Physics Philosophy Assignment
• 1. Does chaos theory overturn the determinism of classical physics?
I do not think chaos theory overturns the determinism of classical physics. Perhaps chaos theory forces the worldview of classical physics to be redrawn, and determinism will also have to be rearticulated, but I am afraid “overturn” is too strong a word.
What is called determinism involves, at the very least, two levels of question. One is ontological, the other operational. Determinism in classical physics first means this: the entire world is determined by strict causal relations; present events are caused by prior ones, and a determinate cause will necessarily lead to a determinate result. Therefore, if the complete state of the world at some moment is determinate, then the complete state of the world at all moments will be uniquely derived from this determinate state, and thus all of them are determinate. To put this determinism in vivid terms, we can say: if I throw a die and get a six now, then this event was already determined tens of millions of years ago.
Determinism on the ontological level does not necessarily mean certainty in the predictive, operational sense. In fact, Christian theology has long contained determinism in this sense. That is to say, everything has been arranged by God; from the very beginning of God’s creation of the world, the omniscient and omnipotent God had already determined everything. A believer in predestination and a believer in classical physics alike would say, “if I throw a die and get a six now, then this event was already determined tens of millions of years ago.”
Chaos theory itself, however, does not overturn determinism on the ontological level. The insolubility of differential equations does not mean that the world is not strictly constrained by equations, and the extreme sensitivity of predictions to initial conditions does not mean that results are not determined by initial conditions. Chaos theory also does not overturn the classical-physics picture that nature is essentially mathematical; on the contrary, fractal mathematics has expanded the range of applicability of mathematical models. In the past, scientists could only use mathematics to describe some simple things, but now even clouds, rivers, and leaves can be simulated mathematically. Although neither classical physics nor chaos theory necessarily demands a Platonic mathematical ontology, chaos theory has clearly not overturned it; perhaps it has, rather, strengthened the mathematization of nature. And if one does not accept intuitionistic mathematics, then according to the mainstream view of mathematics, the mathematical world (that is, the world of essence) is understood as entirely determinate—whether or not a solution can be constructed, the determinate solution nonetheless exists. Intuitionistic mathematics would indeed overturn this belief; however, chaos theory is another matter. Chaos theory itself does not overturn Platonism.
As for determinism in the operational sense, it refers to the idea that by using certain methods, people can predict future situations with certainty. Laplace’s demon is an extreme formulation, and only in such an extreme formulation does operational determinism appear so closely tied to ontological determinism. Chaos theory does indeed overturn the idea expressed by Laplace’s demon; that is to say: even if people possess all initial conditions and equations, we still cannot achieve absolute prediction. However, even in the determinism of classical physics, Laplace’s demon is only the most extreme formulation; no one really believes that human beings can in fact grasp completely precise initial conditions. People do indeed believe that with the help of classical physics, we can make highly accurate predictions, yet no one has ever said that real human beings (rather than God or a demon) can truly make completely deterministic predictions. The accuracy of prediction is an operational question. We may even understand the metaphor of Laplace’s demon as a negative conclusion: since we cannot grasp all the initial conditions of the entire universe, completely determinate prediction is impossible. Therefore, classical physics did not hold that people could obtain determinate predictions; at most it said: the more fully one grasps the initial conditions, the more precisely one may be able to predict. Chaos theory has not denied this; on the contrary, it has more clearly emphasized that whether the initial conditions are specified to three decimal places or six decimal places is extremely important. Of course, chaos theory does not abolish weather forecasting, and as for the practical technique of prediction through initial conditions, chaos theory would certainly not say: retaining three decimal places in prediction is more accurate than retaining six decimal places. In other words, chaos theory would also concede that the more precise the initial conditions one grasps, the more determinate the prediction one obtains; in this respect, it is no different from classical physics.
When Teacher Tian mentioned in class whether one believes in the conviction that the result of tossing a coin can be predicted, I think this conviction has nothing to do with the ontological worldview of determinism; it is only a matter of trust in people’s operational skill. Classical physics does indeed assume that if all initial conditions are known, the heads-or-tails outcome of a coin toss (or the number on a die, and so on) can be predicted with absolute precision. However, this is only a counterfactual conditional sentence. In fact, we know that it is impossible to grasp all initial conditions. Classical physics already had the theory of universal gravitation, and the condition of a single coin is related to all the celestial bodies in the universe. Classical physics has long known that grasping all initial conditions is merely a fiction. What this counterfactual conditional sentence actually means is that by grasping as many initial conditions as possible, we can anticipate the result as precisely as possible. Has chaos theory overturned this? Clearly, it has not.
We need not appeal to classical physics; we can speak of determinacy in the operational sense. For example, we may say: some veteran gamblers may have mastered certain highly skillful techniques; when they throw dice, they can make them show whatever number they wish, and the number that comes up has already been “determined” before the throw. Have chaos theory or any philosophy of science overturned the gambler’s craft? Classical physics, with respect to prediction, is nothing more than such a craft; only this craft is not merely a secret practice passed on by word of mouth and personal example, but something more regularized and universal, using machines to replace the human hand in throwing, and using precise calculation rather than delicate feel to control things. But the result is still deterministic prediction. At this level, the determinism of classical physics is similar to the techniques of a magician or the craft of a chef, and there is no question of whether it has been overturned.
June 27, 2010
Latest Comments
- Jizha
2010-06-29 22:25:09
I don’t really understand what chaos is talking about, but judging from Baidu’s explanation of chaos, it at most only shows that determinism is unworkable, or even meaningless, as long as small changes in initial conditions cause results to diverge. What I’ve never quite understood is this: according to Laplace’s conception, Laplace’s demon only needs to know the “cause” at a certain moment in order to deduce all effects, but human beings have free will, don’t they? At the next second after this moment, isn’t it possible for me to make multiple choices and interfere with the world? How should this contradiction be explained? Where have I misunderstood?
- Gu Dan
2010-06-30 03:22:27
According to Laplace’s-demon-style determinism, human beings are also composed of electrons, atoms, and so on. Free will is an illusion. For example, you think you have made an intervention, but your intervening in just this way and that way was itself already determined long ago. Of course, only Laplace’s demon or God knows everything. They are absolute spectators.
- Jizha
2010-07-03 20:54:38
Oh, so that’s how it is being considered.
- Jizha
2010-07-05 22:49:09
After reading other materials, I found that the significance of chaos theory is far more complex than what I saw on Baidu. I had understood it too simply, and one could even say incorrectly. When I have time, I should study it properly again.
- Gu Dan
2010-07-06 04:09:48
That’s right. In this assignment I said in passing that chaos theory does not overturn the deterministic picture of classical mechanics only because I did not want chaos theory to be understood in some exaggerated and one-sided way, as if it were saying that what used to be mechanical determinism is now chaos and unobservability. That is far too simple. Personally, I think the most important innovation of chaos theory lies in a new understanding of the concept of “natural law.” In the reductionist picture of classical mechanics, the laws of physics determine everything; all phenomena are ultimately determined by the rules governing collisions between atoms. But after new things like chaos theory, systems science, and nonlinear science emerged, the concept of “law” needs to be reconsidered, and the boundary and significance of “order” and “disorder” must also be redefined. “Law” may be some kind of emergent phenomenon, rather than the most basic structure of nature.
Translated from the Chinese original with AI assistance. The original text is authoritative.
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