🚀 go-pugleaf

In article <adh.34.000CFD75@cx.dnv.no> adh@cx.dnv.no (Arne Dehli Halvorsen) writes:

>Has it been settled that Godel's theorem is less valid for analog systems?
>
>I think part of Penrose's argument is that what happens in the brain 
>may be a result of quantum processes which do not follow ordinary commonplace 
>logic. If this is where the difference is, then one could construct 
>intelligent machines by harnessing these quantum effects in any hardware.
>
>(Incidentally, an algorithm for such a quantum machine has recently been shown 
>to be able to factorize large numbers which can not be factorized by *any*
>traditional computer. Realizing the quantum hardware is a different matter...)

Not quite.  Any old computer can factor prime numbers, but it takes a
long time, of the order of something like n * (Log N) **2 or so, if we
don't use Rabin's much faster but not absolutely reliable algorithm.
The proposed quantum computer is theoretically faster.

However, it depends on the superposition of the order of N
simultaneous potential multiplications and, to get the correct answer
in the case of a prime, the implicit NOT detector must reject the
noise of all those superposed 'possible' paths.  I don't know if it's
yet known how to build such a machine with the requisite isolation
from the rest of the universe.  But I firmly doubt that any such
protected environment could be found inside the noisy environment of a
brain. Has Penrose or anyone else suggested why this might be
possible?

Anyway, show me a person who can instantly factor huge numbers (I
suppose, I should also insist on the supervision of the demo by James
Randi) and I'll agree that this hypothesis might be worth thinking
further consideration.  Have you noticed that, right now, computers
are a lot faster than brains at this particular problem?

This whole silly thing seems to turn around an assertion that people
routinely solve computationally intractable problems with enormous
speed.  Darryl McCulloch just pointed out, as I also have repeatedly,
that Penrose' argument of last year foolishly assumed that human
thinking must be consistent and therefore, somehow violates the
Godel-Lucas argument.  This year's Penrose argument foolishly assumes
that people like him can routinely solve computationally intractable
problems.  What will we hear next year.  Quo usque abutere, Roger
Penrose, patentia nostra (if I rightly remember Caesar's words)?