Re: Transactions: good or bad?

"Costin Cozianu" <c_cozianu_at_hotmail.com> wrote in message news:bcsqv8$n2di8$1_at_ID-152540.news.dfncis.de...
> Mikito Harakiri wrote:
> > "Bob Badour" <bbadour_at_golden.net> wrote in message
> > news:Li5Ia.137$vn2.18732148_at_mantis.golden.net...
> > > Where is your proof that all chess games halt? After all, your
assertion
> >
> >>that chess games are finite depends on just such a proof.
> >
> >
> > I beleve there is a chess rule that if position is repeated, then the
game
> > is draw. It is quite obvious that the chess game is finite, then.
> >
> >
>
> I'm amazed that somebody is still following this rant.
>
> However, one of the players have to ask for the draw, it's not a draw
> automatically. There are other similar draw conditions that prevent
> anyone players from being exposed to unnecessary burden.
>
> Bob's claim however was a straw-man even in the absence of those rules,
> because a chess playing game can *prove* if a position is techincally
> winnable by white, or by black, or it is draw (therefore effectively
> calculating a proof in the formal system established by the rule of
> chess), simply by exhaustively applying the min.-max. recursive
> algorithm over the *finitely many* positions of chess.

Your assumption is that no position will ever repeat. If a position repeats, the game will loop indefinitely. You still have not proved that all chess games will halt.

> A theorem prover for a formal system at least as powerful as to encode
> basic arithmetics (therefore also subject to Godel's theorem) does not
> have a finite space to search for and come up with the next best "move"
> (meaning the next best derivation rule to apply on the way to
> constructing the proof). While establishing a proof is effectively
> coming up with the next best move, because for each step of the rule we
> have a next inference rule to apply.
>
> Given that they search in a game with an infinite space, programs have
> to decide whether evaluating a particular branch will be successful,
> without actually going on the branch (because branches are not
> guaranteed to be finite). It is there where they hit the halting problem.

As do humans.

> Evaluation branches in chess are always finite, even if games may be
> infinite,

Nobody asked you to prove that an evaluation branch halts. For your assertions to have validity, you must prove that the entire game halts. The evaluation branch for a turing machine is trivial compared to the evaluation branch for a chess game, and yet turing machines still have the halting problem.

> because the minute you encounter a previous position you no
> longer need to explore the branch.

This, however, won't prevent the game itself from looping endlessly. You still have not met the burden of proof.

> In practice it has been proven that performing an exhaustive search over
> the space bounded by a certain depth of analysis (let's say 20 moves,
> well beyond the reach of a human player) is statistically more than
> enough to approximate the perfect evaluation function in quite many
> position. Still human players get to beat chess programs simply by their
> better intuition.

In other words, your entire position relies on the magic of the ghost in your machine.

> The same way, mathematicians rely on intuition to know where to look for
> a proof, just like a 6 year old gets to recognize hand written
> character "automagically" (including taking the context of the phrase
> into account, the language) while there's no scientific theory to allow
> us to conclude that computers can do the same.

Again, more magic.

> Yet, there's this philosophical belief of some people, that we can
> encode this "intutition" factor as a computable function. That's insofar
> completely unsupported.

What's insofar unsupported is the extistence of "intuition" in the first place. You have some faith in its existence, and I do not. Received on Thu Jun 19 2003 - 20:52:08 CEST