Chess will never be solved, here's why

Or both.  Three situations.
Apparently tygxc oscillates through the three.
And through others too. 
Often acting as if he doesn't understand what is being said to him while actually understanding some or all of it.
This would happen with 'flat earth' positions too.
Again not personal.  Simply addresses his postings.

#3088

"Next to brute-force methods it is often beneficial to incorporate knowledge-based methods in game-solving programs." ++ So I use knowledge to prune like 1 a4 and 1 e4 e5 Ba6.
It would be a waste of resources to look into something we know.

"Yes, but things believed to be true although not proven are conjectures."
++ Yes, formally they are hypotheses or conjectures.
However, there are hypotheses or conjectures with more evidence supporting them.

"If they are used as premises, the result is a conjecture too, not a proof, therefore no solution."
++ Assessing the feasibility of weakly solving chess need not be exact.

"that is just a fallacious circular reasoning."
++ No, that is done in various branches of science, e.g. mathematics and physics.
Example: What is the velocity v of an electron with charge e and mass m accelerated by a voltage V?
Solution: start by the hypothesis: v << c the velocity of light c. Thus use Newtonian mechanics:  eV = mv² / 2 and calculate v = sqrt (2eV / m). Now check if v << c then the hypothesis was true and the calulation valid, else change to relativistic mechanics.

"We have not to believe anything, we have just to find out"
++ In order to find out you have to start with a hypothesis.
E.g. if you try to prove the Riemann Hypothesis, then you start by believing it is true.

Do you even read what I wrote? You pick only what remotely can support your views, ignoring what can contradict them; it's a fallacy. After that statement you find in the paper what type of knowledge is used to find a solution. None of those heuristics cuts off lines arbitrarily the way you do. And you still use "know" to refer to conjectures, that are only believed true.

Whatever, but we need a proof, not a conjecture built upon conjectures.

You play with words. You are describing a process to get a solution, but that "solution" would not meet the criteria of a solution, which is a proof.

 Mmmmh... You maybe right that your assumption that the game-theoretic value is a draw does not lead to circular thinking, but the way you make use of it is fallacious, nonetheless. In the example you give, two different models can be used to answer the question. Both models are not proofs: they are theories, but one of them has been disproven (that is, it is not valid in all cases) the other one is general (so far). However, both models are not built on the premise that v has a particular value; that is, no particular value of v has been used to derive those models and they do not prevent the possibility to be falsified for some particular value of v, as indeed has happened for the classical model. Back to your method to find the solution, you use the conjectured value of the game as a basis to cut off lines, but those lines might actually falsify the conjecture. What I mean is that the conjecture may artificially support itself. If not circular reasoning, it's a form of faulty generalization.

No, why? An hypothesis is just an hypothesis. It may be true, it may be false. To seek objectivity, one should avoid the confirmation bias as much as possible.

#3091

"And you still use "know" to refer to conjectures"
++ "know" is chess knowledge and that is allowed and beneficial to weakly solve chess.
It is known that 1 e4 e5 2 Ba6 loses for white and that 1 a4 is not better than 1 e4 or 1 d4.

"Whatever, but we need a proof, not a conjecture built upon conjectures."
++ That is purism. It is allowed and beneficial to use chess knowledge to weakly solve chess.
It seems minds are changeing. First it was: "chess cannot be weakly solved as there are too many games/positions". Now it is: "no, you are not allowed to prune using chess knowledge."

"You are describing a process to get a solution, but that "solution" would not meet the criteria of a solution, which is a proof."
++ There are two different things:
1) assessing the feasibility, that need not be exact: approximate is enough
2) weakly solving chess. It needs to be exact and a proof, but use of chess knowledge is allowed and beneficial.

"You maybe right that your assumption that the game-theoretic value is a draw does not lead to circular thinking" ++ You begin too see

"but the way you make use of it is fallacious, nonetheless." ++ Fallacious because you say so?

"Both models are not proofs: they are theories, but one of them has been disproven"
++ Both models are knowledge. Both have been disproven. If V is very small, then quantum mechanics is needed. Relativistic quantum mechanics is rarely uses to calculate anything.
There are many more examples in science. E.g. the Maxwell equations are believed to be true. However they are too hard for most problems. In practice low frequency approximations, high frequency approximations, near field approximations, and far field approximations are used. Same methodology. First assume the approximation is valid. Then calculate with it. Then verify the assumed approximation is valid indeed.
The same with fluid mechanics. The Navier-Stokes equations are believed to be true, but are hard to use. Assume the Reynolds number is small. Calculate with the laminar flow hypothesis. Calculate the Reynolds number. If it is small, then the calculation is valid, else use another model. 

"you use the conjectured value of the game as a basis to cut off lines, but those lines might actually falsify the conjecture."
++ No, I do not use the game value. I use chess knowledge to cut of lines. I cut off 1 e4 e5 2 Ba6 because it is known to lose for white. I cut off 1 a4 because it is known not to be better than 1 e4 or 1 d4. I cut off some endgames with opposite colored bishops as these are known draws.

"What I mean is that the conjecture may artificially support itself."
++ Yes, my statement that 4 candidate moves suffice at 17 s/move on a 10^9 nodes/s engine for 1 error in 10^20 moves is based on the hypothesis that chess is a draw.
If that poses a fundamental problem to you, then there is another approach: successive approximations as also often used in other sciences.
First let the engine autoplay and verify it ends in a draw, or taken an ICCF WC drawn game.
Then in a 1st verification pass replace all white moves by the engine 1st alternative and check it is still a draw.
Then in a 2nd verification pass replace all white moves by the engine 2nd alternative and check it is still a draw.
Then in a 3rd verification pass replace all white moves by the engine 3rd alternative and check it is still a draw.
Add some more verification passes if you like.
Each verification pass increases the confidence level.
That is also common in many sciences. E.g. I have measured 1000 screws of a mass production of millions and I can say with 99.96% certainty that none exceeds the tolerance of 25 mm +- 0.1 mm.

"To seek objectivity, one should avoid the confirmation bias as much as possible."
++ There is subjectivity even in mathematics.
Trying to prove the Riemann Hypothesis is completely different from trying to disprove it.
It has nothing to do with bias, but with efficiency.
People trying to prove it are convinced by all failures to disprove it.

Chess "knowledge" is not proven, it's a bunch of conjectures "proven" by examples. For the third time, in the paragraph 5.2 of the paper you quoted, are described four algorithms: if you want to prove that that paragraph supports your claim, you should prove that any of those algorithms prunes 1. e4 e5 2. Ba6; otherwise, you are simply jumping to conclusions.

No. A solution is a proof, therefore it's simply not possible to call "solution" a conjecture, or anytihing based on a conjecture.

I never stated that chess cannot be solved because there are too many games/positions; you are confusing me with someone else.

A solution is a proof that a value v is the game-theoretic value of the game, and s is a strategy to achieve that value. The feasibility to determine s and v is already proven, because it can be done by exhaustive search; however, an exhaustive search would require too much time with current technology. Instead,
1) if you want to prove that a process P can determine s and v in 5 years, then you have to be as rigorous as for any other proof.
2) If you want to theorize that a process P can determine s and v in 5 years, then you have to use as few assumptions as possible and deduce the result rigorously.
3) If you want to theorize that a process P may determine s and v in 5 years, then it's basically worthless. It is a theory of a theory.
The third thing is what your process would accomplish, as explaind below.

Science provides a methodology, but it has to be clear that science does not prove anything. I think that Wikipedia is good enough to explain that:

   "Philosophers, such as Karl R. Popper, have provided influential theories of the scientific method within which scientific evidence plays a central role. In summary, Popper provides that a scientist creatively develops a theory that may be falsified by testing the theory against evidence or known facts. Popper's theory presents asimmetry in that evidence can prove a theory wrong, by establishing facts that are inconsistent with the theory. In contrast, evidence cannot prove a theory correct because other evidence, yet to be discovered, may exist that is inconsistent with the theory. [ . . . ] Alber Einstein said:

   The scientific theorist is not to be envied. For Nature, or more precisely experiment, is an inexorable and not very friendly judge of his work. It never says "Yes" to a theory. In the most favorable cases it says "Maybe", and in the great majority of cases simply "No". If an experiment agrees with a theory it means for the latter "Maybe", and if it does not agree it means "No". Probably every theory will someday experience "No" – most theories, soon after conception."[1]

The only real proof is a mathematical proof. It cannot be disproven if the axioms are not challenged. That's what a game-theoretic solution is. For chess, the axioms are the rules used to play the game.

Not only:

To everyone it is a problem in your theory. I also asked you to express your algorithm in pseudocode, which is more rigorous, instead of using common English. Just translate your statements in pseudocode or simple code with inputs and outputs, black blocks. Then we shall see how it works, even wihtout the details.

I don't know how you can prove how many attempts to prove or disprove the Riemann hypothesis have been made, but of course there is subjectivity in every choice. Nonetheless, a mathematical proof is objective, unless the axioms are challenged. You seem fixated with the Riemann hypothesis, but I was talking in general. Sometimes it is better to directly prove something, sometimes it is more efficient a reductio ad absurdum. This is independent of what one believes. Back to the topic, if you say: "1. e4 e5 2. Ba6 is likely to lose, let's make it the last candidate", it's ok; if you say: "1. e4 e5 2. Ba6 loses for sure, let's prune it immediately", it's not ok, because it is not proven (mathematically, I mean) that it loses.

Sveshnikov acknowledged that chess is an exact mathematical problem and I think he was aware that his idea of "solution" was not a game-theoretic solution, that's why in that interview he used the word "close" instead of "solve" and the word has been enclosed in scare quotes. If he meant a real weak solution he would have just stated that, don't you think?

#3093
Here is the google translation of the last part of the interview:
"What is your coaching credo?
I was able to teach master candidates to understand the opening, to write lectures on openings, materials for the encyclopedia. After all, you yourself wrote a lecture on the Spanish flute with g6, after that you read it to the first-class players and gave them a session in this opening with Black. You won with a score of 8:1 - you have delved into this position so much. And a year later you made a draw in this opening against Tal. And another student, with my help, wrote a lecture on the Panov attack in the Caro-Kann defense. The article is by far the best theoretical work on this option. At that time, my students did not yet use a computer, and only had what was available, plus my games.
The path that I myself walked, I wanted my students to pass. Now I think that the endgame should be studied in parallel with the opening. Chess is an exact mathematical problem, and you need to study it from two sides - the opening and the endgame. There is no such stage as the middle game. A well-studied opening is the middlegame. Often a deeply analyzed opening leads directly to the endgame. This is how Lev Polugaevsky understood chess. Of the great chess players, he is the closest to me. Soon all openings will be given exact scores, and if the variant is correct, it will lead to a technical endgame in which a draw will be achieved with accurate defense.
Today I teach children how to work with a computer. It is now impossible to study the opening without it. Give me five years, good assistants and the latest computers - I will bring all openings to technical endgames and "close" chess. I feel the strength in me.
Questioned by Eldar Mukhametov"

The idea of this weak solution for chess is nonsense and so is the definition quoted earlier. I actually thought the definition given of "weakly solving chess" was a joke.

van den Herik is a games theorist .... presumably one of thousands of them. There's no reason at all to assume that his definition is useful. In general, a weak solution of an equation is given as a weak equation that corresponds to its objects within limits. There are many attemped definitions of weak solutions, within mathematics.

Today I teach children how to work with a computer. It is now impossible to study the opening without it. Give me five years, good assistants and the latest computers - I will bring all openings to technical endgames and "close" chess. I feel the strength in me.
Questioned by Eldar Mukhametov"

They are obviously the words of a nutcase. I also feel the strength in me to know that I'm right about this.

#3093

"Chess "knowledge" is not proven, it's a bunch of conjectures "proven" by examples."
++  We disagree on that. Some chess knowledge is absolute. See for example the scientific paper "Acquisition of Chess Knowledge in AlphaZero" it says knowledge, not conjectures.

"in the paragraph 5.2 of the paper you quoted, are described four algorithms"
++ Yes, the algorithm is brute force and making use of chess knowledge is said to be beneficial

"A solution is a proof" ++ Yes, but we disagree on what proof is acceptable.

"you are confusing me with someone else." ++ I am sorry for that.

"The feasibility to determine s and v is already proven, because it can be done by exhaustive search; however, an exhaustive search would require too much time with current technology."
++ Feasible means it can be done in a reasonable time, like 5 years. 5 million years is not feasible.

"1) if you want to prove that a process P can determine s and v in 5 years, then you have to be as rigorous as for any other proof." ++ No, about 5 years is enough. 5.24 or 4.89 is the same. It is proof of concept necessary as a prerequisite to embark on the solution.
"2) If you want to theorize that a process P can determine s and v in 5 years, then you have to use as few assumptions as possible and deduce the result rigorously." ++ Approximately is OK.
"3) If you want to theorize that a process P may determine s and v in 5 years, then it's basically worthless." ++ If the 'may' is plausible enough then that may be enough to start the solution.

"Science provides a methodology, but it has to be clear that science does not prove anything."
++ Science is a set of knowledge that is proven to satisfaction.

"I Popper provides that a scientist creatively develops a theory that may be falsified by testing the theory against evidence or known facts."
++ That is correct. I claim that evidence and known facts (expert opinions, TCEC, ICCF WC, AlphaZero autoplay, classical WC...) falsify the theories that chess is a forced win for white or for black. The are inconsistent with those theories. In your terms I use reductio ad absurdum to prove chess is not a win for white or for black. It is also what Sveshnikov says: "a draw will be achieved with accurate defense."

"The only real proof is a mathematical proof."
++ I disagree, it would mean that mathematics were the only science. Thermodynamics for example is taught now starting from axioms and using statistics. That is not how it has been developed. It used to be a practical way to predict the behavior of steam engines and the like.

"For chess, the axioms are the rules used to play the game."
++ That is right, but from these axioms Laws of Chess absolute chess knowledge has been deduced over centuries, in part by mathematicians like Anderssen, Steinitz, Lasker. Also Capablanca, Botvinnik and Sveshnikov had engineering backgrounds. So in weakly solving chess we can use that chess knowledge as beneficial. We are not obliged to re-invent all that.

"You seem fixated with the Riemann hypothesis"
++ I just take that as an iconic example of an unsolved mathematical problem.
Maybe the Goldbach Conjecture is a better example as it is simpler to state to the layman.

"This is independent of what one believes." ++ No, a mathematician starts by believing whether a conjecture is true or not and based on that he proceeds trying to prove or disprove it.

éif you say: "1. e4 e5 2. Ba6 loses for sure, let's prune it immediately", it's not ok, because it is not proven (mathematically, I mean) that it loses."
++ We diagree. In my opinion the grandmasters of the past have already proven that starting from the Laws of Chess and AlphaZero has only reconfirmed this knowledge. Likewise they have proven that 1 a4 is not superior to 1 e4 or 1 d4 and AlphaZero has reconfirmed this knowledge.

"in that interview he used the word "close" instead of "solve" and the word has been enclosed in scare quotes." ++ My Russian is not good enough. How is weakly solved in Russian? From the context it is clear he meant a real weak solution.

#3097
"They are obviously the words of a nutcase."
++ That says more about you than about Sveshnikov.
He had a master in engineering and was working on a PhD in engineering, while you dropped out in the first year.
He was a grandmaster and 65+ World Champion, while you are a weak player.
He was a professional chess analyst, you are not.

#3096
"van den Herik is a games theorist "
++ Yes, he is/was the most prominent authority on that subject.
You are neither a mathematician nor a game theoretician.
His definition is the definition. By the way it originates from Allen, the man who solved Connect Four.

Being good at gymnastics doesn't make someone an authority on biophysics.

It talks about me only inasmuch as I can tell there's something very wrong with him. We all "feel the power", occasionally. The point is that Sveshnikov was **so completely wrong**, that what he could feel was clearly in his imagination.

You think I dropped out of mechanical engineering in the first year? No, I passed the first year easily, coming about 9th out of about 81 students, without trying overly hard. I dropped out during my second year. It's obvious that you know a little about me: I wonder where from. But the information you have is garbled. I ended up studying philosophy. That means I can argue rationally.

Calling me a weak player isn't correct and indicates that you have no idea about relative strengths of chess players. I'm weak in comparison with GMs but have been considered a strong player locally and on tournament circuits.

It seems that you have no answers. If you were surer of your position, you wouldn't engage in ad homs. My calling Sveshnikov a nutcase definitely isn't an ad hom. A ad hom is based on a prejudgement. I call him a nutcase because his only justification for his ridiculous prediction is that "he has the power". Well, he clearly didn't have the power and being a professional chess analyst does not indicate that he understood the first thing about analysing chess in the way we are discussing. He clearly didn't.

That paper does not state that the knowledge is "absolute". AZ play is based on probabilities: it knows that playing 1. e4 e5 2. Nf3 gives (in its autoplay) a better expected outcome than playing 1. e4 e5 2. Ba6, but its conclusions are not definitive.

Those algorithms already use "knowledge" which is not really game-specific. They are less brute-force algorithms. After the sentence that you quoted so many times you can read: "The main advantage is providing an appropriate move ordering or selection in the search tree", not to prevent the exploration of some lines like you intend to do.

In my dictioinary, "feasible" means simply that it can be done (it derives from latin facere). That can be interpreted in different ways. Anyway, suffice that we do understand each other.

You say I am a purist? Of course 5 years can be little more or little less. The point is that if you want to prove that chess can be solved in such little time, your proof must be as rigorous any other proof.

If the result is not certain, it is abusive to call it a weak solution. A weak solution cannot be disproven, yours may be.

This statement is ambiguous, like too many other you use.

In your personal conception of what proofs and falsifications are.

No, it means that natural sciences can only diprove things, because they cannot prove them. Again from Wikipedia:

   "Proofs are examples of exhaustive deductive reasoning which establish logical certainity, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds true is not enough for a proof, which must demonstrate that the statement is true in all possible cases."[1]

So, since classical mechanics does not hold true on atomic scale or for speeds comparable with the speed of light c, it is disproven, even if it is obviously used for more common cases. That's why Einstein said that probably every theory will be disproven someday: they are just more or less inaccurate models.

I don't even know what you mean by "absolute knowledge". If you mean that it is proven that the strategic principles hold true in any position, you are for sure wrong, simply because we do not know all the possible cases. That's why a strategy has to be tested against all possible opponent's moves, to prove which is the minimum outcome that that strategy can forcingly achieve.

I don't even know where you take those type of informations. A mathematician can just start from axioms and/or theorems. Other times, they have just a question, not the possible answer, and use axioms and theorems to answer it, without even making hypotheses. Again, you are inclined to overgeneralize special cases.

In your opinion. See above.

I do not know Russian too, but I think he would have used too words, like in English. To me, it is not clear at all that he meant a real weak solution, especially because the word "close" is enclosed in scare quotes. Why use them?

No, it means that natural sciences can only diprove things, because they cannot prove them. Again from Wikipedia:

   "Proofs are examples of exhaustive deductive reasoning which establish logical certainity, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds true is not enough for a proof, which must demonstrate that the statement is true in all possible cases."[1]>>>

Mankind has proved that gravity consists of a mutual attraction of massive bodies which operates as an inverse function of the distance squared. There's no doubt about that, as a very close approximation.

I think, Hikaru, that it's a bit much to claim that we cannot prove but only disprove anything. I understand the idea. It's easier to show something won't work than that it will work, only it isn't working at the moment. But that's talking about "easier" rather than "possible".

I think it is good to keep the distinction between proofs and scientific reasoning clear, but for the proverbial "man in the street", it is convenient to lump them together as reliable ways to arrive at conclusions that can be reliably taken to be true thereafter.

Good point, I'm sad to say.

Chess theoretically can be solved, though that won’t diminish chess as a game. People who follow the engine simply get banned, and humans cannot solve it on their own. So don’t worry, chess will be here for a long, long time. But talking mathematically, computers can crack chess. Hopefully, the community won’t find it boring.