[FOM] Re: Weak "hyper" computers

[Timothy Y. Chow]

Harvey Friedman wrote:
> I didn't make these postings on the FOM just because I am looking for
> something to do with my idle time (I don't have any right now). So I was
> expecting to hear from some of the people who are continuing this general
> area of discussion just how they see my postings might affect - or not
> affect - the discussion.

The part about trying to create Turing machines with few quadruples sounds 
sort of interesting, but perhaps you could provide some more explanation
as to what sort of payoff one might expect from such an effort?  It sounds 
sort of like the efforts to generate ever-larger primes or more digits of 
pi---these projects generate, as byproducts, new mathematical insights.  
However, in the case of Turing machines, I have no intuition as to what 
kinds of byproducts one might expect.  Can you sketch some possible 
examples?

It also seems that one could run a competition along these lines.  Choose
some relatively simple yet profound problem, and have a competition to see 
who can generate the most succinct Turing machine.  This is the sort of 
thing I might be able to convince Prof. Erik Demaine at MIT to host, 
provided I pitch it properly.  However, judging the results might be
too difficult and time-consuming, so I'm not sure if this is really a
good idea.

Tim