The Computer from Pascal to von Neumann - Hardcover

Goldstine, Herman H.

Hardcover

ISBN 10: 0691081042 ISBN 13: 9780691081045

Publisher: Princeton University Press, 1972

Synopsis

In 1942, Lt. Herman H. Goldstine, a former mathematics professor, was stationed at the Moore School of Electrical Engineering at the University of Pennsylvania. It was there that he assisted in the creation of the ENIAC, the first electronic digital computer. The ENIAC was operational in 1945, but plans for a new computer were already underway. The principal source of ideas for the new computer was John von Neumann, who became Goldstine's chief collaborator. Together they developed EDVAC, successor to ENIAC. After World War II, at the Institute for Advanced Study, they built what was to become the prototype of the present-day computer. Herman Goldstine writes as both historian and scientist in this first examination of the development of computing machinery, from the seventeenth century through the early 1950s. His personal involvement lends a special authenticity to his narrative, as he sprinkles anecdotes and stories liberally through his text.

About this title

About the Author

Herman H. Goldstine is currently Executive Officer of the American Philosophical Society.

Excerpt. © Reprinted by permission. All rights reserved.

The Computer from Pascal to von Neumaun

By Herman H. Goldstine

Princeton University Press

Copyright © 1972 Princeton University Press
All right reserved.
ISBN: 978-0-691-08104-5

Contents

Preface (1993)..................................................................................................ixPreface.........................................................................................................xiPART ONE: The Historical Background up to World War II..........................................................11. Beginnings...................................................................................................32. Charles Babbage and His Analytical Engine....................................................................103. The Astronomical Ephemeris...................................................................................274. The Universities: Maxwell and Boole..........................................................................315. Integrators and Planimeters..................................................................................396. Michelson, Fourier Coefficients, and the Gibbs Phenomenon....................................................527. Boolean Algebra: x2 = xx = x......................................................................608. Billings, Hollerith, and the Census..........................................................................659. Ballistics and the Rise of the Great Mathematicians..........................................................7210. Bush's Differential Analyzer and Other Analog Devices.......................................................8411. Adaptation to Scientific Needs..............................................................................10612. Renascence and Triumph of Digital Means of Computation......................................................115PART TWO: Wartime Developments: ENIAC and EDVAC.................................................................1211. Electronic. Efforts prior to the ENIAC.......................................................................1232. The Ballistic Research Laboratory............................................................................1273. Differences between Analog and Digital Machines..............................................................1404. Beginnings of the ENIAC......................................................................................1485. The ENIAC: as a Mathematical Instrument......................................................................1576. John von Neumann and. the Computer...........................................................................1677. Beyond the ENIAC.............................................................................................1848. The Structure of the EDVAC...................................................................................2049. The Spread of Ideas..........................................................................................21110. First Calculations on the ENIAC.............................................................................225PART THREE: Post-World War II: The von Neumann Machine and The Institute for Advanced Study.....................2371. Post–EDVAC Days........................................................................................2392. The Institute for Advanced Study Computer....................................................................2523. Automata Theory and Logic Machines...........................................................................2714. Numerical Mathematics........................................................................................2865. Numerical Meteorology........................................................................................3006. Engineering Activities and Achievements......................................................................3067. The Computer and UNESCO......................................................................................3218. The Early Industrial Scene...................................................................................3259. Programming Languages........................................................................................33310. Conclusions.................................................................................................342APPENDIX: World-Wide Developments...............................................................................349Index...........................................................................................................363

Chapter One

Beginnings

There is of course never an initial point for any history prior to which nothing of relevance happened and subsequent to which it did. It seems to be the nature of man's intellectual activity that in most fields one can. always find by sufficiently diligent search a more or less unending regression back in time of. early efforts to study a problem or at least: to give it some very tentative dimensions. So it is with our field.

Since this is the case, I have chosen somewhat arbitrarily to make only passing references to the history of computers prior to 1600 and to say only the briefest word about the period before 1800. In fact, the only remarks I wish to make about this period are largely anticipatory ones to my main theme which concerns the early electronic digital calculators. The only excuse for this arbitrariness is that to say more on these earlier periods would add very little to our total knowledge of the electronic computer. I shall digress on a few occasions because of the colorfulness of one or another of the intellectual figures involved or because it seems desirable to establish in our minds some feeling for the intellectual, cultural, or social background of a givers period.

Perhaps, however, this choice is not completely arbitrary. If we accept the quite reasonable point of view of scholars such as Needham, we see that in a real sense the date of 1600 may be viewed as a watershed in scientific history. Prior to Galileo (1564–1642) there were of course intellectual giants, but his great contribution was to mathematicize the physical sciences. Ma"y great scientists before him had investigated nature and made measurements, but the world needed Galileo to give these data "the magic touch of mathematical formulation."

It is worth recalling that prior to this time the state of mathematics in. Europe was not substantially more advanced than that in the Arab world, based as it was on European and Chinese ideas and concepts. Then suddenly, as a result of a bringing together of mathematics and physics, something happened in Europe that started science on the path that led from Galileo to Newton. This melding of practical and empirical knowledge with mathematics was the magic touchstone. In about 1580 Francois Vieta (1540–1603) in an earth-shaking discovery introduced the use of letters for unknowns or general parameters into mathematics. The subjects we now call algebra and arithmetic were called by him logistica speciosa and logistica numerosa, respectively. He was followed, from our point of view, by John Napier, Laird of Merchiston (1550–1617), who in 1614 invented logarithms and who also was perhaps the first man to understand, in his Rabdologia in 1617, the use of the decimal point in arithmetical operations; and by Edmund Gunter (1581–1626), who in 1620 invented a forerunner of the slide rule, which was actually invented by William Oughtred (1575–1660) in 1632 and independently by Richard Delamain, who also published the first account of the instrument in 1630. The discovery of René Descartes (1596–1650) of analytical geometry in 1637 is perhaps the next great milestone on the road to the joint discovery of the calculus by Newton and Leibniz. The last stepping stone in that great chain lying between Descartes and Newton and Leibniz is, for our parochial purposes, Pascal's adding machine in 1642.

As Needham says in speaking of the great intellectual revolution that pushed Europe so far ahead of the Arabs, Indians, and Chinese, "No one has yet fully understood the inner mechanism of this development." The mechanism that led to this forward thrust was the confluence of two formerly separate mathematical streams: of algebra, from the Indians and Chinese, and of geometry, from the Greeks. Again, according to Needham, "the marriage of the two, the application of algebraic methods to the geometric field, was the greatest single step ever made in the progress of the exact sciences."

In this great panoply of stars it was Galileo, as we have said, who produced the other great confluence of streams of ideas. He brought together the experimental and mathematical into a single stream "which led to all the developments of modern science and technology." These are the reasons why we have started our account when we did. It is the proper time in the intellectual history of our culture to do so.

In starting at this place we are of course not doing justice to the interesting devices introduced by Moslem scientists very much earlier. The author is much indebted to Professor Otto Neugebauer, the historian of ancient astronomy and mathematics, for calling his attention to some special-purpose instruments invented by an Iranian astronomer and mathematician of the fifteenth century, Jamshid ben Mas'ud ben Mahmud Ghiath ed-Din al-Kashi (1393–1449). He was the head of an astronomical observatory at Samarkand that was set up by Ulugh Beg, Tamerlane's grandson.

Al-Kashi was apparently a Moslem mathematician who made "contributions of a. minor nature dealing with the summation of the fourth powers of the natural numbers, trigonometric computations, approximations.... To him is due the first use of a decimal fraction; ... the value of 2π to sixteen decimal places." His instruments were aids to both astrologers and astronomers in simplifying their calculations. His "Plate of Conjunctions" was a means for finding when two planets would be in conjunction, i.e., when they have the same longitude. Such times were considered to be of peculiar importance by astrologers, and their days of occurrence could be determined from almanacs. Then al-Kashi's plate was used to find the exact hour of occurrence.

His lunar eclipse computer was an ingenious device for simplifying the calculation of the important times associated with lunar eclipses. The method used gives an approximate solution which bears "a sufficiently close relation to reality to be useful."

Finally, his planetary computer was an. instrument for determining the longitudes of the surf, the moon, and the visible planets. In Kennedy's words: "Al-Kdshi's instrument is now seen to be part of an extensive and more or less continuous development of mechanico-graphical scale models of the Ptolemaic system. This development was already well underway in classical times. Bronze fragments of what was probably a (reek planetarium of about 30 B.C. have been recovered. from the Mediterranean.... The existence of a planetarium invented by Archimedes.... The Hypotyposis Astronomicarivn Positionum of Proclus Diadochus (ca. A.D. 450) ... description of a device for finding the longitude and equation of the sun.... In all this the work of al-Kashi is of considerable merit. His elegant constructions ... carry the general methods into branches of astronomical theory where they had not previously been applied."

Our story really opens during the Thirty Years War with Wilhelm Schickard (1592–1635), who was a professor of astronomy, mathematics, and Hebrew in Tübingen. Some years ago (1957) Dr. Franz Hammer, then assistant curator of Kepler's papers, discovered some letters from Schickard to Kepler—both of whom were from Wurtemberg–containing sketches and descriptions of a machine Schickard had designed and built in 1623 to do completely automatically the operations of addition and subtraction and, partially automatically, multiplication and division. The first letter was dated 20 September 1623, and a subsequent one 25 February 1624. In the first one, Schickard wrote of the machine that it "immediately computes the given numbers automatically, adds, subtracts, multiplies, and divides. Surely you will beam when you see how [it] accumulates left carries of tens and hundreds by itself or while subtracting takes something away from them...."

In his letter of 1624 he wrote: "I had placed an order with a local man, Johann Pfister, for the construction of a machine for you; but when half finished, this machine, together with some other things of mine, especially several metal plates, fell victim to a fire which broke out unseen during the night.... I take the loss very hard, now especially, since the mechanic does not have time to produce a replacement soon."

No copy of the machine is extant but Professor Bruno, Baron von Freytag-L6ringhof£, with the help of a master mechanic, Erwin Epple, as well as some others, reconstructed the instrument from the information in the letters and a few working models were made.

The device is ingenious, and it is a great pity that its existence was not known to the world of his day—unfortunately for the world Schickard and all his family died in the plagues brought about by the Thirty Years War. It is interesting to speculate on how his invention might have. influenced Pascal and Leibniz if war had not destroyed both Schickard. and his machine. lie must have been a man of many and great talents; Kepler said of him: "a fine mind and a great friend of mathematics; ... he is a very diligent mechanic and at the same time an expert on oriental languages."

Our next great figure is Blaise Pascal (1623–1662) who, along with his many other acts of genius, had designed and built a small and simple machine in 1642–1644 when he was about twenty years old. His machine formed the prototype for several machines built in France, but all these represented devices of considerable simplicity in terms of their function, which was to effect by counting the fundamental operations of addition and subtraction. In fact the instrument was in some sense not as advanced as Schickard's in that it could not do the non-linear operations: multiplication and division. Apparently both he and his contemporaries viewed this machine as a most remarkable achievement. A version built in 1652 and signed by Pascal is in the, Conservatoire des Arts et Métiers in Paris, and a copy of it is in the Science Museum in South Kensington, London. The machine was described in detail by Diderot in his famous Encyclopédie.

Some thirty years later Gottfried Wilhelm Leibniz (1646–1716), another of the great universalists of his or indeed of all time, invented a device now known as the Leibniz wheel and still in use in some machines. The mechanism enabled him to build a machine which surpassed Pascal's in that it could do not only addition and subtraction fully automatically but also multiplication and division. Leibniz said in comparing his device with Pascal's: "In the first place it should be understood that there are two parts of the machine, one designed for addition (subtraction) the other for multiplication (division) and that they should fit together. The adding (subtracting) machine coincides completely with the calculating box of Pascal." This device was viewed with the greatest interest both by the Académie des Sciences in Paris and by the Royal Society in London, to which Leibniz was elected a Fellow in 1673, the year his machine was completed and exhibited in London. Pascal is reputed to have built his machine as an aid to his father who was the discoverer of a famous curve known as the limagon but who had need for help in computation." In fact his father, Etienne, was a high official in Basse-Normandie, and following a revolt over taxes he reorganized the tax structure of the area.

Curiously at this time the ability to do arithmetic was not generally to be found even among well-educated men. We thus find even such men as Pepys having, as a member of the Admiralty, to teach himself the multiplication tables. Perhaps therefore it was this general state of arithmetical knowledge rather than great filial piety that prompted Pascal to lighten his parent's burden.

In any case, it was Leibniz who summed up the situation very well indeed when he wrote: "Also the astronomers surely will not have to continue to exercise the patience which is required for computation. It is this that deters them from computing or correcting tables, from the construction of Ephemerides, from working on hypotheses, and from discussions of observations with each other. For it is unworthy of excellent men to lose hours like slaves in the labor of calculation which could safely be relegated to anyone else if machines were used."

This notion which already had received such explicit formulation 300 years ago is in a very real sense to be the central theme of our story. It is fully in keeping with the genius of Leibniz that even when the field of computing was so very much in its infancy he already understood the point of the matter with such astonishing clarity. It is also of interest to realize that in the 1670s he had a third copy of his machine built for Peter the Great to send to the emperor of China to show the orientals the arts and industry of the occidentals and thereby increase commerce between the East and West.

It is sad to realize that this great figure in our intellectual life should have had so difficult a time in his own period. Perhaps he was so far ahead of his contemporaries—excepting Newton–that none appreciated his work. On his death in 1716, his only mourner was his secretary, and an eye witness wrote: "He was buried more like a robber than what lie really was, the ornament of his country." In any case his little machine is still preserved in the State Library in Hanover, more as a curiosity than as a very early form of the modern computer. Leibniz's work (lid however stimulate a number of others to build improved machines, many of them ingenious variants of his." Today these machines are still with us and play a significant role for minor calculations. Indeed during World War II they were of greatest importance.

It is also Leibniz, who in the grandeur of his genius realized, at least in principle, his Universal Mathematics. This was also to have greatest importance to our story—but much later. He wrote an essay in 1666 concerning Combinatorics, one of the great branches of mathematics, entitled De Arte Combinatorica. He described it as "a general method in which all truths of the reason would be reduced to a kind of calculation." This work was neglected in his time but was later to be picked up by George Boole and still later by Couturat, Russell, and other logicians. Thus Leibniz contributed very profoundly to computers. Not only by his machine but also by his studios of what is now known as symbolic logic. We will return to this subject later in its appropriate place in our history. In closing our few paragraphs on Leibniz, we feel it is worth emphasizing his four great accomplishments to the field of computing: his initiation of the field of formal logics; his construction of a digital machine; his understanding of the inhuman quality of calculation and the desirability as well as the capability of automating this task; and, lastly, his very pregnant idea that the machine could be used for testing hypotheses. Even today there are only the beginnings of this type of calculation.

(Continues...)

Excerpted from The Computer from Pascal to von Neumaunby Herman H. Goldstine Copyright © 1972 by Princeton University Press . Excerpted by permission of Princeton University Press. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Edition details

• Publisher: Princeton University Press
• Publication date: 1972
• ISBN 10: 0691081042
• ISBN 13: 9780691081045
• Binding: Hardcover
• Language: English
• Number of pages: 365