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Technology and Mathematics pp 79–106Cite as

Mathematics and Mechanical Computation

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Part of the book series: Philosophy of Engineering and Technology ((POET,volume 30))

Abstract

The interplay of mathematics and machine is explored through early physical aids from pebbles to the ‘analytical machines’ of the nineteenth century. The earliest speculations on the nature and potential of computing machines are traced through the work of Charles Babbage for whom calculating engines represented a new technology for mathematics. Babbage’s Analytical Engine, a mechanical embodiment of mathematical analysis, and his Mechanical Notation, a universal language of signs and symbols, are described. Ideas prompted by the intersection of mathematics and machine are discussed: the physicalisation of memory and the implications for coding, algorithmic programming, machine solution of equations, heuristics, computation as systematic method, halting, and numerical analysis. A brief Epilogue links this material to the modern era.

what cannot be investigated and understood mechanically, cannot be investigated and understood at all – Thomas Carlyle (1829)

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Acknowledgement

This work is supported in part by the Leverhulme Trust.

Picture Credits:

Illustrations:

2, 5, 7 – Science Museum/Science and Society Picture Library

1a, 1b, 3, 6, 8 – Doron Swade

4 – Rainer Glaschick

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Authors and Affiliations

  1. Department of Computer Science, Royal Holloway University, London, UK

    Doron Swade

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  1. Doron Swade
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Correspondence to Doron Swade .

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  1. Division of Philosophy, Royal Institute of Technology (KTH), Stockholm, Sweden

    Sven Ove Hansson

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Swade, D. (2018). Mathematics and Mechanical Computation. In: Hansson, S. (eds) Technology and Mathematics. Philosophy of Engineering and Technology, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-93779-3_5

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