(urth) Travelling North aka miscellaneous thoughts on Wolfe

[Adam Thornton]

On Jun 10, 2010, at 6:46 PM, Jeff Wilson wrote:

> 
> There is a mathematical comcept analagous to this called surreal numbers, invented about 1976 and covered in some popular science literature, and the notation employed used a metaphor similar to Zeno's paradox, of traveling an infinite distance in one direction, then one step more, and mapping this additional distance to the side, and repeating that ad infinitum, producing not just a new dimension but all kinds of mathematical structures with suggestive names like transfinite ordered fields that could easily be an influence on the imagery of Yesod.

Invented earlier than that....in 1970 or so (at least, those are the first lectures) by John Horton Conway, whom you may know from the mathematical recreation "The Game Of Life".  Notable because its moniker and first publication came from Don Knuth, who of course is most famous for his Mad Magazine article, "The Potrzebie System of Weights and Measures" (his subsequent career at Stanford University has also been of some minor interest), and is unusual--perhaps unique--for the first public appearance of a mathematical theory in that it is presented in the form of a love story.  That novella (1974) is entitled _Surreal Numbers_ and is still in print, should you wish to order a copy.  The theory is worked out in a more traditional form in Conway's _On Numbers and Games_, published in 1976 and with a second edition in 2001.

It is the most beautiful example of bootstrapping something from very nearly nothing that I know. 

The Wikipedia article at http://en.wikipedia.org/wiki/Surreal_number is a pretty good introduction, but I can't recommend _ONAG_ too highly.  And the "On Games" part?  Well, not to give it away, but a game is a number with certain of the definitory conditions relaxed; it turns out that both numbers and games-which-are-not-numbers (numbers are all games, but not vice-versa) can be used as descriptions of positions in a certain class of what-we-commonly-call-games, namely those in which there are two players, both have perfect knowledge of the game state, and there is no random element.  You can prove all sorts of interesting things with this theory.

Also: regarding Brunians' airship design, I demand that he grow long white whiskers, as it is now impossible for me to visualize him as anything other than the White Knight.  I wonder whether he balances very badly when sliding down pokers.

Adam
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