@Optimissed, firstly, no, I am not stating my "opinion", any more than I would be expressing an opinion if I said that 1+1 is not 3, but is 2. The mathematical sciences are not made up of a set of opinions, they are made up of a set of things that are known to be true. Note that it is not only not an opinion, it is also not "mine". I am communicating what is known.
Are you familiar with the concept of a proof? Are you aware that a weak solution of a game is a proof of the game value? If you look at a paper on the first part of the solution of checkers, you will see a reference to the proof tree (which is the analysis that rigorously proves the result from a given position, by reaching a position with known value at the end of every line). A proof tree does not just deal with opponent moves that seem playable, it deals with all LEGAL opponent moves, because proofs are rigorous.
I am actually rather sure that you understand that @tygxc uses heuristics (vague positional understanding and rough rules) and empirical evidence (game results and unreliable evaluations) to support a conjecture, then describes this as "solving chess". You have drawn attention to this on occasion.
The real discussion between you and tygxc is on a higher level ... on a kind of meta-judgemental or interpretational level. You are stating what is known in the context of your approach to mathematics, which is that of a mathematical purist. tygxc is attempting to state what is known to him, as a scientist-pragmatist. One approach is not "better" than the other.
Yes, ty uses heuristics and they may not all be good. I'm equally sure that there is no possible solution of chess via mathematics. The only possibility is via a more pragmatic, scientific approach. You may disagree with that and you may not like it but I am also stating what is known, by a different process of "knowing" than the deductive one you prefer. All deductive judgements must still be judged to be appropriate and that's where the assumptive thinking may lurk for those who think that syllogistic logic is a be-all-and-end-all.
We're not in much disagreement. There does exist a "mathematical" (i.e. rigorous) solution algorithm - a computer program that would solve chess if it had the resources. It's just impractical to execute.
To be clear, the solution of checkers qualifies as such a mathematical solution, because it was designed to be rigorous and to reach certainty, not an approximation to this.
@12397
"I am not stating my opinion" ++ You are imposing your interpretation. Using some CAPITALS does not make you right. Besides, laughing or insulting are no valid ways of proof.
No, the meaning of proof in the mathematical science is not "mine" or an "opinion", The meaning of "weak solution" in the study of combinatorial games is not "mine" or an "opinion". It's a defined term.
"mathematical sciences are not made up of a set of opinions, they are made up of a set of things that are known to be true." ++ No. The Riemann hypothesis, Goldbach's conjecture and many more are assumed to be true but not yet proven. Ramanujan was famous for producing theorems without proof and claimed a Hindu Goddess told him in his dream.
No. These are not ASSUMED to be true, they are CONJECTURED to be true. Every competent person understands the difference. There is a large class of work in the field that is CONDITIONAL on the truth of the Riemann Conjecture. These results are not proven, they are proven to be true IF the Riemann conjecture is true. Very big difference.
It is very odd that you suggest Ramanujan's conjectures were theorems. A theorem is a proven result, not a conjectured one. Ramanujan was well aware of the difference.
"Are you aware that a weak solution of a game is a PROOF of the game value?" ++ Are you aware that a weak solution of a game is unnecessary for an ultra-weak solution? Example: Hex.
Of course I am. Are you aware that is irrelevant to chess, since there is no ultra-weak solution (nor a hint that one might be found)?
"@tygxc uses heuristics" ++ I use Chess knowledge.
Yes, in addition, you are unaware that chess knowledge of the type you mean is DEFINITELY heuristics.
That is allowed:
It's a free world: you can make as many blunders as you like. Just like in chess.com games.
'Next to brute-force methods it is often beneficial to incorporate knowledge-based methods in game-solving programs.' Games solved: Now and in the future
Now find one competent person who suggests that such methods can be used to solve chess!
"empirical evidence (game results"
++ Yes, 110 draws out of 110 games in the ICCF WC Finals, at average 5 days/move with 2 servers of 90 million positions per second, the strongest chess on the planet.
Yes, empirical evidence. (A tiny amount)
"and unreliable evaluations" ++ No. The 110 ICCF WC Finals games link the initial position to reliably known drawn positions in average 39 moves and in a redundant way.
Stockfish gets the evaluation fatally wrong in a huge number of 7 piece tablebase positions and blunders frequently playing itself in such positions.
What oracle are you using to check its evaluations in much more complex positions?