Science And Math Was: Python's Lisp heritage

[Tim Daneliuk]

arthur.siegel at rsmi.com wrote:
> 
> >>>Ahh, OK. Then I agree completely -- Mathematics *is* larger than its
> >>>would-be applications to the natural sciences. I think it was P. Erdos
> >>>who remarked once that all natural science is conceivably finite - e.g.
> >>>there would be a time when there would be nothing more to learn about
> >>>the universe - but mathematics is literally infinite.
> >
> >>I'm not so sure about the latter assertion, and I'm *definitely* not
> >>certain about the assertion that natural science is finite.
> 
> >The first assertion by Erdos is indeed problematic. The second is not.
> 
> My sense, intution is of mathemetics as infinite only in the sense of allowing
> infinite homologous descriptions of/perspectives on  the One Thing.
> 
> The perspectives are invented.
> 
> The Thing is not.

This is entirely cogent and on-the-mark, IMO, but it still sidesteps the
question of whether or not mathematics can operate on things which do
not exist in the natural realm.  My (unproven/unprovable) claim is that
mathematics is capable of operating on a larger problem set than
that posed by natural science no matter how large/finite/infinite natural
science, in fact, is.

> 
> The modern assumption that increased abstractness brings better perspective
> perhaps reaches a point not only of diminishing, but negative returns.
> 
> But as the opinion of someone who finds the more abstract mathematical
> realms beyond his reach, maybe this represents a Philosophy of Sour Grapes.
> 

I feel your pain ;)  I'm not sure that the assumption is really that
increased abstraction gives better perspective.  I suspect increased
abstraction is pursued by mathematicians because it is intellectually
interesting and new territory to conquer...



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Tim Daneliuk
tundra at tundraware.com