Except that there are a single or small set of moves that are objectively "best" in each position, so the subjective is not really meaningful.
Except that the subjective is nearly always meaningful.
Except that there are a single or small set of moves that are objectively "best" in each position, so the subjective is not really meaningful.
Except that the subjective is nearly always meaningful.
A perfect game has never been established to have happened.
It is not known whether such a game would be a draw.
And both of those facts arise from another fact.
And that fact is that chess has not been solved.
Morocco sounds plausible to me.
I completely forgot about Spanish Sahara. You just reminded me.
A perfect game has never been established to have happened.
It is not known whether such a game would be a draw.
And both of those facts arise from another fact.
And that fact is that chess has not been solved.
Let's agree to differ then. I think it's been solved. According to the poor nomenclature which the poor theorists are forced to use, it's been ultra-weakly solved. We could call it "strategically solved" or maybe something pseudo-clever like "initial-value solved".
My reasoning is that there are theoretical reasons (which I worked out and I think others have reached the same conclusions) which back up the absolute lack of evidence for chess being anyhing but a draw. But there's a further problem, too. If, somehow, chess were found to be something else, such as "a win for white", how could we actually trust that solution? There could be errors in the solution that would never be found and it may even be impossible to find such errors within thousands of years. Or millions, even. Setting an almost infinite set of calculations going is one thing but checking them and working out a proof that they show chess to be one result or other is mind-bogglingly problematic. For that matter, how can it be known that the results haven't been sabotaged? So you see, a deductive proof in the fashion that Elroch demands is impossible, not merely improbable. We have to go with scientifically based proofs instead.
Oh, and scientific proofs are basically "according to all the evidence we can muster, supported by the coherence of whatever theory we are capable of devising".
A perfect game has never been established to have happened.
It is not known whether such a game would be a draw.
And both of those facts arise from another fact.
And that fact is that chess has not been solved.
Let's agree to differ then. I think it's been solved. According to the poor nomenclature which the poor theorists are forced to use, it's been ultra-weakly solved. We could call it "strategically solved" or maybe something pseudo-clever like "initial-value solved".
My reasoning is that there are theoretical reasons (which I worked out and I think others have reached the same conclusions) which back up the absolute lack of evidence for chess being anyhing but a draw. But there's a further problem, too. If, somehow, chess were found to be something else, such as "a win for white", how could we actually trust that solution? There could be errors in the solution that would never be found and it may even be impossible to find such errors within thousands of years. Or millions, even. Setting an almost infinite set of calculations going is one thing but checking them and working out a proof that they show chess to be one result or other is mind-bogglingly problematic. For that matter, how can it be known that the results haven't been sabotaged? So you see, a deductive proof in the fashion that Elroch demands is impossible, not merely improbable. We have to go with scientifically based proofs instead.
A solved state and having a scientific consensus of a certain theoretical outcome are different things. I'm not going to even ask what the scienftific evidence may be, but solved refers to a mathematical solution. Chess being solved and mathematically proven to be a draw should be differentiated from the scientific community agreeing that it is a draw (most likely). You know? It's more precise that way.
Except that there are a single or small set of moves that are objectively "best" in each position, so the subjective is not really meaningful.
Except that the subjective is nearly always meaningful.
Actually, all perceptions of the meaning of objectivity are subjective.
A perfect game has never been established to have happened.
It is not known whether such a game would be a draw.
And both of those facts arise from another fact.
And that fact is that chess has not been solved.
Let's agree to differ then. I think it's been solved. According to the poor nomenclature which the poor theorists are forced to use, it's been ultra-weakly solved. We could call it "strategically solved" or maybe something pseudo-clever like "initial-value solved".
My reasoning is that there are theoretical reasons (which I worked out and I think others have reached the same conclusions) which back up the absolute lack of evidence for chess being anyhing but a draw. But there's a further problem, too. If, somehow, chess were found to be something else, such as "a win for white", how could we actually trust that solution? There could be errors in the solution that would never be found and it may even be impossible to find such errors within thousands of years. Or millions, even. Setting an almost infinite set of calculations going is one thing but checking them and working out a proof that they show chess to be one result or other is mind-bogglingly problematic. For that matter, how can it be known that the results haven't been sabotaged? So you see, a deductive proof in the fashion that Elroch demands is impossible, not merely improbable. We have to go with scientifically based proofs instead.
A solved state and having a scientific consensus of a certain theoretical outcome are different things. I'm not going to even ask what the scienftific evidence may be, but solved refers to a mathematical solution. Chess being solved and mathematically proven to be a draw should be differentiated from the scientific community agreeing that it is a draw (most likely). You know? It's more precise that way.
I've mentioned this before. The best mathematician I know is my son. He tells me that representing chess in terms of mathematical equations is impossible and will remain impossible for the forseeable future. There's no-one on this thread who is more qualified to make that judgement.
This means that chess cannot be mathematically solved. Now, it may be possible to improve on algorithms but to do so would require an entire rethink as to how chess should be analysed.
Generally speaking, scientific proofs are not fundamentally mathematical but they are fundamentally science-based, which means evidence-based. Correlations between variables may be represented mathematically and played around with until a scientific proposition is proven, but it is always proven within limits of accuracy. Sometimes, those limits of accuracy are closer than at other times and I have a strong feeling that, in chess, the limits of accuracy will be problematic, regarding the goal of proof or whatever.
All I'm really saying is that if our goal is mathematical precision in proofs regarding chess, then we're struggling for cognitive coherence.
Except that there are a single or small set of moves that are objectively "best" in each position, so the subjective is not really meaningful.
Except that the subjective is nearly always meaningful.
Context.
Morocco sounds plausible to me.
I completely forgot about Spanish Sahara. You just reminded me.
Ironic, given that British interests in Africa used to concentrate in northern Africa. It's not Morocco, though. I just saw this question elsewhere a few days ago and it's making the rounds, so I won't spoil the fun.
Except that there are a single or small set of moves that are objectively "best" in each position, so the subjective is not really meaningful.
Except that the subjective is nearly always meaningful.
Context.
Agreed.
In some contexts, acknowledgement of the subjective perception of objectivity is little more than a formality.
Except that there are a single or small set of moves that are objectively "best" in each position, so the subjective is not really meaningful.
Except that the subjective is nearly always meaningful.
Context.
Agreed.
In some contexts, acknowledgement of the subjective perception of objectivity is little more than a formality.
By chance, do you believe that when you put your hands over your face, you are invisible to others? That is a good example of what happens when you have not learned to understand objective reality. You could add it to your paranormal panoply of powers, I guess.
Solving chess has nothing to do with the types of positions some players might prefer, whether individual players or computers consider some moves to be "best" while different players/computers have a different opinion, or anything with any subjective matters. The question is: is there or is there not any series of moves that will result in a won position no matter what moves the opponent may play?
Morocco sounds plausible to me.
I completely forgot about Spanish Sahara. You just reminded me.
Ironic, given that British interests in Africa used to concentrate in northern Africa. It's not Morocco, though. I just saw this question elsewhere a few days ago and it's making the rounds, so I won't spoil the fun.
It's stamp collecting that does it. Spanish Sahara, it turns out, is a territory rather than a country.
Seems like my first guess was good except that it still has its old name, amazingly.
Solving chess has nothing to do with the types of positions some players might prefer, whether individual players or computers consider some moves to be "best" while different players/computers have a different opinion, or anything with any subjective matters. The question is: is there or is there not any series of moves that will result in a won position no matter what moves the opponent may play?
But that isn't related to the point he was making.
I've mentioned this before. The best mathematician I know is my son. He tells me that representing chess in terms of mathematical equations is impossible and will remain impossible for the forseeable future. There's no-one on this thread who is more qualified to make that judgement.
This means that chess cannot be mathematically solved. Now, it may be possible to improve on algorithms but to do so would require an entire rethink as to how chess should be analysed.
Generally speaking, scientific proofs are not fundamentally mathematical but they are fundamentally science-based, which means evidence-based. Correlations between variables may be represented mathematically and played around with until a scientific proposition is proven, but it is always proven within limits of accuracy. Sometimes, those limits of accuracy are closer than at other times and I have a strong feeling that, in chess, the limits of accuracy will be problematic, regarding the goal of proof or whatever.
All I'm really saying is that if our goal is mathematical precision in proofs regarding chess, then we're struggling for cognitive coherence.
I assume you do understand that "algorithmically solved" would also include math in significant quantities. Chess is not going to be solved with logical axioms piled one on top of the other, unless you want a proof that also takes millions of years and is so large that nobody can even read it.
I've mentioned this before. The best mathematician I know is my son. He tells me that representing chess in terms of mathematical equations is impossible and will remain impossible for the forseeable future. There's no-one on this thread who is more qualified to make that judgement.
This means that chess cannot be mathematically solved. Now, it may be possible to improve on algorithms but to do so would require an entire rethink as to how chess should be analysed.
Generally speaking, scientific proofs are not fundamentally mathematical but they are fundamentally science-based, which means evidence-based. Correlations between variables may be represented mathematically and played around with until a scientific proposition is proven, but it is always proven within limits of accuracy. Sometimes, those limits of accuracy are closer than at other times and I have a strong feeling that, in chess, the limits of accuracy will be problematic, regarding the goal of proof or whatever.
All I'm really saying is that if our goal is mathematical precision in proofs regarding chess, then we're struggling for cognitive coherence.
I assume you do understand that "algorithmically solved" would also include math in significant quantities. Chess is not going to be solved with logical axioms piled one on top of the other, unless you want a proof that also takes millions of years and is so large that nobody can even read it.
Yes but it doesn't or wouldn't attempt to be a direct representation. This belief in "mathematical proofs" seems obsessive and also misunderstood.
First you have to represent chess in mathematical terms, closely enough that all facets of the game are accurately depicted. Then you have to produce equations that depict the entire dynamics of chess. Finally you have to prove it all.
Pie in the Sky. I agree with you.
Someone help me with this though. How does chess.com not have it?
https://www.chess.com/forum/view/tournaments/tournament-suggestions-non-live-and-bracket-style