tygxc why do you continue to cite definitions that you have no understanding of?
And shouldnt you take the fact that everyone else could understand what elroch was saying while you couldnt as a sign of your own incompetence? not understanding the arguments made by others is literally the first sign that you don't know what you are talking about.
‘Would you say that a ticket in a 1 in a quadrillion lottery could not win? If you answer that it could not, you need a refresher in epistemiology.’
this analogy is faulty because in the lottery, the possibility of winning is slim yet absolute, while the possibility of white winning or even drawing after blundering its bishop is absurd. or iow, the possibility may not exist at all.
Thanks for this observation (which resembles one by @tygxc where he justified his conclusion about the optimal result of chess by saying that was a definite thing with no uncertainty in it. But clearly his thinking was wrong - the fact that a theorem is definitely either true or false does not excuse lack of rigor in a proof).
I hope I can clarify this point by drawing attention to the Bayesian viewpoint. It can be proven that Bayesian probability theory is the only consistent way to quantiify BELIEF about propositions (given some very mild assumptions based on how beliefs need to behave). Not everyone will be familiar with this application of probability theory, which is separate to the more familiar one that has the much narrower scope of "repeatable random events")
In the case of the lottery ticket, viewed from the future, whether the ticket is a winner or not is a definite thing with no uncertainty. But in the past, whether it won was uncertain. The appropriate belief state in the past was one embodying the 1 in a quadrillion chance of winning.
Likewise, for the optimal value of chess, despite what people who inappropriately conflate strong confidence based on empirical evidence and inductive reasoning with certainty say, at the moment the appropriate belief state is an uncertain one. Exactly what probabilities you allocate to a black or white win is a matter of subjective modelling (just like the probability one would allocate to a given very large number being prime, for example), but the probabilities for all three results should be non-zero. With most of the probability on a draw, IMHO!
Likewise for the position 1. e4 e5 2. Ba6, until this position is solved. It may seem absurd to suggest that we don't even know that white is not winning - this is very unlikely - but my logical self demands that I allocate this possibility some tiny probability (for the specific reason that my logical self CANNOT deduce the opposite, and nothing can be truly certain without being deduced. Of course, no-one is ever going to have a problem ignoring really tiny probabilities - in a lifetime it is the difference between zero and tiny is unlikely to have any effect, but the philosophical difference is huge.
Intuitively, it may help to think in terms of log odds. The reason is that the log odds scale extends from -infinity to +infinity, with certain falsehood (0 on the probability scale) being minus infinity on the log odds scale and certain truth (1 on the probability scale) being plus infinity on the log odds scale. I feel this better indicates the very big difference between certainty and high confidence. Big numbers are not infinity!
AIs and neutral networks in general typically work with log odds as raw output (or something similar when there are more than 2 possibilities).
the possibility may not exist at all.
In other words, we might express it as a probability...
express what as a probability? the possibility or our state of knowledge about it?
2.Ba6 doesn't necessarily lose by force... this is extremely easy to understand... the fact that multiple people seem confused by this means this topic should be ignored.
i didn’t say that white lose by force. just think of it for a moment. for you it should be a brief to recognize the subtle nuance. not sure about some others..
@Sillver1, I see now you asked the question that I have just tried to answer (whether rhetorical or not, I can't be sure!).
The thing which we express as a probability is our belief state. That is what Bayesian probability is about.
‘Thanks for this observation’
you welcome.
Note that Bayesian probability is maximally subjective in a sense. It does not prohibit someone from having a prior belief state which is certain. But according to the appropriate cross entropy error function, such a belief is infinitely expensive if it is wrong! So it is fair to say it is inappropriate/unwise to be certain without being able to justify the certainty.
@Sillver1, I see now you asked the question that I have just tried to answer (whether rhetorical or not, I can't be sure!).
The thing which we express as a probability is our belief state. That is what Bayesian probability is about.
it was an attempt to point llama in the right direction. now i can go back to waste my time on something more enjoyable.. lol
Note that Bayesian probability is maximally subjective in a sense. It does not prohibit someone from having a prior belief state which is certain. But according to the appropriate cross entropy error function, such a belief is infinitely expensive if it is wrong! So it is fair to say it is inappropriate/unwise to be certain without being able to justify the certainty.
i can see why you say that, and objectivity speaking that’s ok.
tygxc wrote: @12548
"a major misunderstanding of what mathematics is"
++ Goldbach, Fermat, Riemann, Mersenne, Ramanujan are famous mathematicians for what they conjectured, not for what they proved and certainly not for proofs they criticized.
Besides many proofs were at first faulty and had to be corrected, e.g. the Four color theorem"
LMFAO false on all levels.
all five had many famous proofs, and the four color theorem never had a faulty proof.
""No post of mine has claimed this."
++ I claim 1 a4 cannot be better than 1 e4 and 1 e4 e5 2 Ba6? loses for white.
You vehemently denied this several times, thus claimed the opposite."
never did this. he simply claimed that you do not have rigorous proof of your assertion.
of course, tygxc, with your lack of math education, you could not tell the difference.
I have explained why it was not mathematical induction. You cannot map a crumpet to a falcon. That post. There is no possibility that mathematical induction could be used to prove what you wish to be proven to help your case. It was philosophical induction. If you don't understand, you are just not very bright. Oh I forgot. You may seem very bright to some but unfortunately ..........
Geez, now you can't even come up with your own funny things to compare to...it's like your mind scrambles up everything other people say and then spits it back out in 2 weeks with you taking credit and claiming you said it before anyone else. I used crumpet because it makes a good analogy with your persona...British, pretending to be solid, but full of holes and hot air, softens when butter is added...easy to chew up and spit out.
"No post of mine has claimed this."
++ I claim 1 a4 cannot be better than 1 e4 and 1 e4 e5 2 Ba6? loses for white.
You vehemently denied this several times, thus claimed the opposite.
A perfect example of how your logic about solving chess works. "Thus claimed the opposite" is not a workable leap.
When someone says they notice things that others usually miss, including hidden meaning to ordinary things, that's a common sign of schizophrenia, just sayin' The person assumes they're just more observant, but in reality others don't notice these things because they don't exist.
Just stick Optimissed in his own version of A Beautiful Mind, then put an imaginary secret cartel off to the side whispering in his ear and stoking these delusions...the major plot hole is, Optimissed only imagines himself to be as smart as John Nash, so it all falls apart. Maybe if you retitle it A Mediocre Mind...
jealousy.
Pity mixed with annoyance.
tygxc wrote: @12548
"a major misunderstanding of what mathematics is"
++ Goldbach, Fermat, Riemann, Mersenne, Ramanujan are famous mathematicians for what they conjectured, not for what they proved and certainly not for proofs they criticized.
Besides many proofs were at first faulty and had to be corrected, e.g. the Four color theorem"
LMFAO false on all levels.
all five had many famous proofs, and the four color theorem never had a faulty proof.
Some of those guys were more maths hobbyists than mathematicians (two were 18th century lawyers). Fermat is indeed famous for making a conjecture and calling it a theorem. he made many other claims (which should have been conjectures) that turned out to be wrong. But he also did substantial good work, even if he left more for others to do: 'Fermat's Last Theorem' (FLT) being the most extreme example.
Recklessness was more common in the old days, it seems. Hence the popularity of dueling (which famously killed the excellent mathematician Galois at the age of 20. If he hadn't been an extraordinary prodigy, his name would be forgotten).
BUT, as @tygxc said there were indeed faulty proofs of the four color theorem (4CT). At least two in the 19th century that were believed for a while and then found to be faulty by other mathematicians (seems peer review was even slower in those days). Unlike the first draft of the proof of FLT, they were unfixable, so it took a lifetime before the 4CT was proved.
""No post of mine has claimed this."
++ I claim 1 a4 cannot be better than 1 e4 and 1 e4 e5 2 Ba6? loses for white.
You vehemently denied this several times, thus claimed the opposite."
never did this. he simply claimed that you do not have rigorous proof of your assertion.
of course, tygxc, with your lack of math education, you could not tell the difference.
Perhaps he now understands? Perhaps not.
even fermat has some famous proofs, like fermat's little theorem, which is used extensively in number theory.
"BUT, there were indeed faulty proofs of the four color theorem. At least two in the 19th century that were believed for a while and then found to be faulty by other mathematicians (seems peer review was even slower in those days)."
im counting only ones that passed extended peer review.
Actually, Fermat is not known to have proved his little theorem. Euler did. It's likely Fermat convinced himself of it without proving it. Just realised, I classed him as an 18th century lawyer, but he was a 17th century lawyer. Same century as Shakespeare died. Fermat died in the year of the great plague of London (unconnected, I think).
He was a true genius for sure, getting part way to developing calculus and probability theory, both before others who are known as the originators of these fields. Newton explicitly referred to him inspiring his work on differential calculus!
He also found the deep principle in physics with his name attached.
Actually, Fermat is not known to have proved his little theorem. Euler did. It's likely Fermat convinced himself of it without proving it. Just realised, I classed him as an 18th century lawyer, but he was a 17th century lawyer. Same century as Shakespeare died. Fermat died in the year of the great plague of London (unconnected, I think).
He was a true genius for sure, getting part way to developing calculus and probability theory, both before others who are known as the originators of these fields. Newton explicitly referred to him inspiring his work on differential calculus!
He also found the deep principle in physics with his name attached.
fair, u are correct on that, and that would make sense considering how fermats little theorem isnt even that hard to prove on ur own.
Over a hundred new posts.
With @Optimissed losing again - as he always does.
As he saw he was losing again - he started talking about moderators and 'coded signals' ...
in other words went into his extra-paranoid mode that he always does as he's always defeated.
Similiar in the 'hoax' forum where he's overtly trying to get the opening poster there to block me.
And yes - BC doesn't have O's psychological handicap.
And as also always happens - O is defeated yet again by each and every person he throws stones at.
--------------------------------------
tygxc is then at the center once more as usual and the actual forum topic is then addressed.
tygxc provides 'foils of illogic'.
Noting that tygxc is now using phrases that he is 'after the truth' ...
'the truth'.
Quite a buzz phrase on the net.
In math and in the logic of math - the numbers can't lie.
Numbers don't have that capability.
Of course numbers can be used to support falsehoods though.
Or illogic.
Illogic is not 'truth'.
More central to tygxc's positions is what he has decided 'matters'.
What he 'cares' about and sometimes he uses 'we'.
'We dont care about operations per second of computers'.
He's not going to let anybody tell him what he should prioritize.
Which is understandable and a very common thing.
" 1 e4 e5 2 Ba6? is a white loss, ultra-weakly solved."
objectively false.
a mathematical solution requires the game tree or formal proof.
you obviously dont have the game tree, so where's the proof?