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

Harvey Friedman friedman at math.ohio-state.edu
Wed Feb 4 00:42:06 EST 2004

The following review adds greatly to my confusion.


On 2/3/04 11:26 AM, "Timothy Y. Chow" <tchow at alum.mit.edu> wrote:
> As I thinked
> I've mentioned on FOM before, generalized chess is EXPTIME-complete.  So
> in particular, there is provably no polynomial-time algorithm for solving
> generalized chess.  I regard this as prima facie evidence for option 2.

I think the readers will appreciate hearing about generalized chess, not
played on an 8 x 8 board, and the asymptotic computational complexity
surrounding it. However, the connection with what I was asking about/driving
at, is extremely remote.

I am inquiring about the nature of ordinary 8 x 8 chess

*as a scientific subject*

like topology, rigid body mechanics, macroeconomics, law, political science,
or geology. 

> There may be principles, heuristics, and approximation algorithms that
> capture a lot of what happens in chess, but there will always be a large,
> hard core of tactics that resists simple analysis.

The same is true of any of these other subjects mentioned above. A
foundational exposition of mathematics is not going to remove the need for
technical power in proving many important new results.

>Some other evidence in
> this direction: John Watson's excellent book "Secrets of Modern Chess
> Strategy" goes to great lengths to demonstrate that modern chess, at the
> highest level, explodes with examples where concrete possibilities
> override even the most tried-and-true general principles.  Watson's whole
> book is a treatise *against* the rather naively optimistic views about
> chess theory that many earlier commentators held.

I heard about this book, but don't know how such features should be put into

I don't expect that even some great new 8 x 8 chess theory that changes
forever the way top chess is played strategically, will tell anybody exactly
what the best move is in crucial positions without looking at ad hoc

However, a great new 8 x 8 chess theory could well tell us something new
about how to evaluate quiescent positions properly, and tend to make us be
on the winning side when ad hoc complications erupt.

So I can take the Watson view in different ways.

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.

> Consider also the endgames that have been solved exactly and whose correct
> solutions seem to defy explanation in conceptual terms.

I have long had some calibrated projects concerning this and related things,
but that is obviously a relatively well formed program of an obviously
scientific nature. 

Such things are obviously ripe for scientific research.

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!!
> These show that the EXPTIME-completeness result isn't just an asymptotic
> fact; serious complexities show up already on the 8x8 board.

Can you say something of depth about this matter?

> Having said all this, I do not think that it necessarily precludes 1
> and/or 3 from being true as well.  The fact that theoremhood in ZFC is
> undecidable, or that the existence of a proof of length n (expressed
> in unary) of a given statement is NP-hard, puts a bound on how much
> sense we can make of mathematics, but doesn't stop us from constructing
> lots of beautiful mathematics.  So in principle I think there could be
> such a thing as a "foundational exposition" of chess.

That's better!
> I don't think, however, that chess is "ripe" for such an exposition.

This I don't see. Maybe you offer this as a mere opinion.

> First let's see if we can find polynomial-time algorithms (or
> approximation algorithms) for restricted classes of endgames in
> generalized chess.  If we can't even do that, then I think it's far too
> ambitious to seek the "right" general principles for chess in general.

Again, I think that there is no relevance of this to the issue of ripeness
that I raise. 

Why chess?

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.

Harvey Friedman

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