[FOM] Is Chess ripe for foundational exposition/research?
friedman at math.ohio-state.edu
Mon Feb 2 18:15:29 EST 2004
A top human player combines impressive tactical power with deep positional
understanding. But what is this positional understanding?
I was intrigued by the writings of at least the former over the board World
Champions Emanuel Lasker (also did some algebra and I think, wrote about
philosophy of math, I think) and Max Euwe (at least a Ph.D. in mathematics),
and the contemporary former correspondence World Champion Hans Berliner
(retired Research Associate in CS at CMU, in artificial intelligence), all
three of which proclaimed the absolute (or near absolute) power of general
principles, and wrote works that present general principles. Hans Berliner
comes very close to asserting that adherence to the highest general
principles "solves" chess, in the sense of producing a forced win for White.
I could not quite wrap my brain around these "foundational" works in chess.
It seems that there are often competing general principles that apply to a
given position, and a top player will pick the right one to apply. So I
always looked for even higher general principles that allow me to select
among the competing lower general principles. My initial hope was that Hans
Berliner solved this problem with the right highest general principles, but
I wasn't able to see my way through that.
So here are some possibilities concerning the "true" situation in chess. I
don't have a clue as to what is the case. I know that there are some really
strong over the board and correspondence chess players on the FOM email list
who would know much better than I.
1. There is a steep learning curve of technicalities that are largely
tactical in nature. One FIRST has to be able to easily see this surface
stuff as second nature in real time - perhaps the kind of thing that a
computer program sees instantly. If one has this fundamental tactical
competence - say at the level of an average grandmaster - then chess assumes
the nature of a rich mathematical science, where fundamental principles and
the creative imagination take over, in much the same way that they do in
mathematical science. There is room for spectacularly innovative and deep
new theories, which can at least be productively applied at the very slow
time limits of correspondence chess, and also in opening theory research.
There is a great need and great opportunity for foundational exposition -
just as there is in mathematics, physics, economics, law, probability,
statistics, etc. But the real audience for this is at the grandmaster level.
There is nothing to do at a serious professional level for chess theory
unless one is steeped in a truly MAJOR amount of chess experience. There is
hope for great insights of general intellectual interest in chess, if one
has paid an ENORMOUS amount of dues - but hopeless otherwise.
2. On the contrary, there are only general heuristics - even for the
absolutely top players - which compete for application in crucial chess
positions. Specific tactics rule, and great chess - even in the hands of the
greatest players - is principally a matter of ad hoc deep analysis, centered
around accidental tactical factors, together with a deep knowledge of the
competing general principles (flawed, with limited applicability), and great
experience and concentration. There is no hope for great insights of general
intellectual interest in chess, even if one has paid an enormous - even the
highest - amount of dues.
3. A third possibility, of course, is that what I had hoped for and came to
believe - at one time - through the writings of E. Lasker, M. Euwe, and H.
Berliner, and others, is actually true, and that we don't need any massive
amount of chess experience to get to the foundationally interesting chess
matters. The way this could be reconciled with other "data" is
i) the books these three wrote are a good draft of foundational exposition,
but they are just not sophisticated enough, foundationally. The real most
fundamental principles are not stated at all, or at not stated with
sufficient clarity and power. The situation is like mathematics before
epsilon/delta, or mathematics before f.o.m. E.g., mathematicians at one
point knew how to write rigorous proofs and evaluate other's proofs for
rigor, but couldn't give the right general principles of rigorous proof
ii) the current grandmasters fall into two classes:
a) those who aren't strong enough to really understand the right most
general principles, and got where they are - not quite at the top - on solid
intuition and stunning tactical ability, but no more; and
b) those at the top who know, or at least feel, the right most general
principles, and could articulate them - particularly with the help of
"logicians" or even logicians, BUT CHOOSE NOT TO, since it is not to their
chess advantage. In addition, such foundational exposition is viewed as
being difficult do, and too time consuming for their busy chess life.
If item 3 is true, then it might be very interesting to see what would come
from collaborative efforts by very top players and appropriately deep
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