a lot of my dad's Russian chess scientist co-workers are good at amateur chess.
And a lot are not? I would guess that there is some correlation between math skill and chess skill, but that does not change the existence of a lot of differences.
Below is a short paper of note
Is there a physics professor who thinks this position is about the uncertainty principle?
"... let's look as to why White cannot win. Basically, White can address 'velocity' by chasing down the black h-pawn, or address 'position' by guarding c8 for its own pawn promotion, but not both. White has come up against the 'Uncertainty Principle.' ..." - anonymous
Don't need physics to evaluate this. White's inability to win has nothing to do with the h-pawn. White's inability to win is simply a matter of being unable to save the c-pawn. White's ability to draw is what involves both the c and h pawns. White is able to draw because White is able to both pursue the h-pawn and move to protect the c-pawn. Although our anonymous author does not do so, I suppose it might be argued that Black's dilemma has some resemblance to uncertainty, but White's eventual moves are the result of a Black decision rather than a Black measurement.
... a lot aren't? when I say a lot, I have a tip; I will tell you this: if I say I have a lot, think of it as 75%, so that would obviously mean around 25% aren't. but is 25% 'a lot'? I don't think so.
We can discuss what "a lot" means, but it seems to me to make more sense to consider what actual studies are known to exist on the matter, and what conclusion is claimed. Again, I would guess that there is some correlation between math skill and chess skill, but that does not change the existence of a lot of differences.
Nevertheless, the chess attitude towards scribbling seems to be somewhat different from the physics or math attitude towards scribbling.
Then again farming with goats can drive you mad, chess must therefor have something to do with farming goats.
What I have been saying is that solving-complex-equations-in-one's-head is not a skill that makes one a top mathematician. Publishing is what counts and there is not much concern with how much paper was used to arrive at a published result. Even in a lowly math class, one generally is allowed to use paper as much as one wants. The chess attitude towards scribbling seems to be somewhat different from the math attitude towards scribbling. Again, I would guess that there is some correlation between math skill and chess skill, but that does not change the existence of a lot of differences.
How valuable do you think it was to Edward Lasker to be able to calculate in his head after 1 d4 e6 2 Nf3 f5 3 Nc3 Nf6 4 Bg5 Be7 5 Bxf6 Bxf6 6 e4 fxe4 7 Nxe4 O-O 8 Bd3 b6 9 Ne5 Bb7 10 Qh5 Qe7 ?
I do not feel an obligation to comment on everything that you have written. That has nothing to do with any desire to be right. If you have an objection to some specific statement by me, I suggest that you quote it.
When Edward Lasker faced the position after 1 d4 e6 2 Nf3 f5 3 Nc3 Nf6 4 Bg5 Be7 5 Bxf6 Bxf6 6 e4 fxe4 7 Nxe4 O-O 8 Bd3 b6 9 Ne5 Bb7 10 Qh5 Qe7, it did not matter how much paper was available because chess rules did not allow him to use it. The clock was ticking. (Actually, I think they may have been using something like an hour-glass arrangement.)
The only real calculation that goes on in a Chess game is when there is some tactical action going on. Otherwise positional ideas, and understanding are paramount. Which can be taught in a non mathematical way. However I believe some Geometry is at play here.
I'm not sure what you mean by a non-mathematical way, but ideas and understanding are very important in math.
Math is much more than formulas, and is completely about general ideas. Btw, a game is what chess is.
That kid seemed to think so
Below is a short paper of note
Is there a physics professor who thinks this position is about the uncertainty principle?
"... let's look as to why White cannot win. Basically, White can address 'velocity' by chasing down the black h-pawn, or address 'position' by guarding c8 for its own pawn promotion, but not both. White has come up against the 'Uncertainty Principle.' ..." - anonymous
Don't need physics to evaluate this. White's inability to win has nothing to do with the h-pawn. White's inability to win is simply a matter of being unable to save the c-pawn. White's ability to draw is what involves both the c and h pawns. White is able to draw because White is able to both pursue the h-pawn and move to protect the c-pawn. Although our anonymous author does not do so, I suppose it might be argued that Black's dilemma has some resemblance to uncertainty, but White's eventual moves are the result of a Black decision rather than a Black measurement.
Fixed (I hope)
Thanks
Thanks for the information about Euwe and Lasker. I'll read a little more about them now that I know they are mathematicians.
Another mathematician who played chess is Claude Shannon. But he wasn't a grandmaster - chess was just a hobby of his, and he used math to analyze the game. He wrote a famous paper published in 1950 to show that chess is too complicated to solve by mapping out all games.
His mathematical analysis is still used today by mathematicians who study chess. Since chess is too complicated to be studied by checking all possible games, researchers have worked on other methods to evaluate chess.
One "small" section of the game tree of chess is here: