[FOM] AI Challenge

[Walt Read]

Harvey:

Challenges can be fun for the thought and discussion they generate.
But this challenge seems to have too many under-defined ideas as
posed. In particular, "behave like a real mathematician", "not the way
we do them" and maybe especially "strategy". It's not clear just what
I would have to come up with to meet the challenge. Would I have to
demonstrate somehow that the "computer" had (implicitly? explicitly?)
used the "mathematical theory" as described by Wikipedia?

But before we can get to that question, we have to ask how the game is
going to be defined to the computer.

1. Will it be given a large number of examples (training set) with
criteria for success and be expected to perform successfully on new
examples (test set)? You suggest that that's not like a real
mathematician (but using at least some examples is important even to
real mathematicians) though you allow it as a possibility later. It's
also what most people do most of the time to learn and have been doing
throughout human history. (I recently spent a week playing samba
reggae and maracatu at California Brazil Camp and the music directors
routinely "taught" by playing examples until we were able to copy
them.)

2. Will it be given a set of rules and be allowed to explore
possibilities through, perhaps, exhaustive search? And perhaps with
some obvious heuristics?  Any constraints (time, depth) on the search?
Bounded search is probably how most games are played most of the time
and probably how this was originally played.

3. Will it be given either rules or criteria for success and a set of
definitions/basic strategies/whatever as heuristics (and maybe a few
examples?) and be expected to mutate these into better heuristics?
Maybe basic definitions as in AM or extremely general heuristics as in
GA-type classifier systems? This sounds the closest to what you have
in mind.

Maybe it could be given whatever heuristics people used (the game
seems to be ancient) before the mathematical theory was discovered and
asked to take the further steps. That would seem to be close to what
real mathematicians do.

To succeed by any of these means, will it have to describe the
calculation as we would? Getting the computer to use the standard
"winning strategy" that we're familiar with is almost certainly a lot
easier than getting it to explain how it solved the problem or to
write out a human-oriented rule that would allow other people to
implement the strategy in their own wetware. For it to reproduce, say,
the description in the Wikipedia article, it's going to have to have a
basic set of words and rules for combining them. But it could be
implicitly using the same rule implemented as connections in a neural
net or as heuristics in a classifier system. And that might be our
wetware version of your math.

-Walt