Part 4: Pedestrian Activity and Complex Chaos Theory

Natural Principles 2: Understanding Pedestrian Activity through Complex Chaos Theory

Newton’s third law states, “To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.” In illustration, if a pedestrian is simply standing on the street, the downwards force that the body enacts on the pavement is met with an opposing upwards force that the pavement enacts on the body. A cart vendor who is pushing his halal food cart is exerting a force on the cart, but is inversely having an equal force exerted by the cart onto him. Skimming the surface of Newton’s third law, we can extract the straight sell of applied forces and resistances, but the deeper implications derive an understanding that Newton’s laws of motion operate on the key theme of bodies interacting. This is where chaos theory comes into play.

Betsky’s quote on the ideal world encompasses a close system where architecture, order, people and nature are the only active components. However, the ideal buildings which stand, control, and is, are the dominant force which impinge upon the smaller forces of people and nature. New York City has tried to reject the chaos of nature by closing the system with borderlines of grids and sidewalks, traffic lights and roads. And yet, chaos of the streets is still produced, because of the simple fact that human agency and unpredictable human interactions are complicating factors that were not accounted for. New York City, mapped out, can be considered as an ideal system. Once translated into the every day life however, New York entails a true complex system which opens doors for the chaos theory and an absolute nature-human compatibility.

Chaos in nature can be defined by scientists as “a system behavior which is apparently random even though it is driven by deterministic rules”. Experimental work done by Ruelle and Takens (1971) and later, Swinney (1983), showed that simplicity and determinism could lead to complexity; “that a simple deterministic model, under certain conditions, was able to generate behaviors as complex as those observed in nature”. When working in a complex system of an infinite number of variables, chaotic behavior is said to be likely when the number of variables is equal to or greater than three. The simultaneous presence of counteracting forces create multiple interactions that, though possibly originating as simple relationships, can turn “into a highly complex network of which behavior is impossible to anticipate”. In other words,. increased interactions between multiple bodies can create an apparent randomness, or chaos.

One person darting across the street during a green light when cars are meant to cross and people are not can be viewed as a simple relationship. However, twenty people running across the street–some making it through, others being caught up in front of the car, or others vacillating nervously back and forth from the road to the curb–can produce a chaotic situation if simultaneous. New York City is permissibly a space where a number of variables (people) are simultaneously present and interacting within the given system of sidewalks, and thus anticipates complex relations. In a chaotic state, there is exponential instability; “a small cause can have a big effect,” otherwise known as Lorenz’s butterfly effect. A chaotic system is induced when “small variations in some of the variables might have monumental consequences, consequences which could not have been predicted beforehand.”

Such is the tale of New York pedestrian activities. Consider the following example: a group of tourists is trickling north on 34th Street towards Times Square at a slow velocity and zero acceleration, musing over the grandeur of surrounding sky scrapers. Behind them are three rushed New Yorkers, quickly approaching the group. Coming at both the group of tourists and the triple in the opposite direction are 50 other bodies, all with different velocities and heading straight south, south east, and south west. The two group come to a curb where the light for pedestrians is flashing a caution signal, warning of oncoming car traffic. At this intersection, more bodies are coming from east, north east, south east, west, northwest, and south west, and all with different velocities. If the three rushing New Yorkers travel at the same constant velocity that Newton’s first law suggests, they will run physically into the tourists and their motion will be impinged upon.

They are late, and in a sudden collective decision, they accelerate. One pedestrian sweeps to the left of the group, another through the group, and the third to the right of the group. The pedestrian who steered left collides into another pedestrian. The pedestrian who steered right accelerated enough to run successfully across the street and avoid almost being hit by a car. The pedestrian who traveled through the tourists becomes entangled in the group, and scatters several of the tourists who confusedly collide into other pedestrians.

Sound familiar?

These collisions and dynamic, nonlinear interactions are repeated throughout every day at varying degrees on the streets of New York City. Although sidewalks are meant to enclose behavior with idealized lineaments and regulating traffic lights, human agency and interactions between bodies make pedestrian traffic too complex to be contained on footpaths.

Another characteristic of chaotic systems is that of “attractors,” which create implicit order within chaos. “Apparent random behavior gets ‘attracted’ to a given space and remains within its limits,” and a new form of order is thus created out of chaos. If cars are moving in the roads, pedestrian will become attracted to the sidewalk for safety and be deterministically chaotic in that space. If a car is still far away, pedestrians become attracted to the road and chaotically, for a brief moment until the car approaches, will all pedestrians swarm the intersection to cross the street. The disorderly activities of pedestrians bumping into each other, charging into each other or pushing past slower bodies may seem simplistically random in behavior. However, pedestrians increase or decrease accelerations in response to impinging forces; they learn to predict how to cut across another’s path or to measure the time in between cars to jaywalk, or turn the body to squeeze into between two other bodies so that constant velocities will not be interrupted. To walk in the chaos of the city is to learn the new forms of order that pedestrian traffic demands.

Concluding Comments

To bisect a human into a hierarchy of two polarized parts–mind and body–is too reductionist in simplification. Such Cartesian dualism presupposes that the mind and the body can only be simplified into exclusive substances that make each incompatible, when in fact human existence and nature are far more complex than two extremes of good or bad, rational or chaotic. When man turns to a system of rationalize in city planning, the grids, regulations and delegated spaces of traffic all symbolize the claim that nature is not ordered enough for human existence. Nature is thus negated.

New York City pedestrian activity, however, is a present- day working example of the need to shift normalized thinking from simple dualisms to more complex paradigms of understanding states of individuals. To reject nature as irrational or random is to fail to understand that humans cannot be separated from the natural life. The physics executed in every day life and in the traffic of pedestrians are signs of nature working in us and among us. When man finally comes to terms with the fact that order can beget chaos as chaos can beget order then the science of sidewalks can be better understood. The science of sidewalks calls for a relinquishing of static Cartesian values and relishing of juggling modern day physics and the chaotically but systematically alternations of simple and complex dynamics.

 

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