From: Walter Hicks (wallyshoes@mindspring.com)
Date: Fri Jul 04 2003 - 14:10:02 EDT
Let me argue with this on two fronts. First of
all, you implicitly assume that the only solution
of the salesman problem is obtained by pure trial
and error and that there is no logic or other
physical principles that might be applied. For
example, you did not mention anything about the
relative location of the cities. Suppose that they
were in a relatively straight line, like cities
located on the banks of the Mississippi river. The
conclusion would not follow. Nor would it follow
for any problem where a physical mechanism is
involved.
Secondly, there is far more information in the
universe (at any instant) than the number of
protons in it. The locatio of and formation of
stars, galaxies, etc. yield patterns of
information far in excess of the number of
particles. The distribution is what really matters
IMHO. If I have N particles (grouped so as not to
be absolutely identical), then the number N! can
be expressed and computed even though it is much
larger than N itself. An abacus deals with numbers
much larger than itself and my humble PC can deal
with numbers that are much greater than the number
of memory locations in the computer. In fact we
could not even have this discussion if it were
otherwise.
I read your words but struggle with believing that
they represent a valid concept.
Walt
Glenn Morton wrote:
> Hi Walter, This will also partly answer Wayne
> Dawson,You misunderstood what I said. I said
> that a calculation requires the manipulation of
> a physical object. In a computer it is charged
> particles which are manipulated (usually by the
> bucket full to create a charge which can be
> measured) Inca's used knotted rope. An Abacus
> uses beads. Our brains use voltage potentials
> (and thus are based ultimately on charged
> partcles). My point was not that you can
> 'envision' something but that if you solve a
> traveling salesmen problem for a 100,000 city
> schedule in a time less than the age of the
> universe, (a problem that requres more
> calculations than there are particles in our
> Hubble volume) then one is reasonable to ask
> what particles or objects were manipulated to do
> the calculation. Remember that in order to use
> all the particles in the universe there is
> travel time limited by c. For instance the mass
> of the solar system is close to 2 x 10^33 g and
> a proton weighs 1.6 x 10^-24 gm which says in
> the solar system there are 2.5 x 10^57
> particles. Practically speaking to use for
> calculational problems those in another solar
> system will require 8 years travel time to the
> nearest star and back. In our Galxy there are
> approximately 200 billion times more particles,
> but that brings us only up to 5 x 10^68 or so.
> If a quantum computer can solve a problem
> requiring more particles in a finite time, then
> we have to ask certain questions. Here is an
> example of the Salesman problem.Ivars Petersen
> writes:"For instance, to find the shortest
> possible route to visit 10 cities, a computer
> would have to calculate 362,880
> possiblities...As the number of cities grows,
> the number of possible paths skyrockets. Even
> the fastest computers available would require
> years to handle the (49 x 48 x 47...x 3 x 2 x 1)
> or roughtly 10^62 possible paths in a 50-city
> itenerary." Islands of Truth, (New York: Norton,
> 1990), p. 200-201.And what if we solve a 10^80
> city itinerary, where there are more cities than
> there are particles in the Universe? Where would
> those particles come from? Wayne, it is hard to
> see, at least for me, what other explanation
> could account for such a solution other than
> MWH. Could there be something? Of course, but
> that is doing what the YECs do and hoping that
> the future will solve today's theo-scientific
> problems.
-- =================================== Walt Hicks <wallyshoes@mindspring.com>In any consistent theory, there must exist true but not provable statements. (Godel's Theorem)
You can only find the truth with logic If you have already found the truth without it. (G.K. Chesterton) ===================================
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