I don't believe many of you understand Chris's point. He is saying
that "in principal" the game is solvable. Chris isn't stupid - he
doesn't think it's simple and I knew as soon as he posted it that
everyone would jump on this with their analysis about the size of
the universe and such - the old cliche stuff.
Most science doesn't concerns itself with our perception of things
or the age of the universe, etc. It doesn't care how fast a
computer is or how fast it should be unless you define it as such.
The game is solvable in a theoretical sense. We have a procedure
that can solve it and that procedure is correct.
I would also like to say that you don't really know how long the
universe will last - we have theories that try to predict it and
we have estimates, but they are just theories. We are like
babies in trying to understand how the universe works.
Even so, it doesn't matter how long the sun will last or how
large the universe is or when it will burn out.
There has been a lot of analysis with GO endgames, breaking
them into sub-problems. A much more sophisticated version
of this may yield numbers a few orders of magnitude better
than you are calculating. There may be other techniques
that even make a full solution possible with highly advanced
computers and computer techniques of the future that we can
only dream about now.
- Don
On Fri, 2007-01-12 at 15:57 -0200, Mark Boon wrote:
>
> On 12-jan-07, at 14:16, Chris Fant wrote:
>
> > Plus, some would argue that any Go
> >
> > already is solved (write simple algorithm and wait 1 billion years
> >
> > while it runs).
> >
>
> To 'solve' a game in the strict sense you need to know the best answer
> to every move. And you need to be able to prove that it's the best
> move. To do so you need to look at the following number of positions
> AMP^(AGL/2) where AMP is average number of moves in a position and AGL
> is the average game length. If I take a conservative AGL of 260 moves,
> we can compute the AMP from that, being (365+(365-AGL))/2=235 So we
> get 235^130, which is about 10^300 as a lower bound. The upper bound
> is something like 195^170 (play until all groups have 2 eyes) which my
> calculator is unable to compute, but I think it's roughly 10^400. I'm
> guessing it's questionable whether we'd be able to compute that even
> with a computer the size of this planet before the sun goes out.
> Distributing the work over other planets or star-sysems will only help
> marginally due to the time it takes to send information to Earth by
> the speed of light. So I'd say it's impossible.
>
>
> Mark
>
>
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