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:

> At 1:16 PM -0700 10/25/97, Chris Bogart wrote:
> >On Sun, 26 Oct 1997, HACKER G N wrote:
> [snip]
>
> >> But in terms of actually making the distinction at all, you don't need a
> >> language to do that, you just make the distinction. What a language can do
> >> is find a convenient way of expressing that distinction to others.
> >
> >For me at least, though, it could help me think about the matter more
> >smoothly, and therefore more quickly or more often, at least within a
> >certain category of thinking.
> >
> >This is all very theoretical -- I have no idea how I could ever prove this
> >to myself for sure, much less anyone else.  But I suppose that's an
> >inherent problem when discussing something as immeasurable as "thought".
>
> 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".
>
> Other practical cases of great interest are recounted by Oliver Sachs in
> "The Man Who Mistook His Wife for a Hat." The most interesting for this
> discussion is the artist with achromatopsia. Due to neurological damage, he
> lost not only the ability to see colors, but all memory of what colors
> looked like. He could still describe colors by name and by Pantone matching
> number. It turned out, however, that his knowledge of color went no further
> than names and numbers. All the rest of his understanding of color was
> lost.
>
> The point is that language by itself does not provide the means for
> thought. Language and other mental abilities have to work together so that
> the language refers to something--a memory, a mental model, or whatever,
> which we hope is connected to reality--and the user can work in the
> language or the concepts or both, whichever is more appropriate at the
> moment.

This seems a well-balanced view. So there is thought which is more
language-oriented and thought that is more concept-oriented, and you
switch from one to the other as need be. Fair enough.

Geoff