We are challenged at all levels by complexity. In response, we do our best as scientists and engineers to model system behavior. No matter how far we are along in this process, however, we encounter events which make it clear that the model of behavior does not also model misbehavior. Misbehavior acts differently, and we don’t get to an understanding of that just by refining our existing models. Different models are needed.
 

The Flash Crash
In the world of finance, we have become collectively bedazzled by “efficient market theory,” the idea that market prices immediately reflect the best knowledge that exists about a particular investment. In an ideally functioning market, sellers and buyers are always nearly matched, and volatility is increasingly squeezed out of the system. Volatility is the best measure of attendant risk, hence a robust market is the best assurance we may have that our investment risk is bounded and finite—i.e., quantifiable and of manageable scope.

Indeed the activity of many independent small players can be statistically modeled with fair precision, and it is this realization that led to the dominance of computerized, model-based trading. The fairly predictable success of such trading strategies then led to their increasing dominance in the daily trading realm. This success has perhaps obscured the fact that all such computerized trading violates the core assumption of efficient market theory. The computer program doesn’t know anything about underlying values. It only knows about the statistics of recent trading. Hence, much trading on Wall Street has become entirely self-referential. It has become decoupled from the real world in its moment-to-moment activity.

In the old days, traders on the New York Stock Exchange floor would at times take advantage of knowing where the stop-loss orders were, allow the market price to fall to those levels to trigger those sales. This would be accomplished with a little sand-bagging. Then they would allow the market price to rise once again by removing their own selling pressure. Nowadays, we no doubt have the equivalent, namely smart computer programs trying to trigger another company’s computer programs into programmed sales. It is only too likely that the flash crash was a case like that which simply got out of hand. With computers going up against other computers, algorithm against algorithm, it may indeed have happened without human intervention at all. The significant point is that trading could momentarily become entirely decoupled from market realities—-the very opposite of the foundational assumption of efficient market theory.

There is a second problem that acts much like the first. The cost per transaction is negligible for the large traders, which means that by means of massive trading they can in ordinary times effectively “rectify noise” and make money on small price fluctuations. The strategy has been analogized to “picking up dimes in front of the steamroller.” All that trading activity is thought to be a positive for the markets because it provides liquidity. But this kind of liquidity is ephemeral. It disappears just when the market actually needs it. When the steamroller makes its appearance, one needs real investors to step up who are acting upon the underlying value of the particular investment instrument. Those who are after the dimes will just abandon the casino. As the chief of Citibank has said, as long as the music plays, you have to dance. What does not need to be said is that when the music stops, these people go home.

There is an analogy here to what goes on in seizures. Instead of the efficient market hypothesis we might install here the “efficient control theory,” in which brain networks assure the overall stability of the brain through innumerable contentions between excitatory and inhibitory activity at all levels within the cerebrum. If a part of the system goes out of control for either organic or functional reasons, it can then recruit the whole rest of the brain into the pathological activity, just as a local eddy in the markets can rapidly spread its contagion throughout the system.

The hazard is traceable to the fact that the brain must necessarily live at the edge of stability. It must be in a position to react very fast, and that represents a challenge to stability. Simply slowing down any system makes it more stable. In finance, the prominence of computerized trading has given the markets a hair-trigger response that likewise challenges stability. But here we have a choice. We can simply slow the system down, and in fact we must. The race toward faster trading is just another way of putting our whole society at risk for very limited, very private gain. The financial system has put on exhibit the very worst characteristics of capitalism: it privatizes the profits, externalizes the costs, and socializes the costs of catastrophe.
 

The Soccer Ball
The new soccer ball being used for the first time in the World Cup, the Jabulani from Adidas, has generated controversy throughout its brief life. Top players say that it reacts unpredictably in flight. The developers deny it. It could well be the case that Robert Green’s incredible miscue on Clint Dempsey’s lazy shot on goal during the US-England game was due to the weird flight characteristics of the ball.

So let us take a look at the ball. First of all, it only has eight panels, whereas the earlier version had fourteen, and the traditional soccer ball has 32. With 32 panels, none can play a controlling role. Matters are different if there are only eight. A second observation is that the surfaces are ribbed with tiny ridges, all neatly lined up in circular patterns. Each ridge may individually be negligible, but by having them all lined up in a common pattern, they can give rise to collective motion of the air across the surface of the ball, and thus redirect the flight of the ball. The flaw therefore lies in the fact that the patterns have a collective influence. The small number of larger panels then enters the equation as well, magnifying the overall effect.

We have here another case of a design leading to inadvertent collective activity that is detrimental to overall functioning. Of course the designers are not yet ready to admit their mistake. But that is only a matter of time. The players are not in doubt that there is a problem, and they are far more credible in this matter than the desk jockeys. We have the equivalent in the financial realm among the traders who raise alarms about the impact of uninhibited computerized trading.
 

Schooling Fish
Cornell University mathematics professor Stephen Strogatz presents a lecture in which the simple rules underlying the schooling of fish are demonstrated. (It is available as a TED video.) From the perspective of the individual fish, the chance of being the unlucky victim of a predator is minimized in a crowd. Also, with many eyes looking out, the early detection of the approach of a predator is aided. What looks like an advantage for the schooling fish turns out also to be an advantage for the predator. The predator is more likely to detect a school of fish at a distance than a single fish, and he is more likely to snag one fish out of a crowd of confused fish than to catch a lone individual engaging in evasive maneuvers in the open ocean. It would be energetically expensive for a tuna to be chasing down an individual sardine. On the other hand, a few tuna can whittle down a school of sardines to virtually nothing over the course of many successive passes. The strategy that is optimal for the individual is at the same time fateful for the collective.
 

Lessons for Understanding the Brain
Strangely, the brain finds itself in a bind similar to that of the schooling fish. The brain organizes regulatory function through neuronal collectives. When for one reason or another the regulation of these collectives goes out of control, the results for brain function can be perilous, with seizures only the most obvious example. The action of a lonely neuron in the brain is enhanced by means of coordinated activity—the neuronal synchrony that is everywhere apparent in the brain. At the same time, however, the threat of a runaway condition is ever-present, to the detriment of the integrity of brain function. It will be recognized in time that this kind of misbehavior of neuronal assemblies lies at the heart of mental disorders.

Now when we model the behavior of financial markets or of the brain, the best we can do is describe the system when it is well-behaved. The assumption is that the system is under the influence of many little interactions which collectively keep it on track. The individual behavior is not predictable, but the net outcome will be reasonably bounded. Once such a model is in place, we tend to use it and come to rely upon it, because indeed most viable systems do spend most of their time being well-behaved. Success over time submerges the realization that our models do not cover all of the territory.

If the assumed random behavior ever becomes coordinated, and if that coordinated activity is then positively reinforced, the system goes off into an excursion into anything ranging from mild functional disturbance to complete disruption. In the case of the financial system, the shenanigans in the Wall Street casino took us to the edge of complete collapse. In the case of the brain, we see the whole spectrum from mild functional disturbances all the way out to seizures, catatonia, narcolepsy, and coma.

In the financial markets, the assumption of independent action by many traders is not a bad starting point. In this case, the transition to collective modes of action is analogous to a phase transition between one state of the system and another very different state. The description of behavior in one domain cannot be extrapolated to the other. And yet that is what we are inclined to do because we don’t have a better point of reference. As it happens, we describe normal behavior with what is called the “normal curve,” the Gaussian, and we would like to describe deviant behavior in terms of slight deviations from the Gaussian. In fact, however, the Gaussian model becomes completely inoperative because the assumptions underlying it are no longer met.

In the case of the human brain, the assumption of independent action is not as good because we are dealing with collective activity across the board. In this case even slight deviations from the appropriate collective behavior can lead to functional deficits. So when it comes to the human brain we see the full continuum from slight to gross dysfunction, all traceable to essentially the same mechanism. In the financial markets, by contrast, we see a more obvious demarcation between routine market behavior and incipient catastrophe. There is less middle ground.

In both domains, we have the actual practitioners—the traders in the pit in one case and the clinicians in the other—saying that the model-builders are not accounting for real world experience. In the financial case, the failures are rare but catastrophic. In the case of the modeling of brain functioning, the failure to describe brain-based dysfunctions is more the expectation than the exception. The model that presumes to describe function does not describe dysfunction. In the case of the soccer ball development, the whole issue of potential induction of collective activity was apparently neglected all the way through.

In our increasingly technological world, considerable advantages accrue to the person who comes equipped with models and equations, even if these have crucial shortcomings. One might have thought that the financial catastrophe that we barely avoided would have discredited the quantifiers (the “quants”) that brought the system to its knees. Alas, that did not happen. They are still the only game in town, and they remain completely unchastened by the experience. The traders in the pits raise their objections in futility. Meanwhile, the record is quite clear, according to the Economist Magazine. Academics have demonstrated no ability whatsoever to predict currency markets with their models. Traders in the pit outperform them nearly every time. “The Black Swan,” by Nassim Taleb, tells the story. Taleb gained his essential insights as a currency trader.

In matters of the brain, we have neurofeedback practitioners calling the brain modelers into question. The models just don’t represent what is actually relevant in brain function, which is the dynamics. And the Gaussian description is plainly inadequate to describe the distinctly non-Gaussian behavior of brain-based dysfunctions of all kinds. Just as the flash crash lay totally outside of the models, so does nearly everything that can go wrong in the brain. But the objections of the practitioners in neurofeedback are of no greater avail than that of the traders in the pits. Models carry the day even if they don’t work reliably.

We should recognize that existing models will always fail us in the crunch because they lack the complexity of the systems they are purporting to describe.

Siegfried Othmer, PhD
drothmer.com

This entry was posted on Thursday, June 17th, 2010 at 9:20 pm and is filed under Neurofeedback. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.