On Wed, 7 Jul 2004, Bellview Hospital wrote: > > "If you believe, as many do, that hypercomputational processes are always > merely mathematical, and never physically real, you can't be rational and at > the same time refuse to accept our case for P=NP." > > What does that mean? Believe then I'm not rational, and refuse to accept > case? OR Not believe, and be rational and accept case?
It's perfectly clear, logically speaking.
IF (you believe that hypercomputational processes are not real) THEN (it cannot happen that) (you are rational AND you refuse to accept our case)
In other words,
IF (you believe that all real processes are computational) THEN ((you are irrational) OR (you accept our case))
I think what the paper's authors mean by "hypercomputational" is "not simulatable by a Turing machine (in P?)." They do mention Stephen Wolfram's (crazy) idea that subatomic physics works computationally; they say that IF you believe that the entire universe is a big computer, THEN you must accept that big computers can solve NP-complete problems in P time (because the universe can solve, etc.).
However, it's been pointed out that the soap-bubble method is NOT a solution to the original NP-complete problem; it does not find a global minimum, but only an *approximation* to a *local* minimum. And there exist reasonably well-known algorithms for finding approximate local minima in P, so the paper doesn't show anything interesting.