# David Champernowne

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**David Gawen Champernowne**, (July 09, 1912 - August 19, 2000)

was an English mathematician, statistician and economist who picked a hole in John Maynard Keynes' General Theory of Employment, Interest and Money ^{[2]} and 'built a chess computer' with Alan Turing ^{[3]}, a long-time friend from the time that they were undergraduates together at King's College, Cambridge.

## Contents

# Champernowne constant

In 1933 David Champernowne had noticed and published a simple but new result about normal numbers, introducing the Champernowne constant formed by concatenating positive integers ^{[4]} ^{[5]} ^{[6]}. Kurt Mahler later showed it to also be transcendental ^{[7]}.

C10 = 0.12345678910111213141516... ^{[8]} ^{[9]}

It seems very possible that Turing's interest in the constructive definition of real numbers was stimulated by Champernowne's work, he took up this topic with some new results, and his manuscript notes were written on the back of the typescript of his 1936 paper *On computable numbers* ^{[10]} ^{[11]}.

# Turochamp

In 1948 Turing and Champernowne devised a chess playing program which they called Turochamp, which incorporated important methods of evaluation ^{[12]}. Champernowne later gave this description of Turochamp ^{[13]}:

Most of our attention went to deciding which moves were to be followed up. My memory about this is infuriatingly weak, Captures had to be followed up at least to the point where no further captures was immediately possible. Check and forcing moves had to be followed further. We were particularly keen on the idea that whereas certain moves would be scorned as pointless and pursued no further others would be followed quite a long way down certain paths. In the actual experiment I suspect we were a bit slapdash about all this and must have made a number of slips since the arithmetic was extremely tedious with pencil and paper. Our general conclusion was that a computer should be fairly easy to programme to play a game of chess against a beginner and stand a fair chance of winning or least reaching a winning position.

Turing started to code the Turochamp for Ferranti Mark 1 computer at Manchester University but he never competed the task.

# Round-the-house Chess

Quote from *First Law* ^{[14]}:

Turing played an important role in the development of computers in Britain. Together with his friend David Champernowne he invented "round-the-house" chess: after you move, run around the house, if you get back before your opponent's move you are entitled to a new move.

# Selected Publications

- David Champernowne (
**1933**).*The construction of decimals normal in the scale of ten*. Journal of the London Mathematical Society, Vol. 8, p. 254-260 - David Champernowne (
**1969**).*Uncertainty and estimation in economics*. Holden Day, ISBN-13: 978-0050020067 - David Champernowne, Frank Cowell (
**1998**).*Economic inequality and income distribution*. Cambridge University Press, ISBN-13: 978-0521589598^{[15]}^{[16]}

# External Links

- D. G. Champernowne from Wikipedia
- David Gawen Champernowne, 1912-2000 from The History of Economic Thought
- David Champernowne - The Mathematics Genealogy Project
- Obituary: David Champernowne by Brian Reddaway, The Guardian, September 01, 2000
- Professor David Champernowne, obituary by M. Hashem Pesaran, The Telegraph, September 04, 2000
- David Champernowne (1912-2000), ICGA Journal, Vol. 23, No. 4

# References

- ↑ David Gawen Champernowne, 1912-2000 from The History of Economic Thought
- ↑ Mauro Boianovsky (
**2000**).*Some Cambridge reactions to The General Theory: David Champernowne and Joan Robinson on full employment*. pdf - ↑ Professor David Champernowne, obituary by M. Hashem Pesaran, The Telegraph, September 04, 2000
- ↑ David Champernowne (
**1933**).*The construction of decimals normal in the scale of ten*. Journal of the London Mathematical Society, vol. 8, p. 254-260 - ↑ An easy-to-make sequence that fooled random number checkers
- ↑ All Possible Digital Music By Definition « CHIPFLIP
- ↑ Kurt Mahler (
**1937**).*Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen*. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Ser. A. 40, p. 421-428 - ↑ sequence A033307 in OEIS
- ↑ Champernowne constant - OeisWiki
- ↑ Alan Turing (
**1936**).*On computable numbers, with an application to the Entscheidungsproblem*. pdf - ↑ Alan Turing Scrapbook - Turing Machines - Normal Numbers and the typescript of On Computable Numbers
- ↑ David Champernowne (1912-2000), ICGA Journal, Vol. 23, No. 4
- ↑ Chapter 16, Introduction on 'Chess', in Alan Turing, Jack Copeland (editor) (
**2004**).*The Essential Turing, Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, and Artificial Life plus The Secrets of Enigma*. Oxford University Press, amazon, google books - ↑ Numb3rs 517: First Law
- ↑ Economic inequality from Wikipedia
- ↑ Income distribution from Wikipedia