Have you ever watched the show Tipping Point or played on a coin pusher machine? You drop a coin from the top of the machine and is bounces around a series of pegs before landing on a moving platform. People try and predict where they want the coin to land in order to push the most coins down but it’s rigged (arcades surprisingly don’t want you to win money).
The concept shares similarities with a more interesting contraption known as the Galton Board. Invented by Sir Francis Galton, a 19th century polymath and eugenicist from Birmingham, UK, the probability machine stood at 19.05cm by 11.43cm desktop and demonstrated an important probability distribution in real-time known as the Normal distribution.
It works as follows:
As you rotate the Galton Board on its axis, you set into motion a flow of steel beads that bounce with equal probability to the left or right through several rows of pegs. As the beads accumulate in the bins, they approximate the bell curve, as shown by the yellow line [see video below] on the front of the Galton board.
Sadly, the Galton board didn’t have innocent origins. Galton made it as a way to demonstrate the mathematical principle of regression towards the mean and made part of his eugenist ideology:
Galton coined the term “regression” to describe an observable fact in the inheritance of multi-factorial quantitative genetic traits: namely that traits of the offspring of parents who lie at the tails of the distribution often tend to lie closer to the centre, the mean, of the distribution. He quantified this trend, and in doing so invented linear regression analysis, thus laying the groundwork for much of modern statistical modeling. Since then, the term “regression” has been used in other contexts, and it may be used by modern statisticians to describe phenomena such as sampling bias which have little to do with Galton’s original observations in the field of genetics.
via Wikipedia
From the chaos of randomness comes a uniform curve seen in everything from physics to finance, rainfall, even the growth of hair, nails and teeth—albeit with an ulterior motive. And all that from some beads bouncing against some pegs.
More about the Galton board
- A Galton Board Demonstration of Why All Statistical Models are Misspecified
- The statistics of a Galton Board