Author: José Carlos
Date: 07:33:16 01/17/05
Go up one level in this thread
On January 16, 2005 at 19:54:55, José Carlos wrote:
>On January 16, 2005 at 18:48:10, Ricardo Gibert wrote:
>
>>On January 16, 2005 at 16:30:55, José Carlos wrote:
>>
>>>On January 16, 2005 at 09:19:03, Ricardo Gibert wrote:
>>>
>>>>On January 16, 2005 at 08:54:31, Mike Hood wrote:
>>>>
>>>>>On January 16, 2005 at 08:25:31, Ricardo Gibert wrote:
>>>>>
>>>>>>On January 16, 2005 at 08:09:14, Uri Blass wrote:
>>>>>>
>>>>>>>On January 16, 2005 at 07:34:01, Ricardo Gibert wrote:
>>>>>>>
>>>>>>>>On January 16, 2005 at 05:29:36, Uri Blass wrote:
>>>>>>>>
>>>>>>>>>On January 16, 2005 at 03:16:27, Bruce Moreland wrote:
>>>>>>>>>
>>>>>>>>>>To solve a game is to prove the result with best play for both sides. It's a
>>>>>>>>>>term with precise meaning.
>>>>>>>>>
>>>>>>>>>What if there is no formal proof of the result with perfect play but every game
>>>>>>>>>between top programs ends in a draw?
>>>>>>>>
>>>>>>>>It probably means that if a win exists, they cannot search deeply enough to find
>>>>>>>>it. What else could it mean? I don't like the idea of trying to understand a
>>>>>>>>problem with fanciful probabilies like this. It can be misleading.
>>>>>>>
>>>>>>>By the same logic you can say that maybe white does not win the following
>>>>>>>position and black has a defence or even a win that programs cannot search deep
>>>>>>>enough to see.
>>>>>>>
>>>>>>>[D]1nb1kbn1/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w - - 0 1
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>>I used to think that calling chess a likely draw was a reasonable thing to say,
>>>>>>>>but I've learned the hard way that the really right answer is to simply say we
>>>>>>>>do not know.
>>>>>>>
>>>>>>>What about the more obvious assumption that white does not lose.
>>>>>>>
>>>>>>>I think that there are things that we can say that we know inspite of the fact
>>>>>>>that we are unable to prove them.
>>>>>>
>>>>>>You want to say you *know* the above position to be a win for white, but why not
>>>>>>simply say the truth? That you believe it to be a win even though you do not
>>>>>>know it? Why the need to make a statement that is stronger than the one we are
>>>>>>able to back up with the commensurate facts?
>>>>>>
>>>>>
>>>>>Knowledge vs. Belief?
>>>>>
>>>>>We're wandering into the domain of metaphysics now :)
>>>>
>>>>Nothing metaphysical about it. He believes it to be a win, but does not know it,
>>>>because he cannot prove it. It's as simple as that.
>>>
>>> But I think Uri's idea is interesting. I've thought about it also in the past.
>>>It's pretty much like physics work. You observe, make a theory, try to refute it
>>>by observation and experiment. If you fail to refute it, you accept it.
>>
>>So if a hundred years ago, if someone had proposed the moon were made of cheese
>>and of course nobody could refute it, you would have accepted it?
>
>
> Of course not. You miss a part of the scientific method I summarized:
>experiment. No experiment was possible to prove/refute the statment you
>proposed, so it's not relevant.
> But think carefully about science: it's all made of induction. Deductive
>reasoning is a tool to "prove" induction. For example: hypotesis: "light is made
>of particles" -> deduction: it must remove electrons in an specific rate ->
>experiment: electromagnetic effect -> it works! -> hypotesis not refuted, it
^^^^^^^^^^^^^^^
I meant "photoelectric", of course.
José C.
>passed the test so far.
>
>
>>> It's not
>>>the final and definitive truth, but in physics it has worked so well so far as
>>>to allow us to talk about it in something called internet.
>>> BTW, I personally think chess is not solvable because of the huge graph you
>>>need to explore.
>>
>>For something bigger, check out the link I gave about the traveling salesman
>>problem. For N cities, there are (N - 1)! possible paths. With N = 24978, 24977!
>>= 3.87e98992 completely dwarfs the number of possible positions in chess.
>>Finding an optimal solution for N = 24978 is truly mind boggling, but they did
>>it.
>
>
> I had a quick look. I see no explanation of the algorithm. If I don't see the
>algorithm, I hardly can believe they found a perfect solution for so many
>cities. I've seen impressive programs that "solve" that problem using genetic
>algorithms, but those solutions are not optimal, only "good enough" according to
>some criterium.
> Then again, I don't know if there exists a method to solve chess, but I can't
>imagine it. Exploring the whole graph (well, the relevant part if a mate is
>found) is the only way I can think of, and that's not doable IMO.
>
> José C.
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