When I was a youngster visiting a science museum in my home state what most fascinated me was not the dinosaur displays, or fossils, or insect collections, nor more whizbang exhibits, but a simple large display known as a "Galton Box" (after the 1889 inventor of the first one), or known by some as a "quincunx," (...okay, so I was an odd kid).
Most of you are likely familiar with these enclosed contraptions in which balls drop from a central point at the top onto a symmetrical pegboard where they bounce around until finally falling into columns at the bottom... the majority of balls dropping, by sheer chance, somewhere in the middle columns, and fewer balls bouncing around in a manner depositing them to the outer end columns.
On the glass pane enclosing the balls and peg-grid would be drawn the 'normal' or 'Gaussian' distribution (or 'Bell curve') so central to mathematics/probability, and lo-and-behold, once all the hundreds of balls had been released they would, in the columns below, take on the shape of that normal curve, via of course the 'laws' of sheer chance, not due to any mechanical manipulation. Even as a child, not really understanding much about normal distributions, nor math/probability more generally, somehow that demonstration was very powerful to me; like a magic, unseen hand guiding the fate of those individual spheres --- each one taking a rather random, unpredictable journey, yet the end result being highly predictable and little-changing. Even as a youngster I sensed there was something profound in that. Some kids today construct Galton Boxes or quincunxes for science fair projects. Hooray!, for still to this day I love these apparatuses and their magical outcomes (...the rest of you can go gawk at dinosaur models).
A very quickie YouTube demonstration with a miniature, sand-based quincunx here:
http://www.youtube.com/watch?v=xDIyAOBa_yU
And more on the 'quincunx' here:
http://en.wikipedia.org/wiki/Bean_machine
http://www.mathsisfun.com/data/quincunx.html
finally, more technical info on the normal distribution from Wikipedia here:
http://en.wikipedia.org/wiki/Normal_distribution
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