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“As the nineteenth century advanced, it gradually dawned on theorists that energy is indestructible. The amount of energy in the universe does not change. However, it can change form, and be converted into some other kind of energy at a fixed rate of exchange.”
Jeremy Campbell, Grammatical Man, pg. 36
“For, as Lavoisier said, in nature nothing is created and nothing is lost, everything is transformed.”
Jose Saramago, Death with Interruptions, pg. 115
“The particles themselves have not been made and cannot be destroyed. The patterns of order and disorder in the world are not the product of a divine scheme. Providence is a fantasy.”
Stephen Greenblatt, The Swerve, pg. 187
“We are not stuff that abides, but patterns that perpetuate themselves. A pattern is a message.”
Maria Popova
“There are only patterns, patterns on top of patterns, patterns that affect other patterns. Patterns hidden by patterns. Patterns within patterns. If you watch closely, history does nothing but repeat itself. What we call chaos is just patterns we haven’t recognized. What we call random is just patterns we can’t decipher…”
Chuck Palahniuk, Survivor
“Now that science is looking, chaos seems to be everywhere. A rising column of cigarette smoke breaks into wild swirls. A flag snaps back and forth in the wind. A dripping faucet goes from a steady pattern to a random one. Chaos appears in the behavior of the weather, the behavior of an airplane in flight, the behavior of cars clustering on an expressway, the behavior of oil flowing in underground pipes. No matter what the medium, the behavior obeys the same newly discovered laws.”
James Gleick, Chaos:Making a New Science, pg.44
“Chaos, irregularity, unpredictability. Could it be that such things are not mere noise but have laws of their own? This is what some scientists are now learning. More than that, these scientists are showing how the strange laws of chaos lie behind many if not most of the things we consider remarkable about our world: the human heartbeat and human thoughts, clouds, storms, the structure of galaxies, the creation of a poem, the rise and fall of the gypsy moth caterpillar population, the spread of a forest fire, a winding coastline, even the origins of life itself.”
John Briggs and F. David Peat, Turbulent Mirror: An Illustrated Guide to Chaos Theory and the Science of Wholeness, Foreward
“Chaos theory says that a tiny, insignificant event or circumstance can have outsized influence in shaping the way a large, complex system evolves into the future. Many people are familiar with this so-called butterfly effect, an idea often traced to science fiction author Ray Bradbury’s 1952 story “A Sound of Thunder.” In that tale, a man who has time-traveled into the deep past to hunt a Tyrannosaurus rex inadvertently crushes a butterfly under his foot. When he returns to the present, he discovers that his seemingly trivial act altered the course of history — and not in a good way.”
Nikolai Sinitsyn and Bin Yan, The Quantum Butterfly Effect, 9/21/2020
“For want of a nail, the shoe was lost;
For want of a shoe, the horse was lost;
For want of a horse, the rider was lost;
For want of a rider, the battle was lost;
For want of a battle, the kingdom was lost.”
Benjamin Franklin, Poor Richards Almanack, 1758 (Earlier versions of this date back as far as the 13th century)
“You could not remove a single grain of sand from its place without thereby changing something throughout all parts of the immeasurable whole.”
Johann Gottlieb Fichtein, The Vocation of Man, 1800
I have to admit that I’ve always had a keen interest in how the daily ebb and flow of circumstances in people’s lives can point them in a particular direction, and, to perhaps, ultimately define them as a person. Various fluctuations occur — with some events based on specific, concrete decisions or actions taken by individuals —while others seeming to happen at random or even from out of left field. And, I’ve also wondered how opting to then proceed in one direction rather than another would significantly alter the course of one’s life. (If you’ve read my essay “The Road Taken, or Not…”, you may recall that I’ve already dealt with some aspects of this topic.)
Sometimes there are major happenings that force us to tack abruptly in a markedly different direction from where we were headed. While, on the other hand, there are most probably many minor circumstances we are unaware of that cause us to unknowingly make subtle changes to the route our lives take. Is there a pattern to all of this? Is it all just so random? Is there in fact, a pattern of some kind in the randomness?
When I first began to consider some of these questions, a number of terms popped into my head: order, disorder, matter, atoms, entropy, strange attractors, randomness, patterns, chaos theory. Yes, even the law of conservation of mass, as well as the second law of thermodynamics. Well, I’m not going to bore you with any futile attempts at some kind of high-sounding, science-based scholarship. Don’t have the credentials for that. And, I’d only come across as a pedantic know-nothing.
So, let me begin with my own simple ideas about “chaos theory”, and how it is injected into virtually every part of our daily lives: existing in natural systems like fluid flow, heartbeat irregularities, weather and climate. And, also spontaneously in systems with artificial components such as the stock market, airplane flight, computer science and road traffic. And, as cited in one of the above quotes, even an intrinsic part of such things as human thought, the structure of galaxies and the origins of life itself.
So, I definitely began thinking about some of these forces at work in the universe many, many years ago. How long ago, you ask? Well, here are a few thoughts from a journal I kept back in the day. Specifically, this is an entry from October 4, 1967:
“Life is a constant and continual process of building up and tearing down; of formation and deterioration; of construction and erosion; of order and chaos. e.g.: lawns grow high, given two weeks of indifference; paint wears off of signs and fences; men grow old and wrinkled, haircuts, shaves, baths are constantly a necessity. To just be natural, man would have to let himself go. This is nature’s way — chaotic, a seemingly disorganized assemblage of man, animal, plant and earth. But, there is order to it all. With, or without man, nature has her own order; it is just not man’s order of being measured and planned — but an order nonetheless.”
Frank Fasano, 10/4/1967
Many years earlier, Nathaniel West, in his 1933 classic, Miss Lonelyhearts, seemed to offer some similar thinking to my own:
“Man has a tropism for order. Keys in one pocket, change in another. Mandolins are tuned G, D, A, E. The physical world has a tropism for disorder, entropy. Man against Nature … the battle of the centuries. Keys yearn to mix with change. Mandolins strive to get out of tune. Every order has within it the germ of destruction. All order is doomed, yet the battle is worthwhile.”
Nathaniel West, Miss Lonelyhearts, pg. 104
So, just to confirm for you that my thoughts on matters chaotic and random were not simply a one off when I was just a young lad, I’ll share another sampling from one of the many personal journal entries I’ve kept over the years. Don’t really have a date for this one, but I’m sure it certainly goes back 20 to 30 years at least. These musings deal with my personal theory about chaos:
“Is there some order to disorder? Chaos: can it be predicted? Systems that obey precise laws can still act in random ways. The predictability of randomness? Is there harmony between order and chaos? Oh, and where does entropy fit into all of this?”
Fasano, mid-nineties?
Before continuing on with a discussion of chaos, I’d like to begin at the beginning and say a little something about atoms. Why do atoms matter? (No pun intended. Well, yes, actually, pun intended.) Lucretius, the first century B.C. Roman poet and philosopher, preferred not to use the technical term “atom”, but referred to these foundational “particles” as “first things”, “first beginnings”, “the bodies of matter”, “the seeds of things”. According to historian Stephen Greenblatt:
“Everything is formed of these seeds and, on dissolution, returns to them in the end. Immutable, indivisible, invisible, and infinite in number, they are constantly in motion, clashing with one another, coming together to form new shapes, coming apart, recombining again, enduring.”
Stephen Greenblatt, The Swerve: How the World Became Modern, pg. 185
Third century B.C. Greek philosopher Epicurus reasoned that:
“...in constant motion, atoms collide with each other… and in certain circumstances, they form larger and larger bodies. The largest observable bodies — the sun and the moon — are made of atoms, just as are human beings and waterflies and grains of sand. There are no supercategories of matter; no hierarchy of elements. Heavenly bodies are not divine beings who shape our destiny for good or ill, nor do they move through the void under the guidance of the gods: they are simply part of the natural order, enormous structures of atoms subject to the same principles of creation and destruction that govern everything that exists.”
Greenblatt, Swerve, pg. 74
So, coming together, falling apart, a consistent dynamic that characterizes all of life and living. And, as Greenblatt further stated:
“An infinite number of indestructible particles swerving into one another, hooking together, coming to life, coming apart, reproducing, dying, recreating themselves, forming an astonishing, constantly changing universe.”
Greenblatt, Swerve, pgs. 200-201
With the constant clashing and colliding of atoms, there is “dying”, and, entropy; but, there is also a recreating of life in an ever changing universe. In the following quote, the brilliant German author W.G. Sebald seems to focus only on the darkness and dissolution of life and none of the rebirth:
“Much as in this continuous process of consuming and being consumed, nothing endures, in Thomas Browne’s view. On every new thing there lies already the shadow of annihilation. For the history of every individual of every social order, indeed of the whole world, does not describe an ever-widening, more and more wonderful arc, but rather follows a course which, once the meridian is reached, leads without fail down into the dark.”
W.G. Sebald, The Rings of Saturn, pgs. 23-24
Umberto Eco wrote about the tendency of all living things to make their way toward an ending. In discussing Augustine, he writes:
“Here we should perhaps embark upon a discussion of phenomenological time (Husser) or Heidegger’s notion of time which was not far from objective time or biological time or the physical time of entropy, that time which dictates that all living things tend towards the void.”
Umberto Eco, Time
Pretty bleak stuff, right? But, facts don’t lie. It’s obviously true that as far as human life is concerned, there is a beginning and there is an end. As Eco so succinctly expressed it: “As birth begins the human clock, death ends it.” But, despite the ultimate demise of each and every one of us, the life of the universe will go on. And, as Epicurus reminds us, there is no hierarchy of elements in the universe. Humans are just another category of life composed of atoms; and, after our deaths, we will still contribute, each in our own way, to the ongoing existence of the universe. Here is one more take by Greenblatt regarding the amazing ebb and flow dynamic that is the ongoing characteristic denoting all of existence:
“And so the destructive motions cannot hold sway eternally and bury existence forever; nor again can the motions that cause life and growth preserve created things eternally. Thus in the war that has been waged from time everlasting, the contest between the elements is an equal one: now here, now there, the vital forces conquer and, in turn, are conquered; with the funeral dirge mingles the wail that babies raise when they reach the shores of light; no night has followed day, and no dawn has followed night, which has not heard mingled those woeful wails the lamentations that accompany death and the black funeral.”
Greenblatt, Swerve, pg. 186
Earlier, I promised that I wouldn’t delve very deeply, if at all, into such arcane topics as conservation of mass or the second law of thermodynamics. But, just a brief delving, if you don’t mind, into the work of an Austrian physicist by the name of Ludwig Boltzmann. He was responsible, in the late 1890s, for developing statistical mechanics and the statistical explanation of the 2nd Law. Essentially, he explained that there was a relationship between the increase in entropy and the decrease of knowledge. He felt that entropy was related to “missing information”. (Campbell, Grammatical Man, pg 44)
He also thought that:
“Another way of looking at the second law of thermodynamics is to say that the higher the entropy, the more numerous are the possible ways in which the various parts of the system may be arranged. In this approach, the connection between entropy and probability is plain to see: if there is a large number of possible ways in which the parts of a system may be arranged when the system is in a state of high entropy, then it is improbable that they will be found in any one special arrangement at a particular instant, just as it is unreasonable to expect a pack of cards, while in the process of being shuffled, to return to its original order, because that single, unique arrangement of cards is one out of such an astronomically large number of possible arrangements.
Now stay with me here. You’ve already come this far. I admit that this is the most abstruse and esoteric part of my essay, but it’s damned important, so please don’t stop reading now. Campbell continues:
A muddle is more probable than an arbitrary “order” because there are more, usually many more, ways in which a muddle is treated than there are ways in which an orderly structure is formed. The various parts of a piano can be strewn about at random in a myriad of ways, but there is only one way of putting them all together. It goes without saying that the assembled piano is more valuable and interesting than a litter of parts. This notion can also be applied to words in a language, which are not strung together randomly, but conform to certain rules of structure.”
Jeremy Campbell, Grammatical Man, pg. 44
Essentially, Boltzmann was applying the laws of mechanics and the theory of probability to the motions of atoms. Science was at a point where it was thought that man had developed such a deep understanding of the laws of nature that it had learned how to control the variant and chaotic character of events. This was the thinking at the time:
“Humankind now saw itself as an improbable collision of particles following indifferent universal laws….(and considered themselves as) possessors of knowledge about those laws. By knowing the laws, it was thought, we could learn with increasing deftness to predict and control the entropy that afflicted complicated systems. In practical terms, passive entropic chaos couldn’t be eliminated, perhaps, but it could be minimized or circumvented by an increasingly precise understanding of the universal mechanistic order underlying it.”
Briggs & Peat, Turbulent Mirror, pg 23
According to Ralph Siu, American author and scholar:
“In the Newtonian days of the eighteenth and nineteenth centuries the same set of laws applied to all kinds of systems….They were all supposed to obey the same laws which are considered rigid and unchangeable. What Boltzmann did a century ago was to show that this is not so. Even systems with the same amount of energy are not described forever by a fixed pattern.”
R.G.H. Siu, The Tao of Science, pg. 30
As time went on and new advances were made in technology, it became increasingly obvious that the laws of nature and of science did not always lend themselves to predictability. According to John Briggs and F. David Peat:
Nineteenth-century engineers building their new bridges and steamships and other technological marvels repeatedly encountered disorder in the form of abrupt changes that were quite unlike the slow growth of entropy described by Boltzmann and the science of thermodynamics. Plates buckled1 and materials fractured. These phenomena challenged the powerful mathematics that had forged the Newtonian revolution.”
Briggs & Peat, Turbulent Mirror, pg. 23
This may be the right time to bring up the subject of the so-called “butterfly effect.” It’s simplest definition is: “a sensitive dependence on initial conditions.” Edward Lorenz, a nineteenth century mathematician and meteorologist, coined the term. Initially, he used the concept for predicting weather. He made his discovery when observing various runs of his weather models. When he rounded off his initial condition data in a seemingly inconsequential manner, he found that he failed to reproduce the same results as with unrounded condition data. This showed him that a very small change in initial conditions could create a significantly different outcome. While Lorenz saw the randomness embedded in his weather model, beneath it he also saw a “fine geometrical structure, order masquerading as randomness.” (Gleick, Chaos, pg. 22) He eventually came to discover that there was “a pattern, with disturbances. An orderly disorder.” (Gleick, Chaos, pg.15).
Through the years, there have been a number of examples of the butterfly effect that have shaped our lives and the world we live in. In each case, it was a small detail that led to a dramatic turn of events. One famous example, often cited, has to do with the assassination of Archduke Franz Ferdinand, heir to the Austro-Hungarian Empire. A small group of Serbian nationalists had failed in their initial attempt to assassinate him; the bomb that they tossed bounced off of the car he was riding in with his wife Sophie as they were leaving the train station. A cohort of the bomb thrower, 19-year old anarchist Gavrilo Princip, was leaving town, thinking the mission had failed. He stopped on Franz Joseph Street for a sandwich. Unfortunately for the Archduke, his driver mistakenly made a wrong turn from their planned route which then took them down Franz Joseph Street. Princip witnessed the driver’s error, seized the unexpected opportunity and shot the Archduke and his wife at point blank range, killing both. This one step set off a chain of events that led to World War I.
Another oft-cited example of the butterfly effect was the Cuban Missile Crisis. Tensions were extremely high when JFK was trying to call Khrushchev’s bluff during the blockade of Cuba. The American president had demanded that all Russian missiles be removed from the island only 90 miles from southern Florida. American aircraft and ships began using depth charges to signal a Russian submarine to surface and identify itself. However, the sub was submerged too deep to monitor radio communications; the captain decided that the releasing of depth charges by the Americans meant that war had broken out and he was then prepared to launch a nuclear torpedo. All on board agreed with him — except for a single navy officer named Vasili Arkhipov. He exercised his veto and without total agreement, there was no launch. The result could have been a worldwide nuclear holocaust. Arkhipov has been referred to as “the man who saved the world.”
Certainly, there have been many other examples of the butterfly effect. Some historians wonder how history would have changed dramatically if Adolf Hitler had not been rejected (several times) in his attempt to attend The Academy of Fine Arts in Vienna. And, as terrible as the disaster at Chernobyl was, it could have been so much worse if three, brave plant workers had not volunteered to dive into a basement room filled with radioactive water to turn off underwater valves, preventing a second explosion. Without their heroic act, half of Europe would have been destroyed and rendered uninhabitable.
And, finally, a butterfly effect story that flutters a little bit closer to home:
You see, there was this little girl growing up in Newark, NJ in the early fifties. Unfortunately, there was a major fire in her home and the family had to move. For some reason, her mom and dad decided to buy a house in Madison, NJ — some 15 to 20 miles west of Newark. Going from the city to the suburbs.
Growing up in Madison, the little girl and her siblings attended Catholic schools. As it happened, after a time, the little girl’s parents had a major disagreement with the pastor, Father C. Suffice it to say, this caused the little girl’s parents to take all of their children out of Catholic school (four of them).
By this time, the little girl was now a high school junior. After transferring to Madison High, she began attending a driver’s ed class. There she made the acquaintance of a certain junior boy. And, as you may have guessed, they’ve been driving around together ever since. The rest, as they say, is history. That little girl was my wife Cathy, and that particular junior boy was yours truly.
Here are a few different ways to describe the “butterfly effect”:
• A tiny detail can lead to dramatic change
• There is a sensitive dependence on initial conditions
• Small things can have non-linear impacts on a complex system
I’m fairly certain that if you were to consider some of the more consequential relationships and events in your life, I think you’d be able to see how this phenomenon has affected — and perhaps substantially impacted — your life and the lives of your loved ones and close friends.
I’ll leave you with a statement from Henri Poincare, a late-nineteenth century mathematician, theoretical physicist, engineer and philosopher of science. Long before — perhaps 80 years before — Edward Lorenz coined the term “the butterfly effect,” Poincare described it perfectly. The key to all of this is that even if we think we know the exact starting point of any occurrence, the closest we are ever going to get is just an approximate knowledge of things. So, what we see as a “chance” happening is most likely an inability to identify or even to notice a small cause which can ultimately change everything:
“A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But, even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation “approximately”. If that enabled us to predict the succeeding situation with the “same approximation”, that is all we require, and we should say the phenomenon had been predicted, that it is governed by laws. But, it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.”
Jules Henri Poincare
Click below to listen to an audio recording of this essay
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1Bridge Buckling: Perhaps you’ve seen an old video of a bridge loaded with cars that suddenly launches into an uncontrollable, violent swaying. In some cases, cars and drivers were tossed unceremoniously into the water below. This phenomenon is due to “mechanical resonance” — where harmoniously excited forces contribute to chaos and multiple chaotic motions.
In August of 1831, a brigade of soldiers was marching across the Broughton Bridge in England. And, they were marching “in stride”, as soldiers do. Suddenly the bridge began breaking apart, with dozens of men thrown into the water. After this, the British Army issued new orders, requiring solders to “break stride” when crossing a large bridge.
Over the years, engineers have obviously learned a lot about dealing with such issues. Though structures such as bridges and buildings may seem to be solid and immovable, there is a natural frequency of vibration contained within them. If a force is applied to the object (in this case, soldiers marching across a bridge) and if that force is at the object’s natural frequency, there will be an amplification of the object’s vibration — causing “mechanical resonance.”
Sometimes a phenomenon known as “spontaneous order” can occur. Under the right conditions, chaos spontaneously evolves into a lockstep pattern. The London Millennium Bridge was just such an example. It opened in June, 2000. This pedestrian bridge started to sway alarmingly on opening day when groups of people began to walk over it. Essentially, the natural sway motion of people traversing the bridge caused small, sideways oscillations in the structure. This, in turn, caused people on the bridge to sway in step, increasing the amplitude of the bridge oscillations, continually reinforcing the effect.
The bridge was closed down for two years while modifications were made that mitigated the problem.
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Resonance 