Chaos and the Birth of Order

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 anecdote was neither chaotic nor particularly important, but nonetheless, spontaneous order occurred without an authority to guide it.

We can expand the anecdote to be only slightly larger.

The language and words you are currently reading are not curated by anyone. New words and meanings spring up all of the time. There is no committee nor central planner who invented English or any natural language. Pronunciations, grammar, and words evolve naturally over time as countless people find shared conventions to help themselves coordinate and communicate, not because the system was designed as a whole. Language is an incredibly complex system that develops spontaneously without any official authority to guide it.

Crowds of people in airports or on a sidewalk for example rarely collide. Traffic lanes often form naturally as the people adjust to each other.

The internet you are using right now was developed without a single authority and grew by incremental contributions by engineers, researchers, and users.

Artistic and literary genres grow naturally and without a central authority. When Claude Monet’s ambition led him to document the French countryside, there was no authority dictating to the founder of Impressionism that his brush strokes would be visible, and that he was to emphasize light, atmosphere, and compose casually. Rather he broke the convention and made his philosophy of expressing one’s perceptions of nature a new convention.

One of my favorite medical stories, that is relevant to the Standard of Care, is that of the Boardwalk Babies. In 1904, the New York Times reported on an unusual expo along the Atlantic City Boardwalk. For the cost of $1 ( about $40 today ), you could see the Incubator Babies. The “scientific mother” as the article describes the incubator, was a technology that the contemporary doctors often laughed at. Its effectiveness was proven only as a boardwalk freak show. By the 1940s, over 30 years later, Incubators had finally become the Standard of Care for premature babies in mainstream medicine.

Though the Incubator technology was invented by a French obstetrician, Étienne Stéphane Tarnier, the showman operating the Incubator Babies expo, Martin Arthur Couney, lacked medical credentials or licensure, yet he saved the lives of approximately 7,000 babies, all of whom received free treatment under a free care, paid admission business model for his expo.

It should be clear, that like the violent and random clashing of the beads in the Galton Board, medicine, language, art, and the things that make us Human are all chaotic processes, and they all produce a hidden order.

The problems arise when the process of truth-seeking and natural collaboration are interrupted by institutional violence. In the case of the Covid Pandemic, the shifting Standard of Care, ran a gamut beginning with lockdown, self-isolation, and ventilation, to socially outlawing Ivermectin or Hydroxychloroquine, then onto Remdesivir, monoclonal antibodies, and finally onto Paxlovid and vaccines, and then more vaccines, and finally, vaccine boosters.

Doctors who prescribed — off-label — treatment that was not the institutionally mandated Standard of Care, faced extreme pressure and many lost their medical licensure.

It’s an important point that many of the doubts cast by independent doctors regarding the institutionally mandated Standard of Care are now revealed to have been shared by the bureaucratic leaders of the CDC, NIH, and NIAID, recorded for posterity in their messages to each other. Valid concerns were expressed amongst them about myocarditis, the effectiveness of the vaccines, and even miscarriages. How many doctors had their licensure challenged for expressing these same concerns our bureaucrats acknowledged but casually dismissed?

The world we inhabit today would not allow the Boardwalk Babies.

A fun fact is that my little toy can simulate that world as well by holding it horizontally rather than vertically. This applies an unnatural, outside force to the beads and they no longer distribute themselves chaotically nor randomly. I’m not sure why, but I’ve always felt a subdued dejection when I do that. It’s as if I’m not allowing the toy nor the universe to live up to its full potential.

I’m lucky, though, I guess. I get to flip my simple, little, math toy around; watch as all the little beads collide and distribute themselves; always in the same way, but rarely along the same path. Every time I flip it and watch the chaos unfold, I’m always struck by a sense of wonder. I suppose that is what Galton called the Supreme Law of Unreason.

The wildest confusion somehow marshalled into an unsuspecting yet beautiful form of latent regularity. Regularity derived unreasonably by individuals with the freedom and liberty to act chaotically; randomly; haphazardly.

In its own little irony, every time I flip my little toy, the side of me that loved history comes alive again. Only now the beads tell a story. They fight battles and wars, find glory and destruction, and expand through exploration. Felled and laid to rest in their own dustbins of history, they end in the same normal distribution every, single, time.