Author: Dann Corbit
Date: 13:39:53 12/11/02
Go up one level in this thread
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. >>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).
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