[FOM] Harvey Friedman's, "Number theorist's interest in bounds" (8 Apr)
Timothy Y. Chow
tchow at alum.mit.edu
Mon Apr 10 10:19:24 EDT 2006
Gabriel Stolzenberg wrote:
>> Tim, you're talking about "effective" and "computationally efficient"
>> methods. That's great stuff. I'm with you.
>
> But in saying this, I ignored the fact that, in the statement above,
>"effective" is somehow less good than "computationally efficient." In
>which case, I need to know what is meant here by "effective."
By "effective" I meant "computable." But I think the word I used in a
potentially confusing way was "efficient." By "efficient," I meant more
than "computable"; I meant "computable, with good upper bounds on the
computational complexity."
>But, as I understand it, Harvey is insisting that every bound is, as he
>puts it, "intrinsically" interesting. Every bound.
He can speak for himself, of course, but my understanding wasn't that
*every bound* is interesting, but that passing from *no* bound to *some*
bound is intrinsically interesting.
I feel that I'm aiming at a moving target here. Do I now have to show not
only that number theorists are *interested* in bounds, and I mean *really*
interested in bounds, and I mean really *mathematically* interested in
bounds, but also really mathematically *intrinsically* interested in
*every* bound? What's the next adverb on your list? I'm losing track of
what's being debated.
Tim
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