From: Richard Loosemore (email@example.com)
Date: Fri Nov 25 2005 - 11:38:04 MST
David McFadzean wrote:
> On 11/24/05, Richard Loosemore <firstname.lastname@example.org> wrote:
>>Your phrase "chaotic nature of dynamical complex systems like weather
>>simulations" betrays deep confusion about what a complex system is, what
>>a chaotic system is (not the same, usually) and what the characteristics
>>of weather systems are (partly chaotic, partly normal and predictable)
> Why can't a weather simulation be complex and chaotic?
You are right: weather systems *can* display both complex systems
behavior and chaotic behavior, but what I was trying to get at was the
fact that these really don't happen at the same level, so your comment
about the chaotic nature of complex systems did not make any sense.
A chaotic system tends to wander at random through its state space,
whilst displaying regularity when its trajectory is examined in
particular ways. I would conclude that the global weather system was
chaotic if we all got every kind of weather, at random times, wherever
we lived on the planet, but that certain patterns could be discerned in
the randomness. That clearly does not happen on a fairly broad scale
(we have never had 95 degree weather on a November day in upstate New
York, for example). On the other hand, if we looked at the connection
between millimeter-scale air currents and large weather events (like
tornadoes and hurricanes), we find mostly a random relationship, but on
the other hand it is not completely random because at the origin point
of every hurricane there is almost certainly a millimeter-scale air
movement that looks unusual (a vortex emanating from the flap of a
butterfly wing, for example). This is classic Chaos, of course. But
notice that we had to switch scales to see the chaos.
Complex systems, by contrast, do not wander at random through their
entire state space. They are described as being at "the edge of chaos"
precisely because they show the kind of extremely ordered or restricted
behavior that emerges as you tunr the knob (so to speak) on the
controlling paramters of a chaotic system and turn it back into a
regular, ordered (non-chaotic and non-complex) system. Just before the
parameter change makes the chaotic system regular, there is the
possibility of it being quasi-ordered. If you look at the weather
system at a large scale (storm systems, fronts, tornadoes, hurricanes,
rotating cells, etc), you can see a very crude example of complex
behavior, but it is not a good one (not very systematic complexity).
The emergent features are there (telltale signs of complexity), but they
have poor structure and poor ability to interact with each other -
mostly they just crash and merge when they meet each other, which is not
very "ordered" behavior in my book.
But what really made your comment confusing, for me, was when you said
that "He [Sununu, with his 386 climate simulation] observed how small
changes in the inputs and assumptions led to large changes in the
results and (correctly) reasoned that running on a supercomputer isn't
going to mitigate that problem". The chaotic or complex features of
weather systems do not automatically buy you the conclusion that a small
change in the inputs/assumptions causes large changes in the results.
For a chaotic pendulum, for example, a small change in the initial
conditions gets you nothing at all: the trajectory is different, but
the phase-space portrait is the same. Even a change in the exact
physical parameters of the system (longer or shorter pendulum, different
placement of the trajectory disturbing objects, etc. etc), you would
still observe similar phase-space diagrams. For a big complex adaptive
system like an economics simulation you might change some parameters
and get big global changes, but as you systematically change the
parameters you would not necessarily observe random changes at the
global level. Sometimes the global changes consequent on local or
system parameter changes are small in magnitude (just not very
understandable or obvious or analytically derivable).
Because of the poor correspondence between the global weather system and
a complex system, I would expect to find that when many simulations were
done (by a supercomputer that hadthe power to do them), some fairly
robust relationships between parameters and global trends would emerge.
Now, my understanding of the results is that this *is* what happens.
More simulations and finer scale lead to broadly convergent predictions.
More subtly, the simulations tell us that disturbing the atmosphere
towards (e.g.) greater CO2 concentration causes a tendency toward
unpredictability and wild fluctuations. In other words, the simulations
distinguish between calm regimes and wildly fluctuating regimes, and
they predict that wild fluctuation is what the CO2 problem is inflicting
on the world.
>>You also misunderstand what a supercomputer simulation is used for: not
>>just finer grained modelling, but modelling vast numbers of different
>>variations. Sununu could not possibly have learned anything from his
>>silly little simulation.
> I didn't say he was right necessarily. I said he may not be as stupid
> as someone originally thought. Is it possible?
If someone is purported to be smart, but comes to the conclusion that
their tiny little desktop simulation is as good as a supercomputer, and
if a five minute conversation with a simulation expert could have
revealed that they were profoundly mistaken, then most certainly that
person is stupid.
It is a bit like the kind of macho behavior that occurs when someone
wants to go ice skating on a pond, but dismisses the expert advice (that
the temerature has got to be below a certain level for a certain number
of days) and instead just stamps on the ice at the edge and declares it
to be good enough. That person is stupid.
>>But I think you only made this comment as an excuse to start a political
>>flame war on the subject of global warming ;-)
> I don't see any good reason to impugn my motives. Are you trying to
> make me feel unwelcome here?
Heavens, no. I am sorry you got that impression: I put a facetious
smiley in to indicate that I suspected you were *maybe* trying to be
provocative (as some others have been, just recently, and as some are
being right now, on another branch of this same thread).
There are enough other people on this list who are casually insulting,
that I would be sad if I had descended to the same level of rudeness.
Apologies if it looked like I was being insulting.
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