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From: David Seaman <drseaman.domain.name.hidden>

Date: Fri, 15 Sep 2000 14:36:46 +0100

Maybe the RAC could be a sort of quantum computer which continually

expands itself deeper into the multiverse.

In any case the plenitude should allow all logical possibilities - so

every observer is sure to experience (with very low measure) the

result of every computation however long it takes.

David

At 17:58 +0200 14/9/00, Saibal Mitra wrote:

*> Question: Does the AUH exclude universes in which a RAC can be
*

*>built? The following text explaining the RAC is from the website:
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*>
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*>
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*><http://www.ix.de/tp/english/inhalt/kolu/2414/1.html>http://www.ix.de/tp/english/inhalt/kolu/2414/1.html
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*>
*

*>``Just to see how extreme the Turing-Church Thesis actually is, a
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*>few years ago mathematician Ian Stewart half-jokingly suggested the
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*>idea of what he called, The Rapidly-Accelerating Computer (RAC). His
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*>goal was to show what it is exactly about computing machines that
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*>gives rise to things like the unsolvability of the Halting Problem
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*>and uncomputable numbers. Basically, the problem is the assumption
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*>that it takes a fixed, finite amount of time to carry out a single
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*>step in a computation. For his idealized computer, Turing assumed an
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*>infinite amount of memory. Stewart, on the other hand, considers the
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*>RAC, whose clock accelerates exponentially fast, with pulses
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*>separated by intervals of 1/2, 1/4, 1/8 ...seconds. So the RAC can
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*>cram an infinite number of computational steps into a single second.
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*>Such a machine would be a sight to behold as it would be totally
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*>indifferent to the algorithmic complexity of any problem presented
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*>to it. On the RAC, everything runs in bounded time.
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*>
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*>The RAC can calculate the incalculable. For instance, it could
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*>easily solve the Halting Problem by running a computation in
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*>accelerated time and throwing a switch if and only if the program
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*>stops. Since the entire procedure could be carried out in no more
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*>than one second, we then only have to examine the switch to see if
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*>it's been thrown. The RAC could also prove or disprove famous
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*>mathematical puzzles like Goldbach's Conjecture (every even number
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*>greater than 2 is the sum of two primes). What's even more
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*>impressive, the machine could prove all possible theorems by running
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*>through every logically valid chain of deduction from the axioms of
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*>set theory. And if one believes in classical Newtonian mechanics,
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*>there's not even a theoretical obstacle in the path of actually
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*>building the RAC.
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*>
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*>In Newton's world, we could model the RAC by a classical dynamical
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*>system involving a collection of interacting particles. One way to
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*>do this, suggested by Z. Xia and J. Gerver, is to have the inner
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*>workings of the machine carried out by ball bearings that speed up
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*>exponentially. Because classical mechanics posits no upper limit on
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*>the velocities of such point particles, it's possible to accelerate
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*>time in the equations of motion by simply reparameterizing it so
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*>that infinite subjective time passes within a finite amount of
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*>objective time. What we end up with is a system of classical
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*>dynamical equations that mimics the operations of the RAC. Thus,
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*>such a system can compute the uncomputable and decide the
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*>undecidable.
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*>
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*>Of course, just like Turing's infinite-memory machine, the RAC is
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*>impossible in the real world. The problem is that at the
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*>nitty-gritty level of real material objects like logical gates and
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*>integrated circuits, there is a theoretical upper bound to the rate
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*>of information transfer (i.e., velocities). As Einstein showed, no
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*>material object can exceed the velocity of light. Thus, there is no
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*>RAC and, hence, no devices to complete the incompletable.
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*>
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*>But the fact that we can never construct a RAC in no way precludes
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*>the possibility that some analogue device like a DNA computer or a
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*>quantum machine cannot be made that will allow us to transcend the
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*>Turing limit, and, hence, compute the uncomputable.´´
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*>
*

*>Saibal
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*>
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*>
*

Received on Fri Sep 15 2000 - 06:42:45 PDT

Date: Fri, 15 Sep 2000 14:36:46 +0100

Maybe the RAC could be a sort of quantum computer which continually

expands itself deeper into the multiverse.

In any case the plenitude should allow all logical possibilities - so

every observer is sure to experience (with very low measure) the

result of every computation however long it takes.

David

At 17:58 +0200 14/9/00, Saibal Mitra wrote:

Received on Fri Sep 15 2000 - 06:42:45 PDT

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