Author: Heiner Marxen
Date: 07:53:35 12/12/02
Go up one level in this thread
On December 11, 2002 at 16:39:53, Dann Corbit wrote: >On December 11, 2002 at 15:01:52, Ingo Lindam wrote: >[snip] >>I know exactly what a proof is... and I already said that it would take some >>effort to make it "wasserdicht" (waterproved?) :-). >> >>But it would use the facts (I know it is still not a proof but gives the idea) >>that Black can be sure not to loose the game by playing Bb8 first and than just >>Kg8-h8-g8.... Its possible to prove that black will not lose that game doing so >>and this prove wont cost too much. >> >>Than proof that white can't loose the game either... which is even more simple >>to prove. >> >>And then you are ready because when white can't win and black can't win...game >>must end in a draw. >> >>The prove is more complex that the idea I gave here...but much much less complex >>than the tree of all possible continuations. E.g. in my proof I don't have to >>tell anything about the variation you gave...although it is a possible >>continuation. > >I said a proof would contain (if optimal) the square root of the number of >possible continuations. All possible continuations would be absurdly larger. > >Your proof will not be shorter in steps than the optimal tree. You could use >(of course) theorems to shorten the proof considerably, but they would have been >demonstrated with something equivalent to the tree. A proof can sometimes be much shorter than the explicit optimal tree. You just give a tree generation recipe like the above (Bb8, Kg8-h8-g8 for black, white unrestricted). Such a tree can be sufficient for the proof, but is never explicitly unfolded. Our proof does not inspect all the nodes of the tree, but rather a general property of all the resulting nodes (positions) of the tree. The length of such a proof is independant (!) from the size of the tree, and that size may be quite large. >>>For that matter, our intuition fails us often. Knowing something to be true >>>and proving it are two different things. >> >>Yes, thats true... >>also you can prove that in any logical system there are true facts you can't >>prove within the this system. >> >>>I know that: >>>a^k + b^k = c^k >>>is never true for a,b,c integers greater than zero and k an integer greater than >>>two. >> >>Wow... >> >>>But proving it is beyond my ability. Wiles' proof is hunreds of pages and I >>>can't even follow it. I know the general idea, but even so, I can't prove it. >> >>JUST a few hundreds of pages I hear some people say. >> >>>Similarly, I can say that two rays perpendicular to a plane are parallel in >>>Euclidean geometry. That statement is true, but I have not proved it. It is >>>intuitively obvious. But that is not a proof either. >> >>Right! But doesn't give any points to you in our discussion, sorry. > >The point I was trying to make is knowing something to be true and proving it >are different (sometimes when obvious and sometimes when not obvious). Here I do agree. Cheers, Heiner
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