Sunday, 26 October 2008

Searching for Snarks




The happy band of mathematical warriors above joined me on Thursday night as we set out to the Center for Mathematical Sciences at Cambridge. Our quest was to discover all that Emeritus Gresham College Professor of Geometry Robin Wilson might know about "Lewis Caroll in Numberland." The lecture, which can only be described as "math-lite" was entertaining none the less, and made even better by the good companions who joined me.

Wilson is also, not by coincidence, the author of a book on the topic that is soon to be released in the US (and can be purchased in advance from Amazon at a healthy discount) entitled, Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life.

Wilson explained that if Dodgeson (the real name of Lewis Carroll) had not written the "Alice" stories for which he is so well remembered, he might well be remembered for being one of the pioneering child photographers of the 19th century. And if he had not done either, he might be remembered as an accomplished mathematician and teacher who made contributions in the areas of Logic, algebra, geometry, and the mathematics of elections. Wilson points out that:
"Yet another interest of his was the study of voting patterns. Some of his recommendations were adopted in England, such as the rule that allows no results to be announced until all the voting booths have closed. Others, such as his various methods of proportional representation, were not. As the philosopher Sir Michael Dummett later remarked:

It is a matter for the deepest regret that Dodgson never completed the book he planned to write on this subject. Such was the lucidity of his exposition and mastery of this topic that it seems possible that, had he published it, the political history of Britain would have been significantly different."

He also credits Carroll with the invention of the modern method of seeding tennis matches:
Another interest of Dodgson's was the analysis of tennis tournaments:"At a lawn tennis tournament where I chanced to be a spectator, the present method of assigning prizes was brought to my notice by the lamentations of one player who had been beaten early in the contest, and who had the mortification of seeing the second prize carried off by a player whom he knew to be quite inferior to himself.
Let us take sixteen players, for example, ranked in order of merit, and let us organise a tournament with 1 playing 2, 3 playing 4, and so on. Then the winners of the first round will be 1, 3, 5, and so on; those of the second round will be 1, 5, 9 and 13; the final will then be won by player 1, defeating player 9 who wins the second prize but actually started in the lower half of the ranking.
To avoid this difficulty, he managed to devise a method for re-scheduling all the rounds so that the first three prizes go to the best three players, which presaged the present system of seeding.

For a brief discription of some of his work in Logic diagrams see My page here and for A different version of the Wilson's talk on Lewis Carroll given at Gresham College, look here

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