I think you are fooling yourself. Your statement means that if there were a googleplex of such examples, you would be certain about all of them. You would be wrong about some of them (quite a lot actually, with a googleplex to start with).
Small positive numbers are not zero. Even when they are very small.
No, it's you who makes the assumption. I'm certain about the chess example given. No other has been mentioned. I'm also certain that the entity doesn't exist because I can think more clearly about it than D ever could. If you challenge that assertion, which wouldn't be unreasonable of you, I can explain why I can think more clearly about it.
googolplex. 
@4183
"the probability that an engine misses a best move in its top four choices is (on a logarithmic scale) something like the fourth power of the probability that it misses it on its first move. There is no doubt this happens quite often. I estimate this fourth power to be around 10^-12"
++ You estimate so without any evidence at all.
I calculated that probability from extrapolation from the AlphaZero autoplay paper.
Figure 2. https://arxiv.org/pdf/2009.04374.pdf
At 1 s / move: 11.8% error per game
At 1 min / move: 2.1% error per game
Hence
At 1 h / move: 0.37% error per game
at 60 h / move: 0.066% error per game
Assuming 50 moves / game i.e. 100 positions per game give 1 error per 10^5 positions
The cloud engine running for 15 s corresponds to the engine in the paper for 60 h.
The probability that a 10^9 nodes per second cloud engine running for 15 s misses a best move on its 1st move is thus 1 in 10^5 positions.
The 4th power of that is 1 error in 10^20 positions.
@4182
"Tromp's value (actually 4.8x10^44)"
++ For each position with white to move there is an up/down mirror position with black to move and with the same game-theoretic value.
For each position with lost castling rights there is a left/right mirror position with the same game-theoretic value.
That leaves 1.2 * 10^44 legal positions.
As proven, the vast majority of those is not sensible and plays no role in weakly solving Chess.
Likewise for the Gourion upper bound 3.8521 . . . × 10^37 becomes 1.926 × 10^37 because of left/right symmetry after loss of castling rights
and his estimate of 3 × 10^37 becomes 1.5 × 10^37.
https://arxiv.org/pdf/2112.09386.pdf
"ignored the 3-fold repetition and 50 move rules"
++ The 50-moves rule 9.3 can safely be ignored as it is almost never invoked before the 7-men endgame table base is reached in GM or ICCF games.
Most of these games are over before move 50.
The 3-fold repetition rule 9.2.1 cannot be ignored, as it represents a major drawing mechanism, often invoked in GM and ICCF games.
"position has mostly come to mean the game state in the absence of those rules"
++ No, not at all. From the competition rules:
'9.2.2
Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:
9.2.2.1
at the start of the sequence a pawn could have been captured en passant
9.2.2.2
a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.'
https://handbook.fide.com/chapter/E012018
@4179
"It leaves 10^44 with a bunch of rationalizations"
++ You still do not understand:
10^44 is the number of legal positions needed to strongly solve Chess.
Losing Chess with the same 64 squares and the same 32 men
needed only 10^9 positions to weakly solve it.
@4179
"It leaves 10^44 with a bunch of rationalizations"
++ You still do not understand:
10^44 is the number of legal positions needed to strongly solve Chess.
Losing Chess with the same 64 squares and the same 32 men
needed only 10^9 positions to weakly solve it.
Losing chess is a completely different game with forced captures...stop being disingenuous. That's why it only requires 10^9.
You clearly meant Elroch, not Tygxc, who is on your side of the "assertions are facts" aisle. Whose sell date were you talking about again?
That didn't make any sense. Elroch was agreeing with you regarding your ridiculous assertion that we cannot know that the position we were discussing is lost. I hope that he's reassessing his position. If it were me and I had to choose blind, whether to agree with you and MAR, or with myself over pretty much anything, I'd agree with me.
You habitually confuse things like "x believes that all assertions are facts" and "x asserts a factual statement". Some would call it misrepresentation but it's just confusion. You were making a claim that no-one can know that the said position is a win for black, which is utterly ludicrous. You can and should speak for yourself, as a weak chess player, not competent to judge.
It's far from ludicrous, being the current reality we all live in. You don't know if Ba6 guarantees a black win...you cannot demonstrate it conclusively, nor can any chess player alive or dead, with or without engine assistance.
P.S. You lumped myself and Mar with Tygxc when Elroch is the person you meant...did you even bother to review your post?
@4195
"Losing chess is a completely different game with forced captures"
++ Yes, Losing Chess is a simpler game, that is why Chess needs more than 10^9 positions.
However, it shows that the number of legal positions 10^44 is not related to the number of positions needed to weakly solve a game.
You clearly meant Elroch, not Tygxc, who is on your side of the "assertions are facts" aisle. Whose sell date were you talking about again?
That didn't make any sense. Elroch was agreeing with you regarding your ridiculous assertion that we cannot know that the position we were discussing is lost. I hope that he's reassessing his position. If it were me and I had to choose blind, whether to agree with you and MAR, or with myself over pretty much anything, I'd agree with me.
You habitually confuse things like "x believes that all assertions are facts" and "x asserts a factual statement". Some would call it misrepresentation but it's just confusion. You were making a claim that no-one can know that the said position is a win for black, which is utterly ludicrous. You can and should speak for yourself, as a weak chess player, not competent to judge.
It's far from ludicrous, being the current reality we all live in. You don't know if Ba6 guarantees a black win...you cannot demonstrate it conclusively, nor can any chess player alive or dead, with or without engine assistance.
P.S. You lumped myself and Mar with Tygxc when Elroch is the person you meant...did you even bother to review your post?
Of course I know that Ba6 is won for black. Maybe it's too late to tell you not to be ridiculous. Also, Elroch explained that he had made a simple mistake. Stop behaving like a kid and going on and on about it. Your reading comprehension is currently about zero. You're cracking up and I do mean that.
Of course I know that Ba6 is won for black. Maybe it's too late to tell you not to be ridiculous. Also, Elroch explained that he had made a simple mistake. Stop behaving like a kid and going on and on about it. Your reading comprehension is currently about zero. You're cracking up and I do mean that.
You're not even talking about the same incident, which is par for your course. If you know that Ba6 is won for black, then you can beat Stockfish from that position, on command. Go ahead and demonstrate, without using an engine. You can do it on live chess.
I know that K+R vs. K is won, vs. any engine, and I will happily demonstrate it. If you are claiming to know, 100%, then you are claiming the same level of confidence. You would think after a decade of watching Ponz get pounded for his 99.9999% that you might have learned something about making hyperbolic assertions...but alas, no.
@4195
"Losing chess is a completely different game with forced captures"
++ Yes, Losing Chess is a simpler game, that is why Chess needs more than 10^9 positions.
However, it shows that the number of legal positions 10^44 is not related to the number of positions needed to weakly solve a game.
10^17 will never be the number for any solution of chess. You will be cold in your grave still dreaming about that number.
@4200
I hope you are still alive when Chess is solved with around 10^17 positions.
Of course I know that Ba6 is won for black. Maybe it's too late to tell you not to be ridiculous. Also, Elroch explained that he had made a simple mistake. Stop behaving like a kid and going on and on about it. Your reading comprehension is currently about zero. You're cracking up and I do mean that.
You're not even talking about the same incident, which is par for your course. If you know that Ba6 is won for black, then you can beat Stockfish from that position, on command. Go ahead and demonstrate, without using an engine. You can do it on live chess.
I know that K+R vs. K is won, vs. any engine, and I will happily demonstrate it. If you are claiming to know, 100%, then you are claiming the same level of confidence. You would think after a decade of watching Ponz get pounded for his 99.9999% that you might have learned something about making hyperbolic assertions...but alas, no.
Even if chess was solved and we knew a certain position is winning, more often than not we still wouldnt be able to beat stockfish from there. I'm not sure what this conversation is supposed to prove
Of course I know that Ba6 is won for black. Maybe it's too late to tell you not to be ridiculous. Also, Elroch explained that he had made a simple mistake. Stop behaving like a kid and going on and on about it. Your reading comprehension is currently about zero. You're cracking up and I do mean that.
You're not even talking about the same incident, which is par for your course. If you know that Ba6 is won for black, then you can beat Stockfish from that position, on command. Go ahead and demonstrate, without using an engine. You can do it on live chess.
I know that K+R vs. K is won, vs. any engine, and I will happily demonstrate it. If you are claiming to know, 100%, then you are claiming the same level of confidence. You would think after a decade of watching Ponz get pounded for his 99.9999% that you might have learned something about making hyperbolic assertions...but alas, no.
Can't you, sort of, pretend you know what's going on in a way that makes you look like you have at least some intelligence? You tell me off and say that I can't criticise you without resorting to insults but when you are as confused and generally childish and repetitive as you are, it isn't possible to find anything worth answering. You're just so completely obsessive and you pretend that things you say make sense and are even intelligent. Honestly, you are not worth even trying to answer because you will just find something else completely foolish to say. You're a troll, btickler. You always start your bouts of trolling in the hope that someone will insult you, so you can feel superior.
I know that K+R vs. K is won, vs. any engine, and I will happily demonstrate it.
I'll watch. (With which colour are you going to win?)
Of course I know that Ba6 is won for black. Maybe it's too late to tell you not to be ridiculous. Also, Elroch explained that he had made a simple mistake. Stop behaving like a kid and going on and on about it. Your reading comprehension is currently about zero. You're cracking up and I do mean that.
You're not even talking about the same incident, which is par for your course. If you know that Ba6 is won for black, then you can beat Stockfish from that position, on command. Go ahead and demonstrate, without using an engine. You can do it on live chess.
I know that K+R vs. K is won, vs. any engine, and I will happily demonstrate it. If you are claiming to know, 100%, then you are claiming the same level of confidence. You would think after a decade of watching Ponz get pounded for his 99.9999% that you might have learned something about making hyperbolic assertions...but alas, no.
Even if chess was solved and we knew a certain position is winning, more often than not we still wouldnt be able to beat stockfish from there. I'm not sure what this conversation is supposed to prove
It does prove that, when faced with a chess position which is obviously, clearly and definitely lost for one side, btickler can't tell it's lost. Fair enough, because he's a weak player but next, he tells others that they can't tell it's definitely lost either.
So if Carlsen, Fischer, Kasparov and Capablanca were lined up and agreeing that it's won for black, he'd be telling them that they can't know that. I wonder who has to give him permission, before he can agree that it's won.
Of course I know that Ba6 is won for black. Maybe it's too late to tell you not to be ridiculous. Also, Elroch explained that he had made a simple mistake. Stop behaving like a kid and going on and on about it. Your reading comprehension is currently about zero. You're cracking up and I do mean that.
You're not even talking about the same incident, which is par for your course. If you know that Ba6 is won for black, then you can beat Stockfish from that position, on command. Go ahead and demonstrate, without using an engine. You can do it on live chess.
I know that K+R vs. K is won, vs. any engine, and I will happily demonstrate it. If you are claiming to know, 100%, then you are claiming the same level of confidence. You would think after a decade of watching Ponz get pounded for his 99.9999% that you might have learned something about making hyperbolic assertions...but alas, no.
Even if chess was solved and we knew a certain position is winning, more often than not we still wouldnt be able to beat stockfish from there. I'm not sure what this conversation is supposed to prove
It does prove that, when faced with a chess position which is obviously, clearly and definitely lost for one side, btickler can't tell it's lost. Fair enough, because he's a weak player but next, he tells others that they can't tell it's definitely lost either.
So if Carlsen, Fischer, Kasparov and Capablanca were lined up and agreeing that it's won for black, he'd be telling them that they can't know that. I wonder who has to give him permission, before he can agree that it's won.
I think you're missing the point. As far as I know, nobody is arguing that they believe 2. Ba6 is good for white. However, they are merely pointing out that there is no proof that 2. Ba6 is won for black. It probably is, but that doesn't mean it certainly is. Even if you're 100% sure of something, that doesn't make the probability of it being true 100%.
No, it's you who makes the assumption. I'm certain about the chess example given.
Of course. I understand that you are certain, and that your inappropriate certainty is a result of not understanding the difference between something that is deduced to be true and something that is believed to be true entirely by inductive reasoning.
No other has been mentioned.
For someone who does not already possess adequate intuition about quantifying uncertainty, it is necessary to explain it in this way. For example, someone owns a ticket in a 1 in a trillion lottery (each ticket is a random number from 0 to 999,999,999,999 and so is the winning number) and they express certainty they will not win. You explain to them that if that were correct, they should also be certain of not winning if they possessed a quadrillion randomly numbered tickets. But if they did, they would be almost sure of winning, proving their certainty wrong.
Does anyone not understand my point that when you have something that may have a quantifiable probability of 1 in (say) a trillion of being false it can be reasonable to be certain it is true, even to "know" it is true, but the epistemological situation is that certainty cannot be justified?
An example is the proposition that with an excellent source of random bits (say least significant bit of analog to digital conversion of thermal noise), the next 40 bits will all be zeros.
It's whether or not one agrees with the way you formulate such a situation. I have a problem accepting the legitimacy of formulating it by quantifying odds in such a manner. I think it's impossible to attribute material odds that something is false (for instance) that we very certainly think to be true. The moment that way of looking at it is accepted, of course that constitutes an acceptance that, epistemologically speaking, we cannot know something. I fundamentally disagree with Dawkins, for instance, that there are definite (or indefinite) odds that such and such an entity may or may not exist. I believe it's possible to know and I think that as soon as he plays this trick, because it is a trick, of quantifying odds, he wins the argument. But he's wrong to do so, to begin with. Someone else will have more evidence to work with than he does.
Regarding the 1. e4 e5 2. Ba6 situation, I do not think there is the remotest chance that it isn't a win for black. The chance of that is zero. Yet there are other things I'm uncertain about, which the powers that be take for granted.