On Thu, 10 Nov 1994, Barbara Weitbrecht, Smithsonian wrote:
 
> > Subject:      Re: galton quincunx
>
> Marvelous word, "quincunx".  Those of you who have been putting
> off a trip to the dictionary to look it up should delay no longer.
>
> > The Boston Children's Museum had (years ago) a device that dropped
> > the balls and resulted in the bell shaped curve.  Try them.
>
> So did the wonderful Mathematics exhibit in the Museum of Science
> and Industry in Los Angeles.  That gallery was one of my favorite
> museum spaces when I was a somewhat nerdy child in the L.A. basin.
> It is still there, I wonder?
 
IBM's 'MATHEMATICA' at the Museum of Science in Boston still has
a Galton ball machine.  I think I recall seeing one at the Tech
Museum in San Jose.
 
These devices gave me some insight into Chaotic Dynamics when fractals
hit the fan in '84 - '88.  The Gaussian distribution in the exhibit
is an emergent property.  It is generated by the nonlinear "decisions"
that come about when a ball falls to the left or right of a pin.
And the whole exhibit acts as a powerful amplifier of variation in
initial conditions.
 
I wonder how much of the ball distribution comes about by a Gaussian
distribution of velocities in the incoming balls (and in thermal and sound
vibration in the pins?) Maybe the curve arises because the noise and
vibration in the exhibit guarantee that the balls will make random
decisions when they strike the pins.  If precision initial conditions
could be created, and if the pins were vibrationally isolated from the
exhibit structure, would ALL balls start to take the same path?  Or is the
amplification so great that quantum uncertainty in the balls and pins
would still create a bell shaped curve?  Or maybe it's just because the
balls aren't perfectly round and polished...
 
 
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William Beaty  voice:206-781-3320   bbs:206-789-0775 cserv:71241,3623
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