### The Computer from Pascal to von Neumann

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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 given period. Perhaps, however, this choice is not completely arbitrary. Prior to Galileo — there were of course intellectual giants, but his great contribution was to inathematicize the physical sciences.

Many 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 Francois Vieta — in an earth-shaking discovery introduced the use of letters for unknowns or general parameters into mathematics.

### The Computer from Pascal to von Neumann

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. 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.

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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.

## The Computer from Pascal to von Neumann by Herman H. Goldstine - Book - Read Online

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. This development was already well underway in classical times.

Bronze fragments of what was probably a Greek planetarium of about 30 B. The existence of a planetarium invented by Archimedes…. His elegant constructions … carry the general methods into branches of astronomical theory where they had not previously been applied.

Some years ago Dr.

The first letter was dated 20 September , and a subsequent one 25 February 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 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. 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. He 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 — who, along with his many other acts of genius, had designed and built a small and simple machine in — 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. Apparently both he and his contemporaries viewed this machine as a most remarkable achievement.

Some thirty years later Gottfried Wilhelm Leibniz — , 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 adding subtracting machine coincides completely with the calculating box of Pascal.

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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. 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 correc ing 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 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 s 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.

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Perhaps he was so far ahead of his contemporaries—excepting Newton—that none appreciated his work. 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 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. Not only by his machine but also by his studies 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.

Smith, A Source Book of Mathematics , vol. See also D. Rideres clare, si praesens cerneres, quomodo sinistros denarium vel centenarium supergressos sua sponte coacervet, aut inter subtrahendeum ab eis aliquid suffuretur…. Pfisterum nostratem, sed illud semiperfectum, uno cum aliis quibusdam meis, praecipue aliquot tabellis aeneis conflagravit ante triduum in incendio noctu et ex improvisibi coorto…. His idea was apparently re-invented in by Charles Xavier de Colmar of Alsace.

Through the kindness of Dr. Turski of the Polish Academy of Sciences, I learned of still another interesting machine, or rather series of machines, developed by a Polish scholar, Abraham Stern — His machines handled the four arithmetic operations plus square root in a six-digit unit. The most advanced model was described in a public lecture at the Societas Scientiarum Varsoviensis on 30 April and was published in vol. VIl of the annals of that society. The interested reader may consult R. Couturat, Le Logique de Leibniz Paris, , n, p.

Murray, op.

His machine was basically an early version of the familiar desk calculator. The theme of Leibniz—to free men from slavery by the automation of dull but simple tasks—was next taken up by one of the most unusual figures in modern intellectual history, Charles Babbage — As his biographer has so correctly said of Babbage everything about him was contentious including the date of his birth. According to her, he was born on 26 December , in Devonshire, even though he stated that it was in in London.

The title of her book Irascible Genius is another good clue to his character. In any case, he was born into an upper middle class English home and had the usual advantages, both intellectual and social, of such a background. During his college years he formed close associations with John Herschel, the son of the discoverer of the planet Uranus and himself one of the great astronomers, and George Peacock, who had three wonderful careers—as a mathematician, an astronomer, and later as a divine when he became Dean of Ely.

The importance of these three men to mathematics is attested to by E. In fact, we see him as one of the founding members of the Royal Astronomical Society 12 January and the first recipient of its Gold Medal 13 July for his work on Observations on the Application of Machinery to the Computation of Mathematical Tables. There are, as the Morrisons point out, two different accounts of how young Babbage first hit upon his idea of automating computation.

In his Passages Babbage says:.