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Biology 202
2003 First Web Paper
On Serendip

From Entropy to Avalanching Sand Piles: Important implications for thinking about 'normal' human behavior

Geoff Pollitt

The year is 1967 and Theodore Bundy, an average American college student has fallen in love with Stephanie, a dark haired co-ed of the same state university. He convinces her to go on a few dates, but she quickly loses interest, later citing his lack of ambition. The rejection on his heels, Bundy shifts gears and spends the next six years of his life transforming himself into the law student of her dreams. When they meet again Bundy holds the upper hand and Stephanie falls in love. A short time after the small wedding ceremony Bundy abandons Stephanie during a ski vacation and she never hears from him again.(2)

In the context of this short historical blip from the life of America's most "normal" serial killer the ensuing killing and mutilation spree may be explained in any number of ways. Biologically we could look for an imbalance in neurotransmitter firing or an oversized development in the frontal lobe of his brain. Sociologically we could point to society's need to produce deviants in order to see itself more clearly. A psychoanalyst might notice that Stephanie and most of his victims bore a strange resemblance to Bundy's mother, of whose identity he was deceived until late in adolescence.

Each of these explanations provides its own compelling paradigm for looking at 'abnormal' behavior, then leaves great gaps in the understanding of our own 'normally' irregular behavior. We will forever be attracted to deviance models as a way of examining that which we are not, but 'normal' human behavior is also sporadic. More vigorous models are needed to take in the inconsistency, pick out the places where patterns begin to emerge, and go there to seek a more profound summary of observations.

With the help of these models we will find a place among us for naturally occurring Ted Bundy's, but more importantly is the perspective we gain in looking towards our own variable behavior against the backdrop of millions of years of evolution. At the end we will have few definitive answers, but many notable implications for the way that we perceive our world on many different levels.

For a jumping off point we start with the smallest example of randomness found in nature: the atom. The Second Law of Thermodynamics describes a system beginning with a large but already dissipated amount of energy coming from the breakdown of chemicals in the sun and ending when that energy disperses at the level of each tiny atom whose 'random' movement is propelled by that energy.(10)

The study of Entropy is the study of the amounts of this energy being dispersed in a given process at a certain temperature. Although this is a founding law of nature, life does not rise from nature through entropy but through the blocking of entropy. While each particle carrying a potential amount of energy will unload that energy and spread it to as many other less energetic particles as possible, systems work to use the energy by creating boundaries and walls, both physical and chemical. (10)

The human body presents us with a tangible example of this process in action. Still thinking about tiny particles dispersing their energy to other tiny particles, entropy can be observed in just about every human biological process as there is always energy flowing in or out of the body. The human body therefore exists as an open system in a state that is far-from-equilibrium. This state is marked by the disorderly movement of energy always leaving the system and the constant need for replenishment through the metabolism of food and oxygen. We do contain some of the energy, storing it as proteins and carbohydrate molecules, but it is in the disorder that the true nature of the human body becomes apparent. (10)

If we were to map out human behavior the way we do the behavior of tiny particles, we would find the same trend towards randomness. Whether an individual or an atom, objects under the sun move in ways that we can not predict. The Chaos Theory (CT) centers on this principle.(9)

So named for the chaotic behavior first observed in gaseous molecules, the CT is a misnomer. The bulk of the theory deals with looking at this chaos instead of through linear equations as was previously done, through three-dimensional nonlinear maps. A nonlinear mapping is one way to describe the activity of a system whose multiple pieces interact dynamically over the course of time. Each piece moves without repeating itself, and without direct correlation to any other particular piece in the system. Using this mapping technique scientists observe beautifully ordered patterns emerging from an otherwise chaotic set of data points. These data points are simple representations of the type of structures that make up most of the world's complex systems. (9)

To better understand the idea of a dynamically acting complex system we turn to Per Bak's sand piles and their potential to self-organize, as living systems do, to a point of criticality. The sand pile begins when grains of sand are dropped continuously onto a table. The sand forms a pile within its confines and at some point the pile will crumble, or avalanche. In repeating the dropping of sand over time, it was found that the pile will always organize itself into a predictable sand pile, but the avalanches will never be predictable. In a given time period, there will be a certain number of small and large avalanches, but it is impossible to predict when they will come.(3)

Looking closer at the sand pile we see many tiny grains, each alone acting randomly according to its fall and any number of variables it experiences. Together the grains form a larger, more stable structure. At this point there are two forces acting on the pile. Entropy tells us that a structure approaching its critical point—where it has grown to maximum size and strength—is full of potential energy that will be dispersed if given the right activation boost. At the same time the pile's stability to this point is mediated by forces that will continue to hold the pile stable. Alone, a grain of sand has no say in either process, neither building a stable pile, nor causing one's collapse. These types of results are completely system dependent.

The data this model produces are consistent with that of larger sand piles, like mountains and their tendency to avalanche, as well as stock market activity and other social systems. Bak's most compelling parallel is a translation of the sand pile to a living and evolving ecosystem. In this "landscape," each species acts in relation to greater system the way a grain of sand acts in relation to its pile. The species, defined as a group of individual organisms acting at the same fitness level, is always working towards the critical state characterized by maximum fitness within the ecosystem.(6)

In the ecosystem model, the collapse of the species at its critical level is the extinction of a species or a mutation to a 'new' species. Both of these events are very regular functions of the natural evolution of the ecosystem. Again it does not make sense for a species at its critical level to mutate or become extinct, but in an ecosystem there are countless species all working at the same time for the same goal of maximizing their fitness, which produces a nonlinear network.(6)

When most of the species can stabilize at a high fitness the system will remain in a state of stasis. While any species would like to remain in stasis, there will always be a species with a lower fitness level. Being deficient the barrier set up for this species to go past its criticality will be small and it is likely to mutate or become extinct. This mutation of a seemingly unimportant species does not command much attention in itself, but if we remember the web that makes up the ecosystem we will quickly understand the significance. (6)

If our one species was directly connected to only two other species, the mutation/extinction would upset the immediate landscape of these two and their fitness—previously stable—would have to be reevaluated. Each of the two species has direct connections to two other species and it goes on through the network of both animal and plant species as well as the self-regulated temperature and chemicals making up the ecosystem. The almost immediate result (in terms relative to natural evolution) of this small change is a major shift in a landscape to which each other species' fitness is no longer applicable. (6)

The point to be taken from this model is that the resulting changes and catastrophes are a normal part of the evolution of a landscape and that these changes come from within the network and not from outside influences. The environmental pressure that "causes" the avalanche is constant. The dependent variables are the fitness of a set species and the natural forces, or barrier,* keeping it at its critical state. (6)

Making a quick jump from one complex system to another, we see that the Nervous System (NS) of an individual human being, one of the main communication networks in our bodies, is 99% internal communication and relies little on outside world input. Focusing on the NS and looking to its smallest distinguishable mechanism, we find the nerve to be a self-regulating system.(7)

Along each axon directing information from one neuron to another, there are sets of gated Potassium (K+) gated channels. Particles of K+, following entropy, move towards dispersing their energy, but they can only move as far as the axon walls that contain them. When the gates open up and let the charged K+ through, it flows out and causes a negative charge that pulls it right back in again. The system continues this way until it reaches a threshold, a critical state where the same push comes from within the axon as outside. The system, forming a potential battery, waits in stasis for an activation energy. (7)

That battery is the beginning of an extensive internal system. The end has all ten billion neurons interacting through 1,000 billion synapses. (1) This is not a linear system. It is complex and dynamic with many loops for feedback and self-regulation. With a bit of imagination we can picture a landscape which is the human body, where the resting potential of the axon is the critical state of the neuron and every thought, movement, or reaction is an avalanche.

Neurons fire in all or nothing blasts, but the different firing patterns within the networks of neurons represent climaxes of varied sizes. As with a natural landscape where the species who last evolved is most likely to arrive with low inhibitory barrier and fitness level and be the next to evolve again, full thoughts and muscle motion may very well be the result of cascading bursts of neuronal activity.

At the same time, on a scale a bit more gradual than a neuron firing, we see development in the body, both physically and "mentally," which makes sense in light of the constant extinction/mutation/evolution that goes on according to this model. The neurons do not change physically. Instead, what we see and perceive is always the result of the patterns of those neurons we have had since birth, and the constantly evolving relationships among them.

The human body is always working to maximize its individual fitness and the fitness of the landscape in the context of the larger landscape of the world. The NS is one example of this but it is not the end of the story. Valera includes also the Endocrine and Immune Systems in his model of human cognition and perception. His Santiago theory (with Maturana) states that the mind should not be thought of as an object but a process, involving all of these systems as well as the outside environment. The two scientists do not deny that a physical world exists, but they do not see a separation between us and our perception and that world. (1)

It is our ability to think abstractly that makes the separation. That ability seems to come from the cortex, a subset of our NS. If our three main systems contribute to our perception of the world, we are losing something in abstractly conceptualizing. In simpler organisms, their cognition does not allow abstract reasoning but they still perceive the world enough to get by. There have been interesting experiments with simpler organisms, cited by Paul Grobstein, talking about the increase in "reliable input/output relations in the spinal cord" when parts of the NS are removed from an animal.(11) They perceive more efficiently and so the question is then how is the rest of their perception affected?

We can observe this phenomenon in quadriplegics who have a part of their systems cut off. After observing a reflex reaction of a quadriplegic's foot, that same individual may very well claim that, "I can not move my foot". Though his or her brain functions, their perception of the world is not accurate.(7) A quadriplegic has 'consciousness,' and so observing this behavior we see that consciousness is just a small part of our potential for perceiving the world.

Ted Bundy was asked countless times in many different ways if what he did was wrong, but his answer can only possibly incriminate his consciousness. We speak to a piece of him when we ask the question, the piece that communicates with the world through language. As we have seen, even within humans there is so much more that we are able to readily perceive or articulate.

With or without the conscious opinion of Bundy, our model provides little help in theorizing about the events leading up to any kind of burst of activity or catastrophe. Each one occurs as the result of a network of activity in a landscape, multiple members working towards a state of criticality determined by their natural inclination towards entropy and the self-regulation imposed to fight those forces and utilize the energy handed down by the sun. If we maintain this perspective any conclusions we may make will be nonmaterial and irreducible.

Our models do not offer us conclusive answers. The beauty of this way of thinking is the lack of control it gives us. Nevertheless, there are serious implications for every scientific field, and the subject deserves serious thought. Being that we are all living in a landscape, my questions tend towards how this looks as a mapping of our lives in relation to each other. We like to think of ourselves as existing forever in periods of stasis. I look around and do not a see a species that has maximized its fitness. Wars and serial killers are two quick examples for why the system as we are running it, or participating in it, deserves to be looked at.

*The probability of a species mutating is p=e^(b/t) where b=barrier, t=mutation parameter. Time between mutations is large, but actual mutation is fast. The higher the b, higher fitness of animal, more stability (barrier=stability when species is at its maximum fitness). The lower the b, the easier it will be to make a change.


Non-Web References:

1) Capra, Fritjof. Web of Life. New York: Doubleday, 1996.

2) Rule, Ann. Stranger Beside Me. New York: New American Library 1996.

3) Kauffman, Stuart. At Home in the Universe. New York: Oxford University Press, 1995.

4) W. Softky, W.; Holt G. "A Physicists Introduction to Brains and Neurons". Physics of Biological Systems. New York: Springer, 1997.

5) Bak, P.; Paczuski, M. "Mass Extinctions vs. Uniformitarianism in Biological Evolution." Physics of Biological Systems. New York: Springer, 1997.

6) Flyvbjerg, H.; Bak, P.; Jensen, M.H.; Sneppen, K. "A Self-Organized Critical Model for Evolution." Modelling the Dynamics of Biological Systems. New York: Springer, 1995.

7) Class notes. Bryn Mawr College. Biology 202, Professor Grobstein.

Web References:

8)Introduction to Chaos Theory, short but easy to understand

9)Chaos Theory, very good and comprehensive

10)Second Law of Thermodynamics, for non scientists, very easy to use

11)Variability in Brain Function and Behavior, interesting article by our prof

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