[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.


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