[FOM] Re: Is Chess ripe for foundational exposition/research?

[Timothy Y. Chow]

Harvey Friedman wrote:
> This is an example where there are massively powerful intellectual
> intuitions. Of course they are fallible, and they get mixed together
> with tedious special calculations. But the analysis of powerful
> intellectual intuition seems to be of fundamental importance. Chess
> looks to be a rather attractive place - not the only attractive place by
> any means - to perform such an analysis.

If all that is required for a subject to be "ripe for foundational
exposition" is that there exist powerful intellectual intuitions, then
sure, chess is ripe.  Chess was ripe four hundred years ago, for that
matter; people had powerful intellectual intuitions back then.

I personally think that "powerful intellectual intuitions" by themselves
aren't enough.  It is my ("mere") opinion that, at minimum, one needs to
be able to *evaluate the correctness* of some of those intuitions in a
relatively objective and definitive manner.  Otherwise, all we'll get is
a proliferation of mutually inconsistent "foundational expositions" with
no way to adjudicate between them.

Chess is not at that stage.  I don't know what confuses you about Silman's
review of Berliner; is it that Silman and Berliner disagree?  But this is
the norm in chess.  One grandmaster confidently dismisses "f3?" as a dud;
another grandmaster wins a high-profile game with it, and it becomes
"f3!".  For a long time grandmasters regarded K+Q versus K+R as trivial;
then Belle came along with a complete analysis and bamboozled the
grandmasters.  Andy Soltis, in a column reprinted in the anthology "Karl
Marx Plays Chess," gives plenty of examples of opening lines that were
definitively rejected by top players only to be revived by the next
generation.  This tendency shows no signs of abating.

The only method of definitively settling these debates is exhaustive
tactical analysis, which in spite of advances in computer technology
still leaves most of chess untouched.

> 1. The real powerful principles are more subtle than the ones people
> have been able to carefully enunciate. The super GM's know or at least
> feel great powerful principles/theory that nobody but they can carefully
> enunciate, and they either can't or don't want to do the hard work
> necessary to do it.
>
> 2. There are no real powerful principles except the ones people have
> been able to carefully enunciate, and they have limited application.
> Their utility and power have been exaggerated. The situation will not
> change. The super GM's are simply better athletes.

Watson leans towards 2.  I can't summarize the entire book in a few
sentences, but part of the reason for thinking that the super GM's are
better athletes is that post-mortem analysis of their winning games almost
always reveals that the win was due to something mundane---superior
opening preparation, lower rate of calculational errors, greater mental
toughness, and so on.  I can't think offhand of a practical example that
is like the solved endgames---where both sides maneuver *inexplicably* in
an apparently level, quiet position for dozens of moves with no
discernible mistakes but gradually the position becomes hopeless for the
losing side.  Typically the grandmasters will rely on a rather simple
statement about what the winning chances consist of, if there are any
winning chances, and it's a matter of concrete variations whether the
winning chances can be converted into an actual win.

Watson might be wrong of course; maybe 1 is true.  If super-GM's were
able, for example, to play the 6-piece endgame that I posted previously
nearly perfectly, without memorizing gigabytes of variations and without
being able to articulate carefully what strategic principles they were
following, then I would consider this strong evidence for 1.  (Of course,
they can't.)  Or if the super-GM's did not bother with extensive opening
preparation or studying thousands of current games, that would also be
some evidence towards 1.  Indeed, in the past, Capablanca got away with
doing very little opening preparation, but that was because none of his
opponents did that much of it either (by modern standards).  That approach
just doesn't work any more today.

> But I was talking about much more subtle matters concerning ordinary 8 x
> 8 chess (or extraordinary 8 x 8 chess!), for which ripeness is not at
> all clear. It is also not at all clear what kind of dues need to be paid
> even to find out how ripe it is! And above all, not clear whether these
> dues are worth paying!!

O.K., so maybe we are quibbling over the word "ripe."  I don't see how a
subject can be ripe without its being clear that it is ripe.  If it's not
only unclear whether something is ripe but it's also unclear what it would
take to determine whether it is ripe, then the word "ripe" is surely the
wrong metaphor.

Let me make a more positive suggestion.  Othello is closer to what I think
of as being "ripe."  If you have Windows, you can download WZebra.

  http://www.nada.kth.se/~gunnar/download.html

There is, or used to be, a beefed-up version of WZebra called simply Zebra
that ran on a fast processor and learned from its mistakes and so on.
Zebra, or probably even WZebra, is incomparably stronger than the
strongest human beings.  A much weaker predecessor of Zebra called
Logistello won a match with the human world champion (in 1997 I think)
by a score of 6-0.  People have learned from the computer programs, so
humans are stronger today than they were in 1997, but even so, it is so
thoroughly accepted that the computers are better that nobody even
bothers having human-machine contests any more.

So, we have a tool that gives us relatively definitive assessments of
positions.  For positions with at most 35 empty squares or so, it gives
us exact assessments through exhaustive search.

On the other hand, Othello is far from being "solved" in the strict sense.
So there is still room for analysis.  For example, one concept that is
recognized by practical players as being enormously important in the
endgame is "parity," or the opportunity to make the last move in each
unoccupied region of the board.  This is strikingly suggestive of
combinatorial game theory (especially because many Othello positions
are "cold" in the sense that neither player wants to move).  I asked
David Wolfe if he was interested in looking into this, and he spent some
time on it.  Unfortunately, tactical complexities made it difficult to
make progress.  But I still think there might be something there that is
ripe for foundational analysis.

Tim