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Critical States


Self-organized criticality?!? Sa-weet!


We have written in the past that certain dynamic natural systems - an ecosystem, a swarm of bees, bacterial colonies, etc. - achieve a level of complexity, a level of organization that simply cannot come from any of the particular agents of that system. No individual bird can guide the formation of a flock, no single ant can create or control the development and operation of an ant colony, no single investor (not even the Fed) can control the efficient re-allocation of hundreds of billions of dollars of assets everyday. No, these systems form a level of complexity - a swarm intelligence - despite the ignorance of the individual agents that make up that particular system.

This is what complex systems are all about: ignorance at the agent level, intelligence at the macroscopic level. Somehow, complexity theorists argue, systems consisting of many independent but interacting agents - stars, bacteria, ants, fish, investors - organize themselves into general characteristic states. They remain complex insofar as no specific spatial and temporal relationships exist; only general ones, only scale-invariant ones. Perturb the system the exact same way ten times and you will get ten independent and altogether different responses.

Knowing that such systems are indeed complex is but the first true insight to them. Better still would be to understand the manner in which the forces operating internal (among the agents themselves) and external (from the environment outside of that collection of agents) to that system interact. How do those forces respond to one another? How do they change one another? What is their general behavior?

One of the enticing parallels that such systems have is to equilibrium systems at their critical point. An example of this is water at precisely 0 degrees Celsius. It can be both a liquid and a solid at that temperature. At that precise temperature, water can, depending on the internal and external forces affecting the sample, change between a solid and a liquid instantaneously: all molecules act as "one" in this critical state. In this state, only a small change (say a small heat source on one side of the sample) can instantly propagate throughout the sample size, turning it into a liquid from a solid. And further, the heat decays only algebraically rather than geometrically.

This contrasts radically with a sample of liquid water at 25 degrees Celsius: if you were to heat it up, that heat would only affect the molecules of liquid closest to the heat source. And that energy would propagate slowly from one molecule to its nearest neighbors and from them to their nearest neighbors. And the heat effect would decay geometrically. At water's critical state of 0 degrees Celsius however, that propagation takes place instantly, affects all molecules throughout the sample, and decays algebraically. There is something special about that critical state.

The term that complexity theorists use to describe certain characteristics of complex systems is self-organized criticality. Specifically these types of natural systems show both self-organization (like flocks of birds for example) and critical states (points of bifurcation or points at which the entire system can be altered instantaneously as in the water example above). The term self-organization describes the ability for these systems to develop structures and patterns without external or internal control mechanisms or agents. For example, how do schools of fish maintain the order of their shape without one fish directing the entire group? This is the beauty of self-organization. Almost all natural systems exhibit this type of behavior: we have pointed to the phi-based patterns that abound in nature: conch shells, galaxies, quarks and neutrinos, stocks.

So what does any of this have to do with stocks? We have proposed in previous pieces that we believe that groups of investors - that stock markets - form a complex system. As such it exhibits the behavior of complex systems, specifically self-organization and criticality. The self-organization part is why phi relationships (0.618 and its derivatives) exist in charts. The critical aspect is exhibited when stocks reach what we call bifurcation points: points at which the system becomes balanced (in this case the balance is between buyers and sellers).

We have proprietary ways to analyze this 'self-organization' as well as to determine specific 'critical' levels for stocks and indices. But understanding that negotiated financial instruments exhibit self-organization and criticality is essential for first abandoning your embrace of linear, causal models and secondly finding your own unique models for predicting asset price behavior.

No positions in stocks mentioned.

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