Re: Explanations

[Dusko Pavlovic <dusko@kestrel.edu>]

a friend told me that there was a conference where music critics and professors discussed the visual content of music. on the other side, there are learned essays about the deep links between music and architecture. (hegel in particular wrote about that.)

the question whether a mathematical proof explains the theorem might be of a similar kind. while most proofs of the pythagoras theorem do explain why it is true, wyles' proof of the great fermat theorem (just a slightly different statement) does not seem to be explaining it to too many people.

some proofs yield an explanation, some explanations lead to a proof - but there is a sense in which the *attitudes* leading to one and to the other are *opposite*: while explanations tend to increase the number of words in the world, many people prove things so that we can stop talking about them. 

maybe the situation resembles the discussion between zeno and parmenides: "as parmenides argued that the movement does not exist in the universe, zeno stood up and walked around".

-- dusko

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]