Of course, it *is* impossible to construct such a machine in 'our universe'
since 'time' is a quantum phenomenon (a set of relationships) and cannot be
subdivided indefinitely (from our perspective 10e-43 is smallest quantum of
time).
(And note that there are no 'observers' (sets of observer-moments in time
with an objective identity across them), only monad-like observer-moments.
So this observer-moment, which is all you are, survives 'forever'. I don't
suppose anyone will ever take this seriously this but I can't help saying
it whenever I get the chance.)
James
> -----Original Message-----
> From: Saibal Mitra [SMTP:smitra.domain.name.hidden]
> Sent: Thursday, September 14, 2000 8:56 PM
> To: GSLevy.domain.name.hidden; everything-list.domain.name.hidden.com
> Subject: Re: The Rapidly-Accelerating Computer
>
> George Levy wrote:
>
> > In a message dated 09/14/2000 9:05:44 AM Pacific Daylight Time,
> > smitra.domain.name.hidden writes:
> >
> > > Stewart, on the other hand, considers the RAC, whose clock accelerates
> > > exponentially fast, with pulses separated by intervals of 1/2, 1/4,
> 1/8
> ...
> > > seconds. So the RAC can cram an infinite number of computational steps
> into
> > a
> > > single second.
> >
> > It may be impossible to construct such a machine in our universe, but
> can
> we
> > achieve the same results by slowing down the consciousness of the
> observer
> > observing a conventional computer? In other words, each observer's clock
> > cycle (assuming a computer model for the observer) would double in
> duration
> > in relation to the computer clock. Could there be such an observer in
> our
> > universe? I suspect that there can't be because the construction of the
> > observer's clock woud require smaller and smaller energy packets in the
> > presence of constant background noise.
> >
> > George Levy
> >
> >
> The observer also has to survive ``forever´´. This problem is investigated
> in the context of eternal inflation models in the paper:
>
> http://xxx.lanl.gov/abs/astro-ph/9909143
>
> ABSTRACT:
>
> ``We discuss the large-scale structure of the universe in inflationary
> cosmology and the implications that it may have for the long-term future
> of
> civilizations. Although each civilization is doomed to perish, it may be
> possible to transmit its accumulated knowledge to future civilizations. We
> consider several scenarios of this sort. If the cosmological constant is
> positive, it eventually dominates the universe and bubbles of inflationary
> phase begin to nucleate at a constant rate. Thermalized regions inside
> these
> inflating bubbles will give rise to new galaxies and civilizations. It is
> possible in principle to send a message to one of them. It might even be
> possible to send a device whose purpose is to recreate an approximation of
> the original civilization in the new region. However, the message or
> device
> will almost certainly be intercepted by black holes, which nucleate at a
> much higher rate than inflating bubbles. Formation of new inflating
> regions
> can also be triggered by gravitational collapse, but again the probability
> is low, and the number of attempts required for a positive outcome is
> enormous. The probability can be higher if the energy scale of inflation
> is
> closer to the Planck scale, but a high energy scale produces a tight bound
> on the amount of information that can be transmitted. One can try to avoid
> quantum tunneling altogether, but this requires a violation of quantum
> inequalities which constrain the magnitude of negative energy densities.
> However, the limits of validity of quantum inequalities are not clear, and
> future research may show that the required violation is in fact possible.
> Therein lies the hope for the future of civilizations.´´
>
> You can imagine that a device could be made such that the observer is
> slowing down by a factor of two compared to the previous generation. So,
> maybe the quantum inequalities are a manifestation of the limitations of
> the
> universal Turing machine.
>
> Saibal
>
>
>
Received on Fri Sep 15 2000 - 01:34:45 PDT