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Dead medium: Babbage's Difference Engine
From: nbodley@tiac.net (Nicholas Bodley)

Source(s): Sir David Brewster, *Letters on Natural Magic,* New York, J&J Harper, 1832, pages 263-7 (Quoted by Fred Stahl, on the CALC LIST, CALCLIST-L@techunix.technion.ac.il)

(((bruces remarks: there's a fine melancholy pleasure in reading mindblown pop-science reportage about incredible machinery, especially when that hype pre-dates the utter collapse and obscurity of the Babbage Difference Engine. This Brewster book has received most any number of dead media citations over the years.)))

"Of all the machines which have been constructed in modern times, the calculating machine is doubtless the most extraordinary. Pieces of mechanism for performing particular arithmetical operations have been long ago constructed, but these bear no comparison either in ingenuity or in magnitude to the grand design conceived and nearly executed by Mr. Babbage."

(((bruces remarks: there's a lethal poetic pang in that little word "nearly.")))

"Great as the power of mechanism is known to be, yet we venture to say that many of the most intelligent of our readers will scarcely admit it to be possible that astronomical and navigational tables can be accurately computed by machinery; that the machine can itself correct the errors which it may commit; and that the results of its calculations when absolutely free from error, can be printed off, without the aid of human hands, or the operation of human intelligence."

(((The bold term "computed by machinery" was a stunning neologism at the time.)))

"In all this, I have had the advantage of seeing it actually calculate, and of studying its construction with Mr. Babbage himself. I am able to make the above statement on personal observation. The calculation machine now constructing under the superintendence of the inventor has been executed at the expense of the British government, and is of course their property.

"It consists essentially of two parts == a calculating part and a printing part, both of which are necessary to the fulfilment of Mr. Babbage's views, for the whole advantage would be lost if the computations made by the machine were copied by human hands and transferred to types by the common process."

(((Many people overlook this highly mediated aspect of Babbage's primeval computer: from the get-go, the device was designed to be half-printer, constructed on novel principles.)))

"The greater part of the calculation machinery is already constructed, and exhibits workmanship of such extraordinary skill and beauty that nothing approaching to it has been witnessed.

(((It was permitted to call a computer "beautiful" in those pre-geek days.)))

"In order to execute it, particularly those parts of the apparatus which are dissimilar to any used in ordinary mechanical constructions, tools and machinery of great expense and complexity have been invented and constructed; and in many instances contrivances of singular ingenuity have been resorted to, which cannot fail to prove extensively useful in various branches of the mechanical arts.

(((Babbage was inventing not just a computer, but a new means of highly precise industrial production. His book *Economy of Manufactures* was a major influence on Karl Marx.)))

"The drawings of this machinery, which form a large part of the work, and on which all the contrivance has been bestowed, and all the alterations made, cover upwards of 400 square feet of surface, and are executed with extraordinary care and precision.

"In so complex a piece of mechanism, in which interrupted motions are propagated simultaneously along a great variety of trains of mechanism, it might have been supposed that obstructions would arise, or even incompatibilities occur, from the impracticability of foreseeing all the possible combinations of the parts; but this doubt has been entirely removed, by the constant employment of a system of mechanical notation invented by Mr. Babbage, which places distinctly in view at every instant the progress of motion through all the parts of this or any other machine, and by writing down in tables the times required for all the movements, this method renders it easy to avoid all risk of two opposite actions arriving at the same instant at any part of the engine.

(((Inbuilt crash avoidance == one can't have subparts of the program competing for resources, or overwriting one another.)))

"In the printing part of the machine less progress has been made in the actual execution than in the calculation part. The cause of this is the greater difficulty of this contrivance, not for transferring the computations from the calculating part to the copper or other plate destined to receive it, but for giving to the plate itself that number and variety of movements which the forms adopted in printed tables may call for in practice.

"The practical object of the calculating engine is to compute and print a great variety and extent of astronomical and navigational tables, which could not be done without enormous intellectual and manual labour, and which, even if executed by such labour, could not be calculated with the requisite accuracy.

"Mathematicians, astronomers, and navigators do not require to be informed of the real value of such tables; but it may be proper to state, for the information of others, that seventeen large folio volumes of logarithmic tables alone were calculated at an enormous expense by the French government; and that the British government regarded these tables to be of such national value that they proposed to the French Board of Longitude to print an abridgement of them at the joint expense of the two nations, and offered to advance 5000L. for that purpose."

(((Navigational logarithms were to be the Difference Engine Killer App.)))

"Besides logarithmic tables, Mr. Babbage' machine will calculate tables of the powers and products of numbers, and all astronomical tables for determining the positions of the sun, moon, and planets; and the same mechanical principles have enabled him to integrate innumerable equations of finite differences, that is, when the equation of differences is given, he can, by setting an engine, produce at the end of a given time any distant term which may be required, or any succession of terms commencing at a distant point.

"Besides the cheapness and celerity with which this machine will perform its work, the absolute accuracy of the printed results deserves especial notice. By peculiar contrivances, any small error produced by accidental dust or by any slight inaccuracy in one of the wheels, is corrected as soon as it is transmitted to the next, and this is done in such a manner as effectually to prevent any accumulation of small errors from producing an erroneous figure in the result.

"In order to convey some idea of this stupendous undertaking, we may mention the effects produced by a small trial engine constructed by the inventor, and by which e computed the following table from the formula X**2 + X + 41. The figures as they were calculated by the machine were not exhibited to the eye as in sliding rules and similar instruments, but were actually presented to the eye on two opposite sides of the machine: the number 383, for example, appearing in figures before the person employed in copying.

"Table calculated by a small Trial Engine

41 131 383 797 1373

43 151 421 853 1447

47 173 461 911 1523

53 197 583 971 1601

61 223 547 1033 1681

71 251 593 1097 1763

83 281 641 1163 1847

97 313 691 1231 1933

113 347 743 1301 2021

"While the machine was occupied in calculating this table, a friend of the inventor undertook to write down the numbers as they appeared. In consequence of the copyist writing quickly, he rather more than kept pace with the engine, but as soon as five figures appeared, the machine was at least equal in speed to the writer.

"At another trial thirty-two numbers of the same table were calculated in the space of two minutes and thirty seconds, and as these contained eighty-two figures, the engine produced thirty-three figures every minute, or more than one figure in every two seconds.

(((That would be 0.5 cps, but the thing is made of brass, for heaven's sake.)))

"On another occasion it produced forty-four figures per minute. This rate of computation could be maintained for any length of time; and it is probable that few writers are able to copy with equal speed for many hours together.

"Some of that class of individuals who envy all great men, and deny all great inventions, have ignorantly stated that Mr. Babbage's invention is not new. The same persons, had it suited their purpose, would have maintained that the invention of spectacles was an anticipation of the telescope; but even this is more true than the allegation that the arithmetical machines are precursors of Mr. Babbage's engine. The object of these machines was entirely different. Their highest functions were to perform the operations of common arithmetic. Mr. Babbage's engine, it is true, can perform these operations also, and can extract the roots of numbers, and approximate the roots of equations, and even to their impossible roots.

"But this is not its object. Its function, in contradistinction to that of all other contrivances for calculation, is to imbody in machinery the method of differences, which has never before been done: and the effects which it is capable of producing, and the works which in the course if a few years we expect to see it execute, will place it at an infinite distance from all other efforts of mechanical genius.*

"*A popular account of this engine will be found in Mr. Baggage's interesting volume 'On the Economy of Manufactures,' just published.

Nicholas Bodley (nbodley@tiac.net)