Sobre la perfección

tabular errors, there were no half measures. A table was to be perfect, and known to be perfect, or useless.® Herschel captured the insecurity and the dangers of latent errors in his letter to Henry Goulbum, Chancellor, when he wrote in 1842 that 'an undetected error in a logarithmic table is like a sunken rock at sea yet undiscovered, upon which it is impossible to say what wrecks may have taken place.'® Experts disagreed and empirical method was powerless to provide resolution.

Lardner’s pairing of errors as ‘problem’ with engines as ‘solution’ encourages the notion that the elimination of errors was the essential purpose of automatic calculating engines. While he stops short of attributing these motives directly to Babbage he does nothing to discourage anyone else from so doing.

There is a second seminal account that serves to reinforce the perception that the elimination of errors was the primary purpose of Babbage’s engines. This is the vignette of Babbage and Herschel in 1821 poring over newly calculated tables for the Astronomical Society when, dismayed by the large number of discrepancies, Babbage exclaimed ‘I wish to God these calculations had been executed by steam’.^° Babbage relates how he was seized by the notion of

® In 1821, when Babbage conceived of his engine, his main experience and interest had been in mathematics. His published output to that time consisted entirely of mathematical papers, thirteen of which were published between 1813 and 1821. Lindgren implies that Babbage’s perfectionism, associated with mathematical thinking, was at least partly responsible for his downfall. He also argues that the quest for the "perfect" table was part of the drive to realise calculating engines. He observes that parts for Difference Engine No. 1 were made to a higher precision than was practically necessary and that the same precision was wastefully extended to decorative features. See LEC, pp. 262-3.

9 10

Herschel to Goulburn, September 1842. Royal Society Herschel Archive, Box 27, Item 51. There are three known accounts of this episode written by Babbage: 1822, 1834 and 1839. Quoted in LEC, 14-8. The quotation cited is taken from the third account which appears in the Buxton memoir. (See next footnote). The first account leaves it open as to whether it was

Babbage or Herschel that made the suggestion. In the second and third accounts Babbage claims ownership for himself. All three accounts refer to steam as the agent of redemption. The third account is the most dramatised and is the only one to include direct speech. Peter Ackroyd describes Babbage’s exclamation as "one of the most wonderful sentences of the nineteenth century’. See Ackroyd (1994), p. 116.

calculating engines immediately after this episode and how his near obsession with the “Calculating Engine” made him ill in the following days and weeks/^

Lardner’s article, combined with Babbage’s account of his mechanical epiphany, has had a defining influence on historical accounts of automatic computation, and the perception that Babbage’s primary purpose was the elimination of errors is one that has consolidated over time. It has the appeal of monocausal simplicity and features increasingly in historical accounts to this day."*^ While errors have been emphasised in historical accounts it should not be

assumed that the elimination of error was the sole purpose, or indeed the enduring purpose, or necessarily even the main appeal of the machines to Babbage simply because errors were the trigger to his deliberations and subsequent efforts.

This chapter argues that while the elimination of errors features in Babbage’s own justification for his engines, it does so alongside several other reasons,

benefits and justifications, and far less prominently, than Lardner’s article and historians since have suggested. Secondly, that Lardner’s simplification of purpose by an emphasis on errors can be seen as a product of the need to appeal to

lecture hall audiences. Finally, that the political context of the collapsing fortunes of the engine project disposed Babbage to accept and even endorse Lardner’s

simplification even if it represented a less than complete picture.

Lardner’s article was published in the July 1834 issue of the Edinburgh

Review, thirteen years after Babbage’s first conception of the machine, and after

many of the arguments for and against the utility of the machines, their funding and construction had been played out. Whatever effect the article has had on historians

Babbage’s account of the aftermath of his mechanical epiphany is related in Buxton’s memoir. See Hyman (1988), pp. 46-48. Buxton, a junior colleague of Babbage, was entrusted by Babbage with the task of writing his biography using manuscript sources he supplied. The memoir was written between 1872 and 1880 but not published until 1988. See Hyman (1988), editor’s

Introduction, p. xiii. The political background to the commissioning of these tables is discussed below. See below pp. 125-6.

Chapter 3: Babbage's Expectations 116

since, it had no material influence on the earliest formulations of the purpose and benefits of the machines. To uncouple contemporary accounts from the backward projection of later historical accounts it is necessary to start with Babbage’s earliest papers on the utility of the machines written before Lardner framed utility the way he did.

Babbage’s Early Writings

The documents that are most revealing of Babbage’s earliest notions of the capacities and potential benefits of the machine date from the period between 14 June and 13 December 1822. During this time he wrote five papers, four published close to the time of writing, and one manuscript (Item 3 below) that remained unpublished during his lifetime;

1. “A note respecting the application of machinery to the calculation of astronomical tables.” Memoirs of the Astronomical Society 1 (1822): 309. [Dated 2 June 1822. Read 14 June 1822]

2. “A letter to Sir Humphrey Davy, Bart., President of the Royal Society, on the application of machinery to the purpose of calculating and printing

mathematical tables.” . London: Cradock and Joy, 1822. [Dated 3 July 1822].^^

3. “The science of number reduced to mechanism.” November 1822 [Buxton MS].

See for example Stan Augarten’s account which is typical of many. Augarten (1984), p. 40. Reprinted in Parliamentary Papers. 1823, Vol. 15, pp. 9-14. See editor’s note. Works, Vol. 2, p. 6, ft a. An excerpt of the letter was published in Edinburgh PhilosophicalJournal, Vol. VII, p. 274. See editor’s note. Works, Vol. 2, p. 38.

4. “Observations on the application of machinery to the computation of

mathematical tables.” Memoirs of the Astronomical Society 1 (1822): 311-314. [Read 13 December 1822].

5. “On the theoretical principles of the machinery for calculating tables.”.

Edinburgh PhilosophicalJoumal 8 (1823): 122-128. [Dated 6 November

1822].“

The suite of papers was written after the first trials using a small working model completed in Spring 1822 but before Babbage showed any serious ambition to build an engine."'® The papers derive much of their material from the results of the first experiments and the theoretical speculations stimulated by them. With the exception of the manuscript (Item 3 above) all the papers are short. The notice to the Astronomical Society (Item 1) is barely 300 words long, and the Items 4 and 5 run to only a few pages and are narrowly mathematical.

Though Babbage's writing is voluminous and polymathic the four published papers in this suite, plus an additional one read on 3 May 1824 to the Cambridge Philosophical Society, are his oniy pubiished writing on the Difference Engines apart from fragmentary references in later works."'® While he returns repeatedly in his published work to the collapse of the engine project, the protracted negotiation with successive administrations, and his grievances over the Government’s final

This paper is a pubiished letter from Babbage to David Brewster.

The exact date the model was completed is not known. In a diary entry dated 10 May 1822 Babbage wrote ‘my calculating engine is nearly finished' (Babbage Papers, W aseda University). Collier narrows the date to ‘near the end of May 1822’ {LEC,, pp. 30, 32). On 14 June 1822 Babbage refers to the ‘engine just finished’ {Works, Vol. 2, p. 3). This first model has never been found nor any plans for it. It is known in the literature as ‘DEO’ to signify that it preceded

Difference Engine No. 1. See Taylor (1992); Tee (1994).

For a detailed annotated Bibliography of Babbage’s printed works (six books and some eighty six papers) see van Sinderen (1980). For a complete list of known publications see Bibliography,

Works, Vol. 1, pp. 34-45. The paper read to the Cambridge Philosophical Society in May 1824 was pubiished in 1826 (Babbage (1826), Works, Vol. 2, pp. 61-68). The most substantial of Babbage’s fragmentary writing on the engines is in Passages.