Great Calculators: Mental and Metal and back to Mental

JF Ptak Science Books     Expanding Post 2739

Two months ago I wrote on a paper that I found in a mid-century engineering journal (Minutes of Proceedings of the Institution of Civil Engineers with Abstracts of the Discussions) on the fantastic mental arithmetician George Parker. When I went to retrieve the volume to look for a different paper (on Fresnel lenses for lighthouses) I  flipped the pages to then end of the book to read through the index, and my thumb stopped on a page with a running header, "Mechanical Notations". And lo and behold, the very familiar title was indeed a paper on a report to the Institution on Charles Babbage (1791-1871) and his "mechanical notation", given by his son Henry P. Babbage (1824-1918).

Well.  Babbage over the years proposed several different difference and analytical engines which indeed could be considered the first stored program Turing-complete computers. Never quite being able to get to the end of one project, and no doubt discovering along his various ways even better and more substantial designs (as well as int he pursuit of future money to build not "version 1.0" or "1.1" but "3.0"), Babbage tried within the limits of available technology to produce his heroic beast. His "mechanical notation" appears in full force in his diagrams for the design of his analytical engine, and it is there that we see his self-derived shorthand and symbols that produced and still-produce evident budgets of unknowns. The thing is, with these mechanical notations, is that they were part of a user manual, and the user manual was actually left unwritten and chiefly unexplained. And that is a problem. 

In any event this paper by Henry Provost Babbage makes some attempt in outlining the notation, though for me it is done without success. This is further complicated by almost none of the notation presented in illustration. There were other and earlier illustrated papers (including some by Babbage himself) that stretch back at least to 1821--but this explanation of the notations leaves me a little on the outside. 

And so we moved from the mental calculator George Bidder to the great metallic calculating engines of Charles Babbage, who takes us back to the opening biological/mental part of engineering thought via his manual-less manual, where his instructions and explanations of the interactions of thousands of perfectly manufactured precision gear works is printed but the key to which is left locked in Babbage's head.  

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Here's the part of the post that led to the discovery of the Babbage, both of these papers as I said appearing in the same journal volume: 

George Parker Bidder (1806-1878) gave a lecture (without notes) explaining to the audience at the Institution of Civil Engineers in 1856¹ his interior practices and habits in performing absolutely prodigious and complex arithmetical feats entirely in his head. He was among the first tier of performing human calculators (like Zerah Colburn, b. 1804) mental calculations enchanted large audiences from the stages, answering seemingly impossible questions with accuracy and speed. It is in the 1856 paper (which Martin Gardner refers to as "historic²" and "valuable") that he relates some of the practices which clarify his process--for example, one large element was that he would keep one fact in his head at a time, until it was finished, and then move on. Of course for people who did not have anything even remotely resembling this impossible ability, the information is interesting, though I have no idea how useful it may be...unless you were already a savant, that is.  Some things are just not to be known by mere mortals. Like the probably-apocryphal story of someone asking Hans Bethe how Richard Feynman had solved--on his feet--some impossible something, and Bethe responds: "First he thinks very very hard....and then he gets the answer".) Something like that. 

In any event, here's the article, reproduced by Devonshire Perspectives website. My own copy is in a tightly-bound volume from the proceedings, and no doubt I would have broken the spine trying to copy the thing. That said, if anyone wants to buy this volume, it is for sale--this is a book selling site, sorta, after all.  

The full lecture by Bidder:

https://www.devonperspectives.co.uk/georgebidder/OnMentalCalculation.pdf

Notes:

1. Bidder, George Parker. "On Mental Calculation", in Minutes of Proceedings of he Institution of Civil Engineers with Abstracts of the Discussions, volume XV, Session 1855-6, London, published by the Institution,  pp 251-280 in the 534pp volume. 

2.  Gardner, Martin. "Mathematical Games", in Scientific American, 216/4, April 1967, p. 117. 

Also, I found an interesting biographical treatment of Bidder:

• Bidder, George Parker. Mental Arithmetic. A short account of George Bidder, the celebrated mental calculator: with a variety of the most difficult questions, proposed to him at the principal towns in the kingdom, and his surprising rapid answers, etc. by George Parker BIDDER Rapid Calculator and Engineer., 1821

It seems as though there was a separate edition of this 1856 lecture tens years later, published by Clowes:

• Bidder, George Parker, and Institution of Civil Engineers (Great Britain). On Mental Calculation. Edited by Charles Manby. London: Printed by W. Clowes, 1866.

And another printing somewhat later:

• Bidder, George Parker. On Mental Calculation. London: Printed by W. Clowes, 1886.