jp wrote: ↑Thu Sep 03, 2020 5:41 am
towforce wrote: ↑Tue Sep 01, 2020 9:52 pm
From what's written in the paper, it's not going to be easy to disprove any of the above 3 points. However, I read the whole paper as carefully as I could, and, unless I missed it,
there's actually no proof in there that in complex positions, it's impossible for rules to exist which can tell you quickly whether the game is won or not.
I'm not sure what exactly you mean by that.
You could hope that some subset of positions is easily solved. After all, we already know that we can set up easily solved positions. (e.g. given N & the piece content, you just set up a mate in 1.)
But if you mean simple rules that apply to every position on the NxN board, that's what the result has disproven.
First, second, third and last, I want to emphasise how grateful I am for having been given that paper to read. Once again, a VERY big thank you!
I have read it again (it's a lot easier the second time!), and what I said in
this post is actually exactly right (at the risk of immodesty, I'm giving myself a pat on the back for that, because I found the report confusing the first time I read it!).
What the paper
ACTUALLY proves is that, in worst case scenarios, the shortest path (minimum number of moves) from the current position to the end of the game, given an opponent who is trying their hardest to stop you, can grow exponentially in n on an n*n chessboard (I am not convinced that their case is watertight, but given that disproving it would take a lot of time, I'll grant that assertion as "maybe correct" for the purpose of this discussion).
However, the report makes a mistake: the authors assume that the only way to know that a position is won is to play the game out to checkmate. We all know that this is not true for all positions: there are some positions where rules will accurately tell you whether the position is won or not. The issue under dispute here is for what proportion of positions is is possible to determine whether the position is won by applying a rule. I'm afraid the report says nothing whatsoever about that.
It's completely fair to say, "the proportion of positions which can be evaluated accurately without building a game tree is higher than the proportion of positions which today's best evaluation functions (EF) evaluate accurately".
It's even completely fair to say that it would be possible to write an EF that would evaluate all positions accurately: the problem is, how big would that EF have to be?
I have reasons to think that the size of an "accurate EF" need not be as big as you would expect, and that working out what code to put in it is not an insoluble problem with today's technologies and techniques. I accept that other participants in this thread disagree with this opinion.
I apologise if this sounds negative or churlish: I emphasise again my gratitude for having been given access to that report - I am genuinely grateful!
Writing is the antidote to confusion.
It's not "how smart you are", it's "how are you smart".
Your brain doesn't work the way you want, so train it!