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Charles Babbage as an Algorithmic Thinker

IP.com Disclosure Number: IPCOM000129754D
Original Publication Date: 1992-Sep-30
Included in the Prior Art Database: 2005-Oct-07
Document File: 24 page(s) / 99K

Publishing Venue

Software Patent Institute

Related People

I. GRATTAN-GUINNESS: AUTHOR [+2]

Abstract

While the career of Charles Babbage (1791-1871) shows a remarkable range of interests, strong threads bind together several of the principal ones: algorithmic thinking, with intimate links to algebra and to semiotics. The links connect especially his mathematical researches in functional equations with his work on mathematical tables and on calculating machines, but they are evident also in some of his social and industrial concerns. Evidence is presented to show that Babbage was consciously aware of at least some of these links. Attention to them casts light upon his achievements.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

Copyright ©; 1992 by the American Federation of Information Processing Societies, Inc. Used with permission.

Charles Babbage as an Algorithmic Thinker

I. GRATTAN-GUINNESS

While the career of Charles Babbage (1791-1871) shows a remarkable range of interests, strong threads bind together several of the principal ones: algorithmic thinking, with intimate links to algebra and to semiotics. The links connect especially his mathematical researches in functional equations with his work on mathematical tables and on calculating machines, but they are evident also in some of his social and industrial concerns. Evidence is presented to show that Babbage was consciously aware of at least some of these links. Attention to them casts light upon his achievements.

Categories and Subject Descriptors: K.2 [Computing Milieux]: History of Computing -- People, Theory. General Terms: Algorithms. Additional Terms: Babbage, Algebra, Semiotics, Mathematical Tables.

(Image Omitted: ...the whole of analysis discovered is dependent in great part upon modified algorithms of certain fixed quantities... Leonhard Euler, 17641)

This opinion was quoted in 1822 by Babbage, in a paper on notation which was related to functional equations (p. 1/344) 2 In this article I put forward a general thesis about Babbage's work as a mathematician, engineer, and scientist, of which several elements are exemplified by the quotation. My claim is as follows:

Although Babbage's interests covered a remarkable and indeed polymathic range, many of the most important ones exhibit common threads, in both the choice of problem and the manner(s) of their investigation.

The common threads center around algorithmic procedures in mathematics, science, and other walks of life.

Babbage was consciously aware of some of these common features, especially in his deployment of analogy from one theory in another.

Attention to these common features casts much light upon the character of his achievements, for it shows links within an apparently eclectic range of interests.

The content of this thesis will become clearer in and after the discussion (in the next section) of certain mathematical trends in Babbage's time, but some preliminary expansion on the word "algorithm" is necessary here. I intend it to refer, in a very general range of contexts, to ideas, theories, or procedures in which prominence is given to successive repetitions of a process or maneuver, its reversal, its compounding with other processes, and/or its substitution into itself. In mathematical contexts the words "iteration" and "combination" will also be used (and indeed, quoted).

In addition, two related notions have to be included. First, "algebra" refers both to the branch of mathematics in which Babbage worked (specifically, functional equations) and to certain features of algebraic thinking and proof which also arise elsewhere in his activities. Second, "semioti...