h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

The mathematical equation you speak of at the end of your essay has been misunderstood. Don't think of it as a mathematical equation, but as a computer simulation that knows the position and the speed of every smallest atom in the universe. This simulation would be able to work out how, for example, a sandstorm would proceed, grain by grain. Your thoughts, as electrical signals and chemical reactions, could be predicted before they happened. With information about the external world, this simulation could predict how you are going to react to the stimulus around you.
The theory rests on nothing being random. If there are no effects for which there is no cause, then everything follows the causal chain. The simulation could predict exactly how the world would be one second later, but because there are no random elements which add inaccuracy, it could go on to predict the next second, and the next, and so on, until it can plot out the entire future of your life.

Free will therefore wouldn't exist - if the computer knows what you're going to think, and what decision you're going to come to, then no random, external, unpredictable element will make you choose any different. If you re-wound time to the decision point over and over, you're always going to choose one way.

This computer cannot theoretically exist, mind, but just because nothing is there to -know- what will happen in the future, doesn't mean we can change what will happen in the future.

Exactly. What you point out is what most people opossing Determinism misunderstand.
They tend to limit the extent of the so-called equation.
Also, the Chaos and Free Will Theories explained that way are quite flawed: They dont represent an undetermined future, they merely mix up the concept of unpredictability with lack of knowledge.
It is hardly the same to say that you dont know what is going to happen, than to imply that the outcome of something is unpredictable.
The Cause-Effect thery implies that for every cause there is an effect that will be the same, always, if the conditions are the same.
In this situation, the fact that the equation cant be solved (because of the infinite amount of factors to be taken in consideration) doesnt mean that the answer doesnt exist: it does, even if it is virtually unobteinable.

The Chaos theory is an usefull tool, mind you. Some systems must be examined in a light that equals those answers that cant be obtained with a random outcome.