Chaos and Weak Determinism

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Tom has a very interesting post on determinism as understood by St. Thomas Aquinas. The description is very similar to some aspects of chaos theory. Chaotic systems look random, but they follow a pattern called "weak determinism." The determinism is weak because while the next few steps of the pattern can more or less readily be predicted from knowing initial parameters, small variations in the initial system result in large divergences very rapidly. (The popular name for this is "the butterfly effect"--a term coined by or about the work of meteorologist Edward Lorenz.) Weak determinism is interesting because even though it is weak because predicatability is poor, the determinism includes every variation back to and including the initial stages. That is, the initial stages strongly, if unpredictably, influence the entire "chain of being." What happened in the past is present and influential at every moment. (See Mandelbrot's discussion of the price of cotton in The (Mis)Behavior of Markets.)

The net result of this is that one can start with two objects that to all appearances exist in identical circumstances, subject them to the same influences and still come up with different results because (1) there were differences that were minute, but important in the initial makeup; and (2) there were differences in the influences.

What does this analogy mean for determinism? It means that two people can start at what looks like the same point as far as human eyes can see and wind up at very different places. As Tom points out in his discussion--determinism is in part influenced by free will. That is the choices that we make influence the array of choices that are available to us at the next decision-making nexus. When we choose not to take the job in Seattle--all contingencies based on that job more or less pass away and the path is closed--we are weakly determined by that choice. We may know what lies immediately ahead. What we cannot know is that by not taking the Seattle job we missed out (10 years down the line) on a volcanic eruption that buried our house in 15 feet of ash. That path is closed.

Each choice I make via free will in closes some doors and opens others. When I choose to "sin a little bit" by investing time in pornography, I may find that I subtly alter the current of things in such a way that the door to adultery is opened (or perhaps not). The choice to sin closes some doors (doors leading toward God) and opens others (those leading away) Always keeping in mind, however that all of the doors back to God are never completely closed, there is always at least one wide open--the door of the confessional.

The analogy of weak determinism speaks seems to tread the middle road between complete determinism and complete randomness or free will. Each choice alters parameters and constrains future choices, while at the same time opening other channels. We have some things set in motion about which we can do almost nothing--biochemical factors, certain environmental conditions in youth. However, we do have a choice about how we react to these factors and how much we allow them to guide our lives. An alcoholic may or may not be able to do anything about the biological condition that predisposes him or her to alcohol addiction; however, they can do a great deal about what they choose to do as a result. Free will is not easy, but biological determinism is not the final factor and things can be done to combat predispositions.

This is one reason I'm extremely dubious about the so-called "gay gene" and its deterministic effect on behavior. You may have a predisposition, what you do not have is a requirement to act upon that predisposition--you are, in fact, free. Once again, we should keep in mind that what is freely determined is not necessarily easily undertaken. Carrying the ring to Mt. Doom was freely chosen; however, in the end, it was not easily accomplished. And unfortunately, we all have rings in our lives that need undone--we all have the same quest to undertake to rid our lives of the power of darkness. Christ's yoke is easy, His burden light--choosing to assume them is what is difficult.

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Sensitive dependance on initial conditions is the phrase I have heard used for the 'butterfly effect'. In medicine, especially genetics, we look at what we call multifactorial conditions. We are just at the very beginnings of beginning to understand how genes and environment interact even with the physical diseases. One which I know very well is type 1 diabetes (The one in which the insulin secreting cells of the pancreas are totally destroyed by what seems to be an auto-immune response) aka juvenile diabetes or insulin dependant diabetes. My family has been part of a 4 generation inheritance study on this disease. What they found in my family is that a gene somewhere on the DR locus of the HLA typing system is associated with the diabetes that my father and his only sib both suffer. My uncle developed the disease in 1941, at the age of three, after a bout with influenza. My father devloped the disease in 1963, at the age of 28, after a bout with mumps. My grandfather who also had that gene lived to be 80 something without ever developing the disease. I do not carry that gene, and nor do any of my siblings that were tested. My cousin, however, does, but she has not developed diabetes - BUT - her daughter did. (They think that a viral illness may have triggered the haywire immune response there also, but are less certain than with my parental generation). So, to get this disease, you have to both have the genetics and the environmental stimulus. There are lots of disease conditions like this - breast cancer, the many other auto-immune disorders, even possbily HIV/AIDS. I too, question the 'gay gene' hypothesis. There may be a hormonal or genetic predisposition to same sex attraction but one need not act on it or accept imperfection of this sort. According to the radical feminists biology is not destiny. According to the homosexual lobby, it is. who is right? What is truth?

Dear Alicia,

Yes, all chaotic systems show sensitive dependence on initial conditions. To give you an idea of HOW sensitive, I ran 10,000 iterations of a logistical difference equation used for estimating the population of a species under certain conditions in an ecosystem. I did this twice. The first time I chose the number 2, the second time, I ran the same thing using 1.9. . . out to thirty-two or sixty-four digits, I forget which now. The two systems tracked exactly for the first two iterations. The third iteration showed a minor deviation, by the fourth there was a significant difference and by the sixth or seventh, you would not have know that we started with numbers so close together--that's how powerfully sensitive dependence works. But if we take each iteration as a nexus or choice point and start to vary the numbers at each iteration imagine the deviation. So the system may be weakly deterministic (but none the less deterministic) but from all outside views it looks utterly random or chance. No chance to it at all--all determined, all driven by the initial point and by the choices along the way. And yet at each nexus we have the oppotunity to return to the beginning.



Dear Mr. Riddle,

Are you familiar with Stephen Wolfram's complexity work? His main works in the area can be found here. Forgive me if this is a repeat.

Cheers -




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This page contains a single entry by Steven Riddle published on January 14, 2005 9:13 AM.

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