Mark Peaty wrote:
> Hello Jason,
> please excuse my ignorant interjections here but, as a
> non-mathematician, non-philosopher, I need to work things into a plain
> English version before I can feel that I understand them, and even then
> the edges of things get fuzzy with far more ease than they get straight
> and clear cut. Furthermore I am beginning to wonder if the apparently
> 'straight' and clear cut boundaries to concepts and so forth are not
> merely figments of my imagination. I don't think I go anywhere as far as
> John M. in this but then maybe that is just because I fear to let go of
> my sceptical reductionist walking stick. :-)
>
> Jason: 'perform an infinite number of
> computations with a finite amount of energy, but only if the
> computations done on that computer are logically reversible.'
>
> MP: Surely 'logically reversible' does not necessarily imply no entropy,
> just that for the purposes of the concerned observer, the computing
> system can return to a state that is sufficiently close to the original
> state so that the inputs can be discovered. More or less by definition,
> entropy increases and manifests as deterioration of the substrate and as
> the need to supply more energy to travel through the system than
> otherwise is calculated to be necessary to obtain the minimum changes
> needed to embody the changes of state in the calculating system.
>
Right, logically reversible computations on their own do not imply no
increase in entropy by the computing system, but for a computing system
to operate with no net increase in entropy, the computations it
performs must be logically reversible. This is because: "For a
computational operation in which 1 bit of logical information is lost,
the amount of entropy generated is at least k ln 2, and so the energy
that must eventually be emitted to the environment is E kT ln 2." (
http://en.wikipedia.org/wiki/Reversible_computing#More_on_Landauer.27s_principle
) Note that the computing substrates needed to implement such an
efficient computer are well beyond our current level of technology and
are only theoretical. However there is as of yet, no known reason why
an arbitrarily efficient computer could not be built.
A reversible computation is one that has a 1 to 1 mapping between input
and output. For example if if I compute x=x+3, every input has a
unique output, given the function and the result it is possible to
determine the input. However the same could not be said of a function
defined as x=x modulo 3, or x=0, where there are a finite number of
outputs. These computations are not reversible because it is
inpossible to get the input given function and the output.
> Jason: 'The physical interactions that occur in this universe are also
> reversible. e.g. An electron can accept a photon and move to a higher
> energy state or an electron can emit a photon and move to a lower
> energy state. Does reversible physics imply that a computational model
> of said physics would involve entirely reversible computations? '
>
> MP: This concept of 'reversible' is very useful, but to how great an
> extent is it just a convenient fiction? My understanding is that you
> can't fire *a particular* photon at a particular atom and guarantee that
> your favourite electron will rise to the predicted level. I mean it
> either will or it won't.
By physically reversible I don't mean we as humans can undo anything
that happens, rather physical interactions are time-invertible. If you
were shown a recording of any physical interaction on a small scale, an
elastic collision of particles, the decay of a nucleus, burning of
hydrogen, it would be impossible for you to tell if that recording were
being played in reverse or not, since it is always possible for that
interaction to occur as it does in either direction of time.
> Conversely as I understand it [AIUI] the
> subsidence of an electron to a lower orbital is only predictable in a
> statistical sense. Once again is it not that the real world entities
> must be dealt with in a statistical manner, either as bulk substances,
> predictable due to the averaging of activities of the individual quantum
> particles, or as individual quantum items manifesting radical
> indeterminacy?
Quantum mechanics makes the universe seem random and uncomputable to
those inside it, but according to the many-worlds interpretation the
universe evolves deterministically. It is only the observers within
the quantum mechanical universe that perceive the randomness and
unpredictability, but this unpredictability doesn't exist at the higher
level where the universe is being simulated (assuming many-worlds).
>Either way AIUI, the computational model will manipulate
> symbols denoting the real world physics and there is no guarantee that
> any such computing system could overcome the limits imposed by entropy
> and quantum indeterminacy.
>
I'm not sure what you are saying here. Are you saying that a perfectly
efficient computer could not be built or that the physics of this
universe are not computable?
Jason
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Received on Sun Jan 14 2007 - 07:30:33 PST