Re: Reversible Computation and Experience

From: Lee Corbin (
Date: Thu May 10 2001 - 19:18:42 MDT

At 09:50 PM 5/5/01, Jim Fehlinger wrote:

>> So un-experiencing something would be just as
>> fun as experiencing it... not "un-fun" at all!
>Sounds just like Paul Durham's Theorie de la Poussiere
>(Dust Theory) in Egan's _Permutation City_:

Jim then quotes the bizarre scene that starts on p. 78:

>"Experiment two, trial number one. Reverse order.
>Paul counted, 'One. Two. Three.'... After an initial
>leap into the future...In real time, the first thing to
>be computed would be his model-time-final brain state,
>complete with memories of everything that 'had happened'
>in the 'preceding' ten seconds....
>I wonder if this sort of reversibility Gedanken experiment
>could be parlayed by a mathematician or philosopher into
>evidence that consciousness **cannot**, in fact, be
>implemented as a Turing machine.

Certainly not, and for two reasons. In the first place, what Greg
Egan was talking about was not reversibility in the sense of
reversible computation. He simply ran some scenes in a different
order. If the successive states are denoted A--B--C--D--E, then
he was only talking about having a copy experience D--E, then C--D,
and so on. This is nothing more than slicing up calculations that
are still "forward" going. With reversible computers, of course,
we are talking about sequences such as E--D--C--B--A.

The second reason is that Greg Egan does not appear to be talking
about the kinds of computation, in general, that can be accomplished
by a Turing machine (or a computer). In a very confused way, he
appears to be talking about a restricted kind of computation.

Anyway, let me digress to explain how Egan was probably going wrong.
I used to think that I knew exactly how it happened. If you ask anyone
who is reading this what a good mathematical model of the conscious
development in real time of an organism should be, they'll sooner or
later point you in the direction of non-linear dynamics (chaos theory),
because of the way that our lives, as well as so many other physical
phenomena, exhibit features not found in differential equations.

I mean to say that it wouldn't have occurred to Maxwell to attempt
to model millions of interactions large scale objects using
differential equations. There is a clear non-compressibility
of the entire "calculation" of varies and mixed kinds of objects,
much as one sees in Conway's Life.

Differential equations are a tool useful in non-chaotic calculations.
Yes, it's true that the initial conditions determine the final state
just as in, say, cellular autonoma. Yes, it's true that differential
equations can display sensitive dependence on initial conditions.
But unlike the kind of chaotic development that I'm talking about, in
which each state is necessary for the calculation of all following
states, differential equations often submit to formal symbolic
methods in such a manner that intermediate states (and calculations)
can be ignored.

I think that Greg Egan refers to "differential equations" at least
once, though I can't find it. But on pages 48-49, what he's talking
about is just not clear. He says, first, "His model of a brain was
being fully described at half-second (model time) intervals---but each
description still included the results of everything that "would have
happened" in between". Now from this you would think that the
emulation of Paul Durham was not experiencing each of the little
steps during the half-seconds.

But then on the next page he goes on, "The equations controlling the
model were far too complex to solve in a single step. In the process
of calculating the solutions, vast arrays of partial results were
being generated and discarded along the way. In a sense, these
partial results **implied**---even if they didn't directly represent---
events taking place within the gaps between successive complete
descriptions." And when the whole model was arbitrary, who was to
say that these implied events, buried a little more deeply in the
torrent of data, were any "less real" than those which were directly

It's obvious that he's leaning way too heavily on some very unclear
concepts such as "implied", "represent" and "fully described", or
at least trying to get some strange mileage out of them.

For sure it was sensitive dependence on confused concepts that
led Greg Egan downward into the Theory of Dust. And it's not
impossible that he knew this perfectly well, and was having some
fun, as he seemed to indicate in one interview.

Lee Corbin

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