From: Glenn Morton (glennmorton@entouch.net)
Date: Fri Jul 04 2003 - 14:58:09 EDT
Walter wrote:
>-----Original Message-----
>From: asa-owner@lists.calvin.edu [mailto:asa-owner@lists.calvin.edu]On
>Behalf Of Walter Hicks
>Sent: Friday, July 04, 2003 1:10 PM
>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.
Walter, you are lost in the details. I am speaking of the generalized
traveling salesman problem. We can obviously solve a linear combo of
cities. That isn't the point. The point is that some of the problems are so
complex that it would take the age of the universe and more memory than
exists in our solar system or galaxy to solve.
>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.
Yes, an abacus deals in number larger than itself, but it requires the
movement or manipulation of a physical object for the abacus to do anything.
A wire with beads sitting on the ground not moving, doesn't calculate
anything. It is the calculation that is important here.
You can learn more about the TSP at http://www.math.princeton.edu/tsp/
and the largest one solved to date on a distributed computer
http://www.math.princeton.edu/tsp/d15sol/
As to the concept that calculation requires the manipulation of a physical
object consider this quote about the relation between computers memory and
physical state of the object:
"The kinship with the computer memory now begins to shine through. In a
computer each of the possible logical states is represented by a certain
configuration in the hardware--each of n logical states has its physical
representation in the hardware. Werner R. Lowenstein, The Touchstone of
Life, (New York: Oxford University Press, 1999), p.13
Glenn
>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)
>===================================
>
>
>
This archive was generated by hypermail 2.1.4 : Fri Jul 04 2003 - 14:58:27 EDT