Re: SWH again (was Re: What's going on here?)

[HACKER G N <c9709244@ALINGA.NEWCASTLE.EDU.AU>]

> On Sun, 26 Oct 1997, Edward Cherlin wrote:
>
> > A practical example is Conway's recent recasting of the theory of games in
> > terms of extended non-standard arithmetic. A number is defined as an
> > ordered pair of sets of numbers, where each member of the Left set is less
> > than each member of the Right set. A game is an ordered pair of sets of
> > games, without restriction. Both constructions begin with the number 0 = {
> > |  } in which both Left and Right sets are empty. Then { 0 |  } is a number
> > (1), { 0 | 1 } is a number (1/2), and { 0 | 0 } is a game (*). This game *
> > is infinitesimal, and neither greater than 0, less than 0, or equal to 0.
> >
> > Using this theory, Elwyn Berlekamp, a middle-level amateur, is able to
> > create Go positions in which he can routinely beat the top players in the
> > world with either color. He thinks in the new language (up, star, tiny,
> > miny...), they think in the traditional language of Go (sente, gote...) and
> > he wins, over and over.
> >
> > The concepts cannot be explained in the old terminology, and the
> > distinctions cannot be made without the new terminology. You can think of
> > making one distinction at a time without new language, but not the hundreds
> > required to use the new theory of Go endgames. See "Mathematical Go
> > Endgames: Nightmares for Professional Go Players" by Berlekamp and Wolfe,
> > for details. ISBN  0-923891-36-6. There is also a hardcover edition under
> > the title, "Mathematical Go: Chilling Gets the Last Point".
> >

As a further reflection on this, it will be interesting to see whether
anyone can come up with an application of Lojban that results in improved
thinking in a certain field or activity - let alone one that produces
results as dramatic as this! :)

Geoff