>Certainly, reusing a low number of particles would be slow; however, for
>the problem of factoring a large number, it is only necessary to save
>factors and not non-factors, so less memory is required. I successfully
>ran a computation involving 10^46 possible options on a desktop computer
>(over several days), because several options could be eliminated rather
>quickly. Similarly, if the number to be factored is odd, all even numbers
>can be eliminated as possible factors, and so forth.
> To me, this particular arguement does not seem compelling because
>it is based on the assumption that this quantum computer works fast enough
>to be puzzling, yet it's not known whether it can be built.
Of course this argument assumes that the quantum computer works fast enough to
be puzzling, and of course it assumes that it can be built. That is the
nature of hypotheticals. My understanding of the technology on these things
is that it has been proven that they can THEORETICALLY be built. Whether it
can be done practically is another thing.
However, you and Loren are partially missing the point of my question. Time
and time again, Christianity has been caught unawares and off guard when new
discoveries come along to shake us up. I contend that part of the reason for
this is 1) large segments of the Christian world do not pay any attention to
what is going on, and 2) we avoid doing any contingency planning whatsoever.
I manage a group of geophysicists and as such, I have to plan for unexpected
contingencies. Most never happen. Lots of things I plan for are very
unlikely. That does not negate the usefulness of such contingency planning.
More than once it has saved my cookies at work because I could respond quickly
to a crisis. Should Christianity be any different.
Loren wrote something similar in dismissing this exercise:
>I'll grant that every "calculation" requires a physical operation.
>The critical assumption in the Discover article is that 10^500
>"calculations" are required to factorize a large number. That is true
>when "standard" algorithms are used; it need not be true of other
>algorithms.
>
>A digital computer using standard techniques might require 10^12 physical
>operations to solve a differential equation, while a properly constructed
>analog computer could do it in 10^0 steps. (Well, if you're going to get
>technical, it might be more like 10^6.) Approximately 10^15 computational
>steps have gone into calculating a precise approximation of the helium atom's
>eigenstates. But when two electrons encounter an alpha particle, they
>don't perform all those calculations, they "naturally" find the right
>eigenstates. In the same way, if someone cleverly constructs an artificial
>"atom" in which the quantum eigenstates correspond to the (unknown) factors
>of a large number (which is, I believe, what was proposed), the same
>principle applies. They're just using a very clever algorithm and a
>small number of steps.
Since I would presume that the guys that wrote the program and Deutch who
wants to use the program are able to count, I would further presume that they
are able to give a reasonable estimate of how many calculations are required
for the algorithm in question. I can go to my experts and ask them how many
steps a Kirchoff migration of 3 dimensional seismic data would require and how
many a finite-difference migration would require. They are able to tell me.
What is analogous to David's objection is that the finite difference algorithm
has never been tried. It takes about 100 times the computer power of a
Kirchoff and costs about that much more also. We don't know if it really
works. But these algorithms were written for a computer which does not exist
because we need multi-teraflops to be able to run the finite difference.
If you have read Shor's work and can tell me that they are most definitely
using a "clever algorithm" then I would bow to your assessment. I have not
read Shor's paper and probably wouldn't understand it. But the response seems
weak to me. They state, in the obviously non-technical Discover article, that
Shor worked the problem by having all non factor wavefunctions destructively
interfere. This implies that each non-factor must be calculated.
Even assuming that you are correct, that they are using a "clever algorithm"
which can factor such a large number rapidly, I would be willing to bet that
there is an even LARGER number that would require an equally impossible number
of steps. No matter what algorithm you choose there is some limit to the
number of calculations it can do during the lifetime of the universe.
If you and David don't like the factoring problem, try the traveling salesman
problem. Finding the absolutely shortest/cheapest route between 15,000
cities? This problem can not be solved. Even a 50 city itenerary requires
the comparison of 10^62 paths. For a 15,000 city itenerary, the number of
comparisons is 15,000! which would require too long a time to solve. What if
a quantum computer is able someday to solve it in 10 minutes?
Now my question once again, is what are the theological implications of the
finding of a solution for mathematical problem which exceeds the capacity of
our single universe? And since Loren agrees that a computation requires a
physical operation, if the number of operations in the time frame allowed
given the number of particles within the speed of light distance of the
computer is such, that other physical objects must have been accessed, what
should the Christian response be?
glenn
Foundation,Fall and Flood
http://members.gnn.com/GRMorton/dmd.htm