Thursday, January 04, 2007

Better 10 Axioms Than 1000 Rules

My last post was about proving endgame rules by deducing them from endgame axioms. Interestingly, Dan Heisman, in his last column of 2006, has brought up the same idea. He says that chess axioms are basically common sense and that most chess rules can be simply proven by reducing them to the axioms. DH cannot deny that he is a mathematician.

I like his idea very much. Just two examples.

Axiom 1: Knights are slower than Bishops. Axiom 2: A positional move should maximize the gain in activity. Rule: Move Knights before Bishops in the opening. Prove: A fast piece on his home square is better than a slow piece on his home square, therefore, a Knight gains more activity with his first move than a Bishop. Of course, this holds only if no tactic (safety issue) is involved.

Axiom 1: An inactive piece is better than a lost piece. Axiom 2: Tactics is about piece safety, strategy (positional play) is about piece activity. Rule: Think first tactics, then strategy. Prove: Events like the Kramnik mate-in-one blunder.

It is worth reading Dan Heismans column, because he gives many other examples.

2 Comments:

At 5:49 PM, Blogger Mousetrapper said...

Here is DHs comment on my post (he has no blogger account and sent it by email):

Thanks! I read the blog. Yes, a good source of insight, but probably
impossible from just the two axioms I used. Maybe if you started with a few
more.

Two comments on your blog:

1) the principles are derived from the axioms, not "proven by reducing them
to the axioms"
2) I would not say an axiom is that a positional move should maximize the
gain in activity. I would say that an axiom would be you want to make your
pieces as good as possible. From this we can say that having more activity
is good, so therefore one positional guideline is to make your pieces as
active as possible.

Yes, my B.S. is in Math, my Masters in Engineering. :)

Happy New Year.

Regards,
Dan H

 
At 7:40 PM, Blogger Temposchlucker said...

Interesting idea's. Axiom 3, never trust Zenmaster Larsen when he says a problem is positional:)

 

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