Author: Ingo Lindam
Date: 12:01:52 12/11/02
Go up one level in this thread
On December 11, 2002 at 14:46:00, Dann Corbit wrote: >On December 11, 2002 at 14:34:24, Ingo Lindam wrote: > >>On December 11, 2002 at 14:18:00, Dann Corbit wrote: >> >>>On December 11, 2002 at 14:12:06, Ingo Lindam wrote: >>> >>>>On December 11, 2002 at 13:54:08, Dann Corbit wrote: >>>> >>>>>On December 11, 2002 at 13:46:45, Ingo Lindam wrote: >>>>> >>>>>>On December 11, 2002 at 13:23:23, Dann Corbit wrote: >>>>>> >>>>>>>I never said it 'has to be done with' -- only that they are equivalent and >>>>>>>alternatives will not be superior. >>>>>>> >>>>>>>For that matter, the tree is nothing more than a visualization aid. The steps >>>>>>>will be the same whether or not a tree is used to visualize it. >>>>>> >>>>>>So I understand you right that to prove that following position will end in a >>>>>>draw is impossible by a giving proof less complex (smaller) than that very very >>>>>>big tree of all possible continuations...??? >>>>>> >>>>>>[D] 6k1/bp1p1p1p/8/pPpPpPpP/P1P1P1P1/8/B3K3/8 w - - 0 1 >>>>>> >>>>>>You are just kidding, aren't you? >>>>> >>>>>Of course not. Any *proof* of the forced outcome of this game will be identical >>>>>to the tree proof. >>>> >>>>Hey Dann, please... :-((( !!!! >>>> >>>>you are/were a math major... >>>>it can't be true that you don't see it. >>>> >>>>It hurts... >>>>and I am really crying now... >>>> >>>>You can see the position? >>>>You know the chess rules? >>>>What are the possible results of a chess game? >>>>If white can not win the position and black can not win the position, what is >>>>the only possible result? >>>> >>>>What is needed to win a game? >>>>YES! Mate! >>>>Might there any arguments to prove that white can not mate without promoting a >>>>pawn...? >>>>Might there any arguments to prove that black can not mate without promoting a >>>>pawn...? >>>> >>>>What about strategies to defend against promoting for white/black? >>>> >>>>(ofcourse you can give an equivalent to each proof within a tree, but this is >>>>not the tree of all continuations!!!!) >>>>So, now forget everything you believe to know about the connection between >>>>trees and proofs. >>>> >>>>Take you pencil... >>>>take a sheet of paper... >>>>sit down... >>>>be a nice boy... >>>>and write down the proof!!! >>>> >>>>..and if you do not see it then....!!! >>>> >>>>Then take as much paper as you need >>>>and try to write all possible continuations >>>>on the paper until you finally feel the difference in every >>>>finger and you see... >>>> >>>>"oh, he's right...the is indeed a tiny difference!" >>> >>>The tree proof is identical. >>> >>>What have you done? >>> >>>You looked at the list of possible moves. >>>You looked at the list of possible responses. >>>You continued that logically forward until you saw the outcome. >>>That is what the tree proof does also. There is no difference. If you fail to >>>do this, you do not have a proof. >>> >>>By the way, a win is possible. >>> >>>[D]6k1/bp1p1p1p/8/pPpPpPpP/P1P1P1P1/8/B3K3/8 w - - >>>[D]6k1/bp1p1p1p/1P6/p1pPpPpP/P1P1P1P1/8/B3K3/8 b - - >>>[D]5k2/bp1p1p1p/1P6/p1pPpPpP/P1P1P1P1/8/B3K3/8 w - - >>>[D]5k2/Pp1p1p1p/8/p1pPpPpP/P1P1P1P1/8/B3K3/8 b - - >>>[D]Q4k2/1p1p1p1p/8/p1pPpPpP/P1P1P1P1/8/B3K3/8 w - - >>> >>>And (may I add) "Look -- it's obiously a win!" is not a proof of any sort. >> >>Sorry Dann, >> >>now I am convinced that you can't be a human being. You must be a computer >>programm running on hardware that is just too small and too slow to get it. >> >>My proof is not to say "See it's obviously a draw" and I am sure it will take me >>some effort to put it on a single sheet of paper in a correct way. >>I am also sure that I already proved some more difficult to prove things. >>And last I am sure also this proof wouldn't help you, wouldn't convince you. >> >>Just let my know when surpisingly some day will come a light into your brain >>making you understand. > >It may be "obviously a draw" and yet it is possible for either side to win if >the opponent makes a mistake. Your claim of "it's obviously a draw" is correct. > And yet your claim is most emphatically NOT a proof. Probably, you don't know >what a proof is. When a proof has been presented, there can be no argument >because the conclusion is irrevocable. Handwaving and "it's obvious" are not >allowed, for the most part. 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. >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.
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