BUILD A "BELL CURVE" BOARD

British statistician, Francis Galton (cousin of Charles Darwin, showed us how to build a board with upturned nails that created (in marbles collected at its bottom) the normal distribution curve, popularly known as "the bell curve". (Later, I'll tell you how it became a popular game.)

Galton named this board "the quincunx", by a peculiar Latin derivation.

  1. Take a board about 1 inch by 18 inches by 30 inches and "box" it on all sides by strips extending 1 inch above board surface;
  2. 8 inches from bottom of board, create a row of 1" nails, just fixed into the surface, protruding up, spaced across every inch;
  3. create similar rows of nails up toward top, stopping at least 2 inches from top of board;
  4. at bottom glue or otherwise fix slotting strips (say, 3/8" x 1" x 6") on the 3/8" sides to collect marbles that roll down the board;
  5. finally, use board 1/2" x 1" x 18", driven in, to prop up top of the nail-board.
You roll, one after another, small marbles or small ball bearings from top down the board. When on strikes a nail, it either goes off to the left or to the right to collect in one of the slots at the bottom. (The slot partitions prevent balls sliding of to the side, leveling the bottom output.) It can be shown that there are many more paths toward the middle of the board than toward the sides, so that more marbles collect between the middle slots than betweem those on the sides.

Furthermore, it can be shown that the distribution of paths matches the BINOMIAL DISTRIBUTION (familiar to algebra students in a Pascal Table), and the BINOMIAL DISTRIBUTION is the DIGITAL or DISCRETE FORM which PASSES OVER INTO THE ANALOGIC FORM known as "The Normal Distribution (bell curve)".

Thus, you see how this "curve" arises.

Galton demonstrated his board in public, under the peculiar name, "The Quincunx". Some one got the idea of attaching a device at the bottom right for shooting marbles to the top of the board, to tumble down through the nails.

Still later, holes were put into the board, so that some marbles never reached the bottom slots. Eventually, The Quincux became The Pinball Machine! A statistical demonstration device of Sir Francis Galton became a game-toy!