Eliezer Yudkowsky writes
>Lee Corbin wrote:
>> 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.
>
>The three-body problem is unsolveable for time T without computing all the
>intervening states between now and T. One presumes that the same holds of
>the hundred-trillion-synapse problem. Egan's scenario, which involves
>selectively refusing to compute certain intervening periods, is therefore
>impossible.
In Newtonian mechanics you cannot, of course, compute all the intervening
states between now and T, yet we may obtain arbitrarily precise approximations
(modulo their uselessness for large enough T). Consideration of the three
body problem actually helps Egan's point rather than hinders it. Recall that
I had also quoted:
>> 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. <<
See? Sometimes he's saying (a lot of) intermediate steps are calculated,
and at other times he appears to imply that they're being skipped. Using
the principle of charity obliges us to read him in the strongest way that
we can. Clearly he's using "equations" in the same manner as one would
speak of "differential equations", and their intractability in this case
also suggests something enormously difficult (like the three body problem).
Again, the totally weirdest thing is that anyone but Egan would have
suggested an iterative (chaotic) model, in which the intermediate
calculations don't **approximate** anything, but rather **comprise**
the calculation in question.
By hundred-trillion-synapse problem, I think that you are referring
to an example of the latter iterative model, and not an example of
the former differential equations model. Yes, we certainly think
this also to be incompressible (no short cuts), just in the way
that a Life position is incompressible.
However, speaking again of reversibility, and the n-body problem, I
wonder if there is any way, for some extremely large integer n,
to dismiss the possibility of n bodies acting under Newtonian
gravitation so that they implement a conscious calculation. My
intuition says that this has to be impossible. But just because
there is no entropy increase (Newton's equations are time reversible)
is itself not enough to rule out consciousness, as we know from the
universality of reversible calculation.
Lee Corbin
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