Re: THEORY: OT Syntax (Was: Re: THEORY: phonemes and Optimality Theory tutorial)

On Sat, 18 Nov 2000, John Cowan wrote:

> On Sat, 18 Nov 2000, Yoon Ha Lee wrote:
>
> > <wry g>  From what I can tell the history of mathematics is filled with
> > examples of speculations and ideas that did indeed turn out to be
> > "rubbish."
>
> What's bizarre is that that whole structure of infinitesimals which
> Cauchy & Co. so rightly discarded for epsilon-delta arguments can
> be restored to intellectual respectability by employing nonstandard
> numbers.  ("Nonstandard number" is a technical term here, folks, like
> "imaginary number" -- don't run away with it.)
Huh, that's right--I remember reading about that in _The Mathematical
Experience_ by Davis & Hersh.  I couldn't make heads or tails of it, but
I was in HS at the time, with all the unimpressive background of IBH math
(1st and 2nd semester calculus equivalent).  I should give it another
try.  :-)

I love how the history of mathematical prejudice is recorded in the names
of number-types: rational, irrational, imaginary, complex, nonstandard...<G>

> Wouldn't it be cool if there was a finite proof for G?  Nobody actually
> knows if it's true -- but if it were, nonstandard numbers would be
> *hard-wired* into number theory, willy-nilly.
G?  <puzzled look>  Clarify, please?  I'm mightily curious, but also
rather ignorant.  :-(  (The only thing that comes to mind is "g" in
psychology, which I'm guessing is an entirely different animal.)

YHL, who loves history of math but doesn't quite know enough math
(Actually, I'm not sure anyone does, what with the explosion of
sub-sub-fields and specialists who can't talk to each other.  Some
professors at Cornell have scared me with tales of going to mathematical
conferences where someone would give a paper and only one person in the
audience would pay attention while the rest went out for coffee, because
everyone else had no clue what was going on!)