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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

described?"

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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