I take it that some agreement has been arrived at as to how to define "solved" somewhere. Can anyone recall what it was?
If it means that every conceivable position legally arrived at has to be shown to be a win, loss or draw, it is not going to be done, even by a computer, any time soon.
usually when threads get so long it's buried... can't find any post except in the beginning 5 and the end 5.
https://www.chess.com/forum/view/off-topic/spending-to-much-time-indoors-in-front-of-screens-2?page=1#last_comment
Some mathematician (Ernst Zermelo) actually studied this. It sounds pretty simple, but his work was considered notable because it had some interesting conclusions. Basically, if White can force a win then Black cannot. And vice-versa. Or if neither can force a win, then both can force a draw.
So either chess is a draw, or one player can force a win. Sounds pretty simple.
It's funny that this thread is getting close to 4500 comments and nobody has solved it. And mathematicians haven't figured it out yet either. A crazy problem in game-theory!
Haha! ‘If White can force a win then Black cannot.’ Really? You need to study this as a mathematician to see it?
Of course if White can force a win from move one then Black cannot. And vice versa: if Black can force a win from move one then White cannot.
Vickalan is a little too logic-averse to understand this obvious concept. Any decent chess player that thinks it through for a minute will realize this without any math 
. Sadly, Vickalan doesn't play decent chess, and therefore does not grasp that this is far from an interesting conclusion...maybe he can spruce it up with a graph.
Every axiom is a theorem
Not quite. A theorem can be demonstrated, while an axiom is a statement accepted as a fact without demonstration.
A theorem can be demonstrated. An axiom cannot.
Which is why, without accepting the fundamental equation that 1+1=2 as true, you cannot demonstrate that 2+2=4, 3+3=6, and so on.
I was a mathematician originally, and I can assure you that each axiom is itself a trivial theorem in the formal sense: they are propositions that can be proven from the axioms. It just happens that in this dull case, the proofs involve only one step - exhibiting the axiom.
It is actually surprisingly common for this pattern of verifying a proposition by simply looking it up in a list of assumed true propositions to be used.
For example, consider this set of axioms: "Humans are great apes" "Gorillas are great apes" Chimpanzees are great apes" "Orang utans are great apes".
If presented with the proposition "XXX are great apes" for some species name XXX, the first thing you would do is check your list of axioms to see if the proposition was there, and would consider it proven if it was.
Most mathematics involves more involved reasoning, for sure.
Still, it seems revealing to me that without taking a fact like 1+1=2 for granted, as a fact that cannot be proven through any mathematical means, the subsequent calculations are based on this unprovable equation.
It seems that math is not a system that can stand on its own, but instead relies on accepted truths. For all of its rigorous demonstrations with one thing flowing logically into another, similar to chess but on a bigger scale, it seems disappointing that the logic it uses relies on the illogical consequence of an axiom, which in essence is:
‘ Don’t ask why, it is so’!!
If that is the foundation on which the whole math is built, no wonder we have many scientists drowned in personal beliefs: it is the foundation of their entire work/knowledge ( behind the facade of logic they’ve built over that foundation)!!
Some mathematician (Ernst Zermelo) actually studied this. It sounds pretty simple, but his work was considered notable because it had some interesting conclusions. Basically, if White can force a win then Black cannot. And vice-versa. Or if neither can force a win, then both can force a draw.
So either chess is a draw, or one player can force a win. Sounds pretty simple.
It's funny that this thread is getting close to 4500 comments and nobody has solved it. And mathematicians haven't figured it out yet either. A crazy problem in game-theory!
Haha! ‘If White can force a win then Black cannot.’ Really? You need to study this as a mathematician to see it?
Of course if White can force a win from move one then Black cannot. And vice versa: if Black can force a win from move one then White cannot.
Vickalan is a little too logic-averse to understand this obvious concept. Any decent chess player that thinks it through for a minute...
A minute? Nah, it can be seen instantly if one considers a forced win from the very first move. Then it’s crystal-clear.
...maybe he can spruce it up with a graph.
Are your feelings still hurt?
...maybe he can spruce it up with a graph.
Are your feelings still hurt?
You've never managed to hurt my feelings .
But it is fun to point out your constant gaffes and pratfalls, because you are always overly smug even if the face of your own outright ignorance or lack of understanding.
...it is fun to point out your constant gaffes and pratfalls...
Oops, you made another mistake. Ernst Zermelo is a well respected mathematician and game theorist (look him up). You resorting to insults just makes it seem like you're a crybaby.
well :-)
you guys are talented in chess pratics, mathematics, philososophy, game theory ,theory probability , chess strategy\theory and history...
u make the Mensa a minus habens club.
your parents should be very proud
Still, it seems revealing to me that without taking a fact like 1+1=2 for granted, as a fact that cannot be proven through any mathematical means, the subsequent calculations are based on this unprovable equation.
It seems that math is not a system that can stand on its own, but instead relies on accepted truths. For all of its rigorous demonstrations with one thing flowing logically into another, similar to chess but on a bigger scale, it seems disappointing that the logic it uses relies on the illogical consequence of an axiom, which in essence is:
‘ Don’t ask why, it is so’!!
All this is true. Mathematics can never be proven to be correct. The reason we trust it comes down to two things. The first is that a chosen formal system encapsulates the behaviour of objects we intuitively understand. For example Peano's axioms do a good job of encapsulating the intuitive idea of counting numbers. The fact that however many times you add one to a number, you will never get zero has to be assumed: it is an axiom. There is an inescapable reason for this: if we make a different assumption, we get a different mathematical system. (A classic example is the parallel postulate. This is an axiom which can't be proven. If you replace this axiom, you get spherical or hyperbolic geometry instead of Euclidean geometry).
Secondly, these formal systems are consistent. It is no good having a set of axioms and rules if with them you can prove anything and its negation!
Regarding the consistency issue, it is a well-known theorem that it is impossible to prove the consistency of any mathematical system that includes number theory (this contrasts dramatically with first order logic). So mathematicians rely on an intuitive belief in consistency (consistent with the evidence). In addition, no formal system that includes number theory is complete (again contrasting with first order logic).
Right, but let us be clear: if we change the basic axiom of one system we get another system, also based on a belief, a statement which can’t be proven.
As for numbers, well, if you add one to a number you can never get zero, provided that number is zero or bigger, a positive number. Enlarge that domain to include negative numbers and zero suddenly becomes a possibility.
But the larger implication is that you see mathematicians ( and scientists in general) believing in a supernatural factor, and at first it seems shocking, that a logical person’s whole view of life is based on a superstitious belief.
But seen through this bigger picture that their whole profession is based on a bundle of beliefs, it suddenly seems to make sense, not in the sense of them being correct, but of explaining their outlook on life.
Right, but let us be clear: if we change the basic axiom of one system we get another system, also based on a belief, a statement which can’t be proven.
As for numbers, well, if you add one to a number you can never get zero, provided that number is zero or bigger, a positive number. Enlarge that domain to include negative numbers and zero suddenly becomes a possibility.
True.
I was also thinking of cyclic abelian groups and fields, where (1 + 1 + ... + 1) can equal zero for some number of ones.
But the larger implication is that you see mathematicians ( and scientists in general) believing in a supernatural factor, and at first it seems shocking, that a logical person’s whole view of life is based on a superstitious belief.
This is nonsense. There is belief (eg in consistency) but it is a huge blunder to think all beliefs are "supernatural" or "superstitious".
But seen through this bigger picture that their whole profession is based on a bundle of beliefs, it suddenly seems to make sense, not in the sense of them being correct, but of explaining their outlook on life.
Everything we do is based on beliefs. You eat your lunch because you believe it is not poisoned. Is this a fundamental flaw in your behaviour, perhaps to be described as superstitious?
Not all beliefs are superstitious, based on the supernatural. I did not imply that. I only went directly to that belief, expressed publicly by many mathematicians or scientists in general, and drew a parallel between that deep belief and the fact that their whole profession did not discover something which is beyond belief, just like any non-scientific mind out there.
It seems that a scientist’s mind is operating differently than a layman’s, and it turns out that deeply it doesn’t.
Now, we can go even deeper. Expressed or not, the belief in a supernatural ‘agent’ is a common factor of humanity. Some may call themselves atheists or agnostics, but that is just the facade. In a true crisis, that deeply buried belief will come to life, asking that agent for this or that, regarding their life or that of their loved ones.
As long as a human being has not solved the problem of fear, of mental insecurity, they are bound to believe in a creator, in somebody who looks after them, essentially, in an ideal parent.
As medieval as that is, its root, which is fear, has never been solved, and so this false crutch has always existed, logical thinking on the surface or not.
Because a logical scientist/mathmetician is deeply irrational in his everyday life. At the core of his being, he is irrational, which is why you see them snap, from time to time, and commit horrific crimes, just like anybody else: the irrationality was there all along, snap or no snap. Their entire profession becomes an escape from that fundamental fear, common to all mankind.
But that is well beyond the scope of this thread, which only deals with solving a game created by the same mind which lives with a basic illusion.
...it is fun to point out your constant gaffes and pratfalls...
Oops, you made another mistake. Ernst Zermelo is a well respected mathematician and game theorist (look him up).
Yes, and you failed to understand that his conclusion was obvious, and needn't be stated to chess players, but only to those who don't really understand chess moves or basic logic. Carl Sagan liked to talk about billions and billions of galaxies, and he had great credentials, too. It doesn't mean that every schoolchild who took any Astronomy at all didn't know that there are billions and billions of galaxies...the difference here is that you presented the "billions" equivalent as some profound insight. This is something that is done by somebody that has no understanding of the subject at hand, but likes to makes constant appeals to authority. You toss out names and links to papers, but display a complete lack of understanding whenever you actually are called upon to use your own smarts to interpret anything .
It is inherently obvious to a chess player that gives it any thought that if white has a forced win, black cannot also have one, and vice versa. How could this be a surprising conclusion for you? No, seriously...how?
troy when some calls themselves "atheists" it is NOT a facade.
Are you sure ponz?
You see, it’s the opposite side of the same coin. Which is belief.
A religious person says ‘ I believe that God exists.’
An atheist says: ‘ I believe that God does not exist.’
They both believe, they both don’t know, they both have doubts. Same difference. In fact the same amount of doubt is countered by the same amount of ‘faith’, or counter-doubt. It appears differently only because the conscious and the unconscious percentages vary from person to person—one may exhibit 31% doubt and 69% ‘faith’, consciously, while unconsciously it’s the opposite. The bottom line percentage is always 50-50, just like desire, which always has a counter-desire, if one observes the human psyche closely.
Now, the atheist is simply not aware of his doubts, of his beliefs, of his projections. But in the middle of an acute crisis, the atheist will also invoke a superhuman factor, a creator, someone who has the power to change a sad (for him) destiny. Just watch an atheist in times of crises, or watch yourself if you are one. Even when the prayer to such an entity is repressed, it only indicates the hidden belief in the superstitious factor.
The reason is simple: both the religious and the atheist are not free of fear, of the illusion which produces fear, insecurity and so they both project the same supernatural image, in essence.
...it is fun to point out your constant gaffes and pratfalls...
Oops, you made another mistake. Ernst Zermelo is a well respected mathematician and game theorist (look him up).
Yes, and you failed to understand that his conclusion was obvious, and needn't be stated to chess players, but only to those who don't really understand chess moves or basic logic. Carl Sagan liked to talk about billions and billions of galaxies, and he had great credentials, too. It doesn't mean that every schoolchild who took any Astronomy at all didn't know that there are billions and billions of galaxies...the difference here is that you presented the "billions" equivalent as some profound insight. This is something that is done by somebody that has no understanding of the subject at hand, but likes to makes constant appeals to authority. You toss out names and links to papers, but display a complete lack of understanding whenever you actually are called upon to use your own smarts to interpret anything .
It is inherently obvious to a chess player that gives it any thought that if white has a forced win, black cannot also have one, and vice versa. How could this be a surprising conclusion for you? No, seriously...how?
You have not described Zermelo's theorem correctly. It is that a finite, deterministic two-player, zero sum game of perfect information has a definite result which can be achieved by either player with some deterministic strategy. This result is not true for games that fail to satisfy one of several conditions. I agree it seems obvious, but this is a lucky case where what is obvious happens to be true.
(This is not always so! Eg the "obvious" nature of the parallel postulate of geometry, which one of the greatest mathematicians in human history and all who followed him for over 2000 years failed to see was not actually true, but rather one of three options).
but you cannot prove that 1+1=2, which
I think this statement is incorrect:
You are thinking of the Principia Mathematica, written by Alfred North Whitehead and Bertrand Russell. Here is a relevant excerpt: As you can see, it ends with "From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2
Sure, defined, but not demonstrated. It’s a basic fact in math, everyone knows this, it’s common knowledge in math.