That reads like an excerpt from the Dave Chappelle Show. Little John?
True or false? Chess will never be solved! why?
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btickler wrote:
Thanks, a nice example. According the Mr. Grobe, though, you can't prove an integer is prime unless you try to divide it by every integer less than it. You can't even make a rule saying "even numbers are never prime, skip those", because that would not be enough proof, because somehow it might magically come to pass that there's an even prime number and that the laws of mathematics don't apply at some astonomically high number (kind of like relativity?), so you cannot take shortcuts. You must apply brute force calculation to every number without using square roots to eliminate possibilities, etc. Anything less than that leaves room for doubt.
That's not true at all -- you can prove that a number is prime by attempting to divide it by every other prime up to its square root.
It's still a brute force calculation, but there are some opportunities for de-duplication, as there are in chess (again, rotations and reflections). The problem (in the case of primes, for example) is that these simplifications don't reduce the problem from one that is only solvable in non-polynomial time to one that is solveable in polynomial time. That is, they don't materially impact the problem's complexity.
Any other words you would like to put in my mouth?
By the way, the test for an even number is to attempt to divide it by two -- the first prime that needs testing.
btickler wrote:
Thanks, a nice example. According the Mr. Grobe, though, you can't prove an integer is prime unless you try to divide it by every integer less than it. You can't even make a rule saying "even numbers are never prime, skip those", because that would not be enough proof, because somehow it might magically come to pass that there's an even prime number and that the laws of mathematics don't apply at some astonomically high number (kind of like relativity?), so you cannot take shortcuts. You must apply brute force calculation to every number without using square roots to eliminate possibilities, etc. Anything less than that leaves room for doubt.
No.
Like, no, that's not what he said.
The mathematical theorems that underly primality tests are valid for any number, even big ones. So that is a proof.
But your suggestion of "1.Nc3 2.Nb1 is obviously bad, so let's forget it" is not a proof. "1.g4 e5 2.f3 is mate in one", or "all even numbers except two are non-prime because 2 divides them" is a proof, on the opposite.
Like it used to be a proof that two objects with velocities of 1 receded from each at a rate of 2 and not 1.999999999999999999999999999999999?
I never said "1.Nc3 2.Nb1 is obviously bad, so let's forget it", I said that it could be proved that these moves were not best play without calculating 10^123 possible moves to do it. Completely different. The opposing position is that any such proof is not proof unless it is backed up by 10^123 calculations.
But equally incorrect.
But equally incorrect.
The good news is that we'll still be around when this statement is proved false. The bad news is that your "Chess cannot be solved! 10^123 is the only way!!! Not enough atoms in the universe!!!!!" assertion won't be proved wrong until after we're both gone.
btickler wrote:
I never said "1.Nc3 2.Nb1 is obviously bad, so let's forget it", I said that it could be proved that these moves were not best play without calculating 10^123 possible moves to do it. Completely different. The opposing position is that any such proof is not proof unless it is backed up by 10^123 calculations.
You can twist it as much as you want, either you have to calculate up to a known position (ie a mate or something in the 7-men database), or dismiss some positions on the basis that "it's an obvious win". One way is the one you wanted to avoid, the other is no proof.
There is also not enough data to measure the beauty of an art piece but still our brains can perceive and produce it.
CHESS WILL BE SOLVED. The soultion? Make chess bigger and add more pieces! Problem solved!
AlxMaster wrote:
There is also not enough data to measure the beauty of an art piece but still our brains can perceive and produce it.
And there is enough lemons in the world to fill an oympic pool with lemonade.
But the relevance of the comparison to the current debate is not clear.
Irontiger wrote:
You can twist it as much as you want, either you have to calculate up to a known position (ie a mate or something in the 7-men database), or dismiss some positions on the basis that "it's an obvious win". One way is the one you wanted to avoid, the other is no proof.
But what if we change the definition of proof? That could work, right?
Did you mean if we refute your provided definition of proof in this instance? ;)
Ok, I'm done, I said my piece and now I'm just dancing around with a decaying tooth (yes, I know it is supposed to be a white pepper, but decaying tooth seems more appropo somehow) and a cynical Frenchman to no purpose.
P.S. It's Lil Jon, if I am not mistaken. You're welcome.
My provided definition is the objective mathematical definition. I did not simply make it up. I'd urge you to do a little digging into game theory, and specifically the concept of solved games.
TheGrobe wrote:
But what if we change the definition of proof? That could work, right?
If he can provide a probabilistic argument that yields result like "that position is a win for White with probability X %" with a calculated (not estimated) value of X over -say- 99.9%, I will consider it not as a proof, but still as valuable information.
But as far as he has gone for now, it's "we will find a way to fiddle the things, and be aproximatively sure of the result". A bit weak to my taste.
I've never seen someone so smug about his derping before this thread.
.....oh wait it happens every day here.
Even if it's all of your pieces v.s a king, you can still lose.
Dennis10000 wrote:
Even if it's all of your pieces v.s a king, you can still lose.
Not true, you can only draw or win, not lose. Unless you lose by time, but for that the time is either ludicrously small or you are retarded.
AlxMaster wrote:
Dennis10000 wrote:
Even if it's all of your pieces v.s a king, you can still lose.
Not true, you can only draw or win, not lose. Unless you lose by time, but for that the time is either ludicrously small or you are retarded.
Even if you timeout, it is a draw.
http://www.fide.com/component/handbook/?id=124&view=article (skip to 6.9)
The analogy works as intended. I am merely pointing out that it is impossible to prove anything to someone that refuses to accept it, since the universe only "exists" via each person's perceptions inside their own brain.
No more, no less.
The analogy doesn't work as intended at all. If I refuse to accept something on faith without any evidence at all, it doesn't mean I don't value evidence. Quite the opposite in fact.