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

From: | John Cowan <cowan@...> |

Date: | Saturday, November 18, 2000, 22:50 |

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