Chess will never be solved, here's why

@12535

"it more likely means humans have less and less useful input, and when the engines play each other it's unsurprisingly a draw."
++ No, it is the human that has most input.

LOL. Easily checked: see who wins out of a human without an engine and an engine without a human. Place your bets now.

A top engine adds 1000 points to a 2600-rated human (way more to a weaker player), while even if humans do still add value to engines (not proven until you have a match where one side is pure engine), it is unlikely to be as much as 100 points (as the NN upgrade to Stockfish was). You reckon a human with an out of date engine would beat an up to date engine?

Note that although Elroch depicted it as a full mathematical representation of draughts, it was not that at all.

It was in the correct sense. I can understand why you are confused about this.

So we can understand that at that time, weakly solving it in this way was at the limit of practical possibilities.

Yes, solving checkers took 18 years and over a thousand CPU years. Hundreds of thousands of dollars worth of computing.

Zermelo represented his Theorem as a proof that chess may be solved similarly.

No. He simply presented a mathematical proof that serves for all combinatorial games. [A technicality meant it only applied to chess with a drawing rule which forces games to be finite. Later this was extended to basic chess, where games can go on forever]

Firstly, Elroch has knowingly misrepresented the question, since he had claimed that Zermelo proved that chess could be mathematically represented, which involves representing chess as a series of equations.

This is a major misunderstanding of what mathematics is.

In general mathematics is about abstract truth, In the main this is revealed by the deduction of propositions from sets of axioms that define the properties of an object or a class of objects. For example, you can write a set of axioms that defines a vector space, then derive an infinite number of theorems that apply to all vector spaces. But it also incorporates more specific results, such as the result of an arbitrary calculation like 134798174 * 1382382. Solving a specific game is a bit like the latter.

The representations in Schaeffer's proof are part of the working of the proof that there is a drawing strategy for white and a drawing strategy for black. If you think of it as being like the working of a big arithmetic calculation, you won't go wrong.

This is a rather petty result to mathematics, which is interested in generalities rather than arbitrary examples. But to humans, the solution of a single classic game is of interest. By contrast, Zermelo's result is general. But it does not tell us the result of any game, nor provide any strategies - it just proves they exist! Mathematics is full of existence proofs, as well as more explicit results.

Schaeffer's work is in truth a huge proof most of which is done by a computer. This is perfectly normal - we can easily write a program to check things and be confident of the result even though the working is too big to check. Say a huge arithmetic calculation. Or, for example, the mathematical result that 2^82,589,933 − 1 is prime requires a large amount of computer checking to verify. It is certainly important that programs used to derive mathematical results are checked thoroughly. Ideally redundancy should be used, but the computational cost of results like solving checkers is too big for this to be fully done until the cost falls a lot.

Zermelo's theorem doesn't rely on any representation - it relies on the axioms defining a class of games. 

I am quite sure that it is impossible to expect that a simple proof by mathematical induction demonstrates that a simple, linear game such as noughts and crosses may be mapped to an extremely complex, non-linear (no, that's not a valid use of the term 'non-linear') game such as chess. Zermelo's claim was definitely bogus in this respect.

Let me be quite blunt - that is ignorant narcissism. Zermelo was a mathematician who developed the set theoretic foundation of all of mathematics, and you are a guy who boasts about IQ tests you took when you were young. More importantly, Zermelo's theorem stands today, tested by several generations of mathematicians, all more capable than you. If you disagree, show me your best work.

This is backed up by my son's judgement that representing chess mathematically is completely impossible.

I recall this from a few years back and understand what he meant - that you cannot simplify chess in a way which would permit a compact proof - it is too arbitrary. I think your son would understand that generating the 32-piece tablebase is conceptually possible (just impractical) and you can inform him that in the relevant sense this is "representing chess mathematically". This is the right sense, because it is the sense that determines if a proof is possible. Do discuss tablebases with him.

Elroch is a statistician,

I am not. My original specialisation was in mathematical analysis, and my MMath is in this area. I use probability theory in my work, and am a proponent of Bayesian analysis.

as against a very gifted mathematical analyst

he's a physicist, but I am sure his mathematical skills are good. Here the relevant field is game theory and I am not aware of his level of knowledge. 

who has performed groundbreaking mathematical procedures including representing magnetism mathematically as a product of fermionic spin.

Good for him. And irrelevant to this, to be frank.

I want to say a word about Elroch's behaviour. Elroch constantly switches stories.

I warrant that you are unable to exhibit a single example of two posts of mine that support this.

[deleted drivel]

See, like I said, ICCF players have solved chess... but I wont tell you my definition of "solved."

In any case, it more likely means humans have less and less useful input, and when the engines play each other it's unsurprisingly a draw.

On reflection, I was completely right. The mathematically inductive proof that Zermelo used for his simplistic ideas can only be extended to solving chess via a process of philosophically inductive reasoning, which happens to be false since like isn't being mapped to like. It's as though a crumpet is being mapped to a falcon.

No.

Read what MEGACH3SE wrote and learn something. You seem to have already forgotten that there are two non-overlapping usages of the word "induction", something that can be a problem at advanced ages.

And Bayesian analysis is statistical analysis, Elroch. I'm discussing equation creating and solving. And you have shown yourself too slippery for you to expect that your protestations will be believed by anyone. You shouldn't have used the tactics you tried to use to discredit my arguments, which are good ones.

I haven't read your comment, any of it

You seems to be saying that Playerafar is Elroch's alt. You really shouldn;t go round saying stuff like that you know!

Elroch was taken apart, cooked and served on a plate yesterday. He has no credibility here today, except with the trollish ones ....

And Bayesian analysis is statistical analysis, Elroch. I'm discussing equation creating and solving.

Mathematical analysis (my specialisation as a postgrad). Measure theory is the foundation of probability theory as well as integral calculus. The theory of distributions is supported by functional analysis (analysis in infinite dimensions).

Only your last comment, which was obviously based on desperation. Deleting those pictures; well, you shouldn't have posted them in the first place because they were offensive. Dio took them as a cue to start trolling and he made many off-topic attempted attacks. I realised I'd seen it before and then your mistake was to delete the pictures. I knew then that I was right, not about the bogus Theorem but about you.

OK you're trolling and you're out. You will be disregarded since it's merely attention seeking. Go and play with your toys.

You seems to be saying that Playerafar is Elroch's alt. You really shouldn;t go round saying stuff like that you know!

Elroch was taken apart, cooked and served on a plate yesterday. He has no credibility here today, except with the trollish ones ....

Solved chess does not have to be perfect play

It just has to look like it

I think what you mean is that the games in the ICCF competition merely have to appear correct.

This is true. But the main point is that even if they are all correct, they are about 10^20 times short of a full weak solution of chess, according to the only precise definition of weak solution used in the research community.

I have a very bad feeling there's an error somewhere with how they "solved " it

The ICCF have not come within a million miles of solving chess (according to the definition). They merely play (engine-assisted) chess.

Both coded signals to Dio have now been deleted. This is interesting since it confirms my suspicion that it's a signal and it tends to support the belief that they are prearranged signals. I have seen him employ them previously. There is no doubt that although Elroch portrays tygxc as intellectually dishonest, our eyes should not be on tygxc. It isn't mere intellectual dishonesty but consists of a willingness to do anything to win an argument, which includes deliberately confusing onlookers so they may wrongly imagine that he is winning.

sorry is not a giveaway is a free lottery in

guys! I have seen a very interesting free lottery from a certain Alexchess. They are interactive chess books converted from pdf to chessbase etc. There are also videos. I'll give you the link, I've already signed up!

It is in Spanish but the operation and so on are perfectly understood and there are books in English!

And it is something that was being searched a lot in the forums, such as having the pdf books converted and being able to study them in chessbase for example.

[link removed]

And also :

[link removed]

They could be downloaded here but now it won't let me, the links must be dead but they can be requested and he sent me one!