Author: Robert Henry Durrett
Date: 12:12:01 09/06/98
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On September 06, 1998 at 14:55:16, Robert Henry Durrett wrote: >On September 06, 1998 at 14:27:08, Don Dailey wrote: > >>>>Shall we try it on the group? What is a combination? Give an answer >>>>that has no ambiguity whatsoever. I have never seen one in any book, >>>>but I've seen many attempts. You may be able to come up with a strict >>>>definition of what a combination is, but I'll be many will disagree >>>>about what this definition should be. Your definition will probably >>>>not match peoples perception of what they think a combination is. >>> >>>>- Don >>> >>> >>> An interesting game. I tried to give an objective definition of a >>>combination. at first sight it seemed easier than it was in reality! Here is my >>>attempt : >>> >>> >>>Combination : A series of 2 or more consecutive moves involving the sacrifice or >>>investment of material, and by which the player that initiated it gains some >>>sensible benefits whatever his/her opponent play to counter it. The benefits >>>could be a greater material win in the end or in another form (e.g. a huge space >>>advantage, a strong passed pawn etc.). >>> >>> >>> >>> Having said that, I will now give (I did not look at it before writing mine) >>>the one of IM Nicolas Giffard in his book "Le guide des echecs" (that could be >>>translated as "The Guide of Chess". The translation is from me : >>> >>> >>>Combination: A series of moves from one side provoking forced or almost forced >>>replies, allowing to achieve a concrete goal. A combination correctly realized, >>>this way, could bring a small advantage or as well the checkmate of the >>>opponent. >>> >>>Serge Desmarais >> >> >>Nice try, but not good enough! Not to worry, I don't think I can do >>much better. >> >>The Serge Desmariais definition is more ambiguous than yours! He >>did not even define what a concrete goal is. I suppose it does >>not matter, it's only important that your combination achieves >>whatever you define to be your own personal concrete goal. >> >>Your definition does not tell me anything about when the huge win >>or advantage was achieved. Do you determine this by doing a >>quies search and trusting the results? You have to use a lot >>of human judgement to determine if your move sequence fits the >>definition. In other words it will be possible in principle to >>contruct borderline cases where experts will disagree. >> >>The definition must be completely free of any ambiguious terminology. >>100/100 people should be able to apply your defintion to any >>sequence of moves and determine exactly where a combination starts >>and stops. >> >>- Don > >If you want to be completely rigorous about this you must treat this the same >way a mathematician develops a theory, such as boolian algegra. In every case, >the theory is founded on unproven axioms. Then there is a bunch of definitions >and theorems, connected by proofs. The steps in the proofs must be generally >accepted as being valid, but the validity of the steps in logic cannot be proven >and are like the unproven axioms which form the foundation of any mathematical >theory. > >Note that definitions are never proven! They are selected by those who are >developing the theory. If the theory is being developed by a group of people, >as the case here, then everybody must agree on the ACCEPTABILITY of the >definitions, but not on the "truth or falseness" of the definitions. There is >no such thing as a "true" definition or a "false" definition. But there sure >can be "ambiguous" definitions. These ambiguities become apparent whenever a >proof is attempted in which the assertion to be proven uses the defined term as >part of the definition. Here, I submitted my bulletin too quickly. The above sentence should read "These ambiguities become apparent whenever a proof is attempted in which the assertion to be proven uses the defined term as part of the assertion". > >I suggest that some "reasonable-sounding" definitions be selected and see where >they lead. If a term later proves to be poorly defined, there is always the >opportunity to change the definition. > >But this is the BIG question: Do you guys really want to go through all of >this? I might add: If you "define" a term in such a way that you incorporate unproven assumptions into the definition, then you will be "dead in the water" because any assertion using that term will contain the same flaw. In other words, it is extremely important that definitions not be based on unproven or possibly false assumptions. But there is a good idea someone said: The purpose for all of this is to produce useful workable computer code. Hence, if you can write a program which will evaluate whether or not some sequence of moves fits your "definition," then the definition is probably OK for use in proofs. [If I recall correctly, this is a homomorphism-type of idea or "something like that." (unless my memory is playing tricks on me.)] It is kind of hard to write code to evaluate something which is ambiguously defined.
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