simple example of what ,shannon found out1 suppose that we have two switches1 #a1 #b1 in series 7see ,fig4 #a74 ,when do we get current flowing from the source to the sink8 ,there are #d possible cases and results 7see ,table #i74 ,table #i ,,switch #a ,,is ,,closed ,,switch #b ,,is ,,closed ,,current ,,flows ,yes ,yes ,yes ,no ,yes ,no ,yes ,no ,no ,no ,no ,no ,now what does this table remind us of8 ,it is precisely the truth table for 8,,and40 ,it is just what we would have if we wrote down the truth table of the statement 8,switch #a is closed ,,and switch #b is closed40 ,illustration3 ,,fig4 #b4 ,switches in parallel4 ,illustration3 ,,fig4 #c4 ,switch open--current flowing4 ,suppose that we have two switches #a1 #b in parallel 7see ,fig4 #b74 ,when do we get current flowing from the source to the sink8 ,answer3 when either one or both of the switches are closed4 ,therefore1 this circuit is an exact representation of the statement 8,switch #a is closed or switch #b is closed40 ,suppose that we have a switch that has two positions1 and at any time must be at one and only one of these two positions 7see ,fig4 #c74 ,suppose that current flows only when the switch is open4 ,there are two possible cases and results 7see ,table #aj74 ,table #aj ,,switch #a ,,is ,,closed ,,current ,,flows ,yes ,no ,no ,yes ,this is like the truth table for 8,,not02 and this circuit is an exact representation of the statement 8,switch #a is ,,not closed40 7,note3 ,these examples are in substantial agreement with ,shannon's paper1 although ,shannon uses different conventions47 ,we see1 therefore1 that there is a very neat correspondence between the algebra of logic and automatic switching circuits4 ,thus it happens that3 #a4 ,the algebra of logic can be used in the calculation of some electrical circuits4 #b4 ,some electrical circuits can be used in the calculations of the algebra of logic4 ,this fact is what led to the next step4 ,,logical-,,truth ,,calculation ,,by ,,machine ,in #aidf two undergraduates at ,harvard ,university1 ,theodore ,a4 ,kalin and ,william ,burkhart1 were taking a course in mathematical logic4 ,they noticed that there were a large number of truth tables to be worked out4 ,to work them out took time and effort and yet was a rather tiresome automatic process not requiring much thinking4 ,they had had some experience with electrical circuits4 ,knowing of ,shannon's work1 they said to each other1 8,why not build an electrical machine to calculate truth tables80 ,they took about two months to decide on the essential design of the machine3 #a4 ,the machine would have dial switches in which logical connectives would be entered4 #b4 ,it would have dial switches in which the numbers of statements like #a1 #b1 #c would be entered4 #c4 ,it would scan the proper truth table line by line by sending electrical pulses through the dial switches4 #d4 ,it would compute the truth or falsehood of the whole expression4 ,,construction ,,and ,,completion ,,of ,,the ,,kalin-,,burkhart ,,logical-,,truth ,,calculator ,with the designs in mind1 ,kalin and ,burkhart bought some war surplus materials1 including relays1 switches1 wires1 lights1 and a metal box about #cj inches long by #af inches tall1 and #ac inches deep4 ,from ,march to ,june1 #aidg1 they constructed a machine in their spare time1 assembling and mounting the parts inside the box4 ,the total cost of materials was about #aej4 ,in ,june the machine was demonstrated in ,cambridge1 ,mass41 before several logicians and engineers1 and in ,august it was moved for some months to the office of a life insurance company4 ,there some study was made of the possible application of the machine in drafting contracts and rules4 ,,general ,,organization ,,of ,,the ,,machine ,the logical-truth calculator built by ,kalin and ,burkhart is not giant in size1 although giant in capacity4 ,like other mechanical brains1 the machine is made up of many pieces of a rather small number of different kinds of parts4 ,the machine contains about #de dial switches1 #bc snap switches 7or two-position switches71 #he relays1 #f push buttons1 less than a mile of wire1 etc4 ,the lid of the metal box is the front1 vertical panel of the machine4 ,,units ,,of ,,the ,,machine ,the machine contains #af units4 ,these units are listed in ,table #aa1 in approximately the order in which they appear on the front panel of the machine--row by row from top to bottom1 and from left to right in each row4 ,table #aa ,,units1 ,,their ,,names1 ,,and ,,significance ,,unit ,,row ,,part ,,no4 ,,mark ,,name ,,significance #a #a ,small red #ab -- ,statement truth- ,output3 glows if lights value lights statement is assumed true in the case #b #a #b-position #ab ,statement denial ,input3 if up1 snap switches switches statement is denied #c #b #ad-position #ab ,v ,statement ,input of dial switches switches statements #d #c #d-position #aa k ,connective ,input of dial switches switches connectives3 7and71 7or71 7if-then71 7if and only if7 #e #d #aa-position #aa ,a ,antecedent ,input of dial switches switches antecedents #f #e #aa-position #aa ,c ,consequent ,input of dial switches switches consequents #g #f #b-position #aa ,s ,stop switches ,input3 if up1 snap switches associates connective to main truth-value light #h #f #b-position #aa ,connective denial ,input3 if up1 snap switches switches statement produced by connective is denied #i #g ,red light and #a ,start ,automatic start ,input3 causes the large button calc4 to start down a truth table automatically #aj #g ,red light and #a ,start ,power switch ,input3 turns the #b buttons ,stop power on or off #aa #g #b-position #a ,stop 8,stop-on-true-or- ,input3 causes the snap switch false0 switch calc4to stop and red either on true button cases or on false cases #ab #g ,yellow light #a -- ,main truth-value ,output3 glows if light the statement produced by the main connective is true for the case #ac #g ,large button #a ,man4 ,manual pulse ,input3 causes the ,pulse button calc4 to go to the next line of a truth table #ad #g #aa-position #a k ,connective check ,output3 glows when dial switch switch and light any specified connective is true #ae #g #ac-position #a ,,tt 8,truth-table-row- ,input3 causes the dial switch ,row stop0 switch calc4 to stop on ,stop last row of the the truth table #af ,be- ,continuous #a -- ,timing control ,input3 controls the tween dial knob knob speed at which #f #g and button the calculator scans rows of the truth table ,some of the words appearing in this table need to be defined4 ,connective here means 8,,and10 8,,or10 8,,if ,,then10 8,,if ,,and ,,only ,,if40 ,only these four connectives appear on the machine2 others when needed can be constructed from these4 ,the symbols used for these connectives in mathematical logic are 1 1 1 4 ,these signs serve as labels for the connective switch points4 ,in this machine1 when there is a connective between two statements1 the statement that comes before is called the antecedent and the statement that comes after is called the consequent4 ,,how ,,information ,,goes ,,into ,,the ,,machine ,of the #af units #ac are input units4 ,they control the setup of the machine so that it can solve a problem4 ,of the #ac input units1 those that have the most to do with taking in the problem are shown in ,table #ab4 ,table #ab ,name of ,,kind ,,of ,,unit ,,switches ,,mark ,,switch ,,switch ,,settings #c ,statement ,v to ,dial ,statements #a to #ab or constant ,v ,t or ,f #b ,statement ,snap ,affirmative 7down7 or negative denial 7up7 #d ,connective k to ,dial 7,,and71 k 7,,or71 7,,if-,,then71 7,,if ,,and ,,only ,,if7 #h ,connective ,snap ,affirmative 7down7 or negative denial 7up7 #e ,antecedent ,a to ,dial ,v or various k's ,a #f ,consequent ,c to ,dial ,v or various k's ,c #g ,stop ,s to ,snap ,not connected 7down7 or ,s connected 7up7 ,the first step in putting a problem on the machine is to express the whole problem as a single compound statement that we want to know the truth or falsity of4 ,we express the single compound statement in a form such as the following3 ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v where each ,v represents a statement1 each k represents a connective1 and we know the grouping1 or in other words1 we know the antecedent and consequent of each connective4 ,for example1 let us choose a problem with an obvious answer3 ,,problem4 ,given3 statement #a is true2 and if statement #a is true1 then statement #b is true2 and if statement #b is true1 then statement #c is true2 and if statement #c is true1 then statement #d is true4 ,is statement #d true8 ,how do we express this whole problem in a form that will go on the machine8 ,we express the whole problem as a single compound statement that we want to know the truth or falsity of3 ,if #a and 7if #a then #b7 and 7if #b then #c7 and 7if #c then #d71 then #d ,the #h statements occurring in this problem are1 respectively3 #a #a #b #b #c #c #d #d4 ,these are the values at which the ,v switches 7the statement dial switches1 ,unit #b7 from ,v to ,v are set4 ,the #g connectives occurring in this problem are1 respectively3 ,,and1 ,,if-,,then1 ,,and1 ,,if-,,then1 ,,and1 ,,if-,,then1 ,,if-,,then4 ,these are the values at which the k switches 7the connective dial switches1 ,unit #d7 from k to k are set4 ,a grouping 7one of several possible groupings7 that specifies the antecedent and consequent of each connective is the following3 #a ,,and #a ,,if-,,then #b ,,and #b ,,if-,,then #c ,,and #c ,,if-,,then #d ,,if-,,then #d ------------------ ------------------ ------------------ k k k ------------------------------ ---------------------------------------- ---------- k k ---------------------------------------- ---------------------------------------- -------------- k ---------------------------------------- ---------------------------------------- ---------------------------------- k ,the grouping has here been expressed graphically with lines but may be expressed in the normal mathematical way with parentheses and brackets as follows3 #a ,,and 7#a ,,if-,,then #b7 ,,and 7#b ,,if-,,then #c7 ,,and 7#c ,,if-,,then #d7 ,,if-,,then #d4 ,so the values at which the antecedent and consequent dial switches are set are as shown in ,table #ac4 ,table #ac ,,antecedent ,,consequent ,,connective ,,switch ,,set ,,at ,,switch ,,set ,,at k ,a ,v ,c k k ,a ,v ,c ,v k ,a k ,c k k ,a ,v ,c ,v k ,a k ,c k k ,a ,v ,c ,v k ,a k ,c ,v ,in any problem1 statements that are different are numbered one after another #a1 #b1 #c1 #d 4 ,a statement that is repeated bears always the same number4 ,in nearly all cases that are interesting1 there will be repetitions of the statements4 ,if any statement appeared with a 8,,not0 in it1 we would turn up the denial switch for that statement 7,unit #b74 ,the different connectives available on the machine are 8,,and10 8,,or10 8,,if ,,then10 8,,if ,,and ,,only ,,if40 ,if a 8,,not0 affected the compound statement produced by any connective1 we would turn up the denial switch for that connective 7,unit #h74 ,the last step in putting the problem on the machine is to connect the main connective of the whole compound statement to the yellow light output 7,unit #ab74 ,in this problem the last 8,,if-,,then10 k1 is the main connective1 the one that produces the whole compound statement4 ,so we turn ,stop ,switch #g 7in ,unit #g7 that belongs to k into the up position4 ,there are a few more things to do1 naturally1 but the essential part of putting the information of the problem into the machine has now been described4 ,,how ,,information ,,comes ,,out ,,of ,,the ,,machine ,of the #af units listed in ,table #aa1 #c are output units1 and only #b of these are really important1 as shown in ,table #ad4 ,table #ad ,,unit ,,name ,,of ,,light ,,mark ,,kind ,,of ,,light #a ,statement truth value ,v to ,v ,small1 red #ac ,main truth value ,large1 yellow ,the answer to a problem is shown by a pattern of the lights of ,units #a and #ac4 ,the pattern of lights is equivalent to a row of the truth table4 ,each little red light 7,unit #a7 glows when its statement is assumed to be true1 and it is dark when its statement is assumed to be false4 ,the yellow light 7,unit #ac7 glows when the whole compound statement is calculated to be logically true1 and it is dark when the whole compound statement is calculated to be logically false4 ,the machine turns its 8attention0 automatically to each line of the truth table one after the other1 and pulses are fed in according to the pattern of assumed true statements4 ,we can set the machine to stop on true cases or on false cases or on every case1 so as to give us time to copy down whichever kind of results we are interested in4 ,when we have noted the case1 we can press a button and the machine will then go ahead searching for more cases4 ,a ,,complete ,,and ,,concrete ,,example ,the reader may still be wondering when he will see a complete and concrete example of the application of the logical-truth calculator4 ,so far we have given only pieces of examples in order to illustrate some explanation4 ,therefore1 let us consider now the following problem3 ,,problem4 ,the ,a4 ,a4 ,adams ,co41 ,inc41 has about #ajjj employees4 ,about #fjj of them are insured under a contract for group insurance with the ,i4 ,i4 ,insurance ,co4 ,mr4 ,adams decides that more of his employees ought to be insured4 ,as a part of his study of the change1 he asks his manager in charge of the group insurance plan1 8,what are the possible statuses of my employees who are not insured80 ,the manager replies1 8,i can tell you the names of the men who are not insured1 and all the data you may want to know about them40 ,mr4 ,adams says1 8,no1 ,john1 that won't be enough1 for ,i need to know whether there are any groups or classes that for some basic reason ,i should exclude from the change ,i am considering40 ,so the manager goes to work with the following #e statuses and the following #e rules1 and he produces the following answer4 ,our question is1 8,is he right1 or has he made a mistake80 ,statuses4 ,a status for any employee is a report about that employee1 answering all the following #e questions with 8yes0 or 8no40 #a4 ,is the employee eligible for insurance8 #b4 ,has the employee applied for insurance8 #c4 ,has the employee's application for insurance been approved8 #d4 ,does the employee require a medical examination for insurance8 #e4 ,is the employee insured8 ,rules4 ,the rules applying to employees are3 ,a4 ,any employee1 to be insured1 must be eligible for insurance1 must make application for insurance1 and must have such application for insurance approved4 ,b4 ,only eligible employees may apply for insurance4 ,c4 ,the application of any person eligible for insurance without medical examination is automatically approved4 ,d4 7,naturally7 an application can be approved only if the application is made4 ,e4 7,naturally7 a medical examination will not be required from any person not eligible for insurance4 ,answer by the ,manager4 ,there are #e possible combinations of statuses for employees who are not insured1 as shown in ,table #ae4 ,table #ae ,,possible ,,status #c1 ,,status #d1 ,,combination ,,status #a1 ,,status #b1 ,,application ,,examination ,,status #e1 ,,of ,,statuses ,,eligible ,,applied ,,approved ,,required ,,insured #a ,yes ,yes ,yes ,yes ,no #b ,yes ,yes ,yes ,no ,no #c ,yes ,yes ,no ,yes ,no #d ,yes ,no ,yes ,no ,no #e ,no ,no ,no ,no ,no ,the question may be asked why employees who are eligible1 who have applied for insurance1 who have had their applications approved1 and who require no medical examination 7combination #b7 are yet not insured4 ,the answer is that the rules given do not logically lead to this conclusion4 ,as a matter of fact1 there might be additional rules1 such as3 any sick employee must first return to work2 or any period from date of approval of application to the first of the following month must first pass4 ,the first step in putting this problem on the ,kalin-,burkhart ,logical-,truth ,calculator is to rephrase the rules1 using the language of the connectives that we have on the machine4 ,the rules rephrased are3 ,a4 ,if an employee is insured1 then he is eligible1 he has applied for insurance1 and his application has been approved4 ,,if #e1 ,,then #a ,,and #b ,,and #c ,b4 ,if an employee has applied 7under these rules7 for insurance1 then he is eligible4 ,,if #b1 ,,then #a ,c4 ,if an employee is eligible for insurance1 has applied1 and requires no medical examination1 his application is automatically approved4 ,,if #a ,,and #b ,,and ,,not-#d1 ,,then #c ,d4 ,if an employee's application has been approved1 then he has applied4 ,,if #c1 ,,then #b ,e4 ,if an employee is not eligible1 then he does not require a medical examination 7under these rules74 ,,if ,,not-#a1 ,,then ,,not-#d ,to get the answer we seek1 we must add one more rule for this answer only3 ,f4 ,the employee is not insured4 ,,not-#e ,we now have a total of #d #b #d #b #b #a occurrences of statements1 or #ae occurrences4 ,this is beyond the capacity of the existing machine4 ,but fortunately ,rule ,f and ,rule ,a cancel each other2 they may both be omitted2 and this gives us #aj occurrences instead of #ae4 ,in other words1 all the possible statuses under 8,rule ,b ,,and ,rule ,c ,,and ,rule ,d ,,and ,rule ,e0 will give us the answer we seek4 ,the rephrasing and reasoning we have done here is perhaps not easy4 ,for example1 going from the logical pattern ,only igs may be ows to the logical pattern ,if it is an ow1 then it is an ig as we did in rephrasing ,rule ,b1 deserves rather more thought and discussion than we can give to the subject here4 ,a person who is responsible for preparing problems for the ,logical-,truth ,calculator should know the algebra of logic4 ,choosing an appropriate grouping1 we now set on the machine3 7,,if #b1 ,,then #a7 ,,and ,,if 7#a ,,and #b7 ,,and ,,not-#d1 ,,then #c ,,and 7,,if #c1 ,,then #b7 ,,and 7,,if ,,not-#a1 ,,then ,,not-#d7 ,the setting is as shown in ,table #af4 ,after this setting1 the machine is turned on and set to stop on the 8true0 cases4 ,the ,table #af ,,setting ,,of ,,the ,,problem ,,on ,,the ,,logical-,,truth ,,calculator ,,unit #c ,statement ,dial ,no4 ,v ,v ,v ,v ,v ,v #c ,statement ,dial ,setting #b #a #a #b #d #c #b ,statement ,denial ,switch ,setting -- -- -- -- up -- #d ,connective ,dial ,no4 k k k k k k #d ,connective ,dial ,setting #h ,connective ,denial ,switch ,setting -- -- -- -- -- -- #e ,antecedent ,dial ,no4 ,a ,a ,a ,a ,a ,a #e ,antecedent ,dial ,setting ,v k ,v k k k #f ,consequent ,dial ,no4 ,c ,c ,c ,c ,c ,c #f ,consequent ,dial ,setting ,v k ,v ,v ,v k #g ,stop ,switches1 associating connective to ,main ,truth-,value ,light -- -- -- -- -- up ---------------------------------------- ------------------------- #c ,statement ,dial ,no4 ,v ,v ,v ,v ,v ,v #c ,statement ,dial ,setting #c #b #a #d ,f ,f #b ,statement ,denial ,switch ,setting -- -- up up -- -- #d ,connective ,dial ,no4 k k k k k #d ,connective ,dial ,setting off off #h ,connective ,denial ,switch ,setting -- -- -- -- -- #e ,antecedent ,dial ,no4 ,a ,a ,a ,a ,a #e ,antecedent ,dial ,setting ,v k ,v off off #f ,consequent ,dial ,no4 ,c ,c ,c ,c ,c #f ,consequent ,dial ,setting ,v k ,v off off #g ,stop ,switches1 associating connective to ,main ,truth-,value ,light -- -- -- -- -- possible statuses of employees who are not insured are shown in ,table #ag4 ,as we look down the last column in ,table #ag1 we observe #f occurrences of ,t1 instead of #e as the manager determined 7see ,table #ae74 ,thus1 when we compare the manager's result with the machine result1 we find an additional possible combination to be reported to ,mr4 ,adams1 combination #g3 ,employee eligible1 employee has not applied1 employee's application not approved1 employee requires a medical examination1 employee not insured4 ,table #ag ,,solution ,,of ,,the ,,problem ,,by ,,the ,,calculator ,,legend3 ,a ,,the ,,employee ,,is ,,eligible ,,for ,,insurance ,b ,,the ,,employee ,,has ,,applied ,,for ,,insurance ,c ,,the ,,employee',s ,,application ,,for ,,insurance ,,has ,,been ,,approved ,d ,,the ,,employee ,,requires ,a ,,medical ,,examination ,e ,,the ,,employee ,,is ,,insured ,f ,,case1 ,,or ,,combination ,,no4 ,g ,,the ,,combination ,,does ,,not ,,contradict ,,the ,,rules1 ,i4,e41 ,,the ,,yellow ,,light ,,is ,,on ,a ,b ,c ,d ,e ,f ,g ,status3 #a #b #c #d #e ,t ,t ,t ,t ,f #a ,t ,f ,t ,t ,t ,f #b ,f ,t ,f ,t ,t ,f #c ,f ,f ,f ,t ,t ,f #d ,f ,t ,t ,f ,t ,f #e ,t ,f ,t ,f ,t ,f #f ,f ,t ,f ,f ,t ,f #g ,t ,f ,f ,f ,t ,f #h ,f ,t ,t ,t ,f ,f #i ,t ,f ,t ,t ,f ,f #aj ,f ,t ,f ,t ,f ,f #aa ,f ,f ,f ,t ,f ,f #ab ,f ,t ,t ,f ,f ,f #ac ,f ,f ,t ,f ,f ,f #ad ,f ,t ,f ,f ,f ,f #ae ,t ,f ,f ,f ,f ,f #af ,t ,because of the medical examination1 this additional class of employee would need to be considered rather carefully in any change of the group insurance plan4 ,,an ,,appraisal ,,of ,,the ,,calculator ,in appraising the ,kalin-,burkhart ,logical-,truth ,calculator1 we must remember that this is a first model4 ,it was the only machine of its kind up to the end of #aidh2 and it worked4 ,the cost of the machine1 as stated before1 was about #aej of parts and perhaps #ajjj of labor4 ,this is less than _/ of the cost of the other giant brains described in previous chapters4 ,yet we can properly call this machine a mechanical brain because it transfers information automatically from one part to another of the machine1 has automatic control over the sequence of operations1 and does certain kinds of reasoning4 ,the machine is swift4 ,it can check up to a #ajj cases against a set of rules in less than #a minute4 ,it can check3 #abh cases for #g conditions in #a minutes1 #bef cases for #h conditions in #b minutes1 and #djif cases for #ab conditions in #ch minutes4 ,that is the limit of the present machine4 ,of course1 setting up the machine to do a problem takes some more time4 ,the programming of this machine to do a problem is less complicated than the programming of most of the big machines previously described4 ,of course1 in order to prepare a problem for the machine1 the preparer needs to know a fair amount of the algebra of logic4 ,this1 however1 is not very hard4 ,as to reliability1 the machine has in practice been out of order less than #b per cent of operating time4 ,the big barrier to wide use of the machine1 of course1 is lack of understanding of the field of problems in which it can be applied4 ,even in this modern world of ours1 we are in rather a primitive stage in regard to recognizing problems in logical truth and knowing how to calculate it4 ,here1 however1 is an electrical instrument for logical reasoning1 and it seems likely that its applications will multiply4 ,chapter #aj ,,an ,,excursion3 ,,the ,,future ,,design ,,of ,,machines ,,that ,,think ,in the previous chapters we have described four giant mechanical brains finished by the end of #aidf3 ,massachusetts ,institute of ,technology's ,differential ,analyzer ,no4 #b1 ,harvard's ,,ibm ,automatic ,sequence-,controlled ,calculator1 ,moore ,school of ,electrical ,engineering's ,electronic ,numerical ,integrator and ,calculator 7,eniac71 and ,bell ,telephone ,laboratories' ,general-,purpose ,relay ,computer4 ,all these brains have actually worked long enough to have demonstrated thoroughly some facts of great importance4 ,,what ,,existing ,,machines ,,have ,,proved ,the existing mechanical brains have proved that information can be automatically transferred between any two registers of a machine4 ,no human being is needed to pick up a physical piece of information produced in one part of the machine1 personally move it to another part of the machine1 and there put it in again4 ,we can think of a mechanical brain as something like a battery of desk calculators or punch-card machines all cabled together and communicating automatically4 ,the existing mechanical brains have also proved that flexible1 automatic control over long sequences of operations is possible4 ,we can lay out the whole routine to solve a problem1 translate it into machine language1 and put it into the machine4 ,then we press the 8start0 button2 the machine starts whirring and prints out the answers as it obtains them4 ,mechanical brains have removed the limits on complexity of routine3 the machine can carry out a complicated routine as easily as a simple one4 ,the existing giant brains have shown that a machine with hundreds of thousands of parts will work successfully4 ,it will operate accurately1 it will run unattended1 and it will have remarkably few mechanical troubles4 ,these machines have shown that enormous speeds can be realized3 #ejjj additions a second is ,eniac's record4 ,high speed is needed for many problems in science1 government1 and business4 ,in fact1 there are economic and statistical problems1 now settled by armchair methods1 for which high-speed mechanical brains may make it possible to compute answers rather than guess them4 ,also1 these machines have been shown to be reasonable in cost4 ,the cost of each of the large calculators is in the neighborhood of #bej1jjj to #ejj1jjj4 ,if we assume a ten-year life1 which is conservative1 the cost is about #c to #f an hour for #bd-;hour operation4 ,since each mechanical brain can1 for problems for which it is suited1 do the work of a hundred human computers1 such a machine can save its cost half a dozen times4 ,and these machines are only engineers' models1 built without the advantages of production-line assembly4 ,the cost of giant mechanical brains under design in #aidg and #aidh is in the neighborhood of #ajj1jjj to #bjj1jjj4 ,the main reason for the reduction from the previous cost is the use of cheaper automatic memory4 ,as designs improve and charges for research and development are paid off1 the cost should continue to go down4 ,,new ,,devices ,,for ,,handling ,,information ,in the laboratories working on new mechanical and electronic brains1 scientists are doing a lot of thinking about new devices for handling information4 ,research into devices for storing information shows that magnetic wire as used in sound recording is a rather good storage medium4 ,magnetic ,wire ,for example1 on a hundredth of an inch of fine steel wire we can 8write0 a magnetized spot by means of a small 8writing0 electromagnet4 ,the electromagnet is simply some copper wire coiled around some soft iron shaped in a ,u4 ,when current flows through the coil1 the iron becomes a magnet1 and the tips of the ,u magnetize the little section of the wire between them4 ,the magnetized spot can be of two kinds1 say north-south or south-north1 depending on which way the current flows4 ,we can 8read0 this difference by means of another small 8reading0 electromagnet4 ,we can erase the spot by means of a stronger 8erasing0 magnet that produces a uniform magnetic state throughout the wire4 ,the difference between north-south and south-north corresponds to the difference between #a and #j1 or 8yes0 and 8no10 etc41 and is a unit of information 7see ,chapter #b74 ,many other variations are possible4 ,for example1 the presence or absence of a magnetized spot may be the unit of information1 or the 8writing10 8reading10 and 8erasing0 electromagnets all may be the same4 ,magnetic wire sound recordings made in the #ahij's are still good4 ,this fact shows that magnetic wire may be a more permanent medium for storing information than is paper4 ,stray magnetic forces are likely to have no harmful effect on information stored on magnetic wire1 for these forces would not be strong enough or detailed enough to change greatly the difference between the magnetized spot and its neighboring neutral area4 ,a reel of magnetic wire a mile long and _/ of an inch thick costs about #e4 ,at #hj magnetized spots to the inch1 a mile of wire can store about #e million units of information4 ,hence1 the cost of storing one unit of information is about _/ of a cent4 ,the time needed for changing a magnetized spot from #a to #j or from #j to #a is about _/ of a second4 ,magnetic ,tape ,there is1 however1 a storage device that may be even more useful1 and this is magnetic tape 7see ,fig4 #a74 ,the usual size of such tape is inch wide and #b or #c thousandths of an inch thick4 ,magnetic tape may be made of plastic with magnetic powder all through it1 or it may be of paper coated with magnetic powder1 or it may be of stainless steel or a magnetic alloy1 or it may be of brass or a nonmagnetic alloy coated with a magnetic plating4 ,magnetic tape has the added advantage that from #d to #bj channels across the tape can be filled with magnetized spots1 and the cost then becomes about _/ of a cent per spot4 ,it seems possible that #ajjj units of information can be stored in a quarter of a square inch of magnetic tape4 ,this means that more than #a million units of information can be stored in a cubic inch of space filled with magnetic tape1 and about #b billion units of information in a cubic foot1 except that some of the space should be allotted to the reels and other equipment that hold the tape 7see ,fig4 #b74 ,this is closer packing than printed information in the telephone book1 and yet with magnetic tape we can get to the information automatically4 ,illustration3 ,,fig4 #a4 ,magnetic tape4 ,illustration3 ,,fig4 #b4 ,tape reels4 ,think of the enormous files in libraries1 government1 and business4 ,think of the problems of space and cost and access which these files imply4 ,we can then see that this new development may well be of extraordinary importance4 ,mercury ,tanks ,illustration3 ,,fig4 #c4 ,mercury tank4 ,scientists are investigating other storage devices having still more remarkable properties1 but these have the disadvantage that1 when the power goes off1 the information vanishes4 ,one of these new storage devices is called a mercury tank 7see ,fig4 #c74 ,it consists mainly of a section of iron or steel pipe filled with mercury4 ,at each end of this pipe1 touching the mercury1 is a thin slab of a crystal of quartz4 ,quartz1 which is a common stone1 and which nearly all sand is made of1 changes its shape when pulsed with electricity4 ,we put a pattern of electrical pulses into the quartz slab at one end of the mercury tank2 for example1 we could have the pattern #aaja meaning 8pulse1 pulse1 no pulse1 pulse40 ,the electrical pulses going into the quartz slab make the quartz vibrate4 ,thus ripples are produced in the mercury1 and waves in the pattern #aaja meaning 8wave1 wave1 no wave1 wave0 travel down the tank and strike the quartz slab at the far end4 ,the quartz slab there changes its shape in the rhythm #aaja1 and it converts the waves back into electrical pulses in the same pattern4 ,then we take the pulses out of the far end along a wire1 make them stronger again with an amplifier1 give them the right form again1 and feed them back into the front end of the mercury tank4 ,the mercury tank is a clever use of the principle of an echo1 as when you call across a valley and the rocks answer you back4 ,we can store a pattern of #djj pulses 7each a unit of information1 a #a or a #j1 and each a millionth of a second in duration71 in a mercury tank about #bj inches long4 ,a mercury tank and an echo are examples of delay lines--8lines0 along which waves are 8delayed40 ,electrostatic ,storage ,tube ,another of the memory devices being developed is called an electrostatic storage tube 7see ,fig4 #d74 ,this is a big electronic tube with a screen across one end4 ,the screen may be of two layers3 one of copper1 which conducts electricity1 and one of mica1 a material that does not4 ,in the other end of the tube is a beam of electrons1 which we can turn on and off and shoot at any of #b or #c thousand specific points or spots on the screen4 ,illustration3 ,,fig4 #d4 ,electrostatic storage tube4 ,there are two sizes of electric charge or quantity of electrons2 we can call these #a and #j4 ,in about a millionth of a second1 we can put either size of charge on one of the spots of the screen4 ,with other circuits we can keep it there as long as we want1 if the power does not flicker off4 ,we can 8remember0 perhaps #b or #c thousand units of information in one of these electronic tubes4 ,we can read1 write1 or erase any unit of information in a few millionths of a second4 ,neither the mercury tank nor the electrostatic storage tube had1 by the end of #aidg1 been put into a working mechanical brain4 ,but there is good reason to believe that they will be successful devices and will open up a new era of speed in storing and referring to information4 ,in fact1 several laboratories are developing electronic calculating circuits using these devices which will perform up to #ajj1jjj additions a second or #aj1jjj multiplications a second4 ,our minds certainly stagger at the thought of such speeds4 ,,new ,,operations ,many kinds of combining operations have already been built into one or more mechanical brains4 ,the operations may be arithmetical3 addition1 subtraction1 multiplication1 division1 looking up numbers in tables1 etc4 ,or the operations may be logical3 comparing1 selecting1 checking1 etc4 ,additional logical operations will be built into some of the mechanical brains now being constructed3 sorting1 collating1 matching1 merging1 etc4 ,,new ,,ideas ,,in ,,programming ,programming--the way to give instructions to machines--is also being studied in the laboratories4 ,several new ideas of importance have developed as a result4 ,one idea is that the machine should be able to store its instructions or program or routine in its memory in just the same physical ways as it stores numbers4 ,there is basically no reason why numbers only should be stored in some registers1 and instructions only stored in other registers4 ,another idea is that the machine should have in its permanent memory any subroutine it may need4 ,for example1 a subroutine should always be available in the machine for finding square root4 ,at any time when a square root was needed1 we would only have to call on the machine for the subroutine of square root4 ,the machine would then consult the right part of its memory and carry out the subroutine for square root4 ,a third idea1 and one of the most interesting1 is that the machine should be able to compute its own instructions4 ,for example1 consider a program for finding the product of two matrices 7see ,supplement #b71 each of #ajj terms in an array of #aj columns and #aj rows1 resulting in a new matrix of #ajj terms4 ,the whole program can be made to consist of about #ej orders4 ,only one of them is 8multiply10 and only one of them is 8add02 the other orders consist of how to choose expressions to be multiplied or added1 etc4 ,such problems as these are often fascinating to mathematicians1 who love to play with the intricate ideas needed4 ,,new ,,ideas ,,in ,,reliability ,reliability has a number of aspects3 #a4 ,no wrong results allowed out of the machine4 #b4 ,few failures4 #c4 ,rapid location of failures4 #d4 ,quick repair or replacement of parts that fail4 #e4 ,easy maintenance4 #f4 ,unattended operation overnight4 ,for example1 ,bell ,laboratories proved that mechanical brains can be built so that no wrong results are allowed to come out4 ,in other words1 the machine checks itself all the time as it goes along and stops at once if the check shows that something is wrong4 ,this is likely to be a standard feature of new automatic thinking machinery4 ,the frequency of failures in the machinery being designed in the laboratories may be of the order of one or two mechanical failures a week4 ,for any type of failure an alarm circuit and trouble lights will show what part of the machine needs attention4 ,plug-in parts for replacement are already in use in at least two of the four mechanical brains described and should be available in all the new machines4 ,it is possible to build a machine that will automatically change from failing equipment to properly functioning equipment4 ,for some years though1 this may be too expensive to be reasonable4 ,the use of magnetic tape for storage reduces greatly the number of parts and so increases reliability4 ,for example1 instead of #ah1jjj electronic tubes in an electronic brain1 there may be less than #cjjj4 ,a final degree of reliability is gained when most of the time the machine operates unattended4 ,then1 there is no human operator standing by who may fail to do the correct thing at the moment when the machine needs some attention4 ,in fact1 the motto for the room housing a mechanical brain should become1 8,don't think2 let the machine do it for you40 ,unattended operation from the end of one working day to the beginning of the next1 with the machine changing itself from one problem to another problem1 has already been proved possible on the ,bell ,laboratories machine4 ,,auxiliary ,,devices ,in order to use a mechanical brain1 we have to give it and take from it language that it understands1 machine language4 ,a mechanical brain that can do #aj1jjj additions a second can very easily finish almost all its work at once4 ,how can we1 slow as we are1 keep our friend1 the giant brain1 busy8 ,we have found so far several answers to this question1 none of them yet very good4 ,devices for preparing input will be very important4 ,for each brain1 we shall need a great many of these devices4 ,for1 at best1 we type at a rate1 say1 of #d characters a second1 selecting any one of some #ch keys1 each of which is equivalent to about #f units of information4 ,this is about #hjj units of information per second4 ,the machine1 however1 is likely to be able to gulp information from its input mechanism at the amazing rate of #fj1jjj units of information per second1 equal to #ge people typing with no mistakes and no resting4 ,fortunately1 at least some of the time the machine will be busy computing6 ,for an input-preparation device1 we may get something that can be fastened to an ordinary typewriter and that will produce magnetic tape agreeing with what is printed by the typewriter4 ,since the input information must be carefully verified1 we shall need a second magnetic tape device such as exists for paper tape on the ,bell ,laboratories machine3 the processor4 ,the processor takes two hand-prepared tapes1 compares them1 reports any differences1 and produces a third tape4 ,the third tape copies the two original tapes if they agree1 and it receives corrected information as furnished by a girl at a keyboard if the two original tapes disagree4 ,for information already on punch cards1 we need an input device that will read punch cards and write on magnetic tape4 ,where information is on punched paper tape1 we need a machine that will read punched paper tape and write on magnetic tape4 ,problem data1 tables of numbers1 and routine instructions will go into the mechanical brain4 ,they will all be prepared on regular input devices4 ,the machine will accept information in the form in which it is most convenient for you and me to prepare it4 ,then1 the machine will be instructed to change the information into the form with which it is most convenient for the machine to operate4 ,many output devices will also be needed1 since the machine will be able to produce information very swiftly4 ,these output devices might be cabled to the machine4 ,a kind of traffic control system would govern them4 ,each will have a magnetic tape that will be loaded up swiftly with information4 ,then the output device will unload its information more slowly1 in any form that we may desire3 printing1 graphs1 film1 punch cards1 or punched paper tape4 ,the machine is likely to be able to put out information on magnetic tape at the same high speed of #fj1jjj units of information per second or #aj1jjj characters per second4 ,but the best printing speed of an electric typewriter is about #aj or #ab characters a second4 ,card-punching speed is about #acj characters a second4 ,punch-card tabulator speed can reach a maximum of about #bjj characters a second4 ,thus we see that here1 too1 we may be snowed under with the information that the giant brain puts out1 if we fail to ask the giant only for what we really want4 ,,mechanical ,,brains ,,under ,,construction ,this chapter would not be complete without mention of the great mechanical brains that were actually under construction at the end of #aidg4 ,in power they are intermediate between the machinery now being designed1 described in this chapter1 and the earlier machines described in the previous chapters of this book4 ,the mechanical brains under construction on ,december #ca1 #aidg1 were3 ,harvard's ,sequence-,controlled ,relay ,calculator ,mark ,,ii1 constructed at the ,harvard ,computation ,laboratory1 tested there ,july #aidg to ,january #aidh1 and delivered to the ,naval ,proving ,ground1 ,dahlgren1 ,va41 in #aidh4 ,the ,,ibm ,selective-,sequence ,electronic ,calculator1 constructed in the ,,ibm laboratories1 ,endicott1 ,n4 ,y41 and installed in #aidg at the office of ,international ,business ,machines1 #eij ,madison ,ave41 ,new ,york1 ,n4 ,y4 ,moore ,school of ,electrical ,engineering's ,,edvac 7,electronic ,digital ,variable ,automatic ,computer7 being constructed partly at ,moore ,school and partly elsewhere1 and to be delivered to the ,ballistic ,research ,laboratories1 ,aberdeen1 ,md4 ,harvard's ,sequence-,controlled ,electronic ,calculator ,mark ,,iii1 being constructed at the ,harvard ,computation ,laboratory1 and to be delivered to the ,naval ,proving ,ground1 ,dahlgren1 ,va4 ,we shall cover briefly 7and perhaps a little technically7 some of the main features of the first two of these machines2 for1 during #aidh1 they began to do problems4 ,the other two had not been finished by the end of #aidh and so would be difficult to describe correctly1 for mechanical brains grow1 and design changes go on until they are finished--and even afterwards4 ,some information about these machines can be obtained from the organizations referred to above and from reports that should appear from time to time in some of the journals mentioned in ,supplement #c4 ,there is also a regular section entitled 8,automatic ,computing ,machinery0 in the quarterly ,mathematical ,tables and ,other ,aids to ,computation1 where it is likely that current information may be found4 ,harvard's ,mark ,,ii ,the ,harvard ,sequence-,controlled ,calculator ,mark ,,ii began to do problems under test during ,july #aidg4 ,this machine is at least twelve times as powerful as ,mark ,i 7see ,chapter #f7 and was constructed entirely by the ,harvard ,computation ,laboratory4 ,the machine contains about #ac1jjj relays of a new type that will operate reliably within _/ of a second4 ,numbers in the machine are regularly of #aj decimal digits between #a4jjj1jjj1jjj and #i4iii1iii1iii1 inclusive1 multiplied by a power of #aj between #a1jjj1jjj1jjj1jjj1jjj and #j4jjj1jjj1jjj1jjj1jja1 inclusive4 ,for storage of numbers1 the machine has #ajj relay registers totaling about #abjj decimal digits4 ,also1 it can consult any one of #h tape feeds for numbers and any one of #d tape feeds for instructions4 ,effectively1 the machine can read one number and one instruction from paper tape in _/ of a second4 ,the machine performs all arithmetical and most logical operations4 ,in every second it can carry out #d multiplications1 #h additions 7or subtractions71 and #ab transfers4 ,division is performed by rapid approximation using the other operations4 ,in each second the machine can perform #cj instructions4 ,an instruction is expressed by #f digits between #j and #g which you can select and1 in effect1 by #c more digits fixed by the time 7within the second7 when the machine reads the instruction4 ,for example1 in the #ith instruction of the #cj instructions in each second1 we can specify a multiplicand4 ,but1 if we do not want to multiply right then--a rare event if we are coding wisely--we leave the #ith instruction empty4 ,the machine may operate as a whole1 attending to one problem2 or the machine may be separated into halves1 and each half will attend to its own problem4 ,the ,,ibm ,selective-,sequence ,electronic ,calculator ,the ,,ibm ,selective-,sequence ,electronic ,calculator was announced publicly on ,january #bg1 #aidh1 after some months of trial running4 ,it is a large and powerful mechanical brain1 and it is the intention of ,international ,business ,machines to devote it to solving scientific problems4 ,the staff of the ,watson ,scientific ,computing ,laboratory in ,new ,york will be mainly in charge of the machine4 ,the machine contains about #ab1ejj electronic tubes and about #ba1ejj relays4 ,numbers in the machine are regularly of either #ad or #ai decimal digits4 ,instructions are expressed as numbers4 ,for storage of information1 the machine has a capacity of #h registers totaling #afj decimal digits of very rapid memory in electronic tubes4 ,also1 it has about #aej registers totaling #cjjj decimal digits of less rapid memory in relays4 ,also1 it can consult any one of #ff paper tape feeds2 each row on a paper tape can hold up to #gh punched holes or #ai decimal digits1 and the machine can consult #be rows on one tape in one second4 ,these paper tapes together give the machine about #djj1jjj decimal digits of memory4 ,for arithmetical and logical operations1 the machine has an arithmetical unit using electronic tubes4 ,this unit can carry out about #ej multiplications or about #bej additions per second1 including the transfers of numbers4 ,in each second the machine can read and perform #ej instructions1 and each instruction consists1 usually1 of getting two numbers out of two relay registers1 performing an operation1 and putting the result into a third relay register4 ,eckert-,mauchly's ,binac ,as this book went to press1 another mechanical brain1 the ,electronic ,binary ,automatic ,computer1 or ,,binac1 was announced on ,august #bb1 #aidi4 ,this machine was constructed by the ,eckert-,mauchly ,computer ,corporation1 ,philadelphia1 ,pa41 for ,northrop ,aircraft1 ,inc41 ,hawthorne1 ,calif4 ,this machine has some remarkable properties4 ,it does addition or subtraction at the rate of #cejj per second4 ,it does multiplication or division at the rate of #ajjj per second4 ,the input is from a keyboard or magnetic tape2 the output is to magnetic tape or an electric typewriter4 ,binac has #eab registers of very rapid memory in mercury tanks1 and each register holds #cj binary digits4 ,the machine actually is a pair of twins3 the storage1 the computing element1 and the control are double1 and each twin runs in step with the other and checks every operation of the other4 ,in tests in ,july the machine ran over #aj consecutive hours with no error4 ,each twin has only #gjj electronic tubes4 ,binac handles all numbers in binary notation1 except that the keyboard and the typewriter express numbers in octal notation 7see ,supplement #b74 ,finally1 ,binac is only #e feet high1 #d feet long1 and one foot wide4 ,chapter #aa ,,the ,,future3 ,,machines ,,that ,,think1 ,,and ,,what ,,they ,,might ,,do ,,for ,,men ,the pen is mightier than the sword1 it is often said4 ,and if this is true1 then the pen with a motor may be mightier than the sword with a motor4 ,in the ,middle ,ages1 there were few kinds of weapons1 and it was easy for a man to protect himself against most of them by wearing armor4 ,as gunpowder came into use1 a man could no longer carry the weight of armor that would protect him1 and so armor was given up4 ,but in #aiag1 armor1 equipped with a motor and carrying the man and his weapons1 came back into service--as the tank4 ,in much the same way1 in the ,middle ,ages1 there were few books1 and it was easy for a man to handle nearly all the information that was in books4 ,as the printing press came into use1 man's brain could no longer handle all recorded information1 and the effort to do so was given up4 ,but in #aidd1 a brain to handle information1 equipped with a motor and supporting the man and his reasoning1 came into existence--as the sequence-controlled calculator4 ,in previous chapters we have examined some of the giant mechanical brains that have been finished2 we have also considered the design of such machines4 ,now in this chapter we shall discuss the future significance of machines that think1 of motorized information4 ,we shall discuss what we can foresee if we look with imagination into the future4 ,there are two questions we need to ask3 ,what types of machines that think can we foresee8 ,what types of problems to be solved by these machines can we foresee8 ,,future ,,types ,,of ,,machines ,,that ,,think ,the machines that already exist show that some processes of thinking can already be performed very quickly3 ,calculating3 adding1 subtracting1444 ,reasoning3 comparing1 selecting1444 ,referring3 looking up information in lists1444 ,we can expect other processes of thinking to come up to high speed through the further development of thinking machines4 ,automatic ,address ,book ,nowadays when we wish to send out announcements of an event1 like going to ,south ,america for a year1 we may copy the addresses of our friends onto the envelopes by hand4 ,in the future1 we can see our address book as a spool of magnetic tape4 ,when we wish to send out announcements1 we put a stack of blank envelopes into the machine that will read the magnetic tape1 and we press a button4 ,out will come the envelopes addressed4 ,if we wish to select only those friends of ours whose last names we put down on a list1 we can write the list on another magnetic tape1 place it also in the machine1 and set a few switches4 ,then the machine will read the names on the list1 find their addresses in the address-book tape1 and prepare only the envelopes we want4 ,if a friend's address changes1 we can notify the machine4 ,it will find his old address1 erase it1 and enter the new address4 ,automatic ,library ,we can foresee the development of machinery that will make it possible to consult information in a library automatically4 ,suppose that you go into the library of the future and wish to look up ways for making biscuits4 ,you will be able to dial into the catalogue machine 8making biscuits40 ,there will be a flutter of movie film in the machine4 ,soon it will stop1 and1 in front of you on the screen1 will be projected the part of the catalogue which shows the names of three or four books containing recipes for biscuits4 ,if you are satisfied1 you will press a button2 a copy of what you saw will be made for you and come out of the machine4 ,after further development1 all the pages of all books will be available by machine4 ,then1 when you press the right button1 you will be able to get from the machine a copy of the exact recipe for biscuits that you choose4 ,we are not yet at the end of foreseeable development4 ,there will be a third stage4 ,you will then have in your home an automatic cooking machine operated by program tapes4 ,you will stock it with various supplies1 and it will put together and cook whatever dishes you desire4 ,then1 what you will need from the library will be a program or routine on magnetic tape to control your automatic cook4 ,and the library1 instead of producing a pictorial copy of the recipe for you to read and apply1 will produce a routine on magnetic tape for controlling your cooking machine so that you will actually get excellent biscuits6 ,of course1 you may have other kinds of automatic producing machinery in your home or office4 ,the furnishing of routines to control automatic machinery will become a business of importance4 ,automatic ,translator ,another machine that we can foresee would be used for translating from one language to any other4 ,we can call it an automatic translator4 ,suppose that you want to say 8,how much80 in ,swedish4 ,you dial into the machine 8,how much80 and press the button 8,swedish10 and the machine will promptly write out 8,hur mycket80 for you4 ,it also will pronounce it1 if you wish1 for there would be little difficulty in recording on magnetic tape the pronunciation of the word as spoken by a good speaker of the language4 ,the machine could be set to repeat the pronunciation several times so that the student could really learn the sound4 ,he could learn it better1 probably1 by hearing it and trying to say it than he could by using any set of written symbols4 ,automatic ,typist ,we now come to a possible machine that uses a new principle4 ,this principle is that of being able to recognize signs4 ,this machine would perceive writing on a piece of paper and recognize that all the a's that appear on the paper are cases of a1 and that all the b's that appear on it are instances of b1 and so forth4 ,the machine could then control an electric typewriter and copy the marks that it sees4 ,the first stage of this machine would be one in which only printed characters of a high degree of likeness could be recognized4 ,in later stages1 handwriting1 even rather illegible handwriting1 might be recognizable by the machine4 ,we can call it an automatic typist4 ,the elements of the automatic typist would be the following3 #a4 ,phototubes 7electronic tubes sensitive to the brightness of light71 which could sense the difference between black and white 7these already exist74 #b4 ,a memory of the shapes of #eb letters1 #aj digits1 and punctuation marks4 ,fine distinctions would be required of this memory in some cases--like the difference between the numeral #e and the capital letter ,s4 #c4 ,a control that would cause the machine to tune itself1 so that a good matching between the marks it observed and the shapes it remembered would be reached4 #d4 ,a triggering control so that1 when the machine had reached good enough matching between its observations and its memory1 the machine would proceed to identify the marks1 read them1 and transfer them4 #e4 ,an electric typewriter1 which would respond to the transferred instructions4 7,this also already exists47 ,this machine is perhaps not so farfetched as it might seem4 ,during ,world ,war ,,ii1 gun-aiming equipment using the new technique radar reached a high stage of development4 ,many shots that disabled and sank enemy ships were fired in total darkness by radar-controlled guns4 ,on the glowing screen in the control room1 there were two spots1 one that marked the target and one that reported the point at which the gun was aimed4 ,these two spots could be brought almost automatically into agreement4 ,in the same way1 a report from a phototube telling the shape of an observed mark and a report from the memory of the machine telling the shape of a similar mark could be compared by the machine for likeness and1 if judged enough alike1 could be approved as identical4 ,even the phrase 8enough alike0 can be applied by a machine4 ,during ,world ,war ,,ii1 tremendous advances were made in machinery for deciphering enemy messages4 ,machines observed various features and patterns in enemy messages1 swiftly counted the frequency of these features1 and carried out statistical tests4 ,then the machines selected those few cases in which the patterns showed meaning instead of randomness4 ,a machine like the automatic typist1 if made flexible enough1 would be1 of course1 extremely useful4 ,a great load of dull office work is now being thrown on clerks whose task is to translate from writing and typing into languages that machines can read1 such as punch cards4 ,at the present time1 if punch-card machines are widely used in a big company1 the company must employ large numbers of girls whose sole duty is to read papers and punch up cards4 ,a still bigger chore is the work of typists in all kinds of businesses whose main duty is to read handwriting1 etc41 and then copy the words on a typewriter4 ,illustration3 ,each square in the grill is watched by a phototube4 ,,fig4 #a4 ,scheme for distinguishing ,a and ,h by #ae phototubes4 ,research has already begun on various features of the automatic typist because of its obvious labor-saving value4 ,for example1 many patents have been issued on schemes for dividing the area occupied by a letter or a digit into an array of spots1 with a battery of phototubes each watching a spot4 ,the reports from the phototubes together will distinguish the letter or digit4 ,for example1 if we consider ,a and ,h placed in a grill of fifteen spots1 #e long by #c wide 7see ,fig4 #a71 then the phototubes can distinguish between ,a and ,h by sensing black or white in the spot in the middle of the top row4 ,when we consider how easily and swiftly a human being does this1 we can once more marvel at the recognizing machine we all carry around with us in our heads4 ,automatic ,stenographer ,another development that we can foresee is one that we can call the automatic stenographer4 ,this is a machine that will listen to sounds and write them down in properly spelled ,english words4 ,the elements of this machine can be outlined3 #a4 ,microphones1 which can sense spoken sounds 7these already exist74 #b4 ,a memory storing the #dj 7more or less7 phonetic units or sounds that make up ,english1 such as the #bc consonant sounds1 p b l ng f v m th t d n r s z h y k g w ch j sh zh 7heard in 8pleasure07 and the #ag vowel sounds1 ,,long ,,short ,,other ,a 78ate07 a 78cat07 ar 78are07 ,e 78eat07 e 78end07 aw 78awe07 ,i 78isle07 i 78in07 er 78err07 ,o 78owe07 o 78on07 ow 78owl07 ,u 78cute07 u 78up07 oi 78oil07 ,,oo 78roof07 oo 78book07 #c4 ,a collection of the rules of spelling in ,english1 containing many statements like ,the sound b is always spelled b ,the sound sh may be spelled sh 7ship71 s 7sugar71 ti 7station71 ci 7physician71 ce 7ocean7 or tu 7picture7 and other statements based on context1 word lists1 derivation1 etc4 ,these are the statements by means of which a good ,english speller knows how to spell even words that he hears for the first time4 #d4 ,a triggering control so that1 when the machine reaches good enough matching between its observations of sounds1 its memory of sounds1 and its knowledge of spelling rules1 the machine will identify groups of sounds as words1 determine their spelling1 and report the letters determined4 #e4 ,an electric typewriter1 which would type the reported letters4 ,with this type of machine1 you would dictate your letters into a machine 7now existing7 that would record your voice4 ,then the record would be placed on the automatic stenographer1 and out would come your letters written and spaced as they should be4 ,automatic ,recognizer ,we can foresee a recognizing machine with very general powers4 ,suppose that we call it an automatic recognizer 7see ,fig4 #b74 ,it will have the following elements3 #a4 ,input4 ,this element will consist of a set of observing instruments1 capable of perceiving sights1 sounds1 etc4 ,there will be ways of positioning or tuning these instruments4 #b4 ,memory4 ,this element will store knowledge4 ,it may store the patterns of observations that we are interested in2 or it may store general rules on how to find patterns of observations that we will be interested in4 ,it will contain knowledge about acceptable groups of patterns1 about actions to be performed in response to patterns1 etc4 #c4 ,program #a4 ,the element 8,program #a0 performs a set of standard instructions4 ,under these instructions1 the machine3 ,compares group after group of observations with the information in the memory4 ,compares these groups with patterns furnished1 or seeks to organize the observations into patterns4 ,counts cases and tests frequencies4 ,finds out how much matching with patterns there is4 ,tunes the observing instruments in ways to increase matching4 ,illustration3 ,,fig4 #b4 ,scheme of an automatic recognizer4 #d4 ,program #b4 ,the element 8,program #b0 performs another set of standard instructions4 ,under these instructions1 the machine1 if it is tuned well1 matches sets of observations one after another with the patterns and so reads them4 #e4 ,triggering ,control4 ,this element shifts the control of the machine from ,program #a to ,program #b4 ,it does this when the machine reaches 8good matching40 ,we shall set the meaning of this into the machine in much the same way as we set 8warm0 into a thermostat4 #f4 ,output4 ,this element performs any action that we want1 depending on recognized patterns read and any other knowledge or instructions stored in the memory4 ,the automatic recognizer will be capable of extraordinary tasks4 ,with microphones and a large memory1 this type of machine would be able to hear a foreign language spoken and translate it into spoken or written ,english4 ,with phototubes and with an expanded filtering and decoding capacity as in deciphering machines1 the automatic recognizer should be able to read a dead language1 even those 7such as ,minoan or ,etruscan7 that have so far resisted efforts to read it4 ,the machine would derive rules for the translation of the language and translate any sample4 ,an automatic recognizer could perhaps be equipped with many sensitive1 tiny observing instruments that could be placed around or in the brain and nervous systems of animals4 ,then the machine might enable us to find out what activity in the nervous system corresponds with what activity in the animal4 ,,types ,,of ,,problems ,,that ,,machines ,,will ,,solve ,,in ,,the ,,future ,we turn now to the second question regarding the future of machines that think3 ,what types of problems can we foresee as solved by these machines8 ,problems of ,control ,probably the foremost problem which machines that think can solve is automatic control over all sorts of other machines4 ,this involves controlling a machine that is running so that it will do the right thing at the right time in response to information4 ,for example1 suppose that you are mowing a lawn with a mowing machine4 ,you watch the preceding strip so as to stay next to it4 ,you watch the ends of the strips1 where you turn around4 ,if a stick is caught in the cutting blade1 you stop and take it out4 ,now it is entirely possible to put devices on the mowing machine so that all these things will be taken care of automatically4 ,in fact1 in the case of plowing a large field1 a tractor-plow can be equipped with a device that guides it next to the preceding furrow4 ,thus1 once the first furrow around the edge has been made1 riderless tractors will plow a whole field and stop in the middle4 ,for another example1 take a gas furnace for heating steam to keep a house warm4 ,such a furnace has automatic controls1 which respond to the following information whenever reported3 ,house too warm4 ,house not warm enough4 ,too much steam pressure4 ,not enough water in boiler4 ,gas flame not lit4 ,daytime4 ,nighttime4 ,in fact1 your own meaning of 8warm0 can be put into the control system3 you set the dial on your thermostat at the temperature that 8warm0 is to be for you4 ,in the future many kinds of automatic control will be common4 ,we shall have automatic pilots for flying and landing airplanes4 ,we shall have automatic missiles for destructive purposes1 such as bombing and killing1 and for constructive purposes1 such as delivering mail and fast freight4 ,an article in the magazine ,fortune for ,november #aidf described the automatic factory 7see ,supplement #c74 ,this is a factory in which there would be automatic arms for holding stuff being manufactured1 and automatic feed lines for supplying material just where it is needed4 ,all this factory would be controlled by machines that handle information automatically and produce actions that respond to information4 ,this prospect fills us with concern as well as with amazement4 ,how shall we control these automatic machines1 these robots1 these ,frankensteins8 ,what will there be left for us to do to earn our living8 ,but more of this in the next chapter4 ,problems of ,science ,other problems for which we can foresee the use of machines that think are the understanding1 and later the controlling1 of nature4 ,one of these problems is weather forecasting and weather control4 ,the ,weather ,brain ,we can imagine the following type of machine--a weather brain4 ,a thousand weather observatories all over the country observe the weather at #h ,a4,m4 ,the observations are fed automatically through a countrywide network of communication lines into a central station4 ,here a giant machine1 containing a great deal of scientific knowledge about the weather1 takes in all the data reported to it4 ,at #h3ae the weather brain starts to calculate2 in half an hour it has finished1 having produced an excellent forecast of the weather for the whole country4 ,then it proceeds to transmit its forecast all over the country4 ,by #h3ej every weather station1 newspaper1 radio station1 and airport in the country has the details4 ,in ,october #aide1 ,dr4 ,v4 ,k4 ,zworykin of the ,princeton ,laboratories of the ,radio ,corporation of ,america proposed solving the problem of weather forecasting in this way by a giant brain4 ,the weather brain will have a second stage of application4 ,from time to time and here and there1 the weather is unstable3 it can be triggered to behave in one way or another4 ,for example1 recently1 pellets of frozen carbon dioxide--often called ,dry ,ice--have been dropped from planes and have caused rain4 ,in fact1 a few pounds of ,dry ,ice have apparently caused several hundred tons of rain or snow4 ,in similar ways1 we may1 for example1 turn away a hail storm so that hail will fall over a barren mountain instead of over a farming valley and thus protect crops4 ,or we may dispel conditions that would lead to a tornado1 thus avoiding its damage4 ,both these examples involve local weather disturbances4 ,however1 even the greatest weather disturbances1 like hurricanes and blizzards1 may eventually be directed to some extent4 ,thus the weather may become to some degree subject to man's control1 and the weather brain will be able to tell men where and when to take action4 ,psychological ,testing ,another scientific problem to which new machinery for handling information applies is the problem of understanding human beings and their behavior4 ,this increased understanding may lead to much wiser dealing with human behavior4 ,for example1 consider tests of aptitudes4 ,if you take one of these tests1 you may be asked to mark which word out of five suggested ones is nearest in meaning to a given word4 ,or your test may be #dj simple arithmetical problems to be solved in #be minutes4 ,or you may be given a sheet with #bj circles1 and be asked to put #c dots in the first1 #g dots in the second1 #d dots in the third1 #aa dots in the fourth1 and so on1 irregularly2 you may be given a total of #de seconds to do this as well as you can4 ,now1 if a vocational counselor gives you one of these tests1 and if you get #hd out of #ajj on it1 he needs to know just what he has measured about you4 ,also1 he needs to know whether he can reasonably forecast that1 as a result of your grade of #hd1 you will be good at writing articles1 or good at supervising the work of other people1 or good at designing in a machine shop4 ,he needs to know the records of people with scores of about #hd on this test and to have evidence supporting his forecasts4 ,if we wish to make the most use of the tests1 we need to carry out a good deal of statistics1 mathematics1 and logic4 ,for example1 it will turn out that answers to some questions are much more significant than answers to others1 and so we can greatly improve the quality of the tests by keeping only the more significant questions4 ,powerful machinery for handling calculations will be very useful in the field of aptitude testing4 ,but1 you may ask1 what if the person analyzing your answers has to use interpretations and judgments8 ,if the judgments and interpretations can be expressed in words1 and if the words can be translated into machine language1 then the machine can carry out the analysis4 ,usually the difference between a rule and a judgment is simply this3 a rule in a case in which it is hard to express all the factors being considered is called a judgment4 ,psychological ,trainer ,it is conceivable that machines that think can eventually be applied in the actual treatment of mental illness and maladjustment4 ,consider what a physician does4 ,in treating a psychiatric case1 such as a neurosis1 a physician uses words almost entirely4 ,he asks questions4 ,he listens to the patient's answers4 ,each answer takes the physician nearer and nearer to a diagnosis4 ,by and by the physician knows what most of the difficulty is4 ,then he must present his knowledge slowly to the patient1 gradually guiding the patient to understanding4 ,it is a psychological truth that telling a man in ten minutes what is wrong with him does not cure him4 ,the physician seeks to free the patient from the tormenting circles of habit and worry in which he has been trapped4 ,often the diagnosis is short and the treatment is long2 the reasons for the neurosis may soon be clear to the physician1 but they may take months to become clear to the patient4 ,now let us consider the following kind of machine as an aid to the physician4 ,we might call this kind of machine a psychological trainer1 for in many ways it is like the training machines used in ,world ,war ,,ii for training a pilot to fly an airplane4 ,the psychological trainer would have the following properties3 #a4 ,the machine is able to show sound movies--produce pictures and utter words4 #b4 ,it is able to put before the patient3 situations1 problems1 questions1 experiences1 etc4 #c4 ,it is able to take in responses from the patient4 #d4 ,it is able to receive a program of instructions from the physician4 #e4 ,depending on the responses of the patient and on the program from the physician1 the training machine can select more material to put before the patient4 #f4 ,the training machine produces a record of what it presented and of how the patient responded1 so that the physician and the patient can study the record later4 ,what sort of films would the machine hold8 ,the machine could be loaded with a number of films which would help in the particular type of neurosis from which the patient was suffering4 ,what sort of responses could the patient make8 ,the patient might have buttons in front of him which he could press to indicate such answers as3 ,yes ,i don't know ,repeat ,no ,it depends ,go ahead ,also1 the patient might hold a device--like a lie detector1 perhaps--which would report his state of tenseness1 etc41 and so report what he really felt4 ,where would the machine's questions come from8 ,from one or more physicians very clever in the treatment of mental illness4 ,suppose that the patient is inconsistent in his answers8 ,the machine1 discovering the inconsistencies1 could return to the subject and ask related questions in a different way4 ,as soon as several questions related to the same point are answered consistently1 the machine could exclude groups of questions that no longer apply and could proceed to other questions that would still apply4 ,patients would vary in their ability to go as fast as the machine could4 ,so from time to time the machine would ask questions to test the effect of what it had presented2 and1 depending on the answers1 the machine would go faster or would bring in additional material to clarify some point4 ,this machine might have a few advantages over ordinary treatment4 ,for example1 with the machine1 treatment does not depend on the physician's making the right answer in a split second1 as it may in a personal interview4 ,also1 the patient might be franker with the machine than with the physician1 for it might be arranged that the patient could review his record1 and then decide whether to confess it to his physician4 ,such a machine would enable physicians to treat many more patients than they now can4 ,in fact1 it is estimated that nearly #ej per cent of persons who consult physicians are suffering only from mental illness4 ,such a machine would therefore be a great help4 ,problems of ,business ,another large group of problems for which we can foresee the use of machines that think is found in business and economics4 ,for example1 consider production scheduling in a business or a factory4 ,the machine takes in a description of each order received by the business and a description of its relative urgency4 ,the machine knows 7that is1 has in its memory7 how much of each kind of raw material is needed to fill the order and what equipment and manpower are needed to produce it4 ,the machine makes a schedule showing what particular men and what particular equipment are to be set to work to produce the order4 ,the machine turns out the best possible production schedule1 showing who should do what when1 so that all the orders will be filled in the best sequence4 ,what is the 8best0 sequence8 ,we can decide what we think is the best sequence1 and we can set the machine for making that kind of selection1 in the same way as we decide what is 8warm0 and set the thermostat to produce it6 ,on a much larger scale1 we can use mechanical brains to study economic relations in a society4 ,everything produced in a society is made by consuming some materials1 labor1 equipment1 and skill4 ,the output produced by one man or factory or industry becomes the input for other men1 factories1 industries4 ,in this way all economic units are linked together by many different kinds and degrees of dependence4 ,the situation is1 of course1 complicated3 it changes as time goes on and as people want different things produced4 ,economists have already set up simple models of economic societies and have studied them4 ,but with machines that think1 it will be possible to set up and study far more complicated models--models that are very much like the society we live in4 ,we can then answer questions of economics by calculation instead of by arguments and counting noses4 ,we shall be able to solve definitely such problems as3 8,how will a rise in the price of steel affect the farming industry80 8,how much money must be paid out as wages and salaries so that consumer purchasing power will buy back what industry produces80 ,machines and the ,individual ,what about the ordinary everyday effects of these machines upon you and me as an individual8 ,we can see that the new machinery will apply on a small scale even to us4 ,small machines using a few electronic tubes--much like a radio set1 for example--and containing spools of magnetic wire or magnetic tape will doubtless be available to us4 ,we shall be able to use them to keep addresses and telephone numbers1 to figure out the income tax we should pay1 to help us keep accounts and make ends meet1 to remember many things we need to know1 and perhaps even to give us more information4 ,for there are a great many things that all of us could do much better if we could only apply what the wisest of us knows4 ,we can even imagine what new machinery for handling information may some day become3 a small pocket instrument that we carry around with us1 talking to it whenever we need to1 and either storing information in it or receiving information from it4 ,thus the brain with a motor will guide and advise the man just as the armor with a motor carries and protects him4 ,chapter #ab ,,social ,,control3 ,,machines ,,that ,,think ,,and ,,how ,,society ,,may ,,control ,,them ,it is often easier for men to create a device than to guide it well afterwards3 it is often easier for a scientist to study his science than to study the results for good or evil that his discoveries may lead to4 ,but it is not right nor proper for a scientist1 a man who is loyal to truth as an ideal1 to have no regard for what his discoveries may lead to4 ,this principle is now being widely recognized4 ,many scientists today--both as individuals and as groups1 and especially the atomic scientists--are considering the results of their scientific discoveries2 and they are sharing in the effort to render those results truly useful to humanity4 ,it would be easy to leave out of this book any discussion of how machines that think may be controlled1 any consideration of how they may be made truly useful to humanity4 ,but that would be hardly right or proper4 ,in concluding a book such as this one1 that touches on many aspects of machines that think1 we need to consider what can and should be done to make such machines of true benefit to all of humanity4 ,so1 we come to the most important of all our questions3 ,what sort of control over machines that think do we need in human society8 ,,machine ,,that ,,both ,,thinks ,,and ,,acts ,from a narrow point of view1 a machine that only thinks produces only information4 ,it takes in information in one state1 and it puts out information in another state4 ,from this viewpoint1 information in itself is harmless2 it is just an arrangement of marks2 and accordingly1 a machine that thinks is harmless1 and no control is necessary4 ,although it is true that the information produced only becomes good or evil after other machinery or human beings act on the information1 in reality a machine with the power to produce information is constructed only for the reason of its use4 ,we want to know what such machines can tell us only because we can then proceed to act much more efficiently than before4 ,for example1 a guided missile needs a mechanical brain only because then it can reach its target4 ,in all cases mechanical brains are inseparable from their uses4 ,for the purposes of this chapter1 the narrow view will be rejected because it dodges the issue4 ,we shall be much concerned with the combination of a machine that thinks with another machine that acts2 and we shall often call this combination the robot machine4 ,,reading ,,this ,,chapter ,now1 before launching further into the discussion1 we need to say that the conclusions suggested in this chapter are not final4 ,even if they are expressed a little positively in places1 they are nevertheless subject to change as more information is discovered and as the appraisal of information changes with time4 ,also1 almost any conclusions about social control--including1 certainly1 the conclusions in this chapter--are subject to controversy4 ,but controversy is good3 it leads to thought4 ,the more minds that go to work on solving the problem of social control over robot machines and other products of the new technology--which is rushing upon us from the discoveries of the scientists--the better off we all will be4 ,if1 while stimulating disagreement1 the ideas expressed in this chapter should succeed in stimulating thought and deliberation1 the purpose of this chapter will be well fulfilled4 ,up to this point in this book1 the emphasis has been on possibilities of benefits to humanity that may arise from machines that think4 ,in this chapter1 devoted as it is to the subject of control1 the emphasis is on possibilities for harm4 ,both possibilities are valid1 and the happening of either depends upon the actions of men4 ,in much the same way1 atomic energy is a great possibility for benefit and for harm4 ,it is the nature of control to put a fence around danger2 and so it is natural in this chapter that the weight of attention should shift to the dangerous aspects of machines that think4 ,perhaps a reader may feel that a chapter of this kind is rather out of place in a book1 such as this one1 that seeks to be scientific4 ,if so1 he is reminded that1 in accordance with the general suggestions for reading this book stated in the preface1 he should omit this chapter4 ,,frankenstein ,perhaps the first study of the consequences of a machine that thinks is a prophetic novel called ,frankenstein1 written more than a hundred years ago1 in #ahah4 ,the author1 then only #ba years old1 was ,mary ,w4 ,godwin1 who became the wife of the poet ,percy ,bysshe ,shelley4 ,according to the story1 a young ,swiss1 an ardent student of physiology and chemistry1 ,victor ,frankenstein1 finds the secret of life4 ,he makes an extremely ugly1 clever1 and powerful monster1 with human desires4 ,frankenstein promptly flees from his laboratory and handiwork4 ,the monster1 after seeking under great hardships for a year or two to earn fair treatment among men1 finds himself continually attacked and harmed on account of his ugliness1 and he becomes embittered4 ,he begins to search for his creator for either revenge or a bargain4 ,when they meet3 8,i expected this reception10 said the daemon4 8,all men hate the wretched2 how then must ,i be hated who am miserable beyond all living things6 ,yet you my creator detest and spurn me1 thy creature1 to whom thou art bound by ties only dissoluble by the annihilation of one of us4 ,you purpose to kill me4 ,how dare you sport thus with life8 ,do your duty towards me1 and ,i will do mine towards you and the rest of mankind4 ,if you will comply with my conditions1 ,i will leave them and you at peace2 but if you refuse1 ,i will glut the maw of death1 until it be satiated with the blood of your remaining friends40 ,frankenstein starts to comply with the main condition1 which is to make a mate for the monster2 but ,frankenstein cannot bring himself to do it4 ,so the monster causes the death one after another of all ,frankenstein's family and closest friends2 and the tale finally ends with the death of ,frankenstein and the disappearance of the monster4 ,as the dictionary says about ,frankenstein1 8,the name has become a synonym for one destroyed by his own works40 ,,rossum',s ,,universal ,,robots ,perhaps the next study of the consequences of a machine that thinks is a remarkable play called ,r4,u4,r4 7for ,rossum's ,universal ,robots71 first produced in ,prague in #aiba4 ,karel apek1 the ,czech dramatist who wrote it1 was then only #ca4 ,the word 8robot0 comes from the ,czech word 8robota10 meaning compulsory service4 ,according to the play1 ,rossum the elder1 a scientist1 discovered a 8method of organizing living matter0 that was 8more simple1 flexible1 and rapid0 than the method used by nature4 ,rossum the younger1 an engineer1 founded a factory for the mass production of artificial workmen1 robots4 ,they had the form of human beings1 intelligence1 memory1 and strength2 but they were without feelings4 ,in the first act1 the factory under ,harry ,domin1 ,general ,manager1 is busy supplying robots to purchasers all over the world--for work1 for fighting1 for any purpose at all1 to anyone who could pay for them4 ,domin declares3 8444 in ten years1 ,rossum's ,universal ,robots will produce so much corn1 so much cloth1 so much everything that things will be practically without price4 ,there will be no poverty4 ,all work will be done by living machines4 ,everybody will be free from worry and liberated from the degradation of labor4 ,everybody will live only to perfect himself4444 ,it's bound to happen40 ,in the second act1 ten years later1 it turns out that ,domin and the others in charge of the factory have been making some robots with additional human characteristics1 such as the capacity to feel pain4 ,the newer types of robots1 however1 have united all the robots against man1 for the robots declare that they are 8more highly developed than man1 stronger1 and more intelligent1 and man is their parasite40 ,in the last act1 the robots conquer and slay all men except one--an architect1 ,alquist1 who in the epilogue provides a final quirk to the plot4 ,,fact ,,and ,,fancy ,now what is fact and what is fancy in these two warnings given to us a hundred years apart8 ,of course1 it is very doubtful that a ,frankenstein monster or a ,rossum robot will soon be constructed with nerves1 flesh1 and blood like an animal body4 ,but we know that many types of robot machines can even now be constructed out of hardware--wheels1 motors1 wires1 electronic tubes1 etc4 ,they can handle many kinds of information and are able to perform many kinds of actions1 and they are stronger and swifter than man4 ,of course1 it is doubtful that the robot machines1 by themselves and of their own 8free will10 will be dangerous to human beings4 ,but as soon as antisocial human beings have access to the controls over robot machines1 the danger to society becomes great4 ,we want to escape that danger4 ,escape from ,danger ,a natural longing of many of us is to escape to an earlier1 simpler life on this earth4 ,victor ,frankenstein longed to undo the past4 ,he said3 8,learn from me1 if not by my precepts1 at least by my example1 how dangerous is the acquirement of knowledge1 and how much happier that man is who believes his native town to be the world1 than he who aspires to become greater than his nature will allow40 ,any sort of return to the past is1 of course1 impossible4 ,it is doubtful that men could1 even if they wanted to1 stop the great flood of technical knowledge that science is now producing4 ,we all must now face the fact that the kind of world we used to live in1 even so recently as #aici1 is gone4 ,there now exist weapons and machines so powerful and dangerous in the wrong hands that in a day or two most of the people of the earth could be put to death4 ,giant brains are closely related to at least two of these weapons3 scientists have already used mechanical brains for solving problems about atomic explosives and guided missiles4 ,in addition1 thinking mechanisms designed for the automatic control of gunfire were an important part of the winning of ,world ,war ,,ii4 ,they will be a still more important part of the fighting of any future war4 ,nor can we escape to another part of the earth which the new weapons will not reach4 ,at #cjj miles an hour1 any spot on earth can be reached from any other in less than #dh hours4 ,a modern plane exceeds this speed2 a rocket or guided missile doubles or trebles it4 ,nor can we trust that some kind of good luck will pull us through and help men to escape the consequences of what men do4 ,both ,frankenstein and ,domin reaped in full the consequences of what they did4 ,the history of life on this earth that is recorded in the rocks is full of evidence of races of living things that have populated the earth for a time and then become extinct1 such as the dinosaurs4 ,in that long history1 rarely does a race survive4 ,in our own day1 insects and fungi rather than men have shown fitness to survive and spread over the earth3 witness the blight that destroyed the chestnut trees of ,north ,america1 in spite of the best efforts of scientists to stop it4 ,there seems to be no kind of escape possible4 ,it is necessary to grapple with the problem3 ,how can we be safe against the threat of physical harm from robot machines8 ,,unemployment ,the other chief threat from robot machines is against our economic life4 ,harry ,domin1 in ,r4,u4,r41 you remember1 prophesied3 8,all work will be done by living machines40 ,as an example1 in the magazine ,modern ,industry for ,feb4 #ae1 #aidg1 appeared a picture of a machine for selling books1 and under the picture were the words3 ,another new product in robot salesmen--,latest in the parade of mechanical vending machines is this book salesman4444 ,it is designed for use in hospitals1 rail terminals1 and stores4 ,it offers #ae different titles1 selected manually1 and obtained by dropping quarter in slot4 ,cabinet stores #if books4 ,can you feel the breath of the robot salesman1 workman1 engineer1----1 on the back of your neck8 ,at the moment when we combine automatic producing machinery and automatic controlling machinery1 we get a vast saving in labor and a great increase in technological unemployment4 ,in extreme cases1 perhaps1 the effect of robot machines will be the disappearance of men from a factory4 ,such a factory will be like a modern power plant that turns a waterfall into electricity3 once the machinery is installed1 only one watchman is ordinarily needed4 ,but1 in most cases1 this will be the effect3 in a great number of factories1 mines1 farms1 etc41 the labor force needed will be cut by a great proportion4 ,the effect is not different in quality1 because the new development is robot machinery2 but the amount of technological unemployment coming from robot machines is likely to be considerably greater than previously4 ,the robot machine raises the two questions that hang like swords over a great many of us these days4 ,the first one is for any employee3 ,what shall ,i do when a robot machine renders worthless all the skill ,i have spent years in developing8 ,the second question is for any businessman3 ,how shall ,i sell what ,i make if half the people to whom ,i sell lose their jobs to robot machines8 ,,social ,,control ,,and ,,its ,,two ,,sides ,the two chief harmful effects upon humanity which are to be expected from robot machines are physical danger and unemployment4 ,these are serious risks1 and some degree of social control is needed to guard against them4 ,there will also be very great advantages from robot machines4 ,the monster in ,frankenstein is right when he says1 8,do your duty towards me1 and ,i will do mine towards you and the rest of mankind40 ,and ,harry ,domin in ,r4,u4,r4 is right as to possibility when he says1 8,there will be no poverty4444 ,everybody will be free from worry40 ,social control must also be concerned with how the advantages from robot machines are to be shared4 ,the problem of social control over men and their devices has always had two sides4 ,the first side deals with what we might plan for control if men were reasonable and tolerant4 ,this part of the problem seems relatively easy4 ,the other side deals with what we must ordinarily arrange1 since most men are often unreasonable and prejudiced and1 as a result1 often act in antisocial ways4 ,this part of the problem is hard4 ,let us begin with the easier side first4 ,,types ,,of ,,control--,,if ,,men ,,were ,,reasonable ,in seeking to fulfill wants and achieve safety1 men have used hundreds of types of control4 ,the main types are usually called political and economic systems1 but there are always great quantities of exceptions4 ,the more mature and freer the society1 the greater the variety of types of control that can be found in it4 ,probably the most widely used type of control in this country is private and public control working together1 as private ownership and public regulation--for example1 railroads1 banks1 airlines1 life insurance companies1 telephone systems1 and many others4 ,it would be reasonable to expect private ownership and public regulation of a great many classes of robot machines1 to the end that they would never threaten the safety of people4 ,another common type of control is public ownership and operation2 examples are toll bridges1 airports1 city transit systems1 and water-supply systems4 ,atomic energy was so clearly fraught with serious implications that in #aidf the ,congress of the ,united ,states placed it entirely under public control expressed as the ,atomic ,energy ,commission4 ,there is a class of robot machinery which has already reached the stage of acute public concern3 guided missiles and automatic fire-control4 ,it would be reasonable that in this country all activity in this subdivision should be under close control by the ,department of ,defense4 ,in the international arena1 again1 the problem becomes soluble if we assume men to be reasonable4 ,an international agency1 such as an organ of the ,united ,nations1 would take over inspection and control of robot machine activities closely affecting the public safety anywhere in the world4 ,particularly1 this agency would concern itself with guided missiles1 robot pilots for planes1 automatic gunfire control1 etc4 ,much manufacturing skill is needed to make such products as these3 the factories where they could be manufactured would thereby be determined4 ,also1 a giant brain is a useful device for solving scientific problems about weapons of mass destruction4 ,so the agency would need to inspect the problems being solved on such machines4 ,this agency would be responsible to a legislature or an executive body representing all the people in the world--if men were reasonable4 ,in regard to the effects of robot machines on unemployment1 again1 if men were reasonable1 the problem would be soluble4 ,the problem is equivalent to the problem of abundance3 how should men distribute the advantages of a vast increase in production among all the members of society in a fair and sensible way8 ,a vast increase in production is not so impossible as it may seem4 ,for example1 in #aici1 with #de million employed1 the ,united ,states index of industrial production was at #aji1 and1 in #aidc1 with #eb million employed1 the index of production was at #bci4 ,if men were reasonable1 the net profits from robot machinery would be divided among 7#a7 those who had most to do with devising the new machinery1 and 7#b7 all of society4 ,a rule would be adopted 7probably it could be less complicated than some existing tax rules7 which would take into account various factors such as rewards to the inventors1 incentives to continue inventing1 adequate assistance to those made unemployed by the robot machines1 reduction of prices to benefit consumers1 and contributions to basic and applied scientific research4 ,in fact1 under the assumption 8if men were reasonable10 it would hardly be necessary to devote a chapter to the problem of social control over robot machines6 ,,obstacles ,the discussion above of how robot machines could be controlled supposing that men were reasonable1 seems1 of course1 to be glaringly impractical4 ,men are not reasonable on most occasions most of the time4 ,if we stopped at this point1 again we would be dodging the issue4 ,what are the obstacles to reasonable control8 ,there are1 it seems1 two big obstacles and one smaller one to reasonable types of social control over robot machines4 ,the smaller one is ignorance1 and the two big obstacles are prejudice and a narrow point of view4 ,ignorance ,by ignorance we mean lack of knowledge and information4 ,now mechanical brains are a new and intricate subject4 ,a great many people will1 through no fault of their own1 naturally remain uninformed about mechanical brains and robot machines for a long time4 ,however1 there is a widespread thirst for knowledge these days3 witness in magazines1 for example1 the growth of the article and the decline of the essay4 ,there is also a fairly steady surge of knowledge from the austere scientific fountain of new technology4 ,we can thus see both a demand and a supply for information in such fields as mechanical brains and robot machines4 ,we can expect1 therefore1 a fairly steady decline in ignorance4 ,prejudice ,prejudice is a much more serious obstacle to reasonable control over robot machines4 ,it will be worth our while to examine it at length4 ,prejudice is frequent in human affairs4 ,for example1 in some countries1 but not in all1 there is conflict among men1 based on their religious differences4 ,again1 in other countries1 but not in all1 there is wide discrimination among men1 based on the color of their skin4 ,over the whole world today1 there is a sharp lack of understanding between conservatives1 grading over to reactionaries1 on the one hand1 and liberals1 grading over to radicals1 on the other hand4 ,all these differences are based on men's attitudes1 on strongly held sets of beliefs4 ,these attitudes are not affected by 8information02 the 8information0 is not believed4 ,the attitudes are not subject to 8judgment02 they come 8before judgment03 they are prejudices4 ,even in the midst of all the science of today1 prejudice is widespread4 ,in ,germany1 from #aicc to #aici1 we saw one of the most scientific of countries become one of the most prejudiced4 ,prejudice is often difficult to detect4 ,we find it hard to recognize even in ourselves4 ,for a prejudice always seems1 to the person who has it1 the most natural attitude in the world4 ,as we listen to other people1 we are often uncertain how to separate information1 guesses1 humor1 prejudice1 etc4 ,circumstances compel us to accept provisionally quantities of statements just on other people's say-so4 ,a good test of a statement for prejudice1 however1 is to compare it with the scientific view4 ,prejudice is most dangerous for society4 ,its more extreme manifestations are aggressive war1 intolerance 7especially of strange people and customs71 violence1 race hatred1 etc4 ,in the consuming hatred that a prejudiced man has towards the object of his prejudice1 he is likely to destroy himself and destroy many more people besides4 ,in former days1 the handy weapon was a sword or a pistol2 not too much damage could be done when one man ran amuck4 ,but nowadays a single use of a single weapon has slain #gj1jjj people 7the atom bomb dropped at ,hiroshima71 and so a great many people live anxious and afraid4 ,what is prejudice8 ,how does it arise8 ,how can it be cured1 and thus removed from obstructing reasonable control over robot machines and the rest of today's amazing scientific developments8 ,prejudice is a disease of men's minds4 ,it is infectious4 ,the cause and development of the disease are about as follows3 ,deprive someone of something he deeply needs1 such as affection1 food1 or opportunity4 ,in this way hurt him1 make him resentful1 hostile2 but prevent him from expressing his resentments in a reasonable way1 giving him instead false outlets1 such as other people to hurt1 myths to believe1 hostile behavior patterns to imitate4 ,he will then break out with prejudices as if they were measles4 ,the process of curing the disease of prejudice is about as follows3 ,make friends with the patient2 win his trust4 ,encourage him to pour out his half-forgotten hates4 ,help him to talk them over freely1 by means of questions but not criticisms1 until finally the patient achieves insight1 sees through his former prejudices1 and drops them4 ,in these days prejudice is a cardinal problem of society4 ,it is perhaps conservative to say that a chief present requirement for the survival of human society--with the atom bomb1 bacterial warfare1 guided missiles1 etc41 near at hand--is cure of prejudice and its consequences1 irrational and unrestrained hate4 ,narrow ,point of ,view ,a narrow point of view regarding what is desirable or good is the third obstacle to rational control over robot machines4 ,what do we mean by this8 ,our point of view as a two-year-old is based on pure self-interest4 ,if we see a toy1 we grab it4 ,there is no prejudice about this2 it is entirely natural--for two-year-olds4 ,as we grow older1 our point of view concerning what is good or desirable rapidly broadens3 we think of others and their advantage besides our own4 ,for example1 we may become interested in a conservation program to conserve birds1 or soil1 or forests1 and our point of view expands1 embraces these objectives1 which become part of our personality and loyalties4 ,unfortunately1 it seems to be true that the expanding point of view1 the expanding loyalties1 of most people as they grow up are arrested somewhere along the line of3 self1 family1 neighborhood1 community1 section of country1 nation4 ,an honorable exception is the scientists' old and fine tradition of world-wide unity and loyalty in the search for objective truth4 ,now the problem of rational control over robot machines and other parts of the new technology is no respecter of national boundaries4 ,to be solved it requires a world-wide point of view1 a loyalty to human society and its best interests1 a social point of view4 ,almost all that you and ,i have and do and think is the result of a long history of human society on this earth4 ,all men on the earth today are descendants of other men who lived #ajjj1 #bjjj1 #cjjj 444 years ago1 whether they were ,romans or ,chinese or ,babylonians or ,mayas or members of any other race4 ,to ride in a subway or an airplane1 to talk on the telephone1 to speak a language1 to calculate1 to survive smallpox or the black death1 etc4--all these privileges are our inheritance from countless thousands of other human beings1 of many countries1 and nearly all of whom are now dead4 ,during our lives we pass on to our own children an inheritance in which our own contribution is remarkably small4 ,since each person is the child of two others1 the number of our forefathers is huge1 and we are all undoubtedly blood cousins4 ,because of this relationship1 and because we owe to the rest of society nearly all that we are1 we have a social responsibility--we need to hold a social point of view4 ,each of us needs to accept and welcome a world-wide social responsibility1 as a member of human society1 as a beneficiary and trustee of our human inheritance4 ,otherwise we are drones1 part of the hive without earning our keep4 ,the social point of view is equitable1 it is inspiring1 and it is probably required now in order for human beings to survive4 ,we need to let go of a narrow point of view4 ,,conclusion ,we have now outlined the problem of social control over robot machines1 supposing that human beings were reasonable4 ,we have also discussed the practical obstacles that obstruct reasonable control4 ,it is not easy to think of any yet organized group of people anywhere that would have both the strength and the vision needed to solve this problem through its own efforts4 ,for example1 a part of the ,united ,nations might have some of the vision needed1 but it does not have the power4 ,consequently1 it is necessary and desirable for individuals and groups everywhere to take upon themselves an added load of social responsibility--just as they tend to do in time of war4 ,people often 8want to do their share40 ,through encouragement and education1 the basic attitude of a number of people can contain more of 8,this is our business2 we have a responsibility for helping to solve this problem40 ,we also need public responsibility2 we need a public body responsible for study1 education1 advice1 and some measure of control4 ,it might be something like an ,atomic ,energy ,commission1 ,bacterial ,defense ,commission1 ,mental ,health ,commission1 and ,robot ,machine ,commission1 all rolled into one4 ,when1 at last1 there is an effective guarantee of the two elements physical safety and adequate employment1 then at last we shall all be free from the threat of the robot machine4 ,we can then welcome the robot machine as our deliverer from the long hard chores of many centuries4 ,supplement #a ,,words ,,and ,,ideas ,the purpose of this book is to explain machines that think1 without using technical words any more than necessary4 ,this supplement is a digression4 ,its purposes are to consider how to explain in this way and to discuss the attempt made in this book to achieve simple explanation4 ,,words ,,as ,,instruments ,,for ,,explaining ,words are the chief instruments we use for explaining4 ,of course1 many other devices--pictures1 numbers1 charts1 models1 etc4--are also used2 but words are the prime tools4 ,we do most of our explaining with them4 ,words1 however1 are not very good instruments4 ,like a stone arrow-head1 a word is a clumsy weapon4 ,in the first place1 words mean different things on different occasions4 ,the word 8line10 for example1 has more than fifty meanings listed in a big dictionary4 ,how do we handle the puzzle of many meanings8 ,as we grow older we gather experience and we develop a truly marvelous capacity to listen to a sentence and then fit the words together into a pattern that makes sense4 ,sometimes we notice the time lag while our brain hunts for the meaning of a word we have heard but not grasped4 ,then suddenly we guess the needed meaning1 whereupon we grasp the meaning of the sentence as a whole in much the same way as the parts of a puzzle click into place when solved4 ,another trouble with words is that often there is no good way to tell someone what a word means4 ,of course1 if the word denotes a physical object1 we can show several examples of the object and utter the word each time4 ,in fact1 several good illustrations of a word denoting a physical thing often tell most of its meaning4 ,but the rest of its meaning we often do not learn for years1 if ever4 ,for instance1 two people would more likely disagree than agree about what should be called a 8rock0 and what should be called a 8stone10 if we showed them two dozen examples4 ,in the case of words not denoting physical objects1 like 8and10 8heat10 8responsibility10 we are worse off4 ,we cannot show something and say1 8,that is a 40 ,the usual dictionary is of some help1 but it has a tendency to tell us what some word ,a means by using another word ,b1 and when we look up the other word ,b we find the word ,a given as its meaning4 ,mainly1 however1 to determine the meanings of words1 we gather experience3 we soak up words in our brains and slowly establish their meanings4 ,we seem to use an unconscious reasoning process3 we notice how words are used together in patterns1 and we conclude what they must mean4 ,clearly1 then1 words being clumsy instruments1 the more experience we have had with a word1 the more likely we are to be able to use it1 work with it1 and understand it4 ,therefore explanation should be based chiefly on words with which we have had the most experience4 ,what words are these8 ,they will be the well-known words4 ,a great many of them will be short4 ,,set ,,of ,,words ,,for ,,explaining ,now what is the set of all the words needed to explain simply a technical subject like machines that think8 ,for we shall need more words than just the well-known and short ones4 ,this question doubtless has many answers2 but the answer used in this book was based on the following reasoning4 ,in a book devoted to explanation1 there will be a group of words 7#a7 that are supposed to be known already or to be learned while reading1 and 7#b7 that are used as building blocks in later explanation and definitions4 ,suppose that we call these words the words for explaining4 ,there are at least three groups of such words3 ,group #a4 ,words not specially defined that are so familiar that every reader will know all of them2 for example1 8is10 8much10 8tell40 ,group #b4 ,words not specially defined that are familiar1 but perhaps some reader may not know some of them2 for example1 8alternative10 8continuous10 8indicator40 ,group #c4 ,words that are not familiar1 that many readers are not expected to know1 and that are specially defined and explained in the body of the book2 for example1 8abacus10 8trajectory10 8torque40 ,in writing this book1 it was not hard to keep track of the words in the third group4 ,these words are now listed in the index1 together with the page where they are defined or explained4 7,the index1 of course1 also lists phrases that are specially defined47 ,but what division should be made between the other two groups8 ,a practical1 easy1 and conservative way to separate most words between the first and second groups seemed to be on the basis of number of syllables4 ,all words of one syllable--if not specially defined--were put in ,group #a4 ,also1 if a word became two syllables only because of the addition of one of the endings 8-es10 8-ed10 8-ing10 it was kept in ,group #a1 for these endings probably do not make a word any harder to understand4 ,in addition1 there were put into ,group #a3 #a4 ,numbers2 for example1 8#ahf1jjj02 8_/04 #b4 ,places3 8,philadelphia02 8,massachusetts04 #c4 ,nations1 organizations1 people1 etc43 8,swedish02 8,bell04 #d4 ,years and dates3 8,february02 8#aidf04 #e4 ,names of current books or articles and their authors4 ,of course1 not all these words would be familiar to every reader 7for example1 8,maya071 but in the way they occur1 they are usually not puzzling1 for we can tell from the context just about what they must mean4 ,all remaining words for explaining--chiefly1 words of two or more syllables and not specially defined--were put in ,group #b and were listed during the writing of this book4 ,many ,group #b words1 of course1 would be entirely familiar to every reader2 but the list had several virtues4 ,no hard words would suddenly be sprung like a trap4 ,the same word would be used for the same idea4 ,every word of two or more syllables was continually checked3 is it needed8 can it be replaced by a shorter word8 ,it is perhaps remarkable that there were fewer than #ahjj different words allowed to stay in this list4 ,this fact should be a comfort to a reader1 as it was to the author4 ,now there are more words in this book than words for explaining4 ,so we shall do well to recognize3 ,group #d4 ,words that do not need to be known or learned and that are not used in later explanation and definitions4 ,these words occur in the book in such a way that understanding them1 though helpful1 is not essential4 ,one subdivision of ,group #d are names that appear just once in the book1 as a kind of side remark1 for example1 8a chemical1 called acetylcholine40 ,such a name will also appear in the index1 but it is not a word for explaining4 ,another subdivision of ,group #d are words occurring only in quotations4 ,for example1 in the quotation from ,frankenstein on page #aih1 a dozen words appear that occur nowhere else in the book1 including 8daemon10 8dissoluble10 8maw10 8satiate40 ,clearly we would destroy the entire flavor of the quotation if we changed any of these words in any way4 ,but only the general drift of the quotation is needed for understanding the book1 and so these words are ,group #d words4 ,in this way the effort to achieve simple explanation in this book proceeded4 ,but even supposing that we could reach the best set of words for explaining1 there is more to be done4 ,how do we go from simple explanation to understanding8 ,,understanding ,,ideas ,understanding an idea is basically a standard process4 ,first1 we find the name of the idea1 a word or phrase that identifies it4 ,then1 we collect true statements about the idea4 ,finally1 we practice using them4 ,the more true statements we have gathered1 and the more practice we have had in applying them1 the more we understand the idea4 ,for example1 do you understand zero8 ,here are some true statements about zero4 #a4 ,zero is a number4 #b4 ,it is the number that counts none or nothing4 #c4 ,it is marked #j in our usual numeral writing4 #d4 ,the ancient ,romans1 however1 had no numeral for it4 ,apparently1 they did not think of zero as a number4 #e4 #j is what you get when you take away #ag from #ag1 or when you subtract any number from itself4 #f4 ,if you add #j to #bc1 you get #bc2 and if you add #j to any number1 you get that number unchanged4 #g4 ,if you subtract #j from #dh1 you get #dh2 and if you subtract #j from any number1 you get that number unchanged4 #h4 ,if you multiply #j by #ga1 you get #j2 and if you multiply together #j and any number1 you get #j4 #i4 ,usually you are not allowed to divide by #j3 that is against the rules of arithmetic4 #aj4 ,but if you do1 and if you divide #ab by #j1 for example--and there are times when this is not wrong--the result is called infinity and is marked 1 a sign that is like an #h on its side4 ,this is not all the story of zero2 it is one of the most important of numbers4 ,but1 if you know these statements about zero1 and have had some practice in applying them1 you have a good understanding of zero4 ,incidentally1 a mechanical brain knows all these statements about zero and a few more2 they must be built into it4 ,for us to understand any idea1 then1 we pursue three aims3 #a4 ,we find out what it is called4 #b4 ,we collect true statements about it4 #c4 ,we apply those statements--we use them in situations4 ,we can do this about any idea4 ,therefore1 we can understand any idea1 and the degree of our understanding increases as the number of true statements mastered increases4 ,perhaps this seems to be a rash claim4 ,of course1 it may take a good deal of time to collect true statements about many ideas4 ,in fact1 a scientist may spend thirty years of his life trying to find out from experiment the truth or falsehood of one statement1 though1 when he has succeeded1 the fact can be swiftly told to others4 ,also1 we all vary in the speed1 perseverance1 skill1 etc41 with which we can collect true statements and apply them4 ,besides1 some of us have not been taught well and have little faith in our ability to carry out this process3 this is the greatest obstacle of all4 ,but1 there is in reality no idea in the field of existing science and knowledge which you or ,i cannot understand4 ,the road to understanding lies clear before us4 ,supplement #b ,,mathematics ,in the course of our discussion of machines that think1 we have had to refer without much explanation to a number of mathematical ideas4 ,the purpose of this supplement is to explain a few of these ideas a little more carefully than seemed easy to do in the text and1 at the end of the supplement1 to put down briefly some additional notes for reference4 ,,devices ,,for ,,multiplication ,suppose that we have to multiply #cgb by #dfe4 ,with the ordinary school method1 we write #dfe under the #cgb and proceed about as follows3 #e times #b is #aj1 put down the #j and carry the #a2 #e times #g is #ce1 #ce and #a is #cf1 put down the #f and carry the #c2 #e times #c is #ae1 #ae and #c is #ah1 put down the #h and carry the #a2 444 ,the method is based mainly on a well-learned subroutine of continually changing steps3 #a4 ,select a multiplicand digit4 #b4 ,select a multiplier digit4 #c4 ,refer to the multiplication table with these digits4 #d4 ,obtain the value of their product1 called a partial product4 #e4 ,add the preceding carry4 #f4 ,set down the right-hand digit4 #g4 ,carry the left-hand digit4 ,we can1 however1 simplify this subroutine for a machine by delaying the carrying4 ,we collect in one place all the right-hand digits of partial products1 collect in another place all the left-hand digits1 and delay all addition until the end4 ,for example1 let us multiply #cgb by #dfe with this method3 ,,right-,,hand ,,left-,,hand ,,usual ,,method1 ,,digits ,,digits ,,for ,,comparison #cgb #cgb #cgb #dfe #dfe #dfe ------------ ------------ ------------ #eej #aca #ahfj #hbb #ada #bbcb #bhh #abj #adhh ---------- ---------- ------------ #cgegj #aceda #agbihj ,,final ,,addition #cgegj #aceda ---------------- #agbihj #cgegj is called the right-hand component of the product4 ,it is convenient to fill in with #j the space at the end of #aceda and to call #acedaj the left-hand component of the product4 ,this process is called multiplying by right- and left-hand components4 ,it has the great advantage that no carrying is necessary to complete any line of the original multiplications4 ,some computing machines use this process4 ,built into the hardware of the machine is a multiplication table up to #i #i4 ,the machine1 therefore1 can find automatically the right-hand digit and the left-hand digit of any partial product4 ,in a computing machine that uses this process1 all the left-hand digits are automatically added in one register1 and all the right-hand digits are added in another register4 ,the only carrying that is needed is the carrying as the right-hand digits are accumulated and as the left-hand digits are accumulated4 ,at the end of the multiplication1 one of the registers is automatically added into the other1 giving the product4 ,another device used in computing machines for multiplying is to change the multiplier into a set of digits #j to #e that are either positive or negative4 ,for example1 suppose that we want to multiply #hig by #ahb4 ,we note that #ahb equals #bjj minus #bj plus #b1 and so we can write it as #bbb4 ,the minus over the #b marks it as a negative digit #b4 ,then to multiply we have3 #hig #bbb -------- #agid - #agid #agid ------------ #afcbed ,the middle #agid is subtracted4 ,this process is usually called short-cut multiplication4 ,everybody discovers this trick when he decides that multiplying by #ii is too much work1 that it is easier to multiply by #ajj and subtract once4 ,,binary ,,or ,,two ,,numbers ,we are well accustomed to decimal notation in which we use #aj decimal digits #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i and write them in combinations to designate decimal numbers4 ,in binary notation we use two binary digits #j1 #a and write them in combinations to designate binary numbers4 ,for example1 the first #ag numbers1 from #j to #af in the decimal notation1 correspond with the following numbers in binary notation3 ,,decimal ,,binary ,,decimal ,,binary #j #j #a #a #i #ajja #b #aj #aj #ajaj #c #aa #aa #ajaa #d #ajj #ab #aajj #e #aja #ac #aaja #f #aaj #ad #aaaj #g #aaa #ae #aaaa #h #ajjj #af #ajjjj ,in decimal notation1 #aja means one times a hundred1 no tens1 and one4 ,in binary notation1 #aja means one times four1 no twos1 and one4 ,the successive digits in a decimal number from right to left count #a1 #aj1 #ajj1 #ajjj1 #ajjjj1 444--successive powers of #aj 7for this term1 see the end of this supplement74 ,the successive digits in a binary number from right to left count #a1 #b1 #d1 #h1 #af1 444--powers of #b4 ,the decimal notation is convenient when equipment for computing has ten positions1 like the fingers of a man1 or the positions of a counter wheel4 ,the binary notation is convenient when equipment for computing has just two positions1 like 8yes0 or 8no10 or current flowing or no current flowing4 ,addition1 subtraction1 multiplication1 and division can all be carried out unusually simply in binary notation4 ,the addition table is simple and consists only of four entries4 #j #a ------------ #j #j #a #a #a #aj ,the multiplication table is also simple and contains only four entries4 #j #a ------------ #j #j #j #a #j #a ,suppose that we add in binary notation #aja and #ajja3 ,,binary ,,addition ,,check #aja #e #ajja #i ------------ ------ #aaaj #ad ,we proceed3 #a and #a is #aj2 write down #j and carry #a2 #j and #j is #j1 and #a to carry is #a2 and #a and #j is #a2 and then we just copy the last #a4 ,to check this we can convert to decimal and see that #aja is #e1 #ajja is #i1 and #aaaj is #ad1 and we can verify that #e and #i is #ad4 ,one of the easiest ways to subtract in binary notation is to add a ones complement 7that is1 the analogue of the nines complement7 and use end-around-carry 7for these two terms1 see the end of this supplement74 ,a ones complement can be written down at sight by just putting #a for #j and #j for #a4 ,for example1 suppose that we subtract #aja from #aaaj3 ,,subtraction ,,by ,,direct ,,adding ,,ones ,,subtraction ,,check ,,complement #aaaj #ad #aaaj - #aja -#e #ajaj ---------- -------- ------------ #ajja #i 7#a7ajjj #a ------------ #ajja ,multiplication in the binary notation is simple4 ,it amounts to 7#a7 adding if the multiplier digit is #a and not adding if the multiplier digit is #j1 and 7#b7 moving over or shifting4 ,for example1 let us multiply #aaa by #aja3 ,,binary ,,multiplication ,,check #aaa #g #aja #e ------------ #aaa #aaa ------------ ------ #ajjjaa #ce ,the digit #a in the #fth 7or nth7 binary place from the right in #ajjjaa stands for #a times #b to the #eth 7or n-#a th7 power1 #b #b #b #b #b #cb4 ,the result #ajjjaa is translated into #cb plus #b plus #a1 which equals #ce and verifies4 ,division in the binary notation is also simple4 ,it amounts to 7#a7 subtracting 7yielding a quotient digit #a7 or not subtracting 7yielding a quotient digit #j71 and 7#b7 shifting4 ,we never need to try multiples of the divisor to find the largest that can be subtracted yet leave a positive remainder4 ,for example1 let us divide #ajaj 7#aj in decimal7 into #ajjjaaaj 7#adb in decimal73 #aaaj 7#ad in decimal7 -------------------- #ajaj7ajjjaaaj #ajaj ------------ #aaaa #ajaj ---------- #ajaa #ajaj ---------- #aj 7remainder1 #b in decimal7 ,in decimal notation1 digits to the right of the decimal point count powers of 4 ,in binary notation1 digits to the right of the binary point count powers of 3 1 1 1 _/4444 ,for example1 #j4ajaa equals _/1 or _/4 ,if we were accustomed to using binary numbers1 all our arithmetic would be very simple4 ,furthermore1 binary numbers are in many ways much better for calculating machinery than any other numbers4 ,the main problem is converting numbers from decimal notation to binary4 ,one method depends on storing the powers of #b in decimal notation4 ,the rule is3 subtract successively smaller powers of #b2 start with the largest that can be subtracted1 and count #a for each power that goes and #j for each power that does not4 ,for example1 #hf in decimal becomes #ajajaaj in binary3 #hf #fd #fd goes #a ------ #bb #cb does not go #j #af #af goes #a ------ #f #h does not go #j #d #d goes #a ------ #b #b goes #a #b #a does not go #j ------ #j ,it is a little troublesome to remember long series of #a's and #j's2 in fact1 to write any number in binary notation takes about #c times as much space as decimal notation4 ,for this reason we can separate binary numbers into triples beginning at the right and label each triple as follows3 ,,triple ,,label #jjj #j #jja #a #jaj #b #jaa #c #ajj #d #aja #e #aaj #f #aaa #g ,for example1 #ajajaaj would become #a #jaj #aaj or #abf4 ,this notation is often called octal notation1 because it is notation in the scale of eight4 ,,biquinary ,,or ,,two-,,five ,,numbers ,another kind of notation for numbers is biquinary notation1 so called because it uses both #b's and #e's4 ,essentially this notation is very like ,roman numerals1 ancient style4 ,by ancient style we mean1 for example1 ,,viiii instead of ,,ix4 ,in the following table we show the first two dozen numbers in decimal1 biquinary1 and ancient ,roman notation3 ,,decimal ,,biquinary ,,roman #j #j #a #a ,i #b #b ,,ii #c #c ,,iii #d #d ,,iiii #e #aj ,v #f #aa ,,vi #g #ab ,,vii #h #ac ,,viii #i #ad ,,viiii #aj #ajj ,x #aa #aja ,,xi #ab #ajb ,,xii #ac #ajc ,,xiii #ad #ajd ,,xiiii #ae #aaj ,,xv #af #aaa ,,xvi #ag #aab ,,xvii #ah #aac ,,xviii #ai #aad ,,xviiii #bj #bjj ,,xx #ba #bja ,,xxi #bb #bjb ,,xxii #bc #bjc ,,xxiii ,the biquinary columns alternate in going from #j to #d and from #j to #a4 ,the digits from #j to #d are not changed4 ,the digits from #e to #i are changed into #aj to #ad4 ,we see that the biquinary digits are #j to #d in odd columns and #j1 #a in even columns1 counting from the right4 ,this is the notation actually expressed by the abacus4 ,the beads of the abacus show by their positions groups of #b and #e 7see ,fig4 #a74 ,illustration3 ,,fig4 #a4 ,abacus and notations4 ,,some ,,operations ,,of ,,algebra ,one of the operations of algebra that is important for a mechanical brain is approximation1 the problem of getting close to the right value of a number4 ,take1 for example1 finding square root 7see the end of this supplement74 ,the ordinary process taught in school is rather troublesome4 ,we can set down another process1 however1 using a desk calculator to do division1 which gives us square root with great speed4 ,suppose that we want to find the square root of a number ,n1 and suppose that we have x as a guessed square root correct to one figure4 ,for example1 ,n might be #fg4b and x might be #h1 chosen because #h #h is #fd1 and #i #i is #ha1 and it seems as if #h should be near the square root of #fg4b4 ,here is the process3 #a4 ,divide x into ,n1 and obtain ,n_/x4 #b4 ,multiply x ,n_/x by #j4e and call the result x4 ,now repeat3 #a4 ,divide x into ,n and obtain ,n_/x4 #b4 ,multiply x ,n_/x by #j4e and call the result x4 ,every time this process is repeated1 the new x comes a great deal closer to the correct square root4 ,in fact it can be shown that1 if x is correct to one figure1 then3 ,,approximation ,,is ,,correct ,,to ,,figures x #b x #d x #h x #af ,let us see how this actually works out with #fg4b and a #aj-;column desk calculator4 ,round #a3 #h divided into #fg4b gives #h4d4 ,one half of #h plus #h4d is #h4b4 ,this is x4 ,round #b3 #h4b divided into #fg4b gives #h4aieabb4 ,one half of #h4b plus #h4aieabb is #h4aigefa4 ,this is x4 ,round #c3 #h4aigefa divided into #fg4b gives #h4aigefjbbe4 ,one half of #h4aigefa and #h4aigefjbbe is #h4aigefjfabe4 ,this is x4 ,checking x1 we find that #h4aigefjfabe divided into #fg4b gives #h4aigefjfabf approximately4 ,in this case1 then1 x is correct to more than #aj figures4 ,in other words1 with a reasonable guess and two or three divisions we can obtain all the accuracy we can ordinarily use4 ,this process is called rapid approximation1 or rapidly convergent approximation1 since it converges 7points or comes together7 very quickly to the number we are seeking4 ,another important operation of algebra is interpolation1 the problem of putting values smoothly in between other values4 ,for example1 suppose that we have the table3 x y #e #bf #f #cg #g #ej #h #fe #i #hb ,suppose that we want to find the value that y 7or y7 ought to have when x has the value of #g4b4 ,this is the problem of interpolating y so as to find y at the value of #g4b1 y4 ,one way of doing this is to discover the formula that expresses y and then to put x into that formula4 ,this is not always easy4 ,another way is to take the difference between y and y1 #ae1 and share the difference appropriately over the distance #g to #g4b and #g4b to #h4 ,we can1 for example1 take _/ of #ae #c1 add that to y #ej1 and obtain an estimated y #ec4 ,this is called linear interpolation1 since the difference #j4b in the value of x is used only to the first power4 ,it is a good practical way to carry out most interpolation quickly and approximately4 ,actually here y x #a1 and so the true value of y is 7#g4b #g4b7 #a1 or #eb4hd1 which is rather close to #ec4 ,types of interpolation procedures more accurate than linear interpolation will come much nearer still to the true value4 ,,algebra ,,of ,,logic ,we turn now to the algebra of logic4 ,the first half of ,chapter #i1 8,reasoning0 7through the section 8,logical-,truth ,calculation by ,algebra071 introduces this subject4 ,there the terms truth values1 truth tables1 logical connectives1 and algebra of logic are explained4 ,the part of ,chapter #c1 8,a ,machine ,that ,will ,think10 that discusses the operations greater-than and selection1 also explains some of the algebra of logic4 ,it introduces1 for example1 the formula p ,t7a b7 #a1 #j ,this is a way of saying briefly that the truth value of the statement 8a is greater than b0 equals p2 p is #a if the statement is true and #j if the statement is false4 ,the truth value #a corresponds with 8yes40 ,the truth value #j corresponds with 8no40 ,with mechanical brains we are especially interested in handling mathematics and logic without any sharp dividing line between them4 ,for example1 suppose that we have a register in which a ten-digit number like #a1gfe1dch1hij may be stored4 ,we should be able to use that register to store a number consisting of only #a's and #j's1 like #a1ajj1ajj1jaj4 ,such a number may designate the answers to #aj successive questions3 yes1 yes1 no1 no1 yes1 no1 no1 no1 yes1 no4 ,or it may tell #aj successive binary digits4 ,the register then is three times as useful3 it can store either decimal numbers or truth values or binary digits4 ,we need1 of course1 a way to obtain from the register any desired digit4 ,for this purpose we may have two instructions to the machine3 7#a7 read the left-hand end digit2 7#b7 shift the number around in a circle4 ,the second instruction is the same as multiplying by #aj and then putting the left-most digit at the right-hand end4 ,for example1 suppose that we want the #crd digit from the left in #a1ajj1ajj1jaj4 ,the result of the first circular shift is #a1jja1jjj1aja2 the result of the second circular shift is #j1jaj1jja1jaa2 and reading the left-most digit gives #j4 ,a process like this has been called extraction and is being built into the newest mechanical brains4 ,using truth values1 we can put down very neatly some truths of ordinary algebra4 ,for example3 7the absolute value of a7 a 7the truth of a greater than or equal to #j7 - a 7the truth of a less than #j7 a a ,t7a #j7 - a ,t7a #j7 ,for another example3 ,either a is greater than b1 or else a equals b1 or else a is less than b ,t7a b7 ,t7a b7 ,t7a b7 #a ,many common logical operations1 like selecting and comparing1 and the behavior of many simple mechanisms1 like a light or a lock1 can be expressed by truth values4 ,chapter #d1 on punch-card mechanisms1 contains a number of examples4 99 99 99 99 99 pronoun1 variable ,in ordinary language1 a pronoun1 like 8he10 8she10 8it10 8the former10 8the latter10 is a word that usually stands for a noun previously referred to4 ,a pronoun usually stands for the last preceding noun that the grammar allows4 ,in mathematics1 a variable1 like 8a10 8b10 8x10 8m10 8m0 closely resembles a pronoun in ordinary language4 ,a variable is a symbol that usually stands for a number previously referred to1 and usually it stands for the same number throughout a particular discussion4 multiplicand1 dividend1 augend1 etc4 ,,in ,,the ,,the ,,name ,,the ,,name ,,the ,,name ,,equation3 ,,of a ,,is3 ,,of b ,,is3 ,,of c ,,is3 a b c augend addend sum a - b c minuend subtrahend remainder a b c multiplicand multiplier product a b c dividend divisor quotient ,augend and addend are names of registers in the ,harvard ,mark ,,ii calculator 7see ,chapter #aj74 subtraction by adding1 nines complement ,two digits that add to #i 7#j and #i1 #a and #h1 #b and #g1 #c and #f1 #d and #e7 are called nines complements of each other4 ,the nines complement of a number a is the number b in which each digit of b is the nines complement of the corresponding digit of a2 for example1 the nines complement of #agc is #hbf4 ,ordinary subtraction is the same as addition as of the nines complement1 with a simple correction2 for example1 #efb less #agc 7equal to #chi7 is the same as #efb plus #hbf 7equal to #achh7 less #ajjj plus #a4 end-around-carry ,the correction 8less #ajjj plus #a0 of the foregoing example may be thought of as carrying the #a 7in the result #achh7 around from the left-hand end to the right-hand end1 where it is there added4 ,so the #a is called end-around-carry4 tens complement ,two digits that add to #aj are called tens complements of each other4 ,the tens complement of a number a1 however1 is equal to the nines complement of the number plus #a4 ,for example1 the tens complement of #agc is #hbg4 ,when subtracting by adding a tens complement1 the left-most digit #a in the result is dropped4 ,for example1 #efb less #agc 7equal to #chi7 is the same as #efb plus #hbg 7equal to #achi7 less #ajjj4 power1 square1 cube1 reciprocal1 etc4 ,a power of any number a is a multiplied by itself some number of times4 a a a 444 a where a appears b times is written a and is read a to the bth power4 a1 a to the #bnd power1 is a a and is called a squared or the square of a4 a1 a to the #crd power1 a a a1 is called a cubed1 or the cube of a4 a1 a to the zero power1 is equal to #a for every a4 a1 a to the power #a1 is a itself4 ,the first power is often called linear4 a to some negative power is the same as #a divided by that power2 that is1 a #a_/;a4 a1 a to the power minus #a1 is #a_/;a1 and is called the reciprocal of a4 a1 a to the one-half power1 is a number c such that c c a1 and is called the square root of a and often denoted by a4 table1 tabular value1 argument1 etc4 ,an example of a table is3 #j4jbe #j4jc ------------------------------------ #a #a4jbejj #a4jcjjj #b #a4jejfc #a4jfjij #c #a4jgfhi #a4jibgc ,the numbers in the body of the table1 called tabular values1 depend on or are determined by the numbers along the edge of the table1 called arguments4 ,in this example1 if #a1 #b1 #c are choices of a number n1 and if #j4jbe1 #j4jc are choices of a number i1 then each tabular value y is equal to #a plus i raised to the nth power4 n and i are also called independent variables1 and y is called the dependent variable4 ,the table expresses a function or formula or rule4 ,the rule could be stated as3 add i to #a2 raise the result to the nth power4 constant ,a number is said to be a constant if it has the same value under all conditions4 ,for example1 in the formula3 7area of a circle7 7radius71 is a constant1 equal to #c4adaei 4441 applying equally well to all circles4 infinity ,mathematics recognizes several kinds of infinity4 ,one of them occurs when numbers become very large4 ,for example1 the quotient of #ab divided by a number x1 as x becomes closer and closer to #j1 becomes indefinitely large1 and the limit is called infinity and is denoted 4 equation1 simultaneous1 linear ,an example of two linear simultaneous equations is3 #gx #ht #bb #cx #et #aa x and t are called unknowns--that is1 unknown variables--because the objective of solving the equations is to find them4 ,these equations are called simultaneous because they are to be solved together1 at the same time1 for values of x and t which will fit in both equations4 ,the equations are called linear because the only powers of the unknowns that appear are the first power4 ,values that solve equations are said to satisfy them4 ,it is easy to solve these two equations and find that x #b and t #a is their solution4 ,but it is a long process to solve #aj linear simultaneous equations in #aj unknowns1 and it is almost impossible 7without using a mechanical brain7 to solve #ajj linear simultaneous equations in #ajj unknowns4 derivative1 integral1 differential equation1 etc4 ,see the sections in ,chapter #e entitled 8,differential ,equations10 8,physical ,problems10 and 8,solving ,physical ,problems40 ,there these ideas and1 to some extent1 also the following ideas were explained3 formula1 equation1 function1 differential function1 instantaneous rate of change1 interval1 inverse1 integrating4 ,see also a textbook on calculus4 ,if y is a function of x1 then a mathematical symbol for the derivative of y with respect to x is ,d y1 and a symbol for the integral of y with respect to x1 is y dx4 ,an integral with given initial conditions 7see p4 #hc7 is a definite integral4 exponential ,a famous mathematical function is the exponential4 ,it equals the constant e raised to the x power1 e1 where e equals #b4gahbh4444 ,the exponential lies between the powers of #b and the powers of #c4 ,it can be computed from3 x x e #a x ------------ ------------------ 444 #a #b #a #b #c ,it is a solution of the differential equation ,dy y4 ,see also a textbook on calculus4 ,the exponential to the base #aj is #aj4 logarithm ,another important mathematical function is the logarithm4 ,it is written log x or log x and can be computed from the two equations3 log uv log u log v x x log7#a x7 x - ------------ ------------ - 4441 x #a #b #c ,it is a solution of the differential equation ,dy #a_/y4 ,if y is the logarithm of x1 then x is the antilogarithm of y4 ,the logarithm to the base #aj of x1 log x1 equals the logarithm to the base e of x1 log x1 divided by log #aj4 ,see also textbooks on algebra and calculus4 sine1 cosine1 tangent1 antitangent ,these also are important mathematical functions4 ,the sine and cosine are solutions of the differential equation ,d7,dy7 -y and are written as sin x and cos x4 ,they can be computed from x x sin x x - ------------ ------------------ - 444 #abc #abcde x x cos x #a - ------------ ------------ - 444 #ab #abcd ,the tangent of x is simply sine of x divided by cosine of x4 ,if y is the tangent of x1 then x is the antitangent of y4 ,see also references on trigonometry and on calculus4 ,trigonometric tables include sine1 cosine1 tangent1 and related functions4 ,bessel functions ,these are mathematical functions that were named after ,friedrich ,w4 ,bessel1 a ,prussian astronomer who lived from #aghd to #ahdf4 ,bessel functions are found as some of the solutions of the differential equation x ,d7,dy7 x ,dy 7x - n7y ,o ,this equation arises in a number of physical problems in the fields of electricity1 sound1 heat flow1 air flow1 etc4 matrix ,a matrix is a table 7or array7 of numbers in rows and columns1 for which addition1 multiplication1 etc41 with similar tables is specially defined4 ,for example1 the matrix #a #b #c #d plus the matrix #e #bj #fj #ajj equals the matrix #f #bb #fc #ajd4 7,can you guess the rule defining addition87 ,calculations using matrices are useful in physics1 engineering1 psychology1 statistics1 etc4 ,to add a square matrix of #ajj terms in an array of #aj columns and #aj rows to another such matrix1 #ajj ordinary additions of numbers are needed4 ,to multiply one such matrix by another1 #ajjj ordinary multiplications and #ijj ordinary additions are needed4 ,see references on matrix algebra and matrix calculus4 differences1 smoothness1 checking ,on p4 #bba1 a sequence of values of y is shown3 #bf1 #cg1 #ej1 #fe1 #hb4 ,suppose1 however1 the second value of y was reported as #dg instead of #cg4 ,then the differences of y as we pass down the sequence would not be #aa1 #ac1 #ae1 #ag 7which is certainly regular or smooth7 but #ba1 #c1 #ae1 #ag 7which is certainly not smooth74 ,the second set of differences would strongly suggest a mistake in the reporting of y4 ,the smoothness of differences is often a useful check on a sequence of reported values4 ,supplement #c ,,references ,a book like the present one can cover only a part of the subject of machines that think4 ,to obtain more information about these machines and other topics to which they are related there are many references that may be consulted4 ,there are still few books directly on the subject of machines that think1 but there are many articles and papers1 most of them rather specialized4 ,the purpose of this supplement is to give a number of these references and to provide a brief1 general introduction to some of them4 ,the references are subdivided into groups1 each dealing with a branch of the subject4 ,the references in each group are in alphabetical order by name of author 7with 8anonymous0 last71 and under each author they are in chronological order by publication date4 ,some publications1 especially a forum or symposium1 are listed more than once1 according as the topic discussed falls in different groups4 ,in this supplement1 the sign three dots 7 4447 next to the page numbers for an article indicates that the article is continued on later1 nonconsecutive pages4 ,it seemed undesirable to try to make the group of references dealing with a subject absolutely complete1 so long as enough were given to provide a good introduction to the subject4 ,it proved impractical to try to make the citation of every single reference technically complete1 so long as enough citation was given so that the reference could certainly be found4 ,furthermore1 in a list of more than #bej references1 errors are almost certain to occur4 ,if any reader should send me additions or corrections1 ,i shall be more than grateful4 ,,the ,,human ,,brain ,no one yet knows specifically how particular ideas are thought about in the human brain4 ,the references listed in this section1 however1 contain some information about such topics as3 ,the structural differences1 development1 and evolution of the brains of animals1 apes1 primitive man1 and modern man4 ,the effect on the brain of blood composition1 body temperature1 supply of oxygen1 and other biochemical factors4 ,the structure and physiology of the brain1 the nervous system1 and nerve impulses4 ,the theory of learning1 intelligence1 and memory4 ,,barcroft1 ,,joseph1 ,the ,brain and ,its ,environment1 ,new ,haven3 ,yale ,university ,press1 #aidh1 #aag pp4 ,,beach1 ,,frank ,a41 ,payday for ,primates1 ,natural ,history1 vol4 #ef1 no4 #aj1 ,dec4 #aidg1 pp4 #ddh-dea4 ,,beach1 ,,frank ,a41 ,can ,animals ,reason8 ,natural ,history1 vol4 #eg1 no4 #c1 ,mar4 #aidh1 pp4 #aab-aaf 444 ,,berry1 ,r4 ,j4 ,a41 ,brain and ,mind1 or the ,nervous ,system of ,man1 ,new ,york3 ,the ,macmillan ,co41 #aibh1 #fjh pp4 ,,boring1 ,,edwin ,g41 ,a ,history of ,experimental ,psychology1 ,new ,york3 ,century ,co41 #aibi1 #fii pp4 ,,franz1 ,,shepherd ,i41 ,the ,evolution of an ,idea2 ,how the ,brain ,works1 ,los ,angeles3 ,university of ,california1 #aibi1 #ce pp4 ,,herrick1 ,c4 ,,judson1 ,the ,thinking ,machine1 ,chicago3 ,university of ,chicago ,press1 #aibi1 #cgd pp4 ,,herrick1 ,c4 ,,judson1 ,brains of ,rats and ,men1 ,chicago3 ,university of ,chicago ,press1 #aicj1 #chb pp4 ,,lashley1 ,,karl ,s41 ,brain ,mechanisms and ,intelligence1 ,chicago3 ,university of ,chicago ,press1 #aibi1 #ahf pp4 ,,pieron1 ,,henri1 ,thought and the ,brain1 ,london3 ,kegan1 ,paul1 ,trench1 ,trbner ,co41 #aibg1 #bfb pp4 ,also ,new ,york3 ,harcourt1 ,brace ,co4 ,,schr,,dinger1 ,,erwin1 ,what is ,life81 ,new ,york3 ,the ,macmillan ,co41 #aide1 #ij pp4 ,,sherrington1 ,,charles ,s41 ,the ,brain and ,its ,mechanism1 ,cambridge1 ,england3 ,the ,university ,press1 #aicc1 #ce pp4 ,,tilney1 ,,frederick1 ,the ,brain from ,ape to ,man1 ,new ,york3 ,p4 ,b4 ,hoeber1 ,inc41 #aibh1 #b vol41 #ajge pp4 ,,wiener1 ,,norbert1 ,cybernetics1 or ,control and ,communication in the ,animal and the ,machine1 ,new ,york3 ,john ,wiley ,sons1 #aidh1 #aid pp4 ,,anonymous1 ,ten ,billion ,relays1 ,time1 ,feb4 #ad1 #aidi1 p4 #fg4 ,,mathematical ,,biophysics ,there has recently been another approach to the problem3 ,how does a brain think8 ,a group of men1 many of them in and near ,chicago1 have been saying3 8,we know the properties of nerves1 nerve impulses1 and simple nerve networks4 ,we know the activity of the brain4 ,what mathematical model of nerve networks is necessary to account for the activity of the brain80 ,these men have used mathematics1 statistics1 and mathematical logic in the effort to attack this problem1 and they support a ,bulletin of ,mathematical ,biophysics4 ,,householder1 ,,alston ,s41 ,a ,neural ,mechanism for ,discrimination1 ,psychometrika1 vol4 #d1 no4 #a1 ,dec4 #aici1 pp4 #de-eh4 ,,householder1 ,,alston ,s41 and ,herbert ,d4 ,landahl1 ,mathematical ,biophysics of the ,central ,nervous ,system1 ,bloomington1 ,ind43 ,principia ,press1 #aide4 ,,landahl1 ,,herbert ,d41 ,contributions to the ,mathematical ,biophysics of the ,central ,nervous ,system1 ,bulletin of ,mathematical ,biophysics1 vol4 #a1 no4 #b1 ,june #aici1 pp4 #ie-aah4 ,,landahl1 ,,herbert ,d41 ,,warren ,s4 ,,mcculloch1 and ,,walter ,,pitts1 ,a ,statistical ,consequence of the ,logical ,calculus of ,nervous ,nets1 ,bulletin of ,mathematical ,biophysics1 vol4 #e1 no4 #d1 ,dec4 #aidc1 pp4 #ace-acg4 ,,landahl1 ,,herbert ,d41 ,a ,note on the ,mathematical ,biophysics of ,central ,excitation and ,inhibition1 ,bulletin of ,mathematical ,biophysics1 vol4 #g1 no4 #d1 ,dec4 #aide1 pp4 #bai-bba4 ,,lettvin1 ,,jerome ,y41 and ,,walter ,,pitts1 ,a ,mathematical ,theory of the ,affective ,psychoses1 ,bulletin of ,mathematical ,biophysics1 vol4 #e1 no4 #d1 ,dec4 #aidc1 pp4 #aci-adh4 ,,mcculloch1 ,,warren ,s41 and ,,walter ,,pitts1 ,a ,logical ,calculus of the ,ideas ,immanent in ,nervous ,activity1 ,bulletin of ,mathematical ,biophysics1 vol4 #e1 no4 #d1 ,dec4 #aidc1 pp4 #aae-acc4 ,,rashevsky1 ,n41 ,mathematical ,biophysics1 ,chicago3 ,university of ,chicago ,press4 ,revised edition1 #aidh1 #ffi pp4 ,,rashevsky1 ,n41 ,mathematical ,biophysics of ,abstraction and ,logical ,thinking1 ,bulletin of ,mathematical ,biophysics1 vol4 #g1 no4 #c1 ,sept4 #aide1 pp4 #acc-adh4 ,,rashevsky1 ,n41 ,some ,remarks on the ,boolean ,algebra of ,nervous ,nets in ,mathematical ,biophysics1 ,bulletin of ,mathematical ,biophysics1 vol4 #g1 no4 #d1 ,dec4 #aide1 pp4 #bjc-baa4 ,,rashevsky1 ,n41 ,a ,suggestion for ,another ,statistical ,interpretation of the ,fundamental ,equations of the ,mathematical ,biophysics of the ,central ,nervous ,system1 ,bulletin of ,mathematical ,biophysics1 vol4 #g1 no4 #d1 ,dec4 #aide1 pp4 #bbc-bbf4 ,,rashevsky1 ,n41 ,the ,neural ,mechanism of ,logical ,thinking1 ,bulletin of ,mathematical ,biophysics1 vol4 #h1 no4 #a1 ,mar4 #aidf1 pp4 #bi-dj4 ,,languages3 ,,words ,,and ,,symbols ,,for ,,thinking ,hardly any field of techniques for thinking is more fascinating than language4 ,the following list of references1 of course1 is short2 it is meant chiefly as an introduction pointing out a number of different paths into the field of language and languages4 ,such topics as the following are introduced by the references in this list3 ,the origin of languages and alphabets4 ,the languages of the world1 and speech communities4 ,the comparison of words and structure from language to language4 ,the significance of grammar and syntax4 ,the problem of clear meanings4 ,writing and speaking that is easy to understand4 ,,bloomfield1 ,,leonard1 ,language1 ,new ,york3 ,henry ,holt ,co41 #aicc1 #efd pp4 ,,bodmer1 ,,frederick1 and ,,launcelot ,,hogben1 ,the ,loom of ,language1 ,new ,york3 ,w4 ,w4 ,norton ,co41 #aidd1 #fib pp4 ,,flesch1 ,,rudolf1 ,the ,art of ,plain ,talk1 ,new ,york3 ,harper ,brothers1 #aidf1 #baj pp4 ,,graff1 ,,willem ,l41 ,language and ,languages3 ,an ,introduction to ,linguistics1 ,new ,york3 ,d4 ,appleton ,co41 #aicb1 #dhg pp4 ,,hayakawa1 ,s4 ,i41 ,language in ,action1 ,new ,york3 ,harcourt1 ,brace ,co41 #aida1 #cde pp4 ,,jespersen1 ,,otto1 ,the ,philosophy of ,grammar1 ,new ,york3 ,henry ,holt ,co41 #aibi 7third printing71 #cei pp4 ,,jespersen1 ,,otto1 ,analytic ,syntax1 ,in this book1 by means of a well-contrived system of letters and signs1 the great linguistic scholar ,jespersen depicts all the important inter-relations of ,english words and parts of words in connected speech4 ,,ogden1 ,c4 ,k41 ,the ,system of ,basic ,english1 ,new ,york3 ,harcourt1 ,brace ,co41 #aicd1 #cbj pp4 ,,schlauch1 ,,margaret1 ,the ,gift of ,tongues1 ,new ,york3 ,modern ,age ,books1 #aidb1 #cdb pp4 ,,walpole1 ,,hugh ,r41 ,semantics3 ,the ,nature of ,words and ,their ,meanings1 ,new ,york3 ,w4 ,w4 ,norton ,co41 #aida1 #bfd pp4 ,,languages3 ,,machines ,,for ,,thinking ,for many years1 nearly all references about machines as a language for thinking have been specialized and limited4 ,colleges with scholars who write textbooks usually have not had a variety of expensive and versatile computing machinery4 ,as a result1 the main environment for stimulating possible authors has until recently been missing4 ,the list of references is accordingly brief4 ,,aiken1 ,,howard ,h41 and others1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 #cjb pp4 ,,comrie1 ,,john ,,leslie1 ,the ,application of ,commercial ,calculating ,machines to ,scientific ,computing1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #b1 no4 #af1 ,oct4 #aidf1 pp4 #adi-aei4 ,,crew1 ,e4 ,w41 ,calculating ,machines1 ,the ,engineer1 vol4 #agb1 ,dec4 #aida1 pp4 #dch-dda4 ,,fry1 ,,macon1 ,designing ,computing ,mechanisms1 ,cleveland1 ,ohio3 ,penton ,publishing ,co41 #aidf1 #dh pp4 7,reprinted from ,machine ,design1 ,aug4 #aide through ,feb4 #aidf47 ,,hartree1 ,d4 ,r41 ,calculating ,machines3 ,recent and ,prospective ,developments and ,their ,impact on ,mathematical ,physics1 ,cambridge1 ,england3 ,the ,university ,press1 #aidg1 #dj pp4 ,,horsburgh1 ,e4 ,h41 ,modern ,instruments and ,methods of ,calculation1 ,london3 ,g4 ,bell and ,sons1 ,ltd41 #aiad1 #cdc pp4 ,,lilley1 ,s41 ,mathematical ,machines1 ,nature1 vol4 #adi1 ,apr4 #be1 #aidb1 pp4 #dfb-dfe4 ,,murray1 ,,francis ,j41 ,the ,theory of ,mathematical ,machines1 ,new ,york3 ,king's ,crown ,press1 #aidg1 #aaf pp4 ,the author states that a mathematical machine is a mechanism that provides information concerning the relationships among a specified set of mathematical concepts4 ,,turck1 ,j4 ,a4 ,v41 ,the ,origin of ,modern ,calculating ,machines1 ,chicago3 ,western ,society of ,engineers1 #aiba4 ,recently1 however1 some magazine and newspaper publishers have seen news value in machines that think1 and some good general articles with appeal to a wide audience have appeared4 ,for the references to these articles1 see the section of this supplement entitled 8,digital ,machines--,miscellaneous40 ,,punch-,,card ,,calculating ,,machines ,there are a few general references on punch-card calculating machines3 ,,baehne1 ,g4 ,,walter1 editor1 and others1 ,practical ,applications of the ,punched ,card ,method in ,colleges and ,universities1 ,new ,york3 ,columbia ,university ,press1 #aice1 #ddb pp4 ,this is a collection of many contributions from a number of authors1 describing various applications1 chiefly educational4 ,,eckert1 ,w4 ,j41 ,punched-,card ,methods in ,scientific ,computation1 ,new ,york3 ,columbia ,university1 ,the ,thomas ,j4 ,watson ,astronomical ,computing ,bureau1 #aidj1 #acf pp4 ,this is a scientific treatise1 chiefly relating to the computation of orbits in astronomy4 ,,hartkemeier1 ,,harry ,,pelle1 ,principles of ,punch-,card ,machine ,operation 7,subtitle3 ,how to ,operate ,punch-,card ,tabulating and ,alphabetic ,accounting ,machines71 ,new ,york3 ,thomas ,y4 ,crowell ,co41 #aidb1 #bfi pp4 ,this is based on the author's experience in teaching statistical analysis using ,,ibm tabulators4 ,the book does not deal with the collator or multiplying punch4 ,,hedley1 ,k4 ,j41 ,the ,development of the ,punched-,card ,method1 ,actuarial ,society of ,australasia1 #aidf1 #bj pp4 ,,international ,,business ,,machines ,,corporation1 ,international ,business ,machines 7form no4 ,a-#djcf-f-de71 ,new ,york3 ,international ,business ,machines ,corporation1 #aide1 #fe pp4 ,pages #f to #ca show pictures and brief descriptions of about #bj punch-card machines1 available in #aide4 ,,schnackel1 ,h4 ,g41 and ,h4 ,c4 ,,lang1 ,accounting by ,machine ,methods1 ,new ,york3 ,ronald ,press ,co41 #aici1 #ec pp4 ,,wolf1 ,,arthur ,w41 and ,,edmund ,c4 ,,berkeley1 ,advanced ,course in ,punched ,card ,operations1 ,newark1 ,n4 ,j43 ,prudential ,insurance ,company of ,america1 #aidb1 #ih pp4 ,a useful and authoritative description of ,,ibm punch-card calculating machinery is the following3 ,,international ,,business ,,machines ,,corporation1 ,,department ,,of ,,education1 ,machine ,methods of ,accounting1 ,endicott1 ,n4 ,y43 ,international ,business ,machines ,corporation1 #aicf-da1 #che pp4 ,this is a collection of #bh separate booklets telling the detailed operation of ,,ibm punch-card machinery4 ,they were written for employees of ,,ibm and users of ,,ibm equipment4 ,the following list of the booklets is useful in locating them3 ,,no4 ,,of ,,title ,,form ,,no4 ,,date ,,pages ,machine ,methods of ,accounting--,foreword ,,am #aicf #f ,development of ,,ibm ,corporation ,,am-#a-a #aicf #ad ,principles of the ,electric ,accounting ,machine ,method ,,am-#b #aicf #ab ,the ,tabulating ,card ,,am-#c-a #aicf #bj ,design of ,tabulating ,cards ,,am-#d-a #aicf #af ,preparation and ,use of ,codes ,,am-#e #aicf #bh ,organization and ,supervision of the ,tabulating ,department ,,am-#f #aicf #af ,selection and ,training of ,key ,punch ,operators ,,am-#g #aicf #ab ,accounting ,control ,,am-#h #aicf #h ,punches ,,am-#i #aicf #ab ,alphabetic ,printing ,punches ,,am-#aj #aicf #g ,facts to ,know about ,key ,punches ,,am-#aa #aicf #d ,verifiers ,,am-#ab #aicf #d ,gang ,punches ,,am-#ac #aicf #h ,card-,operated ,sorting ,machines ,,am-#ad #aicf #ab ,facts to ,know about ,sorters ,,am-#ad;a #aicf #d ,electric ,tabulating ,machines ,,am-#ae #aicf #bj ,electric ,accounting ,machines 7,type #bhe and ,type #big7 ,,am-#af #aicf #af ,alphabetic ,direct ,subtraction ,accounting ,machine ,,am-#ag #aicf #bh ,numerical ,interpreters ,,am-#ah #aicf #h ,electric ,punched-,card ,interpreter 7,type #eeb7 ,,am-#ah;a #aida #h ,reproducing ,punches 7,type #eab7 ,,am-#ai #aicf #af ,automatic ,summary ,punches for ,use with the ,numerical ,accounting ,machines 7,type #bhe-big7 ,,am-#bj #aicf #af ,automatic ,summary ,punches for ,use with the ,alphabetic ,accounting ,machines 7,type #dje7 ,,am-#bj;a #aidj #af ,multiplying ,punches ,,am-#ba #aicf #af ,application of ,machines to ,accounting ,functions ,,am-#bb #aicf #bd ,other ,international ,products ,,am-#bc-b #aicf #ai ,the ,international ,automatic ,carriage 7,type #iba7 ,,am-#bd #aich #ae ,the ,department of ,education of ,,ibm has begun a second series of booklets on the principles of operation of punch-card calculating machinery3 ,,international ,,business ,,machines ,,corporation1 ,,department ,,of ,,education1 ,principles of ,operation1 ,endicott1 ,n4 ,y43 ,international ,business ,machines ,corporation1 #aidb and later 7except for one published in #aici74 ,many of the booklets in this series have good examples of machine operation and applications4 ,also1 for the first time1 letters and numbers have been used as coordinates to label the hubs on the plugboards4 ,this series includes the following3 ,,no4 ,,of ,,title ,,form ,,no4 ,,date ,,pages ,,card ,,punches ,,and ,,verifiers ,card-,punching and ,verifying ,machines #eb-cagf-j #aidf #ba ,alphabetical ,verifier1 ,type #jee #eb-cbie-a #aidf #d ,,interpreters ,card ,interpreters1 ,type #eej1 #eea1 and #eeb #eb-cagh-j #aidf #ad ,,reproducers ,automatic ,reproducing ,punch1 ,type #eac #eb-cahj-j #aide #bb ,end ,printing ,reproducing ,punch1 ,type #eai #eb-cbib-a #aidf #bf ,electric ,document-,originating ,machine1 ,june ,type #eai #eb-cbib-b #aidh #bf ,,collators ,collator ,,am-#be #aidc #ca ,collator ,counting ,device ,c4,r4 #iagh #aidb #ab ,,calculating ,,punches ,electric ,multiplier1 ,type #fja #eb-cdjh-a #aidg #dg ,calculating ,punch1 ,type #fjb #eb-cdji-j #aidf #hc ,calculating ,punch1 ,type #fjb #eb-cdji-e #aidg #ic ,calculating ,punch1 ,type #fjb-;,a 7,preliminary ,manual7 #bb-edhi-j #aidh #ei ,electronic ,multiplier1 ,type #fjc #eb-cefa-j #aidf #e ,electronic ,calculating ,punch1 ,type #fjd #bb-ebgi-j #aidh #ea ,,tabulators ,accounting ,machine1 ,type #djb and #djc 7,preliminary ,manual7 #bb-efed-j #aidi #adf ,alphabetical ,accounting ,machine1 ,type #djd #eb-ccie-a #aidf #if ,typical ,applications1 ,alphabetical ,accounting ,machine1 ,type #djd1 with ,multiple ,line ,printing #bb-cgga-a #aidg #dg ,alphabetical ,accounting ,machine1 ,type #dje ,,am #ag 7#a71 #aidc #ij ,revised #a_/a_/dc ,nov4 ,alphabetical ,accounting ,machine1 ,type #dje #eb-cagi-b #aidh #ha ,,automatic ,,printing ,,carriages ,bill ,feed1 ,type #ibj #eb-cahd-j #aide #ba ,form ,feeding ,device #eb-cbce-j #aidf #aa ,automatic ,carriage1 ,type #iba #eb-cahc-j #aide #cf ,tape-,controlled ,carriage 7,preliminary ,manual1 ,revised7 #bb-edae-a #aidh #bg ,,test ,,scoring ,,machine ,test ,scoring ,machine #id-bccc-j #aici #ai ,may ,test ,scoring ,machine #cb-iade-a #aidf #bj ,published ,tests ,adapted for ,use with ,june the ,,ibm ,electric ,test ,scoring ,machine #bg-dbhf-i #aidh #h ,in addition to the new types of punch-card machines referred to in the above list1 an elaborate punch-card calculating machine is described in the following reference3 ,,eckert1 ,w4 ,j41 ,the ,,ibm ,pluggable ,sequence ,relay ,calculator1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bc1 ,july #aidh1 pp4 #adi-afa4 ,a description of punch-card machinery in rather a light vein is contained in3 ,,anonymous1 ,speaking of ,pictures3 ,new ,mechanical ,monsters ,ease ,life's ,growing ,pains1 ,life1 ,sept4 #ae1 #aidg1 pp4 #ae-af4 ,,anonymous1 #edj1 ,chicago3 ,time-,life-,fortune ,magazine1 ,subscription ,fulfillment ,office1 #aidh1 #ae pp4 ,new types of punch-card machinery are continually coming into use4 ,among them are3 machines that take in punch cards and make punched paper tape 7such as teletype tape71 and vice versa--useful for transmitting punch-card information over wires2 an electric typewriter operated by punch cards--useful for preparing almanacs for sea and air navigation1 etc42 a calculator programmed by punch cards1 consisting of an assembly of a tabulator1 an electronic calculating punch1 and an auxiliary storage unit1 all cabled together--useful for some types of long calculation2 etc4 ,for information about such machinery1 the manufacturers may be consulted4 ,,punch-,,card ,,calculating ,,machinery3 ,,applications ,there are many articles in scientific journals on applications of punch-card calculating machinery to technical problems4 ,the fields of engineering1 education1 indexing1 mathematics1 surveying1 statistics1 and others are all represented in the following list of sample references3 ,,alt1 ,,franz ,l41 ,multiplication of ,matrices1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #b1 no4 #ac1 ,jan4 #aidf1 pp4 #ab-ac4 ,,bailey1 ,c4 ,f41 and others1 ,punch ,cards for ,indexing ,scientific ,data1 ,science1 vol4 #ajd1 ,aug4 #bc1 #aidf1 p4 #aha4 ,,bower1 ,e4 ,c41 ,on ,subdividing ,tables1 ,lick ,observatory ,bulletin1 vol4 #af1 no4 #dee1 ,nov4 #aicc1 pp4 #adc-add4 ,,bower1 ,e4 ,c41 ,systematic ,subdivision of ,tables1 ,lick ,observatory ,bulletin1 vol4 #ag1 no4 #dfg1 ,apr4 #aice1 pp4 #fe-gd4 ,,clemence1 ,g4 ,m41 and ,,paul ,,herget1 ,optimum-,interval ,punched-,card ,tables1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #a1 no4 #f1 ,apr4 #aidd1 pp4 #agc-agf4 ,,culley1 ,,frank ,l41 ,use of ,accounting ,machines for ,mass-,transformation from ,geographic to ,military-,grid ,coordinates1 ,washington1 ,d4 ,c43 ,national ,research ,council1 ,american ,geophysical ,union ,transactions of #aidb1 part #b1 pp4 #aij-aig4 ,,deming1 ,w4 ,,edwards1 and ,,morris ,h4 ,,hansen1 ,on ,some ,census ,aids to ,sampling1 ,journal of the ,american ,statistical ,association1 vol4 #ch1 no4 #bbe1 ,sept4 #aidc1 pp4 #cec-ceg4 ,,dunlap1 ,,jack ,w41 ,the ,computation of ,means1 ,standard ,deviations1 and ,correlations by the ,tabulator ,when the ,numbers ,are ,both ,positive and ,negative1 ,proceedings of the ,educational ,research ,forum1 ,international ,business ,machines ,corporation1 ,aug4 #aidj1 pp4 #af-ai4 ,,dwyer1 ,,paul ,s41 ,the ,use of ,tables in the ,form of ,prepunched ,cards1 ,proceedings of the ,educational ,research ,forum1 ,international ,business ,machines ,corporation1 ,aug4 #aidj1 pp4 #abe-abg4 ,,dwyer1 ,,paul ,s41 ,summary of ,problems in the ,computation of ,statistical ,constants with ,tabulating and ,sorting ,machines1 ,proceedings of the ,educational ,research ,forum1 ,international ,business ,machines ,corporation1 ,aug4 #aidj1 pp4 #bj-bh4 ,,dwyer1 ,,paul ,s41 and ,,alan ,d4 ,,meacham1 ,the ,preparation of ,correlation ,tables on a ,tabulator ,equipped with ,digit ,selection1 ,journal of the ,american ,statistical ,association1 vol4 #cb1 #aicg1 pp4 #fed-ffb4 ,,dyer1 ,h4 ,s41 ,making ,test ,score ,data ,effective in the ,admission and ,course ,placement of ,harvard ,freshmen1 ,proceedings of the ,research ,forum1 ,international ,business ,machines ,corporation1 #aidf1 pp4 #ee-fb4 ,,eckert1 ,w4 ,j41 and ,,ralph ,f4 ,,haupt1 ,the ,printing of ,mathematical ,tables1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #b1 no4 #ag1 ,jan4 #aidg1 pp4 #aif-bjb4 ,,feinstein1 ,,lillian1 and ,,martin ,,schwarzchild1 ,automatic ,integration of ,linear ,second-,order ,differential ,equations by ,means of ,punched-,card ,machines1 ,review of ,scientific ,instruments1 vol4 #ab1 no4 #h1 ,aug4 #aida1 pp4 #dje-djh4 ,,hotelling1 ,,harold1 ,some ,new ,methods in ,matrix ,calculation1 ,the ,annals of ,mathematical ,statistics1 vol4 #ad1 no4 #a1 ,mar4 #aidc1 pp4 #a-cd4 ,,international ,,business ,,machines ,,corporation1 editor1 and others1 ,proceedings of the ,educational ,research ,forum1 ,endicott1 ,n4 ,y43 ,international ,business ,machines ,corporation1 #aida4 ,,international ,,business ,,machines ,,corporation1 editor1 and others1 ,proceedings of the ,research ,forum1 ,endicott1 ,n4 ,y43 ,international ,business ,machines ,corporation1 #aidf1 #id pp4 ,,king1 ,,gilbert ,w41 ,punched-,card ,tables of the ,exponential ,function1 ,review of ,scientific ,instruments1 vol4 #ae1 no4 #ab1 ,dec4 #aidd1 pp4 #cdi-cej4 ,,king1 ,,gilbert ,w41 and ,,george ,b4 ,,thomas1 ,preparation of ,punched-,card ,tables of ,logarithms1 ,review of ,scientific ,instruments1 vol4 #ae1 no4 #ab1 ,dec4 #aidd1 p4 #cej4 ,,kormes1 ,,mark1 ,a ,note on the ,integration of ,linear ,second-,order ,differential ,equations by ,means of ,punched ,cards1 ,review of ,scientific ,instruments1 vol4 #ad1 no4 #d1 ,apr4 #aidc1 p4 #aah4 ,,kormes1 ,,mark1 ,numerical ,solution of the ,boundary ,value ,problem for the ,potential ,equation by ,means of ,punched ,cards1 ,review of ,scientific ,instruments1 vol4 #ad1 no4 #h1 ,aug4 #aidc1 pp4 #bdh-bej4 ,,kormes1 ,,mark1 and ,,jennie ,p4 ,,kormes1 ,numerical ,solution of ,initial ,value ,problems by ,means of ,punched-,card ,machines1 ,review of ,scientific ,instruments1 vol4 #af1 no4 #a1 ,jan4 #aide1 pp4 #g-i4 ,,kuder1 ,g4 ,,frederic1 ,use of the ,,ibm ,scoring ,machine for ,rapid ,computation of ,tables of ,intercorrelations1 ,journal of ,applied ,psychology1 vol4 #bb1 no4 #f1 ,dec4 #aich1 pp4 #ehg-eif4 ,,maxfield1 ,d4 ,k41 ,library ,punched ,card ,procedures1 ,library ,journal1 vol4 #ga1 no4 #ab1 ,june #ae1 #aidf1 pp4 #ijb-ije 444 ,,mclaughlin1 ,,kathleen1 ,adding ,machines ,nip ,,aef ,epidemics1 ,new ,york3 ,new ,york ,times1 ,apr4 #bg1 #aide4 ,,mcpherson1 ,,john ,c41 ,on ,mechanical ,tabulation of ,polynomials1 ,annals of ,mathematical ,statistics1 ,sept4 #aida1 pp4 #cag-cbg4 ,,mcpherson1 ,,john ,c41 ,mathematical ,operations with ,punched ,cards1 ,journal of the ,american ,statistical ,association1 vol4 #cg1 ,june #aidb1 pp4 #bge-bha4 ,,milliman1 ,,wendell ,a41 ,mechanical ,multiplication by the ,use of ,tabulating ,machines1 ,transactions of the ,actuarial ,society of ,america1 vol4 #ce1 part #b1 ,oct4 #aicd1 pp4 #bec-bfd2 for discussion see also vol4 #cf1 part #a1 ,may #aice1 pp4 #gg-hd4 ,,royer1 ,,elmer ,b41 ,a ,machine ,method for ,computing the ,biserial ,correlation ,coefficient in ,item ,validation1 ,psychometrika1 vol4 #f1 no4 #a1 ,feb4 #aida1 pp4 #ee-ei4 ,,whitten1 ,c4 ,a41 ,triangulation ,adjustment by ,international ,business ,machines1 ,washington1 ,d4 ,c43 ,national ,research ,council1 ,american ,geophysical ,union ,transactions of #aidc1 part #a1 p4 #ca4 ,the following bibliography may be obtained on request to the ,watson ,scientific ,computing ,laboratory1 ,columbia ,university1 #fab ,west #aaf ,street1 ,new ,york #bg1 ,n4 ,y43 ,,watson ,,scientific ,,computing ,,laboratory1 ,bibliography3 ,the ,use of ,,ibm ,machines in ,scientific ,research1 ,statistics1 and ,education1 ,new ,york3 ,international ,business ,machines ,corporation 7form no4 #ej-chac-j71 ,sept4 #aidg1 #be pp4 ,the organization and equipment of this laboratory are described in3 ,,eckert1 ,w4 ,j41 ,facilities of the ,watson ,scientific ,computing ,laboratory1 ,proceedings of the ,research ,forum1 ,international ,business ,machines ,corporation1 #aidf1 pp4 #ge-hj4 ,,the ,,differential ,,analyzer ,the basic scientific articles on the two differential analyzers at ,massachusetts ,institute of ,technology are3 ,,bush1 ,,vannevar1 ,the ,differential ,analyzer3 ,a ,new ,machine for ,solving ,differential ,equations1 ,journal of the ,franklin ,institute1 vol4 #bab1 no4 #d1 ,oct4 #aica1 pp4 #ddg-dhh4 ,,bush1 ,,vannevar1 and ,,samuel ,h4 ,,caldwell1 ,a ,new ,type of ,differential ,analyzer1 ,journal of the ,franklin ,institute1 vol4 #bdj1 no4 #d1 ,oct4 #aide1 pp4 #bee-cbf4 ,some of the less technical articles about the second differential analyzer at ,m4,i4,t4 are3 ,,caldwell1 ,,samuel ,h41 ,educated ,machinery1 ,technology ,review1 vol4 #dh1 no4 #a1 ,nov4 #aide1 pp4 #ca-cd4 ,,genet1 ,n41 #ajj-,ton ,brain at ,m4,i4,t41 ,scholastic1 vol4 #dh1 ,feb4 #d1 #aidf1 p4 #cf4 ,,anonymous1 ,mathematical ,machine2 ,new ,electronic ,differential ,analyzer1 ,science ,news ,letter1 vol4 #dh1 ,nov4 #aj1 #aide1 p4 #bia4 ,,anonymous1 ,robot ,einstein3 ,differential ,analyzer at ,m4,i4,t41 ,newsweek1 vol4 #bf1 ,nov4 #ab1 #aide1 p4 #ic4 ,,anonymous1 ,m4,i4,t4's #ajj-,ton ,mathematical ,brain is ,now to ,tackle ,problems of ,peace1 ,popular ,science1 vol4 #adh1 ,jan4 #aidf1 p4 #ha4 ,,anonymous1 ,the ,great ,electro-,mechanical ,brain2 ,m4,i4,t4's ,differential ,analyzer1 ,life1 vol4 #bj1 ,jan4 #ad1 #aidf1 pp4 #gc-gd 444 ,,anonymous1 ,all the ,answers at ,your ,fingertips2 in the ,laboratory of ,m4,i4,t41 ,popular ,mechanics1 vol4 #he1 ,mar4 #aidf1 pp4 #afd-afg 444 ,a differential analyzer was built at the ,moore ,school of ,electrical ,engineering3 ,,travis1 ,,irven1 ,differential ,analyzer ,eliminates ,brain ,fag1 ,machine ,design1 ,july #aice1 pp4 #ae-ah4 ,a differential analyzer was built at the ,general ,electric ,company1 ,schenectady1 ,n4 ,y4 ,instead of using a mechanical or electrical amplifier of the motion of the little turning wheel riding on the disc1 this machine follows the motion using polarized light4 ,this machine is described in3 ,,berry1 ,t4 ,m41 ,polarized ,light ,servo ,system1 ,transactions of the ,american ,institute of ,electrical ,engineers1 vol4 #fc1 ,apr4 #aidd1 pp4 #aie-aig4 ,,kuehni1 ,h4 ,p41 and ,h4 ,a4 ,,peterson1 ,a ,new ,differential ,analyzer1 ,transactions of the ,american ,institute of ,electrical ,engineers1 vol4 #fc1 ,may #aidd1 pp4 #bba-bbg4 ,a differential analyzer has been put into use at the ,university of ,california3 ,,boelter1 ,l4 ,m4 ,k41 and others1 ,the ,differential ,analyzer of the ,university of ,california1 ,los ,angeles3 ,university of ,california1 #aidg1 #be pp4 ,a differential analyzer was built at ,manchester ,university1 ,england4 ,it was built first from 8,meccano0 parts1 at a total cost of about #bj pounds1 and later refined for more exact work4 ,some articles dealing with this differential analyzer are3 ,,hartree1 ,d4 ,r41 ,the ,differential ,analyzer1 ,nature1 vol4 #ace1 ,june #h1 #aice1 p4 #idj4 ,,hartree1 ,d4 ,r41 ,the ,mechanical ,integration of ,differential ,equations1 ,the ,mathematical ,gazette1 vol4 #bb1 #aich1 pp4 #cdb-cfd4 ,,hartree1 ,d4 ,r41 and ,a4 ,,porter1 ,the ,construction of a ,model ,differential ,analyser1 ,memoirs and ,proceedings of the ,manchester ,literary and ,philosophical ,society1 vol4 #gi1 ,july #aice1 pp4 #ea-gb4 ,other small scale differential analyzers built in ,england are covered in3 ,,beard1 ,r4 ,e41 ,the ,construction of a ,small ,scale ,differential ,analyser and ,its ,application to the ,calculation of ,actuarial ,functions1 ,journal of the ,institute of ,actuaries1 vol4 #ga1 #aidb1 pp4 #aic-bbg4 ,,massey1 ,h4 ,s4 ,w41 ,j4 ,,wylie1 and ,r4 ,a4 ,,buckingham1 ,a ,small ,scale ,differential ,analyser3 ,its ,construction and ,operation1 ,proceedings of the ,royal ,irish ,academy1 vol4 #de1 #aich1 pp4 #a-ba4 ,a differential analyzer constructed in ,germany is briefly described in the following3 ,,sauer1 ,r41 and ,h4 ,,poesch1 ,integrating ,machine for ,solving ,ordinary ,differential ,equations1 ,engineers ,digest 7,american ,edition71 vol4 #a1 ,may #aidd1 pp4 #cbf-cbh4 ,from the historical point of view there are some interesting papers on a machine for solving differential equations by ,sir ,william ,thomson 7,lord ,kelvin71 including one by his brother ,james ,thomson4 ,they are in the ,proceedings of the ,royal ,society1 vol4 #bd1 ,feb4 #ahgf1 pp4 #bfb-bge4 ,the method of integration by a machine is described1 but the state of machine tools at the time was such that no accurate mechanism was constructed4 ,another interesting paper foreshadowing the differential analyzer is3 ,,wainwright1 ,,lawrence ,l41 ,a ,ballistic ,engine1 ,chicago3 ,university of ,chicago1 thesis for ,master's ,degree1 #aibc1 #bh pp4 ,some of the applications and mathematical limitations of differential analyzers are covered in3 ,,bush1 ,v41 and ,s4 ,h4 ,,caldwell1 ,thomas-,fermi ,equation ,solution by the ,differential ,analyzer1 ,physical ,review1 vol4 #ch1 no4 #aj1 #aica1 pp4 #ahih-aijb4 ,,hartree1 ,d4 ,r41 ,a ,great ,calculating ,machine3 the ,bush ,differential ,analyser and ,its ,applications in ,science and ,industry1 ,proceedings of the ,royal ,institution of ,great ,britain1 vol4 #ca1 #aidj1 pp4 #aea-agj4 ,,hartree1 ,d4 ,r41 and ,a4 ,,porter1 ,the ,application of the ,differential ,analyser to ,transients on a ,distortionless ,transmission ,line1 ,journal of the ,institute of ,electrical ,engineering1 vol4 #hc1 no4 #ejc1 ,nov4 #aich1 pp4 #fdh-fef4 ,,hartree1 ,d4 ,r41 and ,j4 ,r4 ,,womersley1 ,a ,method for the ,numerical or ,mechanical ,solution of ,certain ,types of ,partial ,differential ,equations1 ,proceedings of the ,royal ,society of ,london1 series ,a1 vol4 #afa1 #aicg1 pp4 #cec-cff4 ,,maginniss1 ,f4 ,j41 ,differential ,analyzer ,applications1 ,general ,electric ,review1 vol4 #dh1 no4 #e1 ,may #aide1 pp4 #ed-ei4 ,,shannon1 ,,claude ,e41 ,mathematical ,theory of the ,differential ,analyzer1 ,journal of ,mathematics and ,physics1 ,cambridge1 ,mass43 ,massachusetts ,institute of ,technology1 vol4 #bj1 no4 #d1 #aida1 pp4 #ccg-ced4 ,,harmonic ,,analyzers ,,and ,,synthesizers ,another branch of the analogue calculating machine is the harmonic analyzer and synthesizer4 ,these are machines that study wave motions and related physical and mathematical functions4 ,a brief list of articles on this type of machine follows3 ,,archer1 ,r4 ,m41 ,projecting ,apparatus for ,compounding ,harmonic ,vibrations1 ,journal of ,scientific ,instruments1 vol4 #ad1 #aicg1 pp4 #djh-daj4 ,,brown1 ,s4 ,l41 ,a ,mechanical ,harmonic ,synthesizer-,analyzer1 ,journal of the ,franklin ,institute1 vol4 #bbh1 #aici1 pp4 #fge-fid4 ,,brown1 ,s4 ,l41 and ,l4 ,l4 ,,wheeler1 ,a ,mechanical ,method for ,graphical ,solution of ,polynomials1 ,journal of the ,franklin ,institute1 vol4 #bca1 #aida1 pp4 #bbc-bdc4 ,,brown1 ,s4 ,l41 and ,l4 ,l4 ,,wheeler1 ,use of the ,mechanical ,multiharmonograph for ,graphing ,types of ,functions and for ,solution of ,pairs of ,non-,linear ,simultaneous ,equations1 ,review of ,scientific ,instruments1 vol4 #ac1 ,nov4 #aidb1 pp4 #dic-die4 ,,brown1 ,s4 ,l41 and ,l4 ,l4 ,,wheeler1 ,the ,use of a ,mechanical ,synthesizer to ,solve ,trigonometric and ,certain ,types of ,transcendental ,equations1 and for the ,double ,summations ,involved in ,patterson ,contours1 ,journal of ,applied ,physics1 vol4 #ad1 ,jan4 #aidc1 pp4 #cj-cf4 ,f,,rth1 ,r41 and ,r4 ,w4 ,,pringle1 ,a ,new ,photo-,electric ,method for ,fourier ,synthesis and ,analysis1 ,london1 ,edinburgh and ,dublin ,philosophical ,magazine and ,journal of ,science1 vol4 #ce1 series #g1 #aidd1 pp4 #fdc-fef4 ,,international ,,hydrographic ,,bureau1 ,tide ,predicting ,machines1 ,international ,hydrographic ,bureau1 ,special ,publication #ac1 ,july #aibf4 ,,kranz1 ,,frederick ,w41 ,a ,mechanical ,synthesizer and ,analyzer1 ,journal of the ,franklin ,institute1 vol4 #bjd1 #aibg1 pp4 #bde-bfb4 ,,marble1 ,f4 ,g41 ,an ,automatic ,vibration ,analyzer1 ,bell ,laboratories ,record1 vol4 #bb1 ,apr4 #aidd1 pp4 #cgf-chj4 ,,maxwell1 ,l4 ,r41 ,an ,electrical ,method for ,compounding ,sine ,functions1 ,review of ,scientific ,instruments1 vol4 #aa1 ,feb4 #aidj1 pp4 #dg-ed4 ,,miller1 ,,dayton ,c41 ,a #cb-;,element ,harmonic ,synthesizer1 ,journal of the ,franklin ,institute1 vol4 #aha1 #aiaf1 pp4 #ea-ha4 ,,miller1 ,,dayton ,c41 ,the ,henrici ,harmonic ,analyzer and ,devices for ,extending and ,facilitating ,its ,use1 ,journal of the ,franklin ,institute1 vol4 #ahb1 #aiaf1 pp4 #bhe-cbb4 ,,milne1 ,j4 ,r41 ,a 8,duplex0 ,form of ,harmonic ,synthetiser and ,its ,mathematical ,theory1 ,proceedings of the ,royal ,society of ,edinburgh1 vol4 #ci1 #aiah-ai1 pp4 #bcd-bdb4 ,,montgomery1 ,h4 ,c41 ,an ,optical ,harmonic ,analyzer1 ,bell ,system ,technical ,journal1 vol4 #ag1 no4 #c1 ,july #aich1 pp4 #djf-dae4 ,,raymond1 ,w4 ,j41 ,an ,harmonic ,synthesizer ,having ,components of ,incommensurable ,period and ,any ,desired ,decrement1 ,physical ,review1 vol4 #aa1 series #b1 #aiah1 pp4 #dgi-dha4 ,,robertson1 ,j4 ,m41 ,a ,simple ,harmonic ,continuous ,calculating ,machine1 ,london1 ,edinburgh and ,dublin ,philosophical ,magazine and ,journal of ,science1 vol4 #ac1 #aicb1 pp4 #dac-dai4 ,,somerville1 ,j4 ,m41 ,harmonic ,synthesizer for ,demonstrating and ,studying ,complex ,wave ,forms1 ,journal of ,scientific ,instruments1 vol4 #ba1 ,oct4 #aidd1 pp4 #agd-agg4 ,,straiton1 ,a4 ,w41 and ,g4 ,k4 ,,terhune1 ,harmonic ,analysis by ,photographic ,method1 ,journal of ,applied ,physics1 vol4 #ad1 #aidc1 pp4 #ece-ecf4 ,,wegel1 ,r4 ,l41 and ,c4 ,r4 ,,moore1 ,an ,electrical ,frequency ,analyzer1 ,bell ,system ,technical ,journal1 vol4 #c1 #aibd1 pp4 #bii-cbc4 ,,network ,,analyzers ,a third branch of the analogue calculating machine is the network analyzer4 ,to solve problems1 this machine uses the laws governing a network of electrical circuits4 ,for example1 an electric power company with a system of power lines over hundreds of miles may have a problem about electrical power3 will an accident or a sudden demand cause a breakdown anywhere in the system8 ,in the ,general ,electric ,company in ,schenectady1 ,n4 ,y41 there is a machine called the ,a4,c4 ,network ,analyzer4 ,all the properties of the power company's network of lines can be fed on a small scale into the analyzer4 ,certain dials are turned and certain plugwires are connected4 ,then various kinds of 8accidents0 and 8sudden demands0 are fed into the machine1 and the response of the system is noted4 ,the answers given by the machine are multiplied by the proper scale factor1 and in this way the problem of the power company is solved4 ,there are two kinds of problems that network analyzers are built to solve3 the steady state conditions and the transient conditions4 ,for example1 you may not overload a fuse with an electric iron when it is plugged in and being used1 but as you pull out the cord1 you may blow the fuse3 the steady state does not overstrain the system1 but the transient does4 ,some articles on network analyzers are3 ,,enns1 ,w4 ,e41 ,a ,new ,simple ,calculator of ,load ,flow in ,a4,c4 ,networks1 ,transactions of the ,american ,institute of ,electrical ,engineers1 vol4 #fb1 #aidc1 pp4 #ghf-gij4 ,,hazen1 ,h4 ,l41 and others1 ,the ,m4,i4,t4 ,network ,analyzer1 ,cambridge1 ,mass43 ,massachusetts ,institute of ,technology1 ,department of ,electrical ,engineering1 ,serial ,no4 #fi1 ,apr4 #aica4 ,,kuehni1 ,h4 ,p41 and ,r4 ,g4 ,,lorraine1 ,a ,new ,a4,c4 ,network ,analyzer1 ,transactions of the ,american ,institute of ,electrical ,engineers1 vol4 #eg1 #aich1 pp4 #fg-gc4 ,,parker1 ,w4 ,w41 ,dual ,a4,c4 ,network ,calculator1 ,electrical ,engineering1 ,may #aide1 pp4 #ahb-ahc4 ,,parker1 ,w4 ,w41 ,the ,modern ,a4,c4 ,network ,calculator1 ,transactions of the ,american ,institute of ,electrical ,engineers1 vol4 #fj1 ,nov4 #aida1 pp4 #igg-ihb4 ,,peterson1 ,h4 ,a41 ,an ,electric ,circuit ,transient ,analyzer1 ,general ,electric ,review1 ,sept4 #aici1 pp4 #cid-djj4 ,,varney1 ,r4 ,n41 ,an ,all-,electric ,integrator for ,solving ,differential ,equations1 ,review of ,scientific ,instruments1 vol4 #ac1 ,jan4 #aidb1 pp4 #aj-af4 ,some of the articles on applications of network analyzers to various problems are3 ,,kron1 ,,gabriel1 ,equivalent ,circuits of the ,elastic ,field1 ,journal of ,applied ,mechanics1 vol4 ,a#aa1 ,sept4 #aidd1 pp4 #adf-afa4 ,,kron1 ,,gabriel1 ,tensorial ,analysis and ,equivalent ,circuits of ,elastic ,structures1 ,journal of the ,franklin ,institute1 vol4 #bch1 ,dec4 #aidd1 pp4 #cii-ddb4 ,,kron1 ,,gabriel1 ,numerical ,solution of ,ordinary and ,partial ,differential ,equations by ,means of ,equivalent ,circuits1 ,journal of ,applied ,physics1 vol4 #af1 #aide1 pp4 #agb-ahf4 ,,kron1 ,,gabriel1 ,electric ,circuit ,models for the ,vibration ,spectrum of ,polyatomic ,molecules1 ,journal of ,chemical ,physics1 vol4 #ad1 no4 #a1 ,jan4 #aidf1 pp4 #ai-ca4 ,,kron1 ,g41 and ,g4 ,k4 ,,carter1 ,a4,c4 ,network ,analyzer ,study of the ,schrdinger ,equation1 ,physical ,review1 vol4 #fg1 #aide1 pp4 #dd-di4 ,,kron1 ,g41 and ,g4 ,k4 ,,carter1 ,network ,analyzer ,tests of ,equivalent ,circuits of ,vibrating ,polyatomic ,molecules1 ,journal of ,chemical ,physics1 vol4 #ad1 no4 #a1 ,jan4 #aidf1 pp4 #cb-cd4 ,,peterson1 ,h4 ,a41 and ,c4 ,,concordia1 ,analyzers for ,use in ,engineering and ,scientific ,problems1 ,general ,electric ,review1 vol4 #dh1 no4 #i1 ,sept4 #aide1 pp4 #bi-cg4 ,,machines ,,for ,,solving ,,algebraic ,,equations ,another branch of the analogue calculating machine is a type of machine that will solve various kinds of algebraic equations 7see ,supplement #b74 ,a list of some articles follows4 ,the article by ,mallock describes a machine for solving up to #aj linear simultaneous equations in #aj unknowns1 and the article by ,wilbur1 a machine for solving up to #i4 ,,dietzold1 ,,robert ,l41 ,the ,isograph--,a ,mechanical ,root-,finder1 ,bell ,laboratories ,record1 vol4 #af1 no4 #d1 ,dec4 #aicg1 pp4 #acj-acd4 ,,duncan1 ,w4 ,j41 ,some ,devices for the ,solution of ,large ,sets of ,simultaneous ,linear ,equations1 ,london1 ,edinburgh1 and ,dublin ,philosophical ,magazine and ,journal of ,science1 vol4 #ce1 series #g1 #aidd1 pp4 #ffj-fgj4 ,,frame1 ,j4 ,,sutherland1 ,machines for ,solving ,algebraic ,equations1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #a1 no4 #i1 ,jan4 #aide1 pp4 #ccg-cec4 ,,hart1 ,h4 ,c41 and ,,irven ,,travis1 ,mechanical ,solution of ,algebraic ,equations1 ,journal of the ,franklin ,institute1 vol4 #bbe1 ,jan4 #aich1 pp4 #fc-gb4 ,,herr1 ,d4 ,l41 and ,r4 ,s4 ,,graham1 ,an ,electrical ,algebraic ,equation ,solver1 ,review of ,scientific ,instruments1 vol4 #i1 ,oct4 #aich1 pp4 #caj-cae4 ,,mallock1 ,r4 ,r4 ,m41 ,an ,electrical ,calculating ,machine1 ,proceedings of the ,royal ,society1 series ,a1 vol4 #adj1 #aicc1 pp4 #deg-dhc4 ,,mercner1 ,r4 ,o41 ,the ,mechanism of the ,isograph1 ,bell ,laboratories ,record1 vol4 #af1 no4 #d1 ,dec4 #aicg1 pp4 #ace-adj4 ,,stibitz1 ,,george ,r41 ,electric ,root-finder1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bd1 ,oct4 #aidh1 pp4 #cbh-cbi4 ,,wilbur1 ,j4 ,b41 ,the ,mechanical ,solution of ,simultaneous ,equations1 ,journal of the ,franklin ,institute1 vol4 #bbb1 ,dec4 #aicf1 pp4 #gae-gbd4 ,,analogue ,,machines--,,miscellaneous ,some articles referring to various other kinds of analogue machines and their applications are here listed together3 ,,bush1 ,v41 ,f4 ,d4 ,,gage1 and ,r4 ,r4 ,,stewart1 ,a ,continuous ,integraph1 ,journal of the ,franklin ,institute1 vol4 #bjc1 #aibg1 pp4 #fc-hd4 ,,gray1 ,t4 ,s41 ,a ,photo-,electric ,integraph1 ,journal of the ,franklin ,institute1 vol4 #bab1 #aica1 pp4 #gg-ajb4 ,,hazen1 ,h4 ,l41 ,g4 ,s4 ,,brown1 and ,w4 ,r4 ,,hedeman1 ,the ,cinema ,integraph3 ,a ,machine for ,evaluating a ,parametric ,product ,integral 7two parts and appendix71 ,journal of the ,franklin ,institute1 vol4 #bcj1 ,july #aidj1 pp4 #ai-dd1 and ,aug4 #aidj1 pp4 #ahc-bje4 ,,mccann1 ,g4 ,d41 and ,h4 ,e4 ,,criner1 ,mechanical ,problems ,solved ,electrically1 ,westinghouse ,engineer1 vol4 #f1 no4 #b1 ,march #aidf1 pp4 #di-ef4 ,,myers1 ,d4 ,m41 ,an ,integraph for the ,solution of ,differential ,equations of the ,second-,order1 ,journal of ,scientific ,instruments1 vol4 #af1 #aici1 pp4 #bji-bbb4 ,,pekeris1 ,c4 ,l41 and ,w4 ,t4 ,,white1 ,differentiation with the ,cinema ,integraph1 ,journal of the ,franklin ,institute1 vol4 #bcd1 ,july #aidb1 pp4 #ag-bi4 ,,smith1 ,c4 ,e41 and ,e4 ,l4 ,,gove1 ,an ,electromechanical ,calculator for ,directional-,antenna ,patterns1 ,transactions of the ,american ,institute of ,electrical ,engineers1 vol4 #fb1 #aidc1 pp4 #gh-hb4 ,,yavne1 ,r4 ,o41 ,high ,accuracy ,contour ,cams1 ,product ,engineering1 vol4 #ai1 part #b1 ,aug4 #aidh1 #c pp4 ,,anonymous1 ,electrical ,gun ,director ,demonstrated1 ,bell ,laboratories ,record1 vol4 #bb1 no4 #d1 ,dec4 #aidc1 pp4 #aeg-afg4 ,,anonymous1 ,development of the ,electric ,director1 ,bell ,laboratories ,record1 vol4 #bb1 no4 #e1 ,jan4 #aidd1 pp4 #bbe-bcj4 ,,anonymous1 ,old ,field ,fortune ,teller3 ,electronic ,oil ,pool ,analyzer1 ,popular ,mechanics1 vol4 #hf1 ,sept4 #aidf1 p4 #aed4 ,,harvard ,,ibm ,,automatic ,,sequence-,,controlled ,,calculator ,the basic scientific description of this machine as of ,september #a1 #aide1 is contained in3 ,,aiken1 ,,howard ,h41 and ,,staff ,,of ,,the ,,computation ,,laboratory1 ,a ,manual of ,operation for the ,automatic ,sequence-,controlled ,calculator1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidf1 #efa pp4 ,the machine has changed rather a good deal since ,sept4 #a1 #aide4 ,some circuits have been removed4 ,other circuits have been added4 ,the capacity of the machine to do problems has been greatly increased4 ,the ,computation ,laboratory at ,harvard ,university is cordial towards scientific inquiries1 and some unpublished1 mimeographed information is available at the laboratory regarding the details of these changes4 ,some shorter scientific and technical descriptions of the machine are contained in3 ,,aiken1 ,,howard ,h41 and ,,grace ,m4 ,,hopper1 ,the ,automatic ,sequence ,controlled ,calculator 7#c parts71 ,electrical ,engineering1 vol4 #fe1 nos4 #h1 #i1 and #aj1 ,aug4 to ,nov4 #aidf1 p4 #chd 444 7#ba pp474 ,,bloch1 ,,richard ,m41 ,mark ,i ,calculator1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,harvard ,university ,press1 #aidh1 pp4 #bc-cj4 ,,harrison1 ,,joseph ,o41 ,,jr41 ,the ,preparation of ,problems for the ,mark ,i ,calculator1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,harvard ,university ,press1 #aidh1 pp4 #bjh-baj4 ,,international ,,business ,,machines ,,corporation1 ,,ibm ,automatic ,sequence-,controlled ,calculator1 ,endicott1 ,n4 ,y43 ,international ,business ,machines ,corporation1 #aide1 #f pp4 ,some of the less technical articles regarding the machine are3 ,,genet1 ,n41 ,got a ,problem8 ,harvard's ,amazing ,new ,mathematical ,robot1 ,scholastic1 vol4 #de1 ,sept4 #ah1 #aidd1 p4 #ce4 ,,torrey1 ,v41 ,robot ,mathematician ,knows ,all the ,answers1 ,popular ,science1 vol4 #ade1 ,oct4 #aidd1 pp4 #hf-hi4444 ,,anonymous1 ,giant ,new ,calculator1 ,science ,news ,letter1 vol4 #df1 ,aug4 #ab1 #aidd1 p4 #aaa4 ,,anonymous1 ,mathematical ,robot ,presented to ,harvard1 ,time1 vol4 #dd1 ,aug4 #ad1 #aidd1 p4 #gb4 ,,anonymous1 ,world's ,greatest ,machine for ,automatic ,calculation1 ,science ,news ,letter1 vol4 #df1 ,aug4 #ai1 #aidd1 p4 #abc4 ,,anonymous1 ,superbrain1 ,nation's ,business1 vol4 #cb1 ,sept4 #aidd1 p4 #h4 ,,anonymous1 ,robot ,works ,problems ,never ,before ,solved1 ,popular ,mechanics1 vol4 #hb1 ,oct4 #aidd1 p4 #ac4 ,,eniac1 ,,the ,,electronic ,,numeric ,,integrator ,,and ,,calculator ,there is as yet no full-scale1 published scientific account of the ,eniac4 ,at the ,ballistic ,research ,laboratories1 ,aberdeen1 ,md41 where the machine now is1 there are a few copies of some long mimeographed reports on the machine and the way it works4 ,these were prepared by ,h4 ,h4 ,goldstine and others when at the ,moore ,school of ,electrical ,engineering1 as a part of the contract under which the machine was constructed for the ,u4 ,s4 ,government4 ,it is possible that these reports might be consulted on request by serious students4 ,some scientific descriptions of the machine and its properties are3 ,,burks1 ,,arthur ,w41 ,electronic ,computing ,circuits of the ,,eniac1 ,proceedings of the ,institute of ,radio ,engineers1 vol4 #ce1 no4 #h1 ,aug4 #aidg1 pp4 #gef-gfg4 ,,clippinger1 ,r4 ,f41 ,a ,logical ,coding ,system ,applied to the ,eniac1 ,b4 ,r4 ,l4 ,report ,no4 #fgc1 ,aberdeen1 ,md43 ,ballistic ,research ,laboratories1 ,sept4 #bi1 #aidh1 #da pp4 ,,eckert1 ,j4 ,,presper1 ,,jr41 ,,john ,w4 ,,mauchly1 ,,herman ,h4 ,,goldstine1 and ,j4 ,g4 ,,brainerd1 ,description of the ,,eniac and ,comments on ,electronic ,digital ,computing ,machines1 ,applied ,mathematics ,panel ,report #aga4b,r1 ,washington1 ,d4 ,c43 ,national ,defense ,research ,committee1 ,nov4 #aide1 #gh pp4 ,,goldstine1 ,,herman ,h41 and ,,adele ,,goldstine1 ,the ,electronic ,numerical ,integrator and ,computer 7,,eniac71 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #b1 no4 #ae1 ,july #aidf1 pp4 #ig-aaj4 ,,hartree1 ,d4 ,r41 ,the ,,eniac1 an ,electronic ,computing ,machine1 ,nature1 vol4 #aeh1 ,oct4 #ab1 #aidf1 pp4 #ejj-ejf4 ,,hartree1 ,d4 ,r41 ,calculating ,machines3 ,recent and ,prospective ,developments and ,their ,impact on ,mathematical ,physics1 ,cambridge1 ,england3 ,the ,university ,press1 #aidg1 #dj pp4 7,pages #ad to #bg are devoted to the ,eniac47 ,,tabor1 ,,lewis ,p41 ,brief ,description and ,operating ,characteristics of the ,,eniac1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,harvard ,university ,press1 #aidh1 pp4 #ca-ci4 ,some of the less technical articles on ,eniac are3 ,,rose1 ,a41 ,lightning ,strikes ,mathematics3 ,,eniac1 ,popular ,science1 vol4 #adh1 ,apr4 #aidf1 pp4 #hc-hf4 ,,anonymous1 ,robot ,calculator3 ,,eniac1 ,all ,electronic ,device1 ,business ,week1 ,feb4 #af1 #aidf1 p4 #ej 444 ,,anonymous1 ,answers by ,,eny3 ,electronic ,numerical ,integrator and ,computer1 ,,eniac1 ,newsweek1 vol4 #bg1 ,feb4 #ah1 #aidf1 p4 #gf4 ,,anonymous1 ,adds in _/ ,second3 ,electronic ,computing ,machine at the ,university of ,pennsylvania1 ,science ,news ,letter1 vol4 #di1 ,feb4 #bc1 #aidf1 p4 #aac 444 ,,anonymous1 ,,eniac3 at the ,university of ,pennsylvania1 ,time1 vol4 #dg1 ,feb4 #be1 #aidf1 p4 #ij4 ,,anonymous1 ,it ,thinks with ,electrons2 the ,,eniac1 ,popular ,mechanics1 vol4 #he1 ,june #aidf1 p4 #aci4 ,,anonymous1 ,electronic ,calculator3 ,,eniac1 ,scientific ,american1 vol4 #agd1 ,june #aidf1 p4 #bdh4 ,,bell ,,laboratories ,,relay ,,computers ,as yet no full-scale scientific report is available on the ,bell ,laboratories general-purpose relay computers that went to ,aberdeen and ,langley ,field4 ,however1 there is some information about these and other ,bell ,laboratories relay computing machines in the following articles3 ,,alt1 ,,franz ,l41 ,a ,bell ,telephone ,laboratories' ,computing ,machine 7two parts71 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #ba1 ,jan4 #aidh1 pp4 #a-ac1 and vol4 #c1 no4 #bb1 ,apr4 #aidh1 pp4 #fi-hd4 ,,cesareo1 ,o41 ,the ,relay ,interpolator1 ,bell ,laboratories ,record1 vol4 #bd1 no4 #ab1 ,dec4 #aidf1 pp4 #deg-dfj4 ,,juley1 ,,joseph1 ,the ,ballistic ,computer1 ,bell ,laboratories ,record1 vol4 #be1 no4 #a1 ,jan4 #aidg1 pp4 #e-i4 ,,williams1 ,,samuel ,b41 ,a ,relay ,computer for ,general ,application1 ,bell ,laboratories ,record1 vol4 #be1 no4 #b1 ,feb4 #aidg1 pp4 #di-ed4 ,,williams1 ,,samuel ,b41 ,bell ,telephone ,laboratories' ,relay ,computing ,system1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,harvard ,university ,press1 #aidh1 pp4 #dj-fh4 ,,anonymous1 ,complex ,computer ,demonstrated1 ,bell ,laboratories ,record1 vol4 #ai1 no4 #b1 ,oct4 #aidj1 pp4 v-vi4 ,,anonymous1 ,computer ,mark #bb ,mod4 #j3 ,development and ,description1 ,navord ,report ,no4 #agh-de1 ,washington1 ,d4 ,c43 ,navy ,department1 ,dec4 #f1 #aide1 #bbe pp4 ,,anonymous1 ,relay ,computer for the ,army1 ,bell ,laboratories ,record1 vol4 #bf1 no4 #e1 ,may #aidh1 pp4 #bjh-bji4 ,,the ,,kalin-,,burkhart ,,logical-,,truth ,,calculator ,as yet there are no published references on the ,kalin-,burkhart ,logical-,truth ,calculator4 ,some books covering a good deal of mathematical logic are3 ,,quine1 ,w4 ,v41 ,mathematical ,logic1 ,new ,york3 ,w4 ,w4 ,norton ,co41 #aidj1 #cdh pp4 ,,reichenbach1 ,,hans1 ,elements of ,symbolic ,logic1 ,new ,york3 ,the ,macmillan ,co41 #aidg1 #ddd pp4 ,,tarski1 ,,alfred1 ,introduction to ,logic1 ,new ,york3 ,oxford ,university ,press1 #aida1 #bci pp4 ,,woodger1 ,j4 ,h41 ,the ,axiomatic ,method in ,biology1 ,cambridge1 ,england3 ,the ,university ,press1 #aicg1 #agd pp4 ,chapter #b1 pp4 #ah-eb1 is an excellent and understandable summary of the concepts of mathematical logic4 ,several papers on the application of mathematical logic to the analysis of practical situations are3 ,,berkeley1 ,,edmund ,c41 ,boolean ,algebra 7,the ,technique for ,manipulating 8,and10 8,or10 8,not10 and ,conditions7 and ,applications to ,insurance1 ,record of the ,american ,institute of ,actuaries1 vol4 #bf1 ,oct4 #aicg1 pp4 #cgc-dad4 ,,berkeley1 ,,edmund ,c41 ,conditions ,affecting the ,application of ,symbolic ,logic1 ,journal of ,symbolic ,logic1 vol4 #g1 no4 #d1 ,dec4 #aidb1 pp4 #afj-afh4 ,,shannon1 ,,claude ,e41 ,a ,symbolic ,analysis of ,relay and ,switching ,circuits1 ,transactions of the ,american ,institute of ,electrical ,engineers1 vol4 #eg1 #aich1 pp4 #gac-gbc4 ,this paper has had a good deal of influence here and there on the development of electric circuits using relays4 ,the following report discusses the solution of some problems of mathematical logic by means of a large-scale digital calculator3 ,,tarski1 ,,alfred1 ,a ,decision ,method for ,elementary ,algebra and ,geometry1 ,report ,r-#aji1 ,california3 ,rand ,corporation1 ,aug4 #a1 #aidh1 #fj pp4 ,,other ,,digital ,,machines ,,finished ,,or ,,under ,,development ,the ,aiken ,mark ,,ii ,relay ,calculator ,the ,computation ,laboratory of ,harvard ,university finished during #aidg a second large relay calculator1 called the ,aiken ,mark ,,ii ,relay ,calculator4 ,this machine is alluded to briefly at the end of ,chapter #aj and is described more fully in the following3 ,,campbell1 ,,robert ,v4 ,d41 ,mark ,,ii ,calculator1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #fi-gi4 ,,freeland1 ,,stephen ,l41 ,inside the ,biggest ,man-,made ,brain1 ,popular ,science1 ,may #aidg1 pp4 #ie-ajj4 ,,miller1 ,,frederick ,g41 ,application of ,printing ,telegraph ,equipment to ,large-,scale ,calculating ,machinery1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #bac-bbb4 ,the ,edsac ,the ,edsac is a machine under construction in ,england4 ,,wilkes1 ,m4 ,v41 ,the ,design of a ,practical ,high-,speed ,computing ,machine3 the ,,edsac1 ,proceedings of the ,royal ,society1 series ,a1 vol4 #aie1 #aidh1 pp4 #bgd-bgi4 ,,wilkes1 ,m4 ,v41 and ,w4 ,,renwick1 ,an ,ultrasonic ,memory ,unit for the ,,edsac1 ,electronic ,engineering1 vol4 #bj1 no4 #bde1 ,july #aidh1 pp4 #bjh-bac4 ,the ,edvac ,the ,edvac is a machine under construction at the ,moore ,school of ,electrical ,engineering1 ,philadelphia4 ,,koons1 ,,florence1 and ,,samuel ,,lubkin1 ,conversion of ,numbers from ,decimal to ,binary ,form in the ,,edvac1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bf1 ,apr4 #aidi1 pp4 #dbg-dca4 ,,anonymous1 ,,edvac ,replaces ,,eniac1 ,the ,pennsylvania ,gazette1 ,philadelphia3 ,university of ,pennsylvania1 vol4 #de1 no4 #h1 ,apr4 #aidg1 pp4 #i-aj4 ,the ,,ibm ,selective-,sequence ,electronic ,calculator ,the ,,ibm ,selective-,sequence ,electronic ,calculator was finished and announced in ,january #aidh1 and is alluded to briefly at the end of ,chapter #aj4 ,more information about this machine is in the following references3 ,,eckert1 ,w4 ,j41 ,electrons and ,computation1 ,the ,scientific ,monthly1 vol4 #fg1 no4 #e1 ,nov4 #aidh1 pp4 #cae-cbc4 ,,international ,,business ,,machines ,,corporation1 ,,ibm ,selective-,sequence ,electronic ,calculator1 ,new ,york3 ,international ,business ,machines ,corporation 7form no4 #eb-cibg-j71 #aidh1 #af pp4 ,the ,raytheon ,computer ,the ,raytheon ,computer is a machine under construction at the ,raytheon ,manufacturing ,co41 ,waltham1 ,mass4 ,,bloch1 ,r4 ,m41 ,r4 ,v4 ,d4 ,,campbell1 and ,m4 ,,ellis1 ,the ,logical ,design of the ,raytheon ,computer1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bd1 ,oct4 #aidh1 pp4 #bhf-bie4 ,,bloch1 ,r4 ,m41 ,r4 ,v4 ,d4 ,,campbell1 and ,m4 ,,ellis1 ,general ,design ,considerations for the ,raytheon ,computer1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bd1 ,oct4 #aidh1 pp4 #cag-cbc4 ,a 8,system of ,electric ,remote-,control ,accounting0 ,during the #aicj's a system using connected punch-card machinery was experimented with in a department store in ,pittsburgh4 ,the purpose of the system was automatic accounting and analysis of sales4 ,this system is described in3 ,,woodruff1 ,l4 ,f41 ,a ,system of ,electric ,remote-,control ,accounting1 ,transactions of the ,american ,institute of ,electrical ,engineers1 vol4 #eg1 ,feb4 #aich1 pp4 #gh-hg4 ,the ,univac ,the ,univac is a machine under construction at the ,eckert-,mauchly ,computer ,corporation1 ,philadelphia4 ,a similar but smaller digital computer called the ,binac is also being developed4 ,,eckert-,,mauchly ,,computer ,,corporation1 ,the ,univac ,system1 ,philadelphia3 ,eckert-,mauchly ,computer ,corp41 #aidh1 #h pp4 ,,electronic ,,control ,,co4 7now ,,eckert-,,mauchly ,,computer ,,corp471 ,a ,tentative ,instruction ,code for a ,statistical ,edvac1 ,philadelphia3 ,electronic ,control ,co4 7now ,eckert-,mauchly ,computer ,corp471 ,may #g1 #aidg1 #ai pp4 ,,snyder1 ,,frances ,e41 and ,,hubert ,m4 ,,livingston1 ,coding of a ,laplace ,boundary ,value ,problem for the ,,univac1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #be1 ,jan4 #aidi1 pp4 #cda-cej4 ,the ,zuse ,computer ,the ,zuse ,computer is a small digital computer constructed in ,germany4 ,,lyndon1 ,,roger ,c41 ,the ,zuse ,computer1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #b1 no4 #bj1 ,oct4 #aidg1 pp4 #cee-cei4 ,,the ,,design ,,of ,,digital ,,machines ,following are a number of references on various aspects of the design of digital computing machines3 ,organization ,,burks1 ,,arthur ,w41 ,super-,electronic ,computing ,machine1 ,electronic ,industries1 vol4 #e1 no4 #g1 ,july #aidf1 p4 #fb4 ,,burks1 ,,arthur ,w41 ,,herman ,h4 ,,goldstine and ,,john ,,von ,,neumann1 ,preliminary ,discussion of the ,logical ,design of an ,electronic ,computing ,instrument1 ,princeton1 ,n4 ,j43 ,institute for ,advanced ,study1 #bnd edition1 ,sept4 #aidg1 #db pp4 ,,eckert1 ,j4 ,,presper1 ,,jr41 ,,john ,w4 ,,mauchly1 and ,j4 ,r4 ,,weiner1 ,an ,octal ,system ,automatic ,computer1 ,electrical ,engineering1 vol4 #fh1 no4 #d1 ,apr4 #aidi1 p4 #cce4 ,,forrester1 ,,jay ,w41 ,,warren ,s4 ,,loud1 ,,robert ,r4 ,,everett1 and ,,david ,r4 ,,brown1 ,lectures by ,project ,whirlwind ,staff on ,electronic ,digital ,computation1 ,cambridge1 ,mass43 ,massachusetts ,institute of ,technology1 ,servo-mechanisms ,laboratory1 ,mar4 and ,apr4 #aidg1 #adi pp4 ,,lubkin1 ,,samuel1 ,decimal ,point ,location in ,computing ,machines1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #ba1 ,jan4 #aidh1 pp4 #dd-ej4 ,,patterson1 ,,george ,w41 editor1 and others1 ,theory and ,techniques for ,design of ,electronic ,digital ,computers 7subtitle3 ,lectures ,given at the ,moore ,school #h ,july #aidf-ca ,august #aidf71 ,philadelphia3 ,the ,university of ,pennsylvania1 ,moore ,school of ,electrical ,engineering1 vol4 #a1 lectures #a-aj1 ,sept4 #aj1 #aidg1 #afa pp42 vol4 #b1 lectures #aa-ba1 ,nov4 #a1 #aidg1 #agc pp42 vol4 #c and #d in preparation4 ,,stibitz1 ,,george ,r41 ,relay ,computers1 ,applied ,mathematics ,panel ,report #aga4a,r1 ,washington1 ,d4 ,c43 ,national ,defense ,research ,council1 ,feb4 #aide1 #hc pp4 ,,stibitz1 ,,george ,r41 ,should ,automatic ,computers be ,large or ,small8 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #b1 no4 #bj1 ,oct4 #aidg1 pp4 #cfb-cfd4 ,,stibitz1 ,,george ,r41 ,the ,organization of ,large-,scale ,calculating ,machinery1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #ia-ajj4 ,,stibitz1 ,,george ,r41 ,a ,new ,class of ,computing ,aids1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bc1 ,july #aidh1 pp4 #bag-bba4 ,input and ,output ,devices ,,alexander1 ,,samuel ,n41 ,input and ,output ,devices for ,electronic ,digital ,calculating ,machinery1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #bdh-bec4 ,,fuller1 ,,harrison ,w41 ,the ,numeroscope1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #bch-bdg4 ,o',,neal1 ,r4 ,d41 ,photographic ,methods for ,handling ,input and ,output ,data1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #bfj-bff4 ,,tyler1 ,,arthur ,w41 ,optical and ,photographic ,storage ,techniques1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #adf-aej4 ,,zworykin1 ,v4 ,k41 ,l4 ,e4 ,,flory1 and ,w4 ,s4 ,,pike1 ,letter-,reading ,machine1 ,electronics1 vol4 #bb1 no4 #f1 ,june #aidi1 pp4 #hj-hf4 ,,anonymous1 ,letter-,printing ,cathode-,ray ,tube1 ,electronics1 vol4 #bb1 no4 #f1 ,june #aidi1 pp4 #afj-afb4 ,storage ,devices ,,brillouin1 ,,leon ,n41 ,electromagnetic ,delay ,lines1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #aaj-abd4 ,,forrester1 ,,jay ,w41 ,high-,speed ,electrostatic ,storage1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #abe-abi4 ,,haeff1 ,,andrew ,v41 ,the ,memory ,tube and its ,application to ,electronic ,computation1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bd1 ,oct4 #aidh1 pp4 #bha-bhf4 ,,kornei1 ,,otto1 ,survey of ,magnetic ,recording1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #bbc-bcg4 ,,moore1 ,,benjamin ,l41 ,magnetic and ,phosphor ,coated ,discs1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #acj-acb4 ,,rajchman1 ,,jan ,a41 ,the ,selectron--,a ,tube for ,selective ,electrostatic ,storage1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #b1 no4 #bj1 ,oct4 #aidg1 pp4 #cei-cfa and frontispiece4 ,,sharpless1 ,t4 ,,kite1 ,mercury ,delay ,lines as a ,memory ,unit1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #ajc-aji4 ,,sheppard1 ,c4 ,,bradford1 ,transfer ,between ,external and ,internal ,memory1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #bfg-bgc4 ,programming or ,coding ,,everett1 ,,robert ,r41 ,digital ,computing ,machine ,logic 7memorandum ,m-#fc71 ,cambridge1 ,mass43 ,massachusetts ,institute of ,technology1 ,servo-mechanisms ,laboratory1 ,mar4 #ai1 #aidg1 #dh pp4 ,,goldstine1 ,,herman ,h41 and ,,john ,,von ,,neumann1 ,planning and ,coding of ,problems for an ,electronic ,computing ,instrument1 ,princeton1 ,n4 ,j43 ,institute for ,advanced ,study1 #aidg1 #fi pp4 ,,goldstine1 ,,herman ,h41 and ,,john ,,von ,,neumann1 ,planning and ,coding of ,problems for an ,electronic ,computing ,instrument1 ,princeton1 ,n4 ,j43 ,institute for ,advanced ,study1 part #b1 vol4 #c1 #aidh1 #bc pp4 ,,mauchly1 ,,john ,w41 ,preparation of ,problems for ,edvac-,type ,machines1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #bjc-bjg4 ,,digital ,,machines--,,miscellaneous ,many of the following articles are nontechnical and contain much interesting information about machines that think3 ,,alt1 ,,franz ,l41 ,new ,high-,speed ,computing ,devices1 ,the ,american ,statistician1 vol4 #a1 no4 #a1 ,aug4 #aidg1 pp4 #ad-ae4 ,,bush1 ,,vannevar1 ,as ,we ,may ,think1 ,atlantic ,monthly1 ,july #aide1 pp4 #aja-ajh4 ,,condon1 ,,edward ,u41 ,the ,electronic ,brain ,means a ,better ,future for ,you 7broadcast71 ,columbia ,broadcasting ,system1 ,jan4 #d1 #aidh4 ,,davis1 ,,harry ,m41 ,mathematical ,machines1 ,scientific ,american1 vol4 #ahj1 no4 #d1 ,apr4 #aidi1 pp4 #bi-ci4 ,,lagemann1 ,,john ,k41 ,it ,all ,adds ,up1 ,collier's ,magazine1 ,may #ca1 #aidg1 pp4 #bb-bc 444 ,,locke1 ,e4 ,l41 ,modern ,calculators1 ,astounding ,science ,fiction1 vol4 #eb1 no4 #e1 ,jan4 #aidi1 pp4 #hg-ajf4 ,,maclaughlan1 ,,lorne1 ,electrical ,mathematicians1 ,astounding ,science ,fiction1 vol4 #ec1 no4 #c1 ,may #aidi1 pp4 #ic-ajh4 ,,mann1 ,,martin1 ,want to ,buy a ,brain8 ,popular ,science1 vol4 #aed1 no4 #e1 ,may #aidi1 pp4 #adh-aeb4 ,,newman1 ,,james ,r41 ,custom-,built ,genius1 ,new ,republic1 ,june #bc1 #aidg1 pp4 #ad-ah4 ,,pfeiffer1 ,,john ,e41 ,the ,machine ,that ,plays ,gin ,rummy1 ,science ,illustrated1 vol4 #d1 no4 #c1 ,mar4 #aidi1 pp4 #df-dh 444 ,,ridenour1 ,,louis ,n41 ,mechanical ,brains1 ,fortune1 vol4 #ci1 no4 #e1 ,may #aidi1 pp4 #ajh-aah4 ,,tumbleson1 ,,robert ,c41 ,calculating ,machines1 ,federal ,science ,progress1 ,june #aidg1 pp4 #c-g4 ,,anonymous1 ,almost ,human1 ,home ,office ,news1 ,newark1 ,n4 ,j43 ,prudential ,insurance ,company of ,america1 ,feb4 #aidg1 p4 #h4 ,,applications ,,of ,,digital ,,machines ,some of the problems that mechanical brains can solve1 some of the methods for controlling them to solve problems1 and some of the implications of mechanical brains for future problems are covered in the following references3 ,solving ,problems ,,berkeley1 ,,edmund ,c41 ,electronic ,machinery for ,handling ,information1 and its ,uses in ,insurance1 ,transactions of the ,actuarial ,society of ,america1 vol4 #dh1 ,may #aidg1 pp4 #cf-eb4 ,,berkeley1 ,,edmund ,c41 ,electronic ,sequence ,controlled ,calculating ,machinery and ,applications in ,insurance1 ,proceedings of #aidg ,annual ,conference1 ,life ,office ,management ,association1 ,new ,york3 ,life ,office ,management ,association1 #aidg1 pp4 #aaf-abi4 ,,curry1 ,,haskell ,b41 and ,,willa ,a4 ,,wyatt1 ,a ,study of ,inverse ,interpolation of the ,eniac1 ,b4 ,r4 ,l4 ,report ,no4 #fae1 ,aberdeen1 ,md43 ,ballistic ,research ,laboratories1 ,aug4 #ai1 #aidf1 #ajj pp4 ,,harrison1 ,,joseph ,o41 ,,jr41 and ,,helen ,,malone1 ,piecewise ,polynomial ,approximation for ,large-,scale ,digital ,calculators1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bf1 ,apr4 #aidi1 pp4 #djj-djg4 ,,hoffleit1 ,,dorrit1 ,a ,comparison of ,various ,computing ,machines ,used in ,reduction of ,doppler ,observations1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #be1 ,jan4 #aidi1 pp4 #cgc-cgg4 ,,leontief1 ,,wassily ,w41 ,computational ,problems ,arising in ,connection with ,economic ,analysis of ,interindustrial ,relationships1 ,proceedings of a ,symposium on ,large-,scale ,digital ,calculating ,machinery1 ,cambridge1 ,mass43 ,harvard ,university ,press1 #aidh1 pp4 #afi-age4 ,,lotkin1 ,,max1 ,inversion on the ,eniac ,using ,osculatory ,interpolation1 ,b4 ,r4 ,l4 ,report ,no4 #fcb1 ,aberdeen1 ,md43 ,ballistic ,research ,laboratories1 ,july #ae1 #aidg1 #db pp4 ,,lowan1 ,,arnold ,n41 ,the ,computation ,laboratory of the ,national ,bureau of ,standards1 ,scripta ,mathematica1 vol4 #ae1 no4 #a1 ,mar4 #aidi1 pp4 #cc-fc4 ,,matz1 ,,adolph1 ,electronics in ,accounting1 ,accounting ,review1 vol4 #ba1 no4 #d1 ,oct4 #aidf1 pp4 #cga-cgi4 ,,mcpherson1 ,,james ,l41 ,applications of ,high-,speed ,computing ,machines to ,statistical ,work1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bb1 ,apr4 #aidh1 pp4 #aba-abf4 ,,mitchell1 ,,herbert ,f41 ,,jr41 ,inversion of a ,matrix of ,order #ch1 ,mathematical ,tables and ,other ,aids to ,computation1 vol4 #c1 no4 #bc1 ,july #aidh1 pp4 #afa-aff4 ,,anonymous1 ,revolutionizing the ,office1 ,business ,week1 ,may #bh1 #aidi1 no4 #ajcj1 pp4 #fe-gb4 ,speech ,some of the possibilities of machines dealing with voice and speech are indicated in3 ,,dudley1 ,,homer1 ,r4 ,r4 ,,riesz1 and ,s4 ,s4 ,a4 ,,watkins1 ,a ,synthetic ,speaker1 ,journal of the ,franklin ,institute1 vol4 #bbg1 ,june #aici1 pp4 #gci-gfd4 ,this is an article on the ,voder1 which is an abbreviation of ,voice ,operation ,demonstrator4 ,the machine was exhibited at the ,new ,york ,world's ,fair1 #aici4 ,,dudley1 ,,homer1 ,the ,vocoder1 ,bell ,laboratories ,record1 vol4 #ah1 no4 #d1 ,dec4 #aici1 pp4 #abb-abf4 ,this is a more general type of machine than the ,voder4 ,the ,vocoder is both an analyzer and synthesizer of human speech4 ,,potter1 ,,ralph ,k41 ,,george ,a4 ,,kopp1 and ,,harriet ,c4 ,,green1 ,visible ,speech1 ,new ,york3 ,d4 ,van ,nostrand ,co41 #aidg1 #dda pp4 ,,anonymous1 ,pedro the ,voder3 ,a ,machine that ,talks1 ,bell ,laboratories ,record1 vol4 #ag1 no4 #f1 ,feb4 #aici1 pp4 #agj-aga4 ,weather ,some of the possibilities of machines dealing with weather information are covered in3 ,,lagemann1 ,,john ,k41 ,making ,weather to ,order1 ,new ,york ,herald ,tribune3 ,this ,week1 ,feb4 #bc1 #aidg4 ,,shalett1 ,,sidney1 ,electronics to ,aid ,weather ,figuring1 ,the ,new ,york ,times1 ,jan4 #aa1 #aidf4 ,,zworykin1 ,v4 ,k41 ,outline of ,weather ,proposal1 ,princeton1 ,n4 ,j43 ,radio ,corporation of ,america ,research ,laboratories1 ,oct4 #aide1 #aa pp4 ,,anonymous1 ,weather ,under ,control1 ,fortune1 ,feb4 #aidh1 pp4 #ajf-aaa 444 ,the ,robot ,machine ,,apek1 ,,karel1 ,r4 ,u4 ,r4 7translated from the ,czech by ,paul ,selver71 ,new ,york3 ,doubleday1 ,page ,co41 #aibc4 ,,lagemann1 ,,john ,k41 ,from ,piggly ,wiggly to ,keedoozle1 ,collier's ,magazine1 vol4 #abb1 no4 #ah1 ,oct4 #cj1 #aidh1 pp4 #bj-ba 444 ,,leaver1 ,e4 ,w41 and ,j4 ,j4 ,,brown1 ,machines ,without ,men1 ,fortune1 vol4 #cd1 no4 #e1 ,nov4 #aidf1 pp4 #afe 444 ,,pease1 ,m4 ,c41 ,devious ,weapon1 ,astounding ,science ,fiction1 vol4 #ec1 no4 #b1 ,apr4 #aidi1 pp4 #cd-dc4 ,,shannon1 ,,claude ,e41 ,programming a ,computer for ,playing ,chess1 ,bell ,telephone ,laboratories1 ,oct4 #h1 #aidh1 #cd pp4 ,,shelley1 ,,mary ,w41 ,frankenstein 7in ,everyman's ,library1 ,no4 #faf71 ,new ,york3 ,e4 ,p4 ,dutton ,co41 last reprinted #aide1 #bdb pp4 ,,spilhaus1 ,,athelstan1 ,let ,robot ,work for ,you1 ,the ,american ,magazine1 ,dec4 #aidh1 p4 #dg 444 ,,anonymous1 ,another ,new ,product for ,robot ,salesmen1 ,modern ,industry1 vol4 #ac1 no4 #b1 ,feb4 #ae1 #aidg4 ,,anonymous1 ,the ,automatic ,factory1 ,fortune1 vol4 #cd1 no4 #e1 ,nov4 #aidf1 p4 #afj 444 ,,anonymous1 ,machines ,predict ,what ,happens in ,your ,plant1 ,business ,week1 ,sept4 #be1 #aidh1 pp4 #fh-fi 444 ,,name ,,index ,note3 ,this list of persons mentioned in the text includes names of fictional characters4 ,the subject index1 which follows1 includes all other names4 ,aiken1 ,howard ,h41 #ij-aab1 #agg-h1 #bcb1 #bde-f ,alexander1 ,samuel ,n41 #bea ,alquist1 #bjj ,alt1 ,franz ,l41 #adb1 #bcg1 #bdg1 #bec ,archer1 ,r4 ,m41 #bda ,aristotle1 #aeb ,babbage1 ,charles1 #hi ,baehne1 ,g4 ,walter1 #bcb ,bailey1 ,c4 ,f41 #bcg ,barcroft1 ,joseph1 #bbi ,beach1 ,frank ,a41 #bbi ,beard1 ,r4 ,e41 #hh1 #bdj ,berkeley1 ,edmund ,c41 #bcc1 #bdh1 #bed ,berry1 ,r4 ,j4 ,a41 #bbi ,berry1 ,t4 ,m41 #bdj ,bloch1 ,richard ,m41 #bdf1 #bej ,bloomfield1 ,leonard1 #bca ,bodmer1 ,frederick1 #bca ,boelter1 ,l4 ,m4 ,k41 #bdj ,boole1 ,george1 #aeb ,boring1 ,edwin ,g41 #bbi ,bower1 ,e4 ,c41 #bcg ,brainerd1 ,j4 ,g41 #bdg ,brillouin1 ,leon ,n41 #beb ,brown1 ,david ,r41 #bea ,brown1 ,g4 ,s41 #bde ,brown1 ,j4 ,j41 #bee ,brown1 ,s4 ,l41 #bda-b ,buckingham1 ,r4 ,a41 #bdj ,burkhart1 ,william1 #add1 #aee-f ,burks1 ,arthur ,w41 #bdf1 #bea ,bush1 ,vannevar1 #gb1 #gd1 #bci1 #bda1 #bde1 #bec ,caldwell1 ,samuel ,h41 #gd1 #bci1 #bda ,campbell1 ,robert ,v4 ,d41 #bdi-ej apek1 ,karel1 #aii1 #bee ,carroll1 ,lewis1 #ab ,carter1 ,g4 ,k41 #bdd ,cesareo1 ,o41 #bdh ,clemence1 ,g4 ,m41 #bcg ,clippinger1 ,r4 ,f41 #bdf ,comrie1 ,john ,leslie1 #bcb ,concordia1 ,c41 #bdd ,condon1 ,edward ,u41 #bec ,crew1 ,e4 ,w41 #bcb ,criner1 ,h4 ,e41 #bde ,culley1 ,frank ,l41 #bcg ,curry1 ,haskell ,b41 #bed ,davis1 ,harry ,m41 #bec ,deming1 ,w4 ,edwards1 #bcg ,dietzold1 ,robert ,l41 #bdd ,domin1 ,harry1 #aii ,dudley1 ,homer1 #bed-e ,duncan1 ,w4 ,j41 #bdd ,dunlap1 ,jack ,w41 #bcg ,dwyer1 ,paul ,s41 #bcg ,dyer1 ,h4 ,s41 #bcg ,eckert1 ,j4 ,presper1 ,jr41 #aad1 #agh1 #bdg1 #bea ,eckert1 ,w4 ,j41 #bcc1 #bcf-g1 #bci1 #bej ,edison1 ,thomas ,a41 #ae ,ellis1 ,m41 #bej ,enns1 ,w4 ,e41 #bdc ,everett1 ,robert ,r41 #bea-b ,feinstein1 ,lillian1 #bcg ,flesch1 ,rudolf1 #bca ,flory1 ,l4 ,e41 #beb ,forrester1 ,jay ,w41 #bea-b ,frame1 ,j4 ,sutherland1 #bdd ,frankenstein1 ,victor1 #aih1 #bjj ,franz1 ,shepherd ,i41 #bbi ,freeland1 ,stephen ,l41 #bdi ,fry1 ,macon1 #bcb ,fuller1 ,harrison ,w41 #beb ,frth1 ,r41 #bdb ,gage1 ,f4 ,d41 #bde ,genet1 ,n41 #bci1 #bdf ,godwin1 ,mary ,w4 7,mary ,w4 ,shelley71 #aih1 #bee ,goldstine1 ,adele1 #bdg ,goldstine1 ,herman ,h41 #bdg1 #bea1 #bec ,gove1 ,e4 ,l41 #bde ,graff1 ,willem ,l41 #bca ,graham1 ,r4 ,s41 #bdd ,gray1 ,t4 ,s41 #bde ,green1 ,harriet ,c41 #bee ,haeff1 ,andrew ,v41 #beb ,hansen1 ,morris ,h41 #bcg ,harrison1 ,joseph ,o41 ,jr41 #bdf1 #bed ,hart1 ,h4 ,c41 #bdd ,hartkemeier1 ,harry ,pelle1 #bcc ,hartree1 ,d4 ,r41 #bcb1 #bdj-a1 #bdg ,haupt1 ,ralph ,f41 #bcg ,hayakawa1 ,s4 ,i41 #bca ,hazen1 ,h4 ,l41 #bdc1 #bde ,hedeman1 ,w4 ,r41 #bde ,hedley1 ,k4 ,j41 #bcc ,herget1 ,paul1 #bcg ,herr1 ,d4 ,l41 #bdd ,herrick1 ,c4 ,judson1 #bbi ,hoffleit1 ,dorrit1 #bed ,hogben1 ,launcelot1 #bca ,hollerith1 ,herman1 #dc ,hopper1 ,grace ,m41 #bdf ,horsburgh1 ,e4 ,h41 #bcb ,hotelling1 ,harold1 #bcg ,householder1 ,alston ,s41 #bcj ,jespersen1 ,otto1 #bca ,juley1 ,joseph1 #bdh ,kalin1 ,theodore ,a41 #add1 #aee-f ,kelvin1 ,lord1 #gb1 #bdj ,king1 ,gilbert ,w41 #bch ,koons1 ,florence1 #bdi ,kopp1 ,george ,a41 #bee ,kormes1 ,jennie ,p41 #bch ,kormes1 ,mark1 #bch ,kornei1 ,otto1 #beb ,kranz1 ,frederick ,w41 #bdb ,kron1 ,gabriel1 #bdc-d ,kuder1 ,g4 ,frederic1 #bch ,kuehni1 ,h4 ,p41 #bdj1 #bdc ,lagemann1 ,john ,k41 #bec1 #bee ,landahl1 ,herbert ,d41 #bcj ,lang1 ,h4 ,c41 #bcc ,lashley1 ,karl ,s41 #bbi ,leaver1 ,e4 ,w41 #bee ,leontief1 ,wassily ,w41 #bed ,lettvin1 ,jerome ,y41 #bcj ,lilley1 ,s41 #bcb ,livingston1 ,hubert ,m41 #bej ,locke1 ,e4 ,l41 #bec ,lorraine1 ,r4 ,g41 #bdc ,lotkin1 ,max1 #bed ,loud1 ,warren ,s41 #bea ,lowan1 ,arnold ,n41 #bed ,lubkin1 ,samuel1 #bdi1 #bea ,lyndon1 ,roger ,c41 #bej ,mac,laughlan1 ,lorne1 #bec ,maginniss1 ,f4 ,j41 #bda ,mallock1 ,r4 ,r4 ,m41 #bdd ,malone1 ,helen1 #bed ,mann1 ,martin1 #bec ,marble1 ,f4 ,g41 #bdb ,massey1 ,h4 ,s4 ,w41 #bdj ,mastukazi1 ,kiyoshi1 #ai ,matz1 ,adolph1 #bed ,mauchly1 ,john ,w41 #aad1 #agh1 #bdg1 #bea1 #bec ,maxfield1 ,d4 ,k41 #bch ,maxwell1 ,l4 ,r41 #bdb ,mc,cann1 ,g4 ,d41 #bde ,mc,culloch1 ,warren ,s41 #bcj ,mc,laughlin1 ,kathleen1 #bch ,mc,pherson1 ,james ,l41 #bed ,mc,pherson1 ,john ,c41 #bch ,meacham1 ,alan ,d41 #bcg ,mercner1 ,r4 ,o41 #bdd ,miller1 ,dayton ,c41 #bdb ,miller1 ,frederick ,g41 #bdi ,milliman1 ,wendell ,a41 #bch ,milne1 ,j4 ,r41 #bdb ,mitchell1 ,herbert ,f41 ,jr41 #bed ,montgomery1 ,h4 ,c41 #bdb ,moore1 ,benjamin ,l41 #beb ,moore1 ,c4 ,r41 #bdb ,murray1 ,francis ,j41 #bcb ,myers1 ,d4 ,m41 #bde ,newman1 ,james ,r41 #bec ,ogden1 ,c4 ,k41 #bca ,o',neal1 ,r4 ,d41 #beb ,parker1 ,w4 ,w41 #bdc ,patterson1 ,george ,w41 #bea ,pease1 ,m4 ,c41 #bee ,pekeris1 ,c4 ,l41 #bde ,peterson1 ,h4 ,a41 #bdj1 #bdc-d ,pfeiffer1 ,john ,e41 #bec ,pieron1 ,henri1 #bbi ,pike1 ,w4 ,s41 #beb ,pitts1 ,walter1 #bcj ,poesch1 ,h41 #bdj ,porter1 ,a41 #bdj-a ,potter1 ,ralph ,k41 #bee ,pringle1 ,r4 ,w41 #bdb ,quine1 ,w4 ,v41 #bdh ,rajchman1 ,jan ,a41 #beb ,rashevsky1 ,n41 #bcj ,raymond1 ,w4 ,j41 #bdb ,reichenbach1 ,hans1 #bdh ,renwick1 ,w41 #bdi ,ridenour1 ,louis ,n41 #bec ,riesz1 ,r4 ,r41 #bed ,robertson1 ,j4 ,m41 #bdb ,rose1 ,a41 #bdg ,rossum1 #aii ,royer1 ,elmer ,b41 #bch ,sauer1 ,r41 #bdj ,schlauch1 ,margaret1 #bca ,schnackel1 ,h4 ,g41 #bcc ,schrdinger1 ,erwin1 #bbi ,schwarzchild1 ,martin1 #bcg ,shalett1 ,sidney1 #bee ,shannon1 ,claude ,e41 #aec-e1 #bda1 #bdh1 #bee ,sharpless1 ,t4 ,kite1 #beb ,shelley1 ,mary ,w41 #aih1 #bee ,shelley1 ,percy ,bysshe1 #aih ,sheppard1 ,c4 ,bradford1 #beb ,sherrington1 ,charles ,s41 #bbi ,smith1 ,c4 ,e41 #bde ,snyder1 ,frances ,e41 #bej ,somerville1 ,j4 ,m41 #bdb ,spilhaus1 ,athelstan1 #bee ,stewart1 ,r4 ,r41 #bde ,stibitz1 ,george ,r41 #abi-cj1 #bdd1 #bea ,straiton1 ,a4 ,w41 #bdb ,tabor1 ,lewis ,p41 #bdg ,tarski1 ,alfred1 #bdh-i ,terhune1 ,g4 ,k41 #bdb ,thomas1 ,george ,b41 #bch ,thomson1 ,james1 #bdj ,thomson1 ,william1 #gb1 #bdj ,tilney1 ,frederick1 #bbi ,torrey1 ,v41 #bdf ,travis1 ,irven1 #bci1 #bdd ,tumbleson1 ,robert ,c41 #bec ,turck1 ,j4 ,a4 ,v41 #bcb ,tyler1 ,arthur ,w41 #beb ,varney1 ,r4 ,n41 #bdc von ,neumann1 ,john1 #abd1 #bea ,wainwright1 ,lawrence ,l41 #gb1 #bda ,walpole1 ,hugh ,r41 #bca ,watkins1 ,s4 ,s4 ,a41 #bed ,wegel1 ,r4 ,l41 #bdb ,weiner1 ,j4 ,r41 #bea ,wheeler1 ,l4 ,l41 #bda-b ,whitten1 ,c4 ,a41 #bch ,wiener1 ,norbert1 #bbi ,wilbur1 ,j4 ,b41 #bdd ,wilkes1 ,m4 ,v41 #bdi ,williams1 ,samuel ,b41 #bdh ,wolf1 ,arthur ,w41 #bcc ,womersley1 ,j4 ,r41 #bda ,wood1 ,thomas1 #ai ,woodger1 ,j4 ,h41 #bdh ,woodruff1 ,l4 ,f41 #bej ,wyatt1 ,willa ,a41 #bed ,wylie1 ,j41 #bdj ,yavne1 ,r4 ,o41 #bde ,zworykin1 ,v4 ,k41 #aij1 #beb1 #bee ,,subject ,,index ,notes3 ,phrases consisting of an adjective and a noun1 or of a noun and a noun1 are entered in their alphabetical place according to the first word4 ,for example1 8electrostatic storage tube0 is under e1 and 8punch card0 is under p4 ,a field1 #ii ,a tape1 #hb-c abacus1 #ag-i1 #acc1 #bbj abax 7,greek71 #ah absolute value1 #aja1 #bbb accumulator1 #aae-f accumulator decade1 #aah accuracy1 #fg1 #hi acetylcholine1 #c add output1 #abj addend1 #bbc adder1 #gg adder mechanism1 #gg-h adding1 #bd-e1 #bg1 #cg1 #ee1 #ajj1 #aai1 #aci addition circuit1 #cg ,aiken ,mark ,i ,calculator1 #aj1 #hi-aab1 #bde-f2 see also ,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator ,aiken ,mark ,,ii ,relay ,calculator1 #agf-h1 #bdi ,aiken ,mark ,,iii ,electronic ,calculator1 #agg air resistance coefficient1 #hj-b algebra of logic1 #bf1 #cf1 #ef-fb1 #aje1 #adj1 #aea-b1 #afd1 #bba-c1 #bdh algebraic equations1 machines for solving1 #bdd all-or-none response1 #c alphabet1 #ad alphabetic coding1 #ac1 #ed alphabetic punching1 #df alphabetic writing1 #ac amplify1 #gc analogous1 #fe analogue1 #fe analogue machines 7machines that handle information expressed as measurements71 #fe2 ,,mit ,differential ,analyzer ,no4 #b1 #fe-hh2 references1 #bci-de analytical engine1 #ij analyzer1 #fh1 #bda-d2 see also differential analyzer and1 #adf-h and_/or1 #adi angle-indicator1 #gd-e animal thinking1 #d1 #h1 #ahh annuities1 #hh antecedent1 #aeh antilogarithm1 #aci1 #bbf antitangent1 #aci1 #bbf approximation1 #bbj2 see also rapid approximation aptitude testing1 #aij argument 7in a mathematical table or function71 #if1 #ajc-d1 #abb1 #acf1 #bbd arithmetical operations1 #ee-f1 #agc armor with a motor1 #ahj1 #aie array1 #agc1 #bbg ,atomic ,energy ,commission1 #bjc1 #bjh attitudes1 #bje augend1 #bbc aut 7,latin71 #adi automatic address-book1 #aha automatic carriage1 #ec 8,automatic ,computing ,machinery0 7section in ,mathematical ,tables and ,other ,aids to ,computation71 #agg automatic control3 house-furnace1 #ahi2 lawn-mower1 #ahh2 tractor-plow1 #ahh2 weather1 #ahi automatic cook1 #aha automatic factory1 #ahi automatic library1 #i1 #aha automatic machinery1 #ahb automatic pilot1 #ahi automatic recognizer1 #ahf-g automatic sequence-controlled calculator1 #ij2 see also ,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator automatic stenographer1 #ahe automatic switching circuits1 #bdh automatic translator1 #ahb automatic typist1 #ahb1 #ahd axon1 #c ,b field1 #ii ,b tape1 #hb-c ,ballistic ,research ,laboratories1 #a1 #aac-e1 #abg-h1 #acb1 #adb base e1 #bbf base #aj1 #bbf beam of electrons1 #agb behavior1 #d1 #g-h1 #bi ,bell ,telephone ,laboratories1 #d-e1 #abh-dc1 #bdg-h ,bell ,telephone ,laboratories' general-purpose relay computer1 #abh-dc1 #bdg-h2 cost1 #adb2 reliability1 #ada2 speed1 #adb ,bessel functions1 #aaa1 #bbf ,binac1 #agi binary coding1 #aa1 #ac binary digit1 #ad binary numbers1 #ad1 #baf-i biophysics1 #bcj biquinary numbers1 #acc1 #bai-bj blocks of arguments1 #acg ,boolean algebra1 #aeb1 #bdh2 see also mathematical logic both1 #adi bowwow theory1 #ab brain evolution1 #bbi brain with a motor1 #ahj1 #aie ,,btl frames1 #ach-i bus1 #cb1 #aai button1 #ia1 #id ,c field1 #ii ,c tape1 #hb-c calcis 7,latin71 #ah calculating punch1 #dg1 #ea-b1 #bce calculator frames1 #ach calculator programmed by punch cards1 #bcf cam1 #id-e cam contact1 #ia1 #id-e capacitance1 #aag capacitor1 #aag capacity3 counter1 #ei2 selecting1 #ei carbon dioxide1 #aij card channel1 #dg1 #eb card column1 #dh card feed1 #dh1 #ia card punch1 #ia1 #ig card reader1 #aaf1 #aah card sorter1 #if card stacker1 #dh card station1 #dg ,carnegie ,institution of ,washington1 #aac carry impulse1 #aah cell nucleus1 #b-c census1 #dc1 #ec channel1 #dg1 #eb1 #agj characteristic of a logarithm1 #ajg check counter1 #aje check-marks1 #aea checking1 #aje1 #aaj1 #agi1 #bbg chess game1 #aag chestnut blight1 #bja chortle1 #ab class selector1 #ei clearing1 #ajj codes1 #bi1 #ed1 #if1 #ii coding1 #cj1 #acj1 #beb-c coding line1 #ii column 7in a punch card71 #de connective1 #adh1 #aeh-i connective grouping1 #aei collating1 #ea1 #agc collator1 #dg1 #ea1 #bce collator counting device1 #ea1 #bce combining information1 #ae combining operations1 #agc ,common1 #ei-fj comparer1 #eg-h comparing1 #ej1 #eg-h complement1 #ee2 see also nines complement1 ones complement1 tens complement ,complex ,computer1 #abi-cj complex numbers1 #abh-i computer1 #f1 #bg ,computer #a and ,computer #b1 #acb1 #ach conflicts between statements1 #adi-ej consequent1 #aeh constant1 #bbd constant ratio1 #gg constant register1 #if1 #ii constant switch1 #ii ,constant ,transmitter1 #aaf1 #aah consulting a table1 #ajc1 #abb convergent1 #bba ,converter1 #aae context1 #add continuous annuities1 #hh continuous contingent insurances1 #hh continuously running gear1 #ic control1 #f1 #bh1 #ij-a control brushes1 #ea-b control frames1 #ach-i ,control ,instrument ,company1 #dc control over robot machines1 #aif-bjh control tape1 #bh controversy1 #aig cosine1 #ge1 #he1 #aci1 #bbf cost of mechanical brains1 #hg1 #aji1 #abf1 #adb1 #afe1 #afh counter1 #eb1 #gd1 #ic-d counter position1 #ic counter wheel1 #ic1 #aah counting1 #ee coupling 7numbers71 #ajf cube1 #aje1 #bbd ,current 7input of comparer71 #eg cycle1 #bi1 #de ,cycling ,unit1 #aae-f ,cypriote1 #ac ,dartmouth ,college1 #aca decade1 #aah decimal digit1 #aa1 #ad decimal position1 #aah deciphering1 #ahd1 #ahh decoding1 #ahd1 #ahh definite integral1 #aaa1 #bbe delay lines1 #ag1 #bj1 #aga-b dendrite1 #c denial1 #adg dependent variable1 #ha1 #bbd derivative1 #fh-ga1 #bbe design of mechanical brains1 #afg-gi1 #bea desk calculating machines1 #d1 #aa1 #ag1 #ai detail cards1 #ej dial switch1 #ib1 #ie-f dial telephone1 #ag1 #ai1 #abh differences1 #aaj1 #bbg differential1 #fh1 #gj1 #gh differential analyzer1 #fh1 #gb-hh1 #bci-da ,differential ,analyzer ,no4 #b1 #fe-hh2 accuracy1 #hf2 cost1 #hg2 reliability1 #hg2 speed1 #hg differential equation1 #fh-i1 #ga1 #aaa1 #ada1 #bbe-f differential function1 #gj differential gear assembly1 #gh digit1 #aa1 #ad ,digit ,pickup1 #fj digit selector1 #fj digit tray1 #aai digit trunk lines1 #aai digit trunks1 #aai digital machines 7machines that handle information expressed as digits or letters73 ,bell ,laboratories' general-purpose relay calculator1 #abh-dc2 ,eniac1 #aac-bg2 ,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator1 #hi-aab2 punch-card calculating machinery1 #db-fd2 references1 #bcb-i1 #bde-ee directions1 #bd disc1 #gh-hj discrimination1 #adj discriminator1 #adj-a distance1 #fh-i distinguishing ,a and ,h1 #ahd dividend1 #ajc1 #bbc ,divider-,square-,rooter1 #aae-g dividing1 #ee-f1 #ih1 #ajb1 #aba1 #adj divisor counter1 #ajb doorpost1 #fe-f doubling1 #gf-g1 #ajj doubling mechanism1 #gf-g drafting rules1 #adi drag coefficient1 #hj drive1 #hf ,dry ,ice1 #aij echo1 #aga ,eckert-,mauchly ,computer ,corporation1 #agi1 #bej economic relations1 #aid ,edsac1 #bdi 8educated0 machine1 #aja ,edvac1 #agg1 #bdi ,egyptian1 #ab either1 #adi electric charge1 #agb electric remote-control accounting1 #bej electric typewriter1 #ia1 #ig1 #bcf electromagnet1 #afh ,electronic ,binary ,automatic ,computer1 #agi electronic calculating punch1 #bcf ,electronic ,control ,company1 #bej ,electronic ,numerical ,integrator and ,calculator 7,eniac71 #aac-bg1 #bdf-g2 see also ,eniac electronic tubes1 #ag1 #bj-a1 #agh-i2 ,cathode1 #ba2 ,grid1 #ba2 ,plate1 #ba electrostatic storage tube1 #ag1 #bj1 #agb #aa position1 #de #aa punch1 #eh else1 #adf-g end-around-carry1 #ie1 #bag1 #bbc engine1 #ij ,eniac1 #aac-bg1 #bdf-g2 cost1 #abf2 panels1 #aae2 reliability1 #abf2 speed1 #abe2 unbalance1 #abd 8enough alike10 #ahd ,equal 7output of sequencer71 #fa-b equation1 #fh1 #bbe equivalent1 #ad erase key1 #acd ,etruscan1 #ahh explanation1 #bji-ac explicit equation1 #hf exponential1 #he1 #ajf1 #bbe-f extraction1 #bbb falsity1 #adg farad1 #aag fingers1 #af1 #ah fire-control instrument1 #ag1 #ai1 #fg1 #aca #e impulse1 #ef flights1 #gj flip-flop1 #aai following logically1 #ade form feeding device1 #bcf formal logic1 #aeb formula1 #fh1 #gj1 #bbd ,frankenstein's monster1 #aih function1 #fh1 #gj1 #ha1 #ajc1 #aaf1 #aah1 #bbd function table1 #hj-a1 #aaf1 #aah gang punching1 #ej gearbox1 #gg-h ,general ,electric ,a4,c4 ,network ,analyzer1 #bdc ,general ,electric ,company1 #bdc geographic code1 #ed giant brain1 #a1 #e-h globe1 #fe-f graph1 #ha great circle1 #fi greater-than1 #be-g1 #cg1 #bbb greater-than circuit1 #cg ,greek letters1 #abj guided missile1 #aig1 #bjf gun1 #fi hail storm1 #aij hand perforator1 #acb1 #acd handling information1 #aj-ah harmonic analyzers1 #bda-b harmonic synthesizers1 #bda-b ,harvard ,computation ,laboratory1 #hi1 #agf-g1 #bde1 #bdi ,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator 7,mark ,i71 #aj1 #hi-aab1 #bde-f2 cost1 #aji2 efficiency1 #aaa2 reliability1 #aaj2 speed1 #aji ,harvard ,sequence-,controlled ,electronic ,calculator 7,mark ,,iii71 #agg ,harvard ,sequence-,controlled ,relay ,calculator 7,mark ,,ii71 #agf-h1 #bdi ,harvard ,university1 #a1 #d1 #h1 #hi1 #agf-g1 #bde1 #bdi hatred1 #bjf hoppers1 #ea hub1 #df1 #ih human brain1 #b-d1 #af1 #bbi humidity1 #fc ,,ibm 7,international ,business ,machines71 #dc-fd1 #hi-ij1 #agg1 #bcc-i1 #bdi-ej ,,ibm ,automatic ,sequence-,controlled ,calculator1 #aj1 #hi-aab1 #bde-f2 see also ,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator ,,ibm card-programmed calculator1 #bcf ,,ibm pluggable sequence relay calculator1 #bcf ,,ibm punch-card machinery1 #dc-fd1 #bcc-i ,,ibm ,selective-,sequence ,electronic ,calculator1 #agg-i1 #bdi ideographic writing1 #ab if1 #adf-g if 444 then1 #adi ignorance1 #bje illness1 #aia-b imitative scheme1 #ab in-code1 #ii in-field1 #ii independent variable1 #ha1 #bbd infinity1 #hf1 #acc1 #bab1 #bbe information1 #aj initial conditions1 #hc1 #bbe ,initiating ,unit1 #aae-f input1 #f1 #ij-a input devices1 #age1 #bea-b input register1 #bg instantaneous rate of change1 #gj-a ,institute of ,advanced ,study1 #abd instructions1 #bh1 #hc1 #ig1 #agh-i insurance company1 #db insurance policies1 #db insurance values1 #hh integral1 #fh1 #ga-b1 #bbe integral sign1 #he1 #bbe integrating1 #ga-b1 #gh integrator1 #gh-hj integrator mechanism1 #gh-i ,international ,business ,machines ,corporation 7,,ibm71 #dc2 see ,,ibm ,international ,hydrographic ,bureau1 #bdb ,international ,phonetic ,alphabet1 #ac interpolating1 #aca1 #bba interposing1 #ajb interpreter1 #dg1 #di1 #bce interpreting1 #di interval1 #fh1 #gj intuitive thinking1 #h inverse1 #ga judgments1 #aia ,kalin-,burkhart ,logical-,truth ,calculator1 #add-ff1 #bdh2 cost1 #afe2 reliability1 #aff2 speed1 #aff key punch1 #dg-h1 #if1 #bce keyboard1 #dh knots1 #ag language of logic1 #ef-fb1 #aje1 #adj2 see also mathematical logic languages1 #aj-ba1 #bca latch relay1 #dj-a left-hand components1 #ef1 #aba1 #bae library1 #i1 #aha ,library of ,congress1 #ae lie detector1 #aib line of coding1 #ii linear1 #bbd-e linear interpolation1 #bba linear simultaneous equations1 #ada1 #bbe lobe1 #id-e logarithm1 #fg1 #he1 #ajf-h1 #aci1 #bbe ,logarithm-,in-,out counter1 #ajg logic1 #add2 see also mathematical logic logical choice1 #d2 see also mathematical logic logical connective1 #adh1 #bbb logical operations1 #ef-fb1 #agc logical pattern1 #ade-f logical truth1 #add-ef1 #aff ,logical-,truth ,calculator1 #add-ff2 see ,kalin-,burkhart ,logical-,truth ,calculator loopholes1 #adi ,low ,primary 7output of sequencer71 #fa-b ,low ,secondary 7output of sequencer71 #fa-b ,lower ,brushes1 #eb loxodrome1 #fi-gj machine call number1 #ii machine cycle1 #ef machine language1 #bi1 #ii1 #age1 #aia machines as a language for thinking1 #ai-bj2 references1 #bca-b machines involving voice and speech1 #ahe-f1 #bed magnetic surfaces1 #ag1 #bj1 #afh-gj1 #agi magnetic tape1 #afi-gj1 #agi magnetic wire1 #afh magnetized spot1 #afh-gj main connective1 #afj many-wire cable1 #ej ,mark ,i 7,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator71 #aj1 #hi-aab1 #bde-f2 see also ,harvard ,,ibm ,automatic ,sequence-,controlled ,calculator ,mark ,,ii 7,harvard ,sequence-,controlled ,relay ,calculator71 #agf-h1 #bdi ,mark ,,iii 7,harvard ,sequence-,controlled ,electronic ,calculator71 #agg ,massachusetts ,institute of ,technology1 #a1 #bj1 #fe1 #gb-hh1 #aec ,massachusetts ,institute of ,technology's ,differential ,analyzer ,no4 #b1 #fe-hh2 accuracy1 #hf2 cost1 #hg2 reliability1 #hg2 speed1 #hg master card1 #ej ,master ,programmer1 #aae-f matching1 #agc mathematical biophysics1 #bcj mathematical logic1 #bf1 #cf1 #ef-fb1 #aje1 #adj1 #aea-b1 #afd1 #bba-c1 #bdh matrices1 #agc1 #bbg matrix1 #agc1 #bbg meanings1 #bji1 #bca measurements1 #fe-f1 #fh mechanical brain1 #a1 #e-h1 #bj2 crucial devices for1 #bj mechanical brains under construction1 #agf-i memory1 #bg1 #ij-a mentality1 #bd1 #bg mercury tank1 #aga1 #agi merging1 #agc metal fingers1 #ace mica1 #agb microphone1 #ahe mimeograph stencil1 #af ,minoan1 #ahh miscellaneous field1 #ii mistake1 #acd ,moore ,school of ,electrical ,engineering1 #g1 #aac-bg1 #agg1 #bdi multiplicand1 #bbc multiplicand counter1 #aja multiplication schemes1 #bad-f multiplier1 #aae-f multiplier counter1 #aja multiply-divide unit1 #ajc multiplying1 #ee-f1 #aja1 #aba1 #adj multiplying punch1 #dg1 #eb1 #bce ,national ,advisory ,committee for ,aeronautics1 #abh1 #acb ,naval ,proving ,ground1 #agg negation1 #bd-e1 #bg1 #cd-f negation circuit1 #cf negative1 #adg negative digit1 #bae neon bulb1 #aai nerve1 #b-d nerve cell1 #b1 #c1 #af nerve fiber1 #b1 #c nerve networks1 #bcj nervous system1 #ahh network analyzers1 #bdb-d neurosis1 #aia nine-pulses1 #abj-a nines complement1 #ie1 #aba1 #bbc ,no ,x1 #ei ,northrop ,aircraft1 ,inc41 #agi not1 #adf-h numeric coding1 #ac1 #ed numerical ,x position1 #de numerical ,y position1 #de occupation code1 #ed octal notation1 #agi1 #bai ohm1 #aag ,ojibwa1 #ab ones complement1 #bag only1 #adf-g operation code1 #ajc operations with numbers1 #bd-g or1 #adf-i organization of digital machines1 #bea out-code1 #ii out-field1 #ii output1 #f1 #ij-a1 #bea-b output devices1 #agf1 #bea-b output register1 #bg paper channel1 #eb partial differential equations1 #hg partial products1 #aae1 #bad ,pearl ,assurance ,company1 #hh pebbles1 #ag-h pen with a motor1 #ahj1 #aie permanent table frames1 #ach-i personal income tax1 #ada phonetic writing1 #ac phonograph1 #ae-f phonographic writing1 #ac phototube1 #ha-b1 #ahc-d physical equipment for handling information1 #aa1 #ae-ba1 #ia physical problems1 #fi-gb physical quantities1 #fg-i pictographic writing1 #ab plugboard1 #df1 #ih plug-in units1 #aag-h point of view1 #bjg pooh-pooh theory1 #ab position 7in a punch card71 #de position frames1 #ach-i power1 #dc1 #fe1 #acc1 #baf1 #bbd prejudice1 #bje ,previous 7input of comparer71 #eg ,primary 7input of sequencer71 #fa-b ,primary ,brushes1 #ea1 #fb ,primary ,feed1 #ea1 #fa ,primary ,sequence ,brushes1 #ea printer1 #acg printer frames1 #ach problem frames1 #ach problem position1 #acb1 #ace problem tape1 #acd processor1 #acb1 #acd1 #age product1 #gj1 #ajb1 #bbc product counter1 #ajb production scheduling1 #aic program1 #abb1 #agc1 #beb-c program-control switch1 #abc program pulse1 #abb program-pulse input terminal1 #abc program register1 #ch program tape1 #bh-i program trays1 #aai program trunk lines1 #aai programming method of von ,neumann1 #abd pronoun1 #bbc psychological testing1 #aij psychological trainer1 #aia-b pulses1 #abj1 #aga punch card1 #ag1 #dd-e1 #ie1 #ig punch-card column1 #de punch-card machinery1 #ag1 #bj1 #db-fd1 #bcb-i2 cost1 #fc2 reliability1 #fc-d2 speed1 #fb-c punch feed1 #ea-b punched paper tape1 #ag1 #bc1 #hb1 #ie punching channel1 #ej punching dies1 #dh1 #ea-b pyramid circuit1 #ci quantity of information1 #aa1 #ad-ae quartz1 #aga quotient1 #ih1 #ajc ,r4,u4,r41 #aii radar1 #ahc railroad line1 #f1 #aai rapid approximation1 #ajf-h1 #bbj-a rate of change1 #fh1 #gj-a ratio1 #gg1 #hc ,raytheon ,computer1 #bej reading1 #eg reading brushes1 #ea-b reading channel1 #ej reading of punch cards1 #dd reasoning1 #add rebus-writing1 #ac reciprocal1 #he1 #bbd recognizing1 #h1 #ahb-e recorder1 #acb1 #acg rectifier1 #cb referent1 #ab register1 #bg reject1 #di relay1 #ag1 #bj-a1 #bc1 #ib1 #abi1 #acc1 #agh2 ,common1 #ba2 ,ground1 #ba2 ,normally ,closed1 #ba2 ,normally ,open1 #ba2 ,pickup1 #ba release key1 #dh reliability1 #fc-d1 #aaj1 #abf1 #abh1 #ada-b1 #aff1 #afh1 #agd ,remington-,rand1 #dc reperforator1 #acg rephrasing1 #afc-d reproducer1 #dg1 #di-ej1 #bce reproducing1 #di reset code1 #ajj resetting1 #ajj resistance1 #hj1 #aag resistance coefficient1 #hj resistor1 #aag right-hand components1 #ef1 #aba1 #bae robot machine1 #aig1 #aih-bjh1 #bee robot salesman1 #bja robota 7,czech71 #aii ,roman numerals1 #bab2 ancient style1 #bai room1 #gj ,rossum's ,universal ,robots1 #aii rounding off1 #ee-f routine1 #h1 #afg1 #agc routine frames1 #ach-i routine tape1 #bh1 #acd rules1 #aia1 #bbd satisfy1 #bbe scale factor1 #gd1 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