Author: Rolf Tueschen
Date: 04:15:08 09/09/02
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On September 09, 2002 at 04:58:21, Ingo Althofer wrote: >(...)the reader gets the impression that the author >has not a very high opinion of Jonathan Schaeffer's work in the Chinook project. > >As I saw similar ways of thinking or argumenting in other areas of research let >me start explaining by an analogy from my own discipline. In mathematics we have >the expression "there is a right of the first proof". Look at some difficult >problem (for instance P !=? NP) and assume that someone has proved an answer. >His proof may be as lengthy or awkward as imaginable - as long as it is >logically correct, it is a fantastic result and the author deserves full honors. >Later, other scientists may come and find shorter or more elegant or more >general proofs. This will not diminish the honors of the first prover. He was >the one to find the bridge. It is much easier to polish or smoothen an awkward >proof than to find the proof as a pioneer. There might be principal reasons to challenge the analogy with mathematics. First of all in experimental sciences one has no proofs. It always depends on the chosen conditions. Now there is no principal question of truth because truth exists until the first refutation. And different to maths there is no way to prove that the actual truth is the final truth. Also in experimental sciences there is a problem of economy of experimental designs, especially because of sponsoring from big business. Then the question of coming first is different in experimental sciences because of the invention of always new and more powerful tools and machines. Is the one the best who's being allowed to make the first experiments with the novelties? Of course not. We understand that neither elegance nor the mere fact of being the first user is enough. Experimental sciences is a universe of theories, conjectures and refutations. And the actual "best" in a field is the one who did something that refutated some old truth, or opened lots of new perspectives of research, or who did something surprising that was normally judged as most stupid for the last years or decades. It's always a mixture of nature, tools, genius and spirit, and also psychological factors. Therefore by force it's always by chance when a person has the luck to find all the necessary conditions in combination with the required personality. All this means that mathematics is in a way much easier, because finding proofs is almost always a question of individual genius while sciences depend much more on cooperation in teams and other synergy effects. Perhaps that's the answer why mathematical novelties almost always are discovered by very young talents. Absolute domination of creativity in maths while the moment you are depending on experiments other talents are needed in plus to extreme creativity. >Claude Shannon for instance was a man >of ugly first proofs. When you read through some of his work in information >theory you can laugh about his (sometimes) awkward ways of argumenting - and >sometimes third-year students do this. Then I explain the right of the first >proof and try to encourage them "Come on! Find your own first proofs!" (...) This is one way, I would like to add another choice. One can have "weaknesses" in details but still be a great thinker. That is a further message. It seems as if the difference between maths and experimental sciences is reclusion with infinite final truths vs openess without final truths. If we would keep in mind the important paradigma of the absence of final truths it would be progress in our human affairs. Perhaps then loud laughs could change into more sophisticated humour. Not the worst for human relationships. Rolf Tueschen
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