Recently, there has been much research into the chaotic dynamics of complex systems in many different fields.
Complexity theory provides great analytical insights into the structures of “hard” sciences such as biology and also social sciences such as economics. It can even reveal dyamic properties that will serve as predictive indicators across both of the two fields (and perhaps many others). It should be noted that “predictive” doesn’t necessarily mean a specific result will always follow, but that it becomes significantly more likely to occur.
The following article will explore a relatively simple indicator which identifies high probabilities of instability in both the human circulatory system (specifically cardiac) and financial markets. Let’s start this discussion with a short quiz. Take a look at the following four graphs of heartbeats per minute over a 30-minute interval, and see if you can guess which one(s) belongs to a healthy patient and which one belongs to a patient facing sudden cardiac death:
Many people would presume the first graph belonged to a patient with severe heart problems, but they would be incorrect. In fact, the first one is that of a healthy person at sea level, the second of a healthy person at high altitude, the third of a person with obstructive sleep apnia and the fourth of a person with ventricular fibrillation. 
The key observation here is that the variability of time intervals between heartbeats decreases as the subject’s cardiac and respiratory functions become more unstable. Variability is not the same as randomness, however, and is actually the product of an underlying complex mathematical structure. We can describe it as “deterministic chaos”, where the initial conditions of the sympathetic and parasympathetic nervous systems (influenced by thermo-regulation, hormones, sleep-wake cycles, meals, stress, etc.)  give rise to beat time intervals that are locally unpredictable, but exhibit a globally identifiable pattern.
It is the intricate “music” that results from a complex orchestra of underlying instruments and notes, rather than the “noise” which would result from random tones. .
The time series of a healthy human heartbeat is a fractal structure, since it is an irregular pattern with fractional dimensions that exhibits “self-similarity” at different scales of resolution. We observe fractal structures in many different natural systems, whether it be a continental coast line, branching tree, human circulatory system or even impulses generated from biological processes. The fractal structures that arise from processes of the heart dynamically interact with all other rhythms of the body and help maintain a stable lifeform.
Although these rhythms each exhibit a deterministic variability of their own, they also synchronise with each other so that different parts of the body can work together while staying within a bounded range of operation. An unhealthy human heart, on the other hand, is characterised by a collapse of inter-communication with other signals and a return to a regular, intrinsic rhythm that has lost its emergent order. .
It is important to understand that complex dynamics leading to emergent order may also endogenously lead to instability and collapse. Human beings with healthy hearts may be able to perform many activities within a given day. Perhaps some of those activities and interactions will lead to significant amounts of stress, which negatively influences the peoples’ eating and/or exercise habits.
As their circulatory system becomes less efficient, they require more energy to simply maintain the level of activity they have become accustomed to. The people turn to more food and/or other substances to acquire this energy, and eventually they are caught in a destructive cycle which undermines the heart’s stability.
Of course, this example is just one potential nonlinear path of cardiac evolution, and there are obviously many examples of people maintaining relatively healthy hearts for much of their lives. This endogenous emergence of fragility is much more frequent and evident in complex financial markets where, as Hyman Minsky would say, stability breeds instability. .
Given the above information, one may conclude that we are currently on the verge of the stock market equivalent of “sudden cardiac death”, but that’s not entirely accurate. Although the dominance of HFT in the market has helped destroy healthy variability, it is not the root cause of systemic instability. That designation is more appropriately reserved for the decades-long credit (complexity) bubble which has ensued all around the world, but especially in the United States.
The reality is that the “critical point” for U.S. financial markets was already reached in 2008, and as most Americans are aware, the markets almost died back then. Cue the federal government and federal reserve, which provided trillions in “liquidity” to artificially create the variability that had been lost. The politicians and central bankers would like to think of themselves as the defibrilator that has sparked the financial “heart” back into a healthy rhythm.
However, that analogy is simply not accurate, as evidenced by the current equity market’s painfully boring microstructure. They are more like the artificial respirator that is keeping the brain-dead markets “technically” alive. Their tireless efforts are simply masking the terminal reality that lies underneath, and now we’re all just waiting for someone or something to finally pull the plug.
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