don't need to be constrained to inhabit a world of mathematical purism, which is an ideal world, only loosely related to reality
perfect
Except for the part where we are trying to solve chess...a process that has strictly defined solutions, all of which require "ideal", i.e. not imperfect, efforts.
It's a ridiculous statement in this context. Maybe if you are trying to tell your kids that they are human beings and it's okay not to be perfect, it works...
"You are saying that it is axiomatic that chess can be mathematically solved, aren't you? Not only that but that's it's a CORE AXIOM OF MATHEMATICAL PROOF."
never said that
I thought he was talking to me. But we surely agree on this issue.
basically optimissed's argument that chess cannot be solved mathematically is that he casts doubt on the very nature of such a proof, however the way he casts doubt makes no distinction between chess and any other math proof that could exist. I was pointing that out, and optimissed thought that I meant that the proof itself was just an axiom, even though we agree it is in fact derived directly from axioms.
tbh tho this thread hasnt required any more than the mathematics I learnt in middle school (tbf i was a couple years ahead and did competitions that focused heavily on game theory topics but still)
there's no calculus required here. no vectors, fields, or groups.
^^ Again, you're making assumptions regarding the correct application of mathematical expertise. Those assumptions are subject to questioning. Merely your complete insistence that you're right raises questions regarding the assumptions you must have made for you to be so sure.
Lol...this applies to Tygxc, and to you. Not to anyone sticking with the defined parameters of solving games.
Anyone that "knows" chess is a forced draw (your stated position) is the undisputed king of "your complete insistence that you're right raises questions regarding the assumptions you must have made for you to be so sure".
OK that's a fair comment but ty is entitled to his utter rejection of a mathematical approach. He says he has trained to be a mathematician. It is because my son is a mathematician that I do realise its importance and am willing to meet you halfway. Incidentally, son claims he is now a data scientist. He certainly has a wonderful array of large screens in the new office he just had their garage converted into. One of them is even curved, which is really impressive.
I thought he was an engineer, so I was mistaken.
Glad you found out what your son does for a living...kudos.
You are easily impressed. Curved monitors have been around for 10 years now. You can buy them at Costco.
Tygxc is in no way "entitled" to makes claims about solving chess using his faulty methods. What he is entitled to is his personal opinion. Every time he states "chess can be solved by 10^17 blah blah blah..." in response to people, he is knowingly lying at this point, in much the same way that when you claim to have paranormal powers, you are willfully saying something you know to be false no matter how much you wish to believe it.
Humility discourages me
thatsa first lol ! just teezing L♥
any combinatorial game
it can be (transpositional) but its more like a big giant permutation.
don't need to be constrained to inhabit a world of mathematical purism, which is an ideal world, only loosely related to reality
PERFECT ! (just 4u dodo due)
don't need to be constrained to inhabit a world of mathematical purism, which is an ideal world, only loosely related to reality
PERFECT ! (just 4u dodo due)
Repeating the ridiculous does not make it any more correct. But otherwise, kudos for actually asking some basic questions and engaging after only 620+ pages.
"Can you prove that chess can be exactly represented as a set of equations??"
"My son says it's almost certainly impossible"
I can almost guarantee a misunderstanding between you and your son. your son probably believes that you are referring to some positional algorithm of a solution, which is almost impossible.
the mathematical representation of chess literally exists within the code used in chess.com.
a game to be represented mathematically is not necessarily a solution of the game directly from a mathematical framework, but just an explanation of the rules of the game as a mathematical object.
"Says who? If you can't prove it then it's an axiom"
the definition literally dictates that it has been proven already, unless there is some miscommunication relating to you.
That's more like it. Axioms are fundamental building blocks, necessary for deductions to be made. The idea that it's axiomatic, which means that we may assume it to be the case since it's obvious, that chess may be solved mathematically, is quite ridiculous. It also assumes that which we're trying to establish, as to whether chess can be represented mathematically by means of sets of equations. It assumes it to be the case, which is of course is the problem with the game theory stuff.
<<THEOREM: There is a methodical way to find optimal strategies for any combinatorial game. The procedure can be implemented as a program.>>
Says who? If you can't prove it then it's an axiom and we've just rejected axioms which put the cart before the horse. Can you prove that chess can be exactly represented as a set of equations?? My son says it's almost certainly impossible. He should know.
You are talking about apples and oranges. Programming a solution that solves chess and reducing chess in its entirety to mathematical equations are not equivalent in any way. The latter might be required for your premise of a pure algorithmic solution to chess, not but for solving chess via a combination of brute force and pruning. Your son is correct, your approach is actually harder to complete as things sit. Now if brute force produces enough quantifiable truisms over the centuries, maybe the algorithmic approach will become more plausible. As is the case for a number of games, though, brute force and proper pruning (*not* 27 orders of magnitude of vague casting off of positions) may solve the game, at which point backing into a pure logic and rules-based solution of chess that fits your bill might be possible. But certainly not within our lifetimes with any foreseeable technology we are working on currently.
Dio, I am so much more intelligent than you that you would not have the faintest idea when, how or why I'm right. Everything is so completely beyond you.
This argument is, of course, completely empty (as most of yours tend to be). There's not a single word after "Dio" that is not pure opinion and conjecture on your part. Not one iota of data. Not one ounce of supporting detail. This is your method of analysis and exposition in general...bereft and empty.
well he outsmarts u all day. and thats a fact !
esp when u bumble out s/t 1900's dum like this:
certainly not within our lifetimes with any foreseeable technology we are working on
its ok to be behind...we u/s lol !
He outsmarts everyone according to criteria he sets himself and his own judgements. Whether these have any real value is questionable.
i love to see scientists debating
Especaly when they pretend they know more about a subject than a math nerd
Anyway, I asked Elroch to prove that it's correct, according to a theorem of combinatorial games theory, that chess can be solved mathematically.
He just told us that it wasn't an axiom, by the way, MEGA. I thought we were making some progress. However, you were more correct than Elroch, seemingly, because if he can't prove that it can be solved mathematically (and that proof has to be a syllogistic proof, which is what he always demands of others) then it's a axiom.
Having an axiom that chess can be solved mathematically is exactly equivalent to an axiom that states that mankind will reach other galaxies in their space exploration. Now, I'm not saying it's impossible but I strongly doubt it. The axiom is based on "mankind can travel, therefore mankind can travel to other galaxies" and is exactly equivalent to "simple combinatorial games can be solved mathematically: therefore chess can." I would require a proof, please, or you've lost the argument.
You would lose the argument since you would not have responded in kind. You required deductive proofs from tygxc but you cannot give them to defend your own far less reasonable claims.
@Optimissed, this theorem even has its own wikipedia page.
If you want a formal proof, here is one (it's half a page long after the definitions have been made):
The original paper was published in 1913 (in German), and apparently it was the first published paper on game theory. It needed an addition published in 1927 to be a truly rigorous proof for basic chess (where there are a finite number of possible positions, but games can be indefinitely long).
Interestingly, this is the same Zermelo who has his name attached to the Zermelo-Fraenkel axiomatisation of set theory that is perhaps the most popular foundation for mathematics.
[Remark: It strikes me that Zermelo's theorem can be easily generalised to a game where there is a general finite ordered set of outcomes].
It's not axiomatic, it's a theorem of the relevant branch of game theory.
THEOREM: There is a methodical way to find optimal strategies for any combinatorial game. The procedure can be implemented as a program.
I could certainly write such a program. It's not difficult if you don't add other constraints. It's not worth the effort since all of us know it requires impractical resources to get to the answer.