The age of the universe is 13.8 billion years ( 4.3*10^17 seconds ):
http://en.wikipedia.org/wiki/Age_of_the_universe
An Earth size super computer if it started working at the Big Bang, could finish by now solving the halting problem of a computer with 307 bits of memory:
http://www.wolframalpha.com/input/?i=log%284.3*10%5E17*10%5E75%29%2Flog%282%29
Anyone ever see the Big Bang ? Anyone ? Anyone at all ?
First Class Gobbledygook!
Yes, complete and utter Gödeldybook.
Anyone ever see the Big Bang ? Anyone ? Anyone at all ?
You can deny the established results of physics at will. It is not against the law. There is free speach.
You can deny the established results of physics AND still call your viewpoint scientific in the following case:
You submit a theory which can account for the known facts of physics at least as well as established physics, plus on or more of the following is true: there are additional facts which your theory can explain; it can explain the known facts with better precision; or it can predict facts that are not predicted by the current theory and those facts are testable experimentally and indeed are tested experimentally.
Let me give you an example:
You can argue, that the Big Bang can not exist because the world was created by God six thousand years ago.
Now, starting from this premise, calculate how the spectrum of the cosmic microvawe background should look like, with at least the precision as the established theory ( that assumes a Big Bang ) does.
Let me give you an example:
You can argue, that the Big Bang can not exist because the world was created by God six thousand years ago.
Now, starting from this premise, calculate how the spectrum of the cosmic microvawe background should look like, with at least the precision as the established theory ( that assumes a Big Bang ) does.
It takes a special kind of mind to see this as an example relating to the question of whether computers will solve chess.
Indeed, He's So Special.
And he's (apparently) already answered this question, earlier this year -- http://www.chess.com/blog/watcha/limits-of-quantum-computing-in-solving-chess
But (apparently) no one was listening, at that time.
Did the universe ever start ? Maybe for those believing that anything created must have a beginning. Who is there to say the universe had to be created ? Elementary stuff my dear Watson.
Please. Speak about the possibility of solving chess.
I want to learn new things.
The problem with chess is that it is too boring. So the solution is obvious.
The problem with chess is that it is too boring. So the solution is obvious.
Why are you in this thread?
Case closed. Period.
For curiosity's sake ( http://en.wikipedia.org/wiki/Computer_memory ):
So ENIAC, the first real computer already had 10^200 states ( 20 ten digit decimal numbers have 200 decimal digits, each digit representing 10 possible states ).
The halting problem of even this stone age computer is unsolvable by any practical computer that can ever be built.
This is a warning sign that theoretical limits are for real and someone not familar with them can commit big mistakes. This is why I say that one should know some basic facts about the limits of computation in order to be able to attack the problem of solving chess.
I think that chess on a 5 x 6 board is solvable by current technology:
Why 5 x 6 board? Because there are 5 non pawn pieces that have to be placed on the base ranks, and you need at least two empty ranks to be able to push a pawn by two squares in the starting position. So this game already has the feeling of chess ( apart from castling - you have to add an other file with a rook for castling to make sense ).
It would be instructive to solve this toy model of chess completely and draw conclusions from the solution.
3x4 chess has been solved, 4x4 chess has been solved up to nine pieces, and one variant (Gardner minichess, identical setup as watcha's board with one less empty rank) of 5x5 chess has been weakly solved.
A variant called Chess Attack uses watcha's board.
There is a Noughts & Crosses/Tic-Tac-Toe Position that even All the Worlds most Powerful Computers together Cannot Solve!
How many People would like Me to Post the Position ? and how Much would you bet Me that I am Wrong ?
We don't care...and the ARB chess system is a sham.
No, since stockfish only works with evaluations (win probabilities of some sort). A solution would be "moves e4, e4, c4, Nf3, g3 draws, other moves lose". Or when asked to demonstrate a win, it would show how to forcefully acheive a position that is heuristically deemed as a win (like a rook up in a quiet position).
It just occured to me that a quiet position with a rook up can be a draw, so if Stockfish knows all too well that it is a win, then Stockfish is wrong.
Stockfish actually happens to think it is a win:
This shows that heuristics can always leak.
Even if I accept that there are unshakable heuristics, these can not reduce the search space in a significant enough way.
This is a draw
I qoute from the Wikipedia article on Bremermann's limit ( http://en.wikipedia.org/wiki/Bremermann's_limit ):
"a computer with the mass of the entire Earth operating at the Bremermann's limit could perform approximately 10^75 mathematical computations per second."
Now, an Earth size super computer can perform 3.15*10^7*10^75 operations in a year. If you calculate a memory of what size has this number of states, you get 275 bits:
http://www.wolframalpha.com/input/?i=log%283.15*10%5E7*10%5E75%29%2Flog%282%29
Even if your lab computer has only 275 bits of memory, its halting problem can only be solved by a super computer of the size of the Earth in one year.
Since your lab computer has much more than 275 bits of memory ( at least Mbytes of memory ), the super computer of the size of the Earth will not be capable of solving its halting problem even during the entire age of the universe.