By Charles Krblich at Brownstone dot org.
Growing up, I never cared for Mathematics. It was too logical, bland, boring, difficult, and when contrasted against the stories, battles, wars, glory, destruction, growth, and exploration that was History, I never gave it a fair chance. So it was one of the little ironies of life, that I came to do Mathematics for a living.
Focused study softened the difficulty, and armed with growing knowledge, bland and boring transformed to mildly charming. With new perspective, I discovered what has since become my favorite toy, a Galton Board.
The toy is a small window into our experience over the last several years in which our free and independent lives have clashed broadly against arcane, top-down rules conceived by bureaucrats.
The phrase Standard of Care had already filtered into everyday health decisions made by healthcare providers. As with any bureaucratic phrase it is itself an equivocation — the deliberate use of ambiguous language in order to mislead, deceive, or conceal the truth. The Pandemic was a view into how Standards of Care are often decided simply by the opinion of unelected, unaccountable, and lifelong federal bureaucrats.
My favorite toy, on the other hand, takes an opposite approach, and yet it reveals a hidden fact about life. In plain view, but unseen by all those around us: chaos produces spontaneous order.
The creator of my toy, Sir Francis Galton, has a mixed and fascinating history. He was the originator of eugenics, popularized the phrase "nature versus nurture," developed the first weather map, introduced the use of questionnaires and surveys for collecting data on human communities, and he also developed the statistical concept of correlation. Most importantly, he developed my favorite toy.
Galton's Board is just a simple vertical board with interleaved rows of pegs. At the top is a small container storing a mass of small, spherical beads, and at the bottom are bins to collect the beads after they fall through the pegs. That doesn't sound too fancy, and it is not.
The magic happens when the beads are released from their container at the top of the board. Gravity is applied to the Potential Energy of the beads in the container. The energy becomes Kinetic. In fact, for a few moments, there is mass pandemonium. The beads are falling everywhere. The pegs they hit violently redirect their motion into other beads, other pegs, and finally into the bin where the bead finds its final resting place.
The result of the violent and random clashing of the beads is always — always — the same thing: A Normal Distribution.
I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the Law of Frequency of Error. The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand and marshalled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.
—Francis Galton, Natural Inheritance, 1889
The naive among us may attribute it to being simply a nifty, mathematical trick, but the evidence is all around us in our everyday lives.
I remember one time I was on vacation with my wife in Key West, FL. They have a fairly ugly landmark that is colorful and marks the Southernmost Point in the United States. We were walking down the road and were surprised to find a line. Neatly queued up along a sidewalk, no business or event to indicate anything unusual to line up for, no authorities managing the line, nor enforcing it, yet there was the neatly ordered line: everyone, without any discussion, naturally queued up waiting their turn to take a picture at the landmark.
Maybe you'll say that ...