Re: I'm new to the list...

[Don Smith <dasmith at rotse2_physics.lsa.umich.edu>]

Hi,

Okay, I'm afraid I have to go into physics teacher mode for just a minute...

Gina wrote:
> I've heard that even a butterfly's wings flapping in America can influence
> the weather patterns in Asia...I don't know if it's true, but it makes a good
> point

This isn't really what the butterfly metaphor is about, although it gets used
that way a lot.  The butterfly metaphor is supposed to demonstrate what's
called "sensitive dependence on initial conditions" which is one of the
hallmarks of a chaotic system.  Let's say you have a nice, simple, non-chaotic
system, like a perfect sphere rolling down a perfectly smooth inclined plane.
If you move the spere a teeny-tiny bit to the left before you let it go at
the top, it will end up at the bottom a teeny-tiny bit to the left of where it
would have been otherwise.  But if you make the plane or the sphere all bumpy,
that teeny-tiny shift at the start will result in the ball ending up in a
*completely* different place, and the longer it rolls, the more different
those two end states will tend to be. 

So someone once exaggerated this effect to make a vivid analogy: he or she took
a very small difference at the start (a butterfly flapping or not flapping) of
a chaotic system (weather), took that system through a long development (around
the world) and a very huge difference at the end (hurricane versus no
hurricane) and used those images to represent the idea that chaotic systems
will diverge from tiny differences in initial conditions rather than run in
parallel.  There's no evidence that butterflies really influence weather
patterns; it's just an illustration.  This is why you *can't* model chaotic
systems on a computer and get useful predictions: computers at some level
*have* to round off the numbers, and even if you can go to 12 decimal places,
the difference in the 13th decimal place between the model and reality will
ultimately result in the real system being completely different from your
model.

One could, I suppose, argue that since the critical difference between the two
hypothetical paths for the system to develop is this butterfly, then the
butterfly is in some sense the cause of the hurricane, but that's not really
the point of the analogy.  Besides, there are a gazillion (excuse the technical
term, please. ;-)) steps between the butterfly and the hurricane, during which
uncountable things can influence the system more than the butterfly.  Did
moving the ball a little to the left determine where it ended up, or did all
the bumps and irregularities of the surface determine that?

So, while your point about one person or ten making a difference is a good one,
the butterfly metaphor is perhaps not the best one to use.  Although maybe it
is, because the introduction of one person onto a mailing list of hundreds may
seem like a small change, but it could lead to huge, unpredictable developments
a few years down the line.  :-)  This mailing list sure seems chaotic at times. 

Physics teacher mode off...

I hope this didn't come across as trying to put you down; I'm just trying to 
be helpful in providing more information.  Welcome to the chaos!  Glad you
decided to get your feet wet!  :-)  And did you know that in quantum mechanical
systems, you can't even *look* without influencing the state of the system
you're trying to observe?  So don't stay aloof!  :-)

Yours,
-- 
Don Smith                           Robotic Optical Transient Search Experiment
donaldas at umich_edu                                 http://xte.mit.edu/~dasmith/

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