Re: [computer-go] Search = Bad!

[Paul Pogonyshev <pogonyshev@xxxxxxx>]

Frank de Groot wrote:
> From: "Paul Pogonyshev" <pogonyshev@xxxxxxxxxxxxxxxxx>
>
> From your point of view, chess, Amazons and all other two-player
> deterministic board games with full knowledge should be solvable by
> ``pondering'' on fractals and deriving a ``magical'' mathematical
> formula that is easy to compute.  Somehow, I seriously doubt that's
> possible.
>
>
> As a naside, I am firmly convinced that the reason that comp. Go is in a
> slump is the ego of the Go players.
>
> You for example, are not interested in the idea of Go as a fractal, because
> it is not your own idea.

No, I'm not interested because I don't think it is an idea that will
bring anything of value and because I can see absolutely no way of
what to do with it (that, of course, may be a limitation of my own.)

> Therefore you assume that the person coming forward with the idea has a low
> intelligence.

That's simply not true.  Just coming up with a new idea takes certain
intelligence.  I just not happen to think it is a worthy idea, but then,
I can be proven wrong eventually, right?

> Thsi becomes clear from your allegation (confabulation) that I claimed that
> there was an "easy to compute" formula. I alledged that there was a
> formula. I never said it was "easy to compute".

I chose non-clear words here.  I meant a formula that can be computed
quickly.  For instance, in a year, which would be a tremendous improvement
over global search.

> My guess is that the formula would take infinite - 1 operations to computer
> perfectly (accurately), but that, for example, a hundred billion CPU cycles
> would be enough to keep withing the path that leads to victory, as long as
> you start woth a position that is already won.

Go board has a finite number of states and, finite number of possible
moves and possible games, even if extremely large.  I doubt you can
capture a _discreet_ regularity with continuous functions...

> And yes, I think all games I know of of full information are fractals and
> yes, I as a chess player think that the game of chess has nothing to do
> with capturing, king safety, pawn structure, development of pieces etc. but
> ONLY with navigating the fractal space.

But all the regularity of that space comes exactly from the rules of the
game.  You may happen to find a simpler restatement of them, reduce them
to simpler rules, but in the end you either take the tree/fractal of all
possible games as given, discarding all domain-specific knowledge, or
accept that this tree/fractal can be generated with game rules.

Let me rephrase your statement that Go is only about navigating fractal
space.  Consider the set of all legal Go board states, we'll name it B.
Let set M be the set of all moves (i.e. a set with 361 elements from
``A1'' to ``T19''.)  Finally let's introduce a function f : B -> M, that
will associate a move with every board state.  We'll call it a strategy.
Obviously, only those strategies that associate a legal move to each
board state are interesting.

Now, the set S of all strategies f : B -> M is finite.  What if I claim
that the game of Go is all about choosing a strategy f0 from S that will
generate the best possible move in every possible position?  How is this
``restatement of goals'' worse than yours?  Is it helpful in any way?

> The fact that Chess is simple enough that a surrogate method works (search
> with pruning, using heuristics for an evaluation function), is not proof
> that my opinion about this is incorrect.
>
> In comp. Go such a primitive and inefficient method will not work.
>
> I suggest finding & defining the regularity in Go-fractal space by
> pre-computing a few small board sizes and analyzing what the fractals have
> in common, then to derive a formula (I am bad at mathematics but this
> formula will be huge, it will have many variables and recursive or
> whatever, in any case it will take a terribly long time to compute).
>
> The really exciting thing about solving small boards is not that it "has
> been done" and a record has been broken, (time-wise or size-wise), the real
> interest lies in comparing the fractal space of ascending sizes and finding
> the regularities so that general rules can be derived for navigating that
> fractal space.

Maybe you should start with a simpler task.  Lay out all natural numbers
in a spiral like this:

                 <---- 13
               5  4  3 12
               6  1  2 11
               7  8  9 10

Now, if you paint all prime numbers white and the rest---black, you'll
notice certain regularity.  One could even call this a fractal, maybe.
How about finding a formula that, given number n, computes p so that
p is prime, p > n and for each k, n < k < p, k is composite?

To study regularity, you could, say, lay out 100 first numbers, then
1000 or 100000 of them.  Eventually something useful should turn up,
right?

Paul

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