ould be important to shape the final outcome.
Finally, the outcome itself must serve a purpose on its own. For a chair, it might be something to sit on, for a statue it might be something to be marveled at.
However, Aristotle also admits that luck and chance can play an important role that do not fit the causal framework in its own right. Some things do happen by chance or luck. Chance is a rare event, it is a random event and it is typically brought out by some purposeful action or by nature.
We had briefly discussed the Laplace demon and he summarized this wonderfully: “We ought then to consider the resent state of the universe as the effect of its previous state and as the cause of that which is to follow. An intelligence that, at a given instant, could comprehend all the forces by which nature is animated and the respective situation of the beings that make it up if moreover it were vast enough to submit these data to analysis, would encompass in the same formula the movements of the greatest bodies of the universe and those of the lightest atoms. For such an intelligence nothing would be uncertain, and the future, like the past, would be open to its eyes.” He thus admits to the fact that we lack the vast intelligence and we are forced to use probabilities in order to get a sense of understanding of dynamical systems.
It was Maxwell in his pivotal book “Matter and Motion” published in 1876 lay the groundwork of chaos theory.
“There is a maxim which is often quoted, that “the same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more than once, so that the causes and effects cannot be the same in all respects. There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts “That like causes produce like effects.” This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied: but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the points cause a railway train to run into another instead of keeping its proper course.” What is interesting however in the above quote is that Maxwell seems to go with the notion that in a great many cases there is no sensitivity to initial conditions.
In the 1890’s Henri Poincare was the first exponent of chaos theory. He says “it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.” This was a far cry from the Newtonian world which sought order on how the solar system worked. Newton’s model was posted on the basis of the interaction between just two bodies. What would then happen if three bodies or N bodies were introduced into the model. This led to the rise of the Three Body Problem which led to Poincare embracing the notion that this problem could not be solved and can be tackled by approximate numerical techniques. Solving this resulted in solutions that were so tangled that is was difficult to not only draw them, it was near impossible to derive equations to fit the results. In addition, Poincare also discovered that if the three bodies started from slightly different initial positions, the orbits would trace out different paths. This led to Poincare forever being designated as the Father of Chaos Theory since he laid the groundwork on the most important element in chaos theory which is the sensitivity to initial dependence.
In the early 1960’s, the first true experimenter in chaos was a meteorologist named Edward Lorenz. He was working on a problem in weather prediction and he set up a system with twelve equations to model the weather. He set the initial conditions and the computer was left to predict wha