[...]
>
>Glenn, a question for you (since I'm not an expert in nonlinear dynamics):
>While chaos theory describes the way a system's time-evolution is quite
>sensitive to initial conditions, aren't there also mathematical equations
>of motion which lead to very similar time evolution no matter what the initial
>conditions? (Is this a "strange attractor"?) The existence of such systems
>could be appealed to by those who seek to blunt the force of an anthropic
>principle which depends on "fine-tuning" of initial conditions.
>
>What do you think? And you, Brian?
>
This is a very interesting question. We've already heard some good
responses by Glenn and David. Here I'll give a few of my own
random thoughts. I remember Stu Kauffman talking at great length
about initial conditions and how he has devoted a great deal of effort
trying to find models that do interesting things without being
overly sensitive to the initial conditions. I don't recall Kauffman
discussing any metaphysical implications of this. One thing we might
take from Kauffman's experience goes along the lines of what Glenn
said. There are apparently a great number of models falling within
the generic class of models that Kauffman is considering with only
a very few of them having the property of giving a robust response
without being overly constrained by the initial conditions. So
again we have an apparent fortuitousness upon which anthropic
principles are based. Also, the strange attractors seem to be
located at very convenient places ;-).
Your question reminded me of something I read in John Barrow's
(excellent) book <The World Within the World>. He has a very
interesting discussion of initial conditions in the context
of the inflationary cosmological model. This is a good example
of what we are discussing here since the primary goal of this
model seems to be to remove the high sensitivity to initial
conditions inherent in other models. Whether it is successful
is another matter entirely. I seem to recall that this model
has a number of parameters that must be finely tuned so one
is just exchanging one type of fine-tuning for another. In
effect, I believe this is what Kauffman was doing in the example
above. Anyway, this is interesting but not really what I
wanted to mention at this point. Here I wanted to discuss
the motivation for seeking this type of model. What we are
inclined to suspect is that the motivation is uneasiness
regarding the metaphysical implications of finely tuned
initial conditions. While this is undoubtedly true in some
cases, I would like to argue that its not necessarily the
case and that there is a very practical reason for preferring
models that become uncoupled from their initial conditions,
a reason that has nothing to do with metaphysics. The reason
is simply that these types of models are more useful. Since
I don't know much about cosmology, I'll illustrate this from
my own field of expertise. This has a bonus in that no one
should be suspicious of ulterior metaphysical motives since
there are no metaphysically deep implications hidden in the
models I use.
I'll try to keep my illustration brief as I suspect those who
have read this far are getting bored :). Basically, what I do
is try to develop models which describe the time dependent
(evolutionary :-) mechanical behavior of polymers. All the models
that I use and indeed can even think of have a particular type
of history dependence commonly referred to as fading memory
(we can all identify with that concept!). In a nutshell, the idea
is that the behavior of the polymer is most sensitive to what
happened in the recent past. The future behavior is very precisely
tuned to what happened in the last 10 minutes, but very insensitive
to what happened 10 days ago. Of course, one reason models have
this feature is because this is the way polymers behave. But suppose
they didn't. Unfortunately, in this case I dare to say that it
would be impossible to have any model for polymers that had any
practical use at all. For example, to predict the behavior of the
polymers in my computer chips I would have to know precisely everything
that happened to them from the time they were manufactured.
I realize that my illustration suffers in the sense that we can
do repeatable experiments on polymers but not on universes. Thus
there will probably always be some uncertainty about which type
of model is appropriate to cosmology. My point here is that we
should avoid jumping to conclusions regarding someone's metaphysics.
A particular model that we may not particularly like for our
own metaphysical reasons may be preferred by someone else for
purely pragmatic reasons.
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Brian Harper | "People of that kind are academics, scholars,
Associate Professor | and that is the nastiest kind of man I know."
Applied Mechanics | -- Blaise Pascal
Ohio State University |
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