Re: paper claiming p=np and soap bubbles

From: Craig Feinstein (cafeinst_at_msn.com)
Date: 07/09/04 

Date: 8 Jul 2004 20:11:30 -0700

>>
> >> They don't. Soap films find a local minimum. They don't always find
> >> a global minimum. Other algorithms can also find local minima quickly.
> >> This does not help much with NP-complete problems.
> >>
> >> Robert Israel israel@math.ubc.ca

>
> Leaving the question of "choice" unaddressed, I will guess that the
> system simply evolves along the gradient of the appropriate potential
> function until it reaches a local (not necessarily global) minimum.
> Perhaps (we're talking nature here, right?) things are further
> sophisticated by (natural, not simulated) "annealing" (again, of
> an appropriate sort), say, thermal noise that is very likely to
> rather quickly kick the configuration of soap bubbles out of a
> sufficiently shallow local-not-global minimum and set it off
> down the flowlines of the gradient again. That still wouldn't
> necessarily guarantee reaching a global minimum in every case.
>
> Lee Rudolph

Have experiments been done to show that it is only a local minimum
that is reached by soap bubbles and not a global minimum or is this
just the party line? I'd like to believe that nature was designed to
be smarter than we give it credit.

I'd be willing to make a gentleman's bet that no one can site a paper
which describes an experiment that shows that the global minimum is
not always acheived with soap bubbles.

Craig

Relevant Pages

  • Re: paper claiming p=np and soap bubbles
    ... > system simply evolves along the gradient of the appropriate potential ... > down the flowlines of the gradient again. ... that is reached by soap bubbles and not a global minimum or is this ... I'd like to believe that nature was designed to ...
    (sci.math)
  • Re: paper claiming p=np and soap bubbles
    ... > system simply evolves along the gradient of the appropriate potential ... > down the flowlines of the gradient again. ... that is reached by soap bubbles and not a global minimum or is this ... I'd like to believe that nature was designed to ...
    (comp.theory)
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