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Newton, Determinism, and Complexity

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"For whoever knows the ways of Nature will more easily notice her deviations; and, on the other hand, whoever knows her deviations will more accurately describe her ways"
- Francis Bacon

"The investor's worst enemy is likely to be himself."
- Benjamin Graham

There is little in the way of clear consensus about how to define complex systems. But broadly speaking, the study of complexity is the study of many actors (or agents) and their interactions. These actors can be at all degrees of scale: atoms, bacteria, plants, bees, ants, birds, fish, people, organizations, galaxies. And the resulting interactions among these actors (or agents) have a common set of characteristics or properties; these characteristics allow us to generalize about the forces at work between and among these agents. The study then of the entire system of individual agent-based interaction and the resulting global behavior patterns that develop, is deemed complexity theory.

For readers who would prefer a more precise definition, we think Camazine et al. provide as complete an overview as we have come across:

"Self organization is a property of certain dynamical mechanisms whereby structures, patterns, and decisions appear at the global level of a system based on the interactions among its lower level components. The rules specifying interactions among the system's constituent units are executed on the basis of purely local information, without reference to the global pattern. The overall pattern then is an emergent property of the system rather than a property imposed on the system by an external ordering influence."

We have found that in our conversations with colleagues that examples are the best way to relay what a complex system is. As noted above, examples of complex systems include things like ant colonies, bee hives, schools of fish, flocks of birds, etc. At this point you might be asking yourself what an ant colony has to do with the stock market. To this you might be interested to know that the biologist Charles Darwin credited the economists Adam Smith and Thomas Malthus as the inspirations for his development of the theory of natural selection. So the connection between biological systems and economics goes back centuries. At their heart, these two disciplines - biology and economics - do share some very striking commonalities. It is important for readers to understand how complexity theory itself got started and where this emerging discipline stands in relation to other notable achievements in science: from the development of Newton's Laws of motion centuries ago to the development of chaos theory in the 1960s.

Understood as simply a way to describe interesting things like ant colonies and asset markets, complexity would be an interesting thing to know. But the true power of this argument - that the science of complexity may be at the heart of understanding all natural, non-linear systems - lies in understanding that scientists have been grappling with this question for centuries. And more importantly, the recent acceptance of complexity in natural systems is in fact a giant evolutionary step forward in science itself.

Ancient Greek philosophers struggled to understand if the universe was deterministic or random. That is, they wanted to know if the world around them was defined by a set of immutable laws of nature or a world defined by complete randomness. In their day neither the deterministic nor the random model provided a satisfactory answer, and ever since, scientists and philosophers alike have struggled with this question. Socrates, Epicurus, Kant, Heidegger, and Einstein: all struggled with and wrote about the dichotomy between a macroscopic world where planets, events, and humans were all ordered by deterministic physical laws and a microscopic world where randomness and chaos prevailed. This mystery has consumed scientists for centuries.

By and large however, most scientists had come to accept a deterministic world view, where a set law of nature prevailed. There are a large and diverse set of reasons for this: religious, social, economic, and scientific. This paper is not the proper venue for detailing why the deterministic view has remained dominant, but there was a key discovery that cemented this deterministic world view in scientific communities and academic disciplines of the day. That key discovery? Newton's three laws of motion. Newton's laws, expressible in only a few short sentences, could accurately predict the motion of a remarkably wide variety of systems with unheard of accuracy.

Once understood and applied to the environment, Newton's laws tipped the scales decidedly toward the deterministic view of the world. Indeed, Newton's laws are to this day widely believed to be one of the single most important advances in the history of man. Such laws, for the first time in human history, allowed humans to control large parts of nature, to understand and predict ocean tides and planet movements, to build structures, and to create tools that provided a human mastery over the environment undreamed of for centuries. According to the deterministic view of science, backed up by Newton's laws, the world unfolds in time like a perfect machine without deviation from the predetermined laws of cause and effect. This idea, and the obvious benefits that accrued to civilization from the application of and extension of Newton's laws, would make a deterministic view of the world, as opposed to a chaotic, random view, the norm for the next several hundred years.

But what, precisely, is a 'deterministic' view of the world? And how does this compare to its opposite, a world of apparent randomness and chaos? At its most basic, these two competing views of natural systems can be summed up by a few examples that readers will be familiar with. Deterministic systems are ones that act according to Newton's laws and the resulting theories based upon them (like quantum mechanics). A pendulum swinging back and forth, a bullet shot from a gun, the planets orbiting the sun, the tide moving in and out on a beach; each are deterministic physical systems. The motion of each of these can be easily and relatively precisely modeled with Newton's laws. Given an initial set of conditions (position, speed, direction of motion and any forces acting on the object) one can predict precisely where and when that feather will land, how that pendulum will oscillate, or the periodicity of a planet around the sun. Thus, Newton's laws, in applying to all objects everywhere and at all times, served to reinforce the idea that the world was governed by a set of immutable natural laws whose continued application and refinement would allow man to have nearly limitless control over his environment.

The phraseology "at all times" used above is very important in understanding the differences between the deterministic view and the chaotic, non-linear view. In the above examples of a pendulum and a bullet, the idea of "time" has no real meaning. More precisely time is reversible in these systems. What does that mean? Time reversible processes can be reverse engineered: the same initial conditions will always produce the same precise outcome. That pendulum will always act in a given way as long as the initial conditions (position, speed, direction and forces) remain the same. Though time differences matter, time itself does not matter. Newtonian laws work backward and forward at all times.

There is much more to be said on this subject, specifically how all of this relates to asset markets. Future articles will attempt to continue this thought process more fully.
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