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

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.)

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.

> Theoretical math involves a lot more intuition and guesswork
> than I realized when I was in high school, when math was just something
> given to the world etched into a bunch of stone tablets (or such was my
> impression).  Conjectures and proofs rise and fall as new generations of
> scholars find new ways of thinking.
"Mathematics is perhaps the only science in which foundational work can
be replaced at will."  --I forget who

> "Proof" in math can be pretty darn ephemeral sometimes!
"Almost all proofs have bugs, but almost all theorems are true."
        --A math/CS friend of mine

> To my knowledge calculus stayed around 'cause it worked, and because
> later mathematicians were able to find a much more solid theoretical
> foundation for it.
Just so.

--
John Cowan                                   cowan@ccil.org
One art/there is/no less/no more/All things/to do/with sparks/galore
        --Douglas Hofstadter