The Logic Off Topic list

Thoughts from the mind of Kool Musick, 09-11-2001:

>  >Actually most mathematicians believe the beauty of mathematics in and of
>>itself without any regard to real world applications.
>???? !!!! ****

Yes, he's right (hey GA: see!  again I agree!  That's already 3 times 
this week!)

>"One would have to have completely forgotten the history of mathematics so
>as to not remember that the desire to know nature has had the most constant
>and also the happiest influence on its development".
>Henri Poincare

Not to the point.  GA says, rightfully, that most math-heads believe 
in, or are able to appreciate, the beauty of mathematics "in itself" 
-- contrary to most mathematical "laymen" who think mathematics is 
just a boring bunch of formulas and incomprehensible stuff, without 
any inherent "quality" or esthetics.

That doesn't mean they (mathematicians) don't care for applications, 
and it doesn't mean they can't be inspired by nature or any other 
real-world phenomena, or can't rejoice in the applicability of their 
discoveries.

>"The scientist does not study nature because it is useful; he studies it
>because he delights in it, and he delights in it because it is beautiful.

Which is not at all opposed to what GA says.  "Delight in nature" 
doesn't exclude the possibility to delight in pure abstract form as 
well.  Lots of people delight in nature, but very few delight in pure 
abstractions.

>"The profound study of nature is the most fertile of all sources of
>mathematical discoveries".
>Jean Baptiste Fourier

Ditto.

>"Mathematics compares the most diverse phenomena and discovers the secret
>analogies that unite them".
>Jean Baptiste Fourier

"Phenomena" could as well refer to abstract phenomena -- i.e. "pure" 
mathematics.

>"Mathematical Analysis is as extensive as nature herself".
>Jean Baptiste Fourier

Which, again, is not an argument.

Sorry Kool, but I think you missed the point this time...


tata,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html