Linas Vepstas wrote:
On Wed, Oct 03, 2007 at 12:20:10PM -0400, Richard Loosemore wrote:
Second, You mention the 3-body problem in Newtonian mechanics. Although
I did not use it as such in the paper, this is my poster child of a
partial complex system. I often cite the case of planetary system
dynamics as an example of a real physical system that is PARTIALLY
complex, because it is mostly governed by regular dynamics (which lets
us predict solar eclipse precisely), but also has various minor aspects
that are complex, such as Pluto's orbit, braiding effects in planetary
rings, and so on.
Richard, we had this conversation in private, but we can have it again
in public. J Storrs Hall is right. You can't actually say that the
3-body problem has "various minor aspects that are complex, such as
Pluto's orbit". That's just plain wrong.
The phonomenon you are describing is known as the "small divisors
problem", and has been studied for several hundred years, with a
particularly thick corpus developed about 150 years ago, if I remember
rightly. The initial hopes of astronomers were that planetary motion
would be exactly as you describe it: that its mostly regular dynamics,
with just some minor aspects, some minor corrections.
This hope was dashed. The minor corrections, or perturbations, have
a denominator, in which appear ratios of periods of orbits. Some of
these denominators can get arbitrarily small, implying that the "small
correction" is in fact unboundedly large. This was discovered, I dunno,
several hundred years ago, and elucidated in the 19th century. Both
Poincare and Einstein made notable contributions. Modern research
into chaos theory has shed new insight into "what's really going on";
it has *not*, however, made planetary motion only a "partially
complicated system". It is quite fully wild and wooly.
In a very deep sense, planetary motion is wildly and insanely
unpredicatable. Just becaouse we can work out numerical simulations
for the next million years does not mean that the system is complex
in only minor ways; this is a fallacious deduction.
Note the probabilites of pluto going bonkers are not comparable
to the sun tunneling into bloomingdale's but are in fact much, much
higher. Pluto could fly off tommorrow, and the probability is big
enough that you have to actually account for it.
The problem with this whole email thread tends to be that many people
are willing to agree with your conclusions, but dislike the manner in
which they are arrived at. Brushing off planetary motion, or the
Turing-completeness of Conway's life, just basically points to
a lack of understanding of the basic principles to which you appeal.
Linas,
The difficulty I sometimes have with discussions in this format is that
it is perfectly acceptable for people to disagree with the ideas, but
they should keep personal insults OUT of the discussion -- and
accordingly, in my reactions to other people, I *never* introduce ad
hominem remarks, I only *respond* to ad hominem insults from others. I
responded that way when Josh decided to disagree by using extremely
insulting language. To anyone who disagrees politely, I will put in
huge amounts of effort to meet their criticisms, help clarify the
issues, apologize for any lack of clarity on my part, etc.
Now, to the subject at hand.
I hear what you are saying about the 3-body problem. [I would have been
happier if YOU had managed to phrase it without making assertions about
what I do and do not understand, because I earned a physics degree, with
a strong Astronomy component, back in 1979, and I have been aware of
these issues for a very long time].
Even though you assertively declare that my use of the example of
plenetary orbits is "just plain wrong", I knew exactly what I was doing
when I picked the example, and it is precisely correct.
I will explain why.
The core issue has to do with what I actually mean when I say that
planetary orbits contain a "small amount of complexity". You are
interpreting that statement one way, but I am using in a different way.
It is my usage that matters, because this discussion is, after all,
about my paper, the way I used the phrase in that paper, and the way
that other people who talk about "amounts of complexity" would tend to
use that phrase.
The "amount of complexity" is all about the exactness of an overall
scientific explanation for a system. It is about the extent to which a
normal, scientific explanation can be set down and used to explain the
system. Is it possible to find an explanation that covers the state of
that system very accurately for a very large fraction of that system's
lifetime? If the answer is yes, then the system does not have much
complexity in it. If the vast bulk of the lifetime of that system
cannot be understood by any normal scientific explanation (i.e. cannot
be predicted), and if the behavior is not completely random, then we
would say that the system has a "large degree of complexity".
Liquid flow is another example. So long as it is in the non-turbulent
regime, we can build a great deal of regular explanatory apparatus to
describe it. But in that relatively small fraction of the cases where
it goes turbulent, we have a great deal more trouble. Again, a small
amount fo complexity.
There is not any precise measure of "amount of complexity", but
nevertheless it is a clear concept: this is all about the coverage of a
scientific explanation that allows us to make predictions about the
system's behavior.
So, do planetary orbits contain a "small amount of complexity". Of
course they do: in the sense in which I have just defined "small amount
of complexity", and in the sense in which I very clearly use it in my
paper (if you read the paper carefully) the motion of the planets is
governed by a scientific explanation that allows us to predict that
motion with exquisite accuracy.
But you are implicitly using a different interpretation of "small amount
of complexity". An interpretation that has nothing to do with the way I
used it in my paper. You are talking about whether the complex effects
cause NUMERICALLY SMALL amounts of fluctation in the states of the
system. So, in the case of our solar system, things will go humming
along nicely for several hundred million years, and then Pluto will go
bonkers and everything will shift into a new state, and after the
realignment the NUMERICAL position will not be slightly different than
it would have been predicted before the change, it will be massively
different.
This is all true, but it simply does not impact anything because, as I
say, I was quite clear in my usage in the paper -- it is all about
whether *explanations* can be found for global behavior, and the
coverage of those explanations, and nowhere is there even a hint that it
might be about the numerical accuracy of such explanations.
I do not mind in the least if this aspect of the paper is misunderstood
by you or anyone else -- I am only human, and my attempts to explain
these difficult ideas are not perfect, so I expect my writing will
always be less than clear to somebody, and perhaps even less than clear
to a lot of people.
But what just happened was that someone (initally Josh, and now you)
misunderstood the idea, and then came out and decided that they were so
sure they were right that they could START OFF their response to me
telling me that I don't know what I am talking about. You were so sure
I was wrong that you could tell me, personally, that I do not
understand. Instead of challenging the example and asking questions,
you made personal remarks.
That combination of mistaken understanding, combined with arrogance and
an opening salvo of ad-hominem insults directed at me, is what earned
Josh the response that I gave. He deserved it.
Is my clarification of your question clear enough, or do you have
further questions about it?
Richard Loosemore
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