An expense of both time and money, 1822
But will it slice a pineapple?
To bring to perfection the various machinery which I have contrived would require an expense of both time and money…
A slightly different format this time, in order to look at the challenges faced by one of history’s great inventors.
Two hundred years ago this week – on 14th June 1822 – a brief paper was read to the Royal Astronomical Society entitled ‘Note on the Application of Machinery to the Computation of Astronomical and Mathematical Tables’. Below is the full text:
It is known to several of the members of this society that I have been engaged during the last few months in the contrivance of machinery which, by the application of a moving force, may calculate any tables that may be required. I am now able to acquaint the society with the successful results at which I have arrived; and although it might at the first view appear a bold undertaking to attempt the construction of an engine which should execute operations so various as those which contribute to the formation of the numerous tables that are constantly required for astronomical purposes, yet to those who are acquainted with the method of differences the difficulty will be in a considerable degree removed.
I have taken the method of differences1 as the principle on which my machinery is founded; and in the engine which is just finished I have limited myself to two orders of differences. With this machine I have repeatedly constructed tables of square and triangular numbers, as well as a table from the singular formula
which comprises amongst its terms so many prime numbers.
These, as well as any others which the engine is competent to form, are produced almost as rapidly as an assistant can write them down. The machinery by which these calculations are effected is extremely simple in its kind, consisting of a small number of different parts frequently repeated.
In the prosecution of this plan, I have contrived methods by which type shall be set up by the machine in the order determined by the calculation; and the arrangements are of such a nature that, if executed, there shall not exist the possibility of error in any printed copy of tables computed by this engine. Of several of these latter contrivances I have made models; and, from the experiments I have already made, I feel great confidence in the complete success of the plans I have proposed.
The author of this “bold undertaking” was Charles Babbage (1791–1871) and the machinery in question, powered by cranking a handle, was the first iteration of his Difference Engine, now known as ‘No. 0’ – a fairly time-consuming ‘minimum viable product’ which he had started back in 1820 and ended up being the only version of the machine he actually finished. Nonetheless, it marks a landmark in the history of computing, and was arguably the first working device of that kind,2 at least for solving certain kinds of mathematical problems. Sadly no pictures of the completed device seem to have survived,3 although Babbage did describe it in more detail than his later incomplete efforts (the 12,000-part No. 1 was abandoned, and only about a seventh survives today; No. 2 was only fully completed in 2002; and he managed to build just a fragment of his later Analytical Engine before he died).
Babbage wrote an autobiography, Passages from the Life of a Philosopher, in which he explains the genesis of his idea, which he says came around 1812 or 1813:
One evening I was sitting in the rooms of the Analytical Society, at Cambridge, my head leaning forward on the Table in a kind of dreamy mood, with a Table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, “Well, Babbage, what are you dreaming about?” to which I replied, “I am thinking that all these Tables (pointing to the logarithms) might be calculated by machinery.”
He explains the core principles (e.g. “the power of adding one digit to another, and also of carrying the tens to the next digit”) but refers to No. 0 only briefly before telling the story of No. 1. We have Babbage’s youngest son Henry to thank for many of the details which survive: in 1888 Henry gathered as many documents as he could to tell the full story in a volume published in 1899 as Babbage’s Calculating Engines.4
As well as the note above, this book contains a letter Babbage senior wrote to Sir Humphry Davy, then president of the Royal Society (and now mainly remembered for inventing a safety lamp for miners), on 3rd July 1822, i.e. only a couple of weeks after he had announced No. 0. Babbage describes the technical challenges of the project in some detail, but the core points are perhaps these:
The intolerable labour and fatiguing monotony of a continued repetition of similar arithmetical calculation, first excited the desire and afterwards suggested the idea, of a machine, which, by the aid of gravity or any other moving power, should become a substitute for one of the lower operations of human intellect…
To bring to perfection the various machinery which I have contrived would require an expense of both time and money, which can be known only to those who have themselves attempted to execute mechanical inventions.
Thereby hangs a tale. A year later, Babbage had managed to coax £1,700 out of the government to support the development of No. 1 as it was interested in the applications of this technology. By the time it was abandoned a decade later, the sum had grown tenfold (a vast sum in today’s money – certainly millions), with no finished product. Babbage’s notes suggest he was filled with an abundance of ideas but not a great deal of output – which isn’t in any way to decry his great intellect. (Another of his inventions was the cow-catcher fender at the front of trains – but, er, he never actually made one.)
And of course there was scepticism at the time. Last year I wrote about the adventures of politician and author John Wilson Croker (see here, here and here), and one of the ‘out-takes’ from my research into him was the following exchange of letters between Croker and Robert Peel, then Home Secretary and later Prime Minister, about Babbage’s invention…
8th March 1823, Peel to Croker
You recollect that a very worthy seafaring man declared that he had been intimate in his youth with Gulliver, and that he resided (I believe) in the neighbourhood of Blackwall. Davies Gilbert [an engineer and politician who succeeded Davy as president of the Royal Society] has produced another man who seems to be able to vouch at least for Laputa [the flying island inhabited by scientists in Swift’s Gulliver’s Travels]. Gilbert proposes that I should refer the enclosed to the Council of the Royal Society, with the view of their making such a report as shall induce the House of Commons to construct at the public charge a scientific automaton, which, if it can calculate what Mr. Babbage says it can, may be employed to the destruction of Hume… [David Hume, the philosopher who was sceptical of scientific rationalism] I should like a little previous consideration before I move in a thin house of country gentlemen, a large vote for the creation of a wooden man to calculate tables from the formula
21st March, Croker to Peel
Mr. Babbage’s invention is at first sight incredible, but if you will recollect those little numeral locks which one has seen in France, in which a series of numbers are written on a succession of wheels, you will have some idea of the first principles of this machine, which is very curious and ingenious, and which not only will calculate all regular series, but also arranges the types for printing all the figures. At present indeed it is a matter more of curiosity than use, and I believe some good judges doubt whether it ever can be of any. But when I consider what has been already done by what were called Napier’s bones and Gunter’s scale, and the infinite and undiscovered variety of what may be called the mechanical powers of numbers, I cannot but admit the possibility, nay the probability, that important consequences may be ultimately derived from Mr. Babbage’s principle. As to Mr. Gilbert’s proposition of having a new machine constructed, I am rather inclined (with deference to his very superior judgment in such matters) to doubt whether that would be the most useful application of public money towards this object at present.
I apprehend that Mr. Babbage’s present machine, which however I have not seen, answers the purposes which it is intended for sufficiently well, and I rather think that a sum of money given to Mr. Babbage to reward his ingenuity, encourage his zeal, and repay his expenses would tend eventually to the perfection of his machine. It was proposed at the Board of Longitude to give him £500 out of the sum placed at our disposal for the reward of inventions tending to facilitate the ascertaining the Longitude. But the Board doubted that the invention was likely to be practically useful to a degree to justify a grant of this nature.
I think you can have no difficulty in referring the matter to the Council of the Royal Society (of which, although unworthy, I have the honour to be one), which by the assistance of its scientific members will give you the best opinion as to the value of the invention, and when that is obtained, it may be considered whether another machine should be made at the public expense, or whether Mr. Babbage should receive a reward either from Parliament or the Board of Longitude.
Babbage himself was understandably sensitive to criticism, which like many pioneers he saw as endemic in his society. In a preface to an edition of his book Thoughts on the Principles of Taxation, he grumbled:
Propose to an Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it. If you speak to him of a machine for peeling a potato, he will pronounce it impossible: if you peel a potato with it before his eyes, he will declare it useless, because it will not slice a pineapple.
In 1946, another computing pioneer, Leslie John Comrie wrote in Nature that the British government deserved a “black mark” for failing to support Babbage’s engines through to completion and this “cost Britain the leading place in the art of mechanical computing”. Swedish inventor Per Georg Scheutz did go on to build a ‘calculation engine’ based on Babbage’s, and the British government bought some from him in the 1850s. Could more funding for Babbage himself have led to the sort of steampunk society that many authors have imagined? Or would he have somehow never quite finished them anyway? We’ll never know, but his place as the father of computing seems secure, and at least we know from modern re-creations that his machines could certainly have worked.
Let’s not get into the Antikythera mechanism here, and there were some adding machines invented in the 18th century.
A 2009 article by Denis Roegel, ‘Prototype Fragments from Babbage’s First Difference Engine’, does speculate that fragments of No. 1 held in various museums actually contain parts from No. 0.