@13494
"1000+ move games"
++ The 112 ICCF WC finals draws, >99.992% certain to be perfect games with optimal play from both sides end in certain draws in average 39 moves.
since when is high probability accepted as proof in mathematical journals?
Someone who can't tell the difference between finite and infinite is probably not the sharpest tool in the box.
The person who's 'failing' to distinguish - is O. Not Elroch.
O - always obsessing over his misinterpretations of intelligence.
It doesn't even 'seem' to have crossed his mind that Elroch understood exactly ...
with O doing a kind of tygxc ?
Failing to understand mathematical objectivity?
Having disdain for same?
More like - O just trolling again - looking for any semantics opportunity to do so. What percentage of his own personalizing nonsense does he actually believe?
Probably very close to his name. O percentage.
Whereas others - not having his insecurity - don't need to lie and therefore don't.
Someone who can't tell the difference between finite and infinite is probably not the sharpest tool in the box.
Correct. For instance, Elroch believes that the infinite can be counted even though "infinite" literally means "cannot be counted", since finite means countable.
I know that you haven't been sharpened for about 30 years so I know you won't understand what I'm talking about either. I think you've found your level quite nicely.
Narcissism is a problem for you in situations like this because, unlike balanced people, you are unable to comprehend that the knowledge and understanding of the entire mathematical world for a century or so is enormously superior to your own.
If you did want to start to catch up (and had the capability to do so - this seems unlikely, since you are having problems even with the simple distinction between finite and infinite cardinality) any authoritative source would be able to help.
Cardinal numbers (Wikipedia)
Cardinal numbers (Wolfram Mathworld)
Cardinal numbers (The Encyclopedia of Mathematics)
If you had more self respect, you would understand that you can make whatever argument you wish to make by yourself. I have no intention of reading your junk because I know very well that you will misrepresent it.
Perhaps you don't understand how links work. You click on them and read them without any possibility for me to interfere. If you do this right you will then understand things you patently do not without clicking. My prediction - you don't click and you remain ignorant.
Make an argument in your own words.
See below. Ask any mathematically literate person if I have done a good job.
The type of people you gather round you show you for what you are. If any of them were in any way intellectually capable, they would stay well clear of you.
Incidentally, you told me a while back you had been employed as a scientist. I had a look and noted that you were working as a mechanical engineer, doing some experiments and related theory on natural ventilation for sites, maybe 20 years ago. That's very worthwhile. Fluid mechanics and a bit of thermodynamics = mechanical engineering. It's good because it requires experimentation, probably with models and maybe also on site with wind speed devices positioned all over the place. Measurements help you keep your runaway ideas in check.
However, what you are attempting to pronounce upon here is simply your opinion and we know from experience that you always deny there are theoreticians who disagree with those you agree with. Unfortunately, it seems impossible to have a proper conversation with you. If you don't understand something, you deny it exists and that has been noted often. So I'm afraid you're required to make a verbal argument, say, regarding how you can measure or count something that is defined as infinite.
So, let's get this straight. Every time some ignoramus spouts nonsense denying some part of mathematical knowledge, proclaiming that all of mathematics is wrong because he is a self-proclaimed genius and therefore complete ignorance of the subject and lack of any useful intuition is no barrier to the superiority of his proclamations, there is an immediate obligation for others to overwhelm the massive barrier of his ego and lack of understanding and to convince him of textbook facts?
No, there is no such obligation.
Despite that, here is a brief introduction to cardinality and why you should understand that different infinite sets have different sizes. I've even provided handy links to definitions of very basic mathematical terms.
First, lets define a relation >= on the class of all sets by:
A >= B means that there exists a surjective function from A to B
[Exercise for reader: show that this relation is transitive and reflexive. This makes it what is called a preorder]
This relation (like all preorders) generates an equivalence relation on the class of all sets by the definition:
A == B means that A>=B and B >=A
[Exercise for reader - verify that it is an equivalence relation]
There is a famous theorem that shows that for any two such sets there is a bijection between the two sets (I had to look up the name of the theorem but I could recall the neat proof).
This equivalence relation defines cardinality. If two sets are in the same equivalence class - i.e. there exists surjections in both directions - then they are of the same cardinality, i.e. size. This definition applies to all finite and infinite sets.
All that is left is to show there are two infinite sets with different cardinality.
Take the set of natural numbers and the set of decimal numbers between 0 and 1. If there was a surjection between the natural numbers N and this set of decimal numbers S, say
f: N -> S
then define a new decimal number x as follows.
if the n'th digit of f(n) is 7, let x have an n'th digit of 8
otherwise, let x have an n'th digit of 7.
It is easy to see that x is NOT one of the list of numbers (it differs from the n'th number at digit n, so it differs from all of the numbers, and there is no risk that it has a sequence of 9s or 0s afterwards (the only way that a decimal number can be the same as another with a different set of digits).
[Exercise for reader - make a similar, but neater proof showing the set of subsets of the natural numbers has bigger cardinality than the set of natural numbers]
This is first year undergraduate stuff (at least where I studied) and is not difficult (and nor are the necessary parts referred to. We don't actually even need the Schroeder-Bernstein theorem.
So now, @Optimissed, you have no valid excuse for not understanding the basic fact that different infinite numbers have different size.
With regard to the last statement in your last post, the truth is that while everyone is aware that you have a extraordinarily high opinion of your own intelligence, you often refute your own claims and are actually rather dull-witted by comparison with say a decent undergraduate mathematician. I suspect that you will be unable to understand the above (or to fix this by independently studying something which could be just part of a single lecture).
Fisher 960 exists 😎
hey opt, how about you answer the extremely basic and falsifiable question instead of childish insults? surely if you had any sort of, worth, you would have addressed it?
Elroch, you seem to keep forgetting that optimissed has likely never covered, or completely forgotten abstract math language of any type, and because of his narcissism, will choose to not try to understand it because he cannot accept the fact that someone would know something he doesn't. I can predict with almost complete certainty that optimissed will fail to understand the concept.
his claim that an infinity's magnitude needs to be "Assessed" to determine differences is literally self contradicting. The infinity is literally the magnitude. in addition, it's not even true of even non-infinities.
its funny how he claims no infinity can be countable when there is literally a class of infinity called "countable infinity". the fact that optimissed's language includes "Elroch believes that the infinite can be counted even though "infinite" literally means "cannot be counted", since finite means countable." means that he has no understanding of infinities or what it means for something to be "countable".
While maths uses precise language, the vagueness of @Optimissed's language is an issue. He is very likely using "countable" incorrectly as a synonym of "finite". It is likely that he never has understood or even known the correct definition. To my knowledge, he never clicks on a link like that to fix the inadequacy of his basic knowledge.
@13470
"Only if you want to ignore reality"
++ You are the one who ignores reality. With unlimited thinking time the unguided engine reaches the depth to find the forced checkmate.
Thus the error rate at unlimited time is zero. So you fitted the wrong curve.
You should fit a curve with an asymptote error = 0 at time approaching infinity.
The 17 ICCF World Championship finalists at 5 days/move would play this endgame perfectly even without table base or computer. Troitsky did and he had no computers.
It is no coincidence that the late GM Sveshnikov first asked for good assistants and only then for modern computers. Give me five years and I will solve chess.
@13470
"Only if you want to ignore reality"
++ You are the one who ignores reality. With unlimited thinking time the unguided engine reaches the depth to find the forced checkmate.
Thus the error rate at unlimited time is zero. So you fitted the wrong curve.
You should fit a curve with an asymptote error = 0 at time approaching infinity.
The 17 ICCF World Championship finalists at 5 days/move would play this endgame perfectly even without table base or computer. Troitsky did and he had no computers.
It is no coincidence that the late GM Sveshnikov first asked for good assistants and only then for modern computers. Give me five years and I will solve chess.
"Thus the error rate at unlimited time is zero. So you fitted the wrong curve.
You should fit a curve with an asymptote error = 0 at time approaching infinity."
the curve was determined by the datapoints, he didnt choose the curve to fit his argument. also, the curve you propose is literally what you are trying to argue as the truth, so thats a circular logic fallacy.
the whole point is that our machines arent programmed to approach chess with mathematical certainty in every position, not that our current machinse cant be modified or made powerful enough to achieve perfection in some positions, or all positions if set to analyze the whole table base. but thats not what the engines do.
Sveshnikov never mentions the word "solve". he says "close". hes not talking about any mathematical solution, and you would realize that had you both:
a) any understanding of mathematical proof. b) read the article you cite.
@13470
"Only if you want to ignore reality"
++ You are the one who ignores reality. With unlimited thinking time the unguided engine reaches the depth to find the forced checkmate.
Thus the error rate at unlimited time is zero. So you fitted the wrong curve.
You should fit a curve with an asymptote error = 0 at time approaching infinity.
The curve will reach zero in geological time, but seems to be generally increasing in a practical timescale. The predicted value in the graph is unlikely to be accurate because the curve is hardly a curve at all. The point is that you can't assume that the blunder rates at 5 days think time are any better than at 5 seconds from those positions or especially from the starting position.
An alpha beta search is only as good as it's static evaluations. If those lead you up the garden path, then thinking longer can just lead you further up the garden path.
You're the one asserting that 5 days think time will produce blunder free games from the starting position. You have no basis for that.
The fact that SF14's blunder rate with 37 minutes think time was over five times its blunder rate with 1 second think time in my sample games should at least give you pause for thought.
The 17 ICCF World Championship finalists at 5 days/move would play this endgame perfectly even without table base or computer. Troitsky did and he had no computers.
Troitsky probably played the endgame as a whole perfectly under basic rules. Nothing but Syzygy can play the endgame as a whole perfectly under competition rules (ICCF rules without tablebase). Many positions are orders of magnitude harder under competition rules (including the position shown in the SF14 graph). Your 17 ICCF World Championship finalists at 5 days/move would score 17 ducks against Syzygy.
It is no coincidence that the late GM Sveshnikov first asked for good assistants and only then for modern computers. Give me five years and I will solve chess.
He was quite good as humans go I hear.
@13470
"Only if you want to ignore reality"
++ You are the one who ignores reality. With unlimited thinking time the unguided engine reaches the depth to find the forced checkmate.
Thus the error rate at unlimited time is zero. So you fitted the wrong curve.
You should fit a curve with an asymptote error = 0 at time approaching infinity.
Presumably you believe all functions are monotone. And the behaviour "near infinity" is not the point of interest. That is the behaviour of real engines.
Moreover, though it is reasonable to assume a reasonable extrapolation of computational power would lead to perfection at some finite point, there is great uncertainty where this is. You can't put a point on a graph when you have no idea what the x-co-ordinate is, even to within a factor of a million!
The 17 ICCF World Championship finalists at 5 days/move would play this endgame perfectly even without table base or computer. Troitsky did and he had no computers.
It is no coincidence that the late GM Sveshnikov first asked for good assistants and only then for modern computers. Give me five years and I will solve chess.
Yes, all claims by chess players are reliable. For example: "I could give God pawn and move and beat him"
"Nobody has an advantage in playing strength"
++ Over the board 2 of the 17 finalists are IM, 1 is FM, and others untitled.
I mean playing strength, in terms of engine analysis. The ICCF competitors are all almost certainly using the top engines available - which means all the players are performing at the same level.
Which means that draws are practically inevitable.
I don't believe human playing strength matters at this point, due to how high engines have climbed.
A 2300-rated human won't have anything to offer, in terms of chess understanding, to improve the playing strength of a 3600-rated engine.
Just as a 1500-rated club player won't have anything to offer, in terms of chess understanding, to improve the playing strength of Magnus Carlsen ...
Now to be fair, I do believe chess is a draw. So if that's your argument, then I completely agree with you. It should be a draw, anyway - that's how the game is designed. Both players should begin on equal footing. Otherwise, the game would be flawed.
But I don't consider ICCF games to be proof that chess is "solved". I consider them proof that humans using top engines will draw against other humans who are using the same top engines.
It's ... not exactly a surprise outcome ...
"Nobody has an advantage in playing strength"
++ Over the board 2 of the 17 finalists are IM, 1 is FM, and others untitled.
I mean playing strength, in terms of engine analysis. The ICCF competitors are all almost certainly using the top engines available - which means all the players are performing at the same level.
theres a thing where russians reportedly have reduced hardware but played well, although during the timeframe where it was confirmed that russians had reduced hardware (ie the timespan of the interview tygxc cited) russians played considerably worse.
@13526
"The ICCF competitors are all almost certainly using the top engines available"
++ Different engines, different tuning, different hardware (the Russians have worse hardware because of sanctions, but nevertheless 4 of the 17 finalists are Russian), different time per move (50 days per 10 moves, but one may take 2 days on a move and the other 10 days).
"I don't believe human playing strength matters at this point, due to how high engines have climbed." ++ 4 Russians qualified for the World Championship finals, despite worse hardware.
"A 2300-rated human won't have anything to offer, in terms of chess understanding, to improve the playing strength of a 3600-rated engine."
++ 'the key is planning, which computers do not do well — Petrosian-like evaluations of where pieces belong, what exchanges are needed, and what move orders are most precise within the long-term plan.' SIM Jon Edwards wins 32nd World Correspondence Championship
'How many ideas can you interactively throw at the computer in one hour is the key question'
'It takes chess wisdom to escape with a draw even though Stockfish and co have calculated 2+ scores most of the middle game.'
Interview with ICCF 26th World Champion
"chess is a draw" ++ Yes
"Otherwise, the game would be flawed." ++ Losing Chess and Connect Four are first player wins.
@13526
"The ICCF competitors are all almost certainly using the top engines available"
++ Different engines, different tuning, different hardware (the Russians have worse hardware because of sanctions, but nevertheless 4 of the 17 finalists are Russian), different time per move (50 days per 10 moves, but one may take 2 days on a move and the other 10 days).
Worse engines effectively equates to shorter think times. See my last post.
...
@13530
"strategies which could, conceivably, produce a forced win" ++ They try to win, but they draw.
"games of around 200 moves" ++ After average 39 moves it ends in a draw.
"white concentrates on keeping the pieces on where possible and useful and also on making one-step pawn moves" ++ They concentrate on the best possible moves, and draw.
"the idea that black has a forced win to be immaterial"
++ White has the initiative, an advantage of +1 tempo = +0.33 pawn, not enough to win.
Each further move dilutes the +1 tempo advantage, so the advantage gradually evaporates.
"what they need to do to make any possible progress" ++ They try to win, but draw.
@13530
"strategies which could, conceivably, produce a forced win" ++ They try to win, but they draw.
...
Tell me about it.
@13525
"there is great uncertainty where this is"
++ No, when the thinking time reaches depth 2x, a checkmate in x is found with certainty.
@13530
"strategies which could, conceivably, produce a forced win" ++ They try to win, but they draw.
...
Tell me about it.
It's basically the same as @tygxc trying to solve chess.
Syzygy can play the endgame as a whole perfectly under competition rules
how do u know that ?...has a/o ever ran a check on ziggy ?...do we have some value software on it ?
i ran a 10-ply (opening game) against shannons 69+x10^12 report. I got 54+x10^12. still tryn2figure out their parametres. whos right ?...probably them. but some vfyn software still needsta be run right ? [ty github, stack OF 
]
dude its so funny seeing optimissed getting middle school math concepts completely wrong. I dont even need to argue against them he makes a big enough fool himself.
optimissed thinks that there is some sort of disagreement when elroch and the others are listing what are known for over 100 years to be mathematical facts.
optimissed claims there's theoreticians that disagree, but where are they exactly?