Butterflies

["GiNa" <purpleonion at prodigy_net>]

From: Don Smith <dasmith at rotse2_physics.lsa.umich.edu>

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.

Well goodness, I certainly didn't see that one coming...wow.  As I read,
though, it pretty much confirmed that the butterfly metaphor *was*
appropriate for the idea I was trying to express.

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?

Oh man!  That's *exactly* what I was trying to say, that the smallest of
things...even a thought!...can influence the way something evolves.
Granted, the degree of chaos already existing on a given path can also
influence how things change...no argument there...I was just trying to
encourage input while reminding myself that being in the game is worth the
occasional bruising that comes from contact.

I do think physics is fascinating--thank you for the input and for welcoming
me!  : )
                    ______________________________________

"Take it easy, all he did was kick up some dirt."

Embedded in the mud, glistening green and gold and black, was a
butterfly, very beautiful and very dead.

It fell to the floor, an exquisite thing, a small thing that could upset
balances and knock down a line of small dominoes and then big dominoes
and then gigantic dominoes, all down the years across Time.
                    ______________________________________

Yes, that's it!  Yay!  Thank you for passing the story along!

Fluttering my wings,
Gina



----- Original Message -----
From: Don Smith <dasmith at rotse2_physics.lsa.umich.edu>
To: Over the Rhine List <Over-the-Rhine at actwin_com>
Sent: Saturday, December 21, 2002 5:36 AM
Subject: Re: I'm new to the list...


> 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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