The butterfly effect and markets (part 1)

People often don't understand the “Butterfly Effect,” in which a microscopic change at the beginning can later lead to very unpredictable consequences. Understanding how this effect works can provide a different perspective on investing and trading, business, marketing, politics and much more.

“You cannot move one grain of sand from its place without thereby changing something in all parts of the immeasurable whole.” – Fichte, The Vocation of Man (1800).

In one of Stephen King's works, a young man named Jake discovers a portal that takes him back to 1958. After several experiments, Jake finds out that it is possible to change the course of events in history. Despite how much he remains in the past, only 2 minutes pass in the present time. He decides to live in the past before 1963 to prevent the assassination of President John F. Kennedy. Jake believes this action will greatly benefit humanity. After years of pursuing Lee Harvey Oswald, he was able to prevent Kennedy's assassination.

Upon returning to the present, Jake hopes to see a world that is better than before. Instead, the opposite happened. There are earthquakes everywhere, nothing is left of his house, a nuclear war has destroyed almost the entire world. Bewildered by what he saw, Jake returns to 1958 once again and leaves everything as it was.

We saw something similar in the cult film of the 80s “Back to the Future”. These examples from science fiction are a classic example of how everything in the world is interconnected.

The butterfly effect is when a small event can have a non-linear effect on the entire system. The concept of the effect is often thought of as the flapping of a butterfly's wing, which starts a tornado in another part of the world.

The concept of nonlinearity was introduced at the turn of the 19th and 20th centuries by the French mathematician Henri Poincaré, according to which arbitrarily small uncertainties in the initial state of a system can increase over time along a nonlinear trajectory and predicting the future becomes impossible. Nonlinearity, according to Poincaré, is a serious argument that limits the limits of predictability. He suggested that even if the laws of nature revealed all their secrets to us, we would not be able to know exactly the initial position of the Universe. In such a case, even a small insignificant or microscopic uncertainty in the initial conditions that escapes our attention will always cause a significant effect leading to a significant change in the output results that we cannot help but notice.

As UK astrophysicist John Gribbin writes in Deep Simplicity: “Some systems are very sensitive to their initial conditions. A small difference in the initial “push” you give them makes a big difference in where the systems end up. Feedback is triggered – the system itself begins to influence its own behavior and increase the discrepancy.”

Benjamin Franklin, the one whose portrait adorns the $100 bill, was not only a politician and scientist, but also an entrepreneur and journalist. He published a yearbook called “Poor Richard's Almanac” and published in it a lot of advice for every day. Many of these tips have become catchphrases.

For example, the famous phrase “time is money” comes from Franklin’s article “Advice for a Young Entrepreneur.” Benjamin Franklin is the author of a famous parable that very well describes the Butterfly Effect. You should remember her from childhood, thanks to Samuil Marshak:

“There was no nail – the horseshoe was gone,

There was no horseshoe – the horse went lame,

The horse went lame – the commander was killed,

The cavalry is defeated, the army is fleeing.

The enemy enters the city, not sparing prisoners,

Because there was no nail in the forge.”

The absence of such a small thing as a nail could cause the loss of an entire war!

Here it is appropriate to recall the words of General Stanley McChrystal, who in his book about the complex world of Team of Teams clarifies:

“In popular culture, the term “butterfly effect” is almost always misused. It has become synonymous with “leverage” – the idea that there is some small event that has a big impact on the consequences. And that, having leverage, it can be manipulated to achieve a desired goal. Here “misses the point of Lorentz, the creator of Chaos Theory. The reality is that small things in a complex system can often have no effect, or they can have a big effect, making it almost impossible to know what will happen next.”

Edward Lorenz and the discovery of the butterfly effect

It used to be that events that changed the world were things like big bombs, maniacal politicians, huge earthquakes or mass population movements, but it is now clear that this is not entirely true. According to Chaos Theory, the events that change the world are very often tiny events. A butterfly flaps its wings in the Amazon jungle and subsequently half of Europe is destroyed by a storm.” – from Good Omens by Terry Pratchett and Neil Gaiman.

The concept of the “butterfly effect” is attributed to Edward Lorenz (1917–2008). Lorenz was a meteorologist and mathematician who successfully combined the two disciplines to create Chaos Theory.

Lorenz's interest in chaos began by chance while he was working on weather prediction in the 1960s. The principle of the Lorenz model was actually very simple: based on input parameters of weather conditions, the computer model could provide a forecast for a short period of time. The data from this calculation became the basis for subsequent calculations and so on. He was interested in some feature of the solution that arose in the middle of the counting interval, and therefore he repeated the calculations from that moment. The results of the re-count would obviously coincide with the results of the initial count if the initial values ​​for the re-count were exactly equal to the previously obtained values ​​for this point in time.

Lorenz performed weather modeling on one of the first computers, which were extremely low-performance. Therefore, to save time, he ran the simulation, reducing the number of decimal places for key parameters (pressure, temperature, wind force, etc.). For example, the value 0.731127 was printed as 0.731. The difference is only 0.000127! To his surprise, the weather the machine began to predict was completely different from the weather it had previously predicted. This minor difference should have had virtually no effect. The newly calculated solution agreed well with the old one for some time. However, as the count progressed, the discrepancy increased, and the new solution resembled the old one less and less.

That is, if you take and simulate the weather with certain initial values ​​of temperature, wind speed and humidity and other parameters, and then repeat the experiment with another weather system, which, according to the initial conditions, is practically no different from the first, then the second system will behave completely differently like the first one. Over time, their behavior will differ more and more, and very soon they will be two completely different systems, not at all similar to each other. Storm with thunder and lightning instead of calm sunny weather.

He began to look for the cause of the error, even checking the vacuum tubes of the computers. But in the end I realized the reason was rounding to the third digit. From his point of view, the latest numbers could have the same effect on the final weather forecast as the flapping of a butterfly's wings in Brazil on the weather in Texas.

This went against the principles of Newtonian mechanics, which states that small disturbances at the input should lead to small changes at the output.

What Lorentz observed is now called the very essential dependence on the initial conditions that Poincaré spoke about. Small changes in the initial conditions cause large changes in the result. And even if we make wonderful mathematical models of weather behavior, even if we build supercomputers that can calculate them perfectly, and place weather stations in every square kilometer or meter of the Earth, this will still allow us to increase the accuracy of weather forecasts just a little – by a couple of days .

Simply put, Lorenz suggested that weather forecasting models are inaccurate because it is impossible to know the exact initial conditions, and a slight change in them can spoil the results. To make the concept understandable to a non-scientific audience, Lorenz began using a butterfly analogy.

A small error in the original data increases over time. The same conclusion applies to forecasts of the state of all complex systems, especially super complex ones, which include all systems with human participation. The financial market comes first. Yes, a private investor from Moscow selling several shares, theoretically, could cause a sharp drop on all exchanges in the world.

Another example is billiard balls. We hit the billiard ball with a cue, and it begins to roll across the table, bouncing off the sides. Theoretically, this is an extremely simple system, almost Newtonian. And if you know exactly the force with which the ball was hit, the mass of the ball and the angle at which this ball hits the walls, then you can easily calculate the further behavior of the ball. In theory, we can predict the behavior of the ball for a very long time if it constantly hits the sides of the table, to the point that we can accurately locate the ball, say, three hours from the starting point. But in fact, it turns out that you can reliably predict the behavior of the ball only for a few seconds. Because almost immediately the behavior of the ball begins to be affected by very small accidents – unevenness on its surface, small inclusions in the woolen covering of the table… And very soon these random little things destroy all the most accurate calculations. With each new collision, errors accumulate, and even the smallest impact quickly reaches macroscopic proportions. One of the main properties of chaos is the exponential growth of errors. This is how it turns out that even a very simple system of billiard balls on a table behaves almost unpredictably. And if the corners of the table are rounded, the system becomes chaotic after the first bounce of the ball from the board. Her condition cannot be predicted almost immediately.

Lorenz always emphasized that it was impossible to know what exactly failed the system. A butterfly is a symbolic representation of an unknown quantity.

He sought to challenge the use of predictive models that assume linear, deterministic progression and ignore the possibility of trajectory change. Even the smallest error in the initial setup renders the model useless as the inaccuracies compound over time. This happens in most systems, regardless of their simplicity or complexity.

The butterfly effect is somewhat humiliating – a model that exposes the shortcomings of other models. This shows that science is less accurate than we assume because we have no means of making accurate predictions due to the exponential growth of errors.

When computers first appeared, many people believed they would help us understand complex systems and make accurate predictions. People have been slaves to the weather for thousands of years, and now they want to take control of everything. With one innocent mistake, Lorenz shook the world of forecasting, sending ripples that spread far beyond the confines of meteorology.

Lorentz's discovery was so significant that the famous physicist Richard Feynman even called chaos theory one of the three triumphs of human thought in the 20th century – along with the theory of relativity and quantum mechanics.

Ray Bradbury and the butterfly effect

Ray Bradbury's classic science fiction story “The Sound of Thunder.” Set in 2055, it follows a man named Eckels who travels 65 million years into the past to shoot a dinosaur. Warned not to deviate from the guide's plan, Eckels (along with his guide and assistant guide) sets out to kill the Tyrannosaurus Rex, who will soon die anyway when a falling tree hits him. Eckels panics at the sight of the creature and leaves the trail, leaving his guide to kill the T. Rex. The guide becomes furious and orders Eckels to remove the bullets before the trio return to 2055. Upon arrival, they are confused and find that the world has changed. The language has been changed and there is now an evil dictator in charge. Confused, Eckels notices a crushed butterfly stuck to his shoe and realizes that by going astray, he killed the insect and changed the future. Bradbury writes:

Eckels felt himself falling into his chair. He fiddled madly with the thick slime on his boots. He picked up a clod of earth: “No, this cannot be. Not such a small thing. No!”

In the mud, sparkling green, gold and black, there was a butterfly buried, very beautiful and dead.

“Not such a small thing! Not a butterfly! – Eckels exclaimed.

It fell to the floor, an exquisite thing, a small thing that could upset the balance and knock down a line of small dominoes, then large dominoes, and then giant dominoes, throughout the years of Time. Eckels' thoughts began to spin. It couldn't change anything. Killing one butterfly is not that important!

Bradbury believed that the passage of time was fragile and could be disrupted by minor changes. The butterfly effect, chaos theory, determinism, free will, time travel have captured the imagination of many since their discovery. Films from It's a Wonderful Life to Donnie Darko and the eponymous Butterfly Effect explore the complexities of cause and effect. Once again, it is important to note that works of art tend to consider precisely that very symbolic butterfly as the cause of the effect. According to Lorenz, the point is that small details can tip the scales to a completely unpredictable result, while being almost imperceptible.

Butterfly effect in markets

The stock market is also a chaotic system. Very often, large price fluctuations are caused by tiny, completely unnoticeable factors. This makes it impossible to predict the future. The successes and failures of companies seem to be random, periods of economic growth and decline appear out of nowhere. This is the result of the exponential impact of microscopic stimuli – the economic equivalent of the butterfly effect.

We live in an interconnected, or rather hyper-connected, world. Organizations and markets behave like networks. This causes chaotic and complex rather than linear behavior.

Preparing for the future and seeing logic in the chaos of stock prices, companies themselves, and consumers is not easy. The once powerful giants (General Motors, General Electric, Nokia) are collapsing, falling behind the times. Tiny startups rise out of nowhere and take over entire sectors. Small changes in existing conditions and technologies change the way people live, just as the advent of the iPad once had an impact on the market for childcare services – the demand for nannies fell. COVID-19 has taken Zoom, FAANG companies and delivery services to the skies.

And remember the sensational story in January with the rise in the price of GameStop shares. When, in fact, one person, with the help of a social network, contributed to an upward reversal in the prices of shares of a small company, which was gradually heading towards bankruptcy. And within a few days, its capitalization grew to the level of the world's largest corporations, bringing some hedge funds to their knees. It became the wing of that same Lorenz butterfly.

By their nature, all markets are chaotic, and seemingly insignificant changes can push a business and stock up or down. Globalization and frequent shifts in consumer preferences for products and services have accelerated the creation of chaos in the market due to the influx of firms, products and business strategies. Chaos theory in markets examines the strategic and dynamic actions of competing firms, which are highly sensitive to existing market conditions, causing the butterfly effect.

The initial conditions (economic, social, cultural, political) in which a business is created significantly influence its success or failure. Lorenz discovered that the slightest change in preconditions leads to a different outcome in weather forecasts, and we can consider the same to be true for business and stock markets. The first few months and years are the critical time when failure rates are highest and the organization's core business model is formed. We can say that any of the early decisions, achievements or mistakes can become the very flap of the wing that creates a storm and a new Facebook or Tesla.

(to be continued)

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