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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 One art/there is/no less/no more/All things/to do/with sparks/galore --Douglas Hofstadter