I love the Matrix movies. I know some people feel differently; but to me, they present a panoramic view over our entire mankind. To me, they provide a deep insight in what a simulated world must look like. It combines elements of machine-like mathematical purity with the chaotic and emotional mankind; the unification of which is not unlike the deep and paradoxical notions of quantum physics.

The Matrix movies make a deep and fundamental statement about free will. Throughout history, philosophers argue whether mankind really has a free will; if we can at any moment choose between different choices (no regard taken to whether we actually use that choice or not in practice), or if the universe is completely deterministic. If mathematical rules govern the movement of celestial bodies, keep the planets orbiting in perfect trajectories – so that it is possible to determine the exact location of Jupiter 10000 years from now – are there similar rules that govern our behavior? The mere fact that we seem to make logical decisions may not mean that the decision was not already decided beforehand, without our knowledge. Spoken mathematically, if S and S’ represent two different states, is the transition t(S, S’) between those two states governed by rules to the extent that it is possible – given all relevant circumstances – to determine exactly what I will do thirty years from now?

It only gets more difficult if we take into account such statements that God may know exactly who gets saved in the end and who doesn’t. Isn’t that deterministic? Is it predetermined – and how can God cast judgement if so – or is it foreseen? If it is possible to look at a world without being bound by time, so the entire history of man is laid out in full view, do we still have a free will?

I belong to the school that says, yes, we do. And I think the advances in quantum theory and chaos theory may one day prove me right. Isaac Asimov’s books about the Foundation offers an interesting view on the topic through its “psychohistory” – that it’s possible to determine a society’s development through sufficiently well-defined principles and equations, but that it’s also impossible to predict the decisions of a single individual (I love the notion of “achaotic equations”). It corresponds nicely with the Heisenberg uncertainty principle: That it’s impossible to know both the exact position and momentum of a particle at the same time. I believe there is a similar notion (whether it can in fact be proved or not is an exercise I happily leave to the reader) with human beings: While there are a certain type of “Newtonian” laws (such as economics) that predict how our society is progressing, it is also impossible to determine exactly the future of a single individual. Once again, spoken mathematically, it is impossible to derive a future state S’ exactly from a given present state S and a transition function t because of the inherent fundamental uncertainty properties of t itself.

The Matrix movies seem to make even a further suggestion: That we human beings crave that uncertainty, that we cannot function without it. That mankind in a fully deterministic universe would not only fail to accept the given world but even reject it. Nowhere is this more interestingly explained than in the final fight scene in Matrix Revolutions between the two nearly omnipotent characters Neo and Agent Smith:

Agent Smith: Why, Mr. Anderson? Why do you do it? Why get up? Why keep fighting? Do you believe you’re fighting for something? For more that your survival? Can you tell me what it is? Do you even know? Is it freedom? Or truth? Perhaps peace? Yes? No? Could it be for love? Illusions, Mr. Anderson. Vagaries of perception. The temporary constructs of a feeble human intellect trying desperately to justify an existence that is without meaning or purpose. And all of them as artificial as the Matrix itself, although only a human mind could invent something as insipid as love. You must be able to see it, Mr. Anderson. You must know it by now. You can’t win. It’s pointless to keep fighting. Why, Mr. Anderson? Why? Why do you persist?

Neo: Because I choose to.

Even the Architect, the program that created the Matrix world itself, acknowledges: “The problem, as you so adequately put it, is choice.”

Time travel does not make things easier, as demonstrated in another movie, Twelve Monkeys, which demonstrates the Novikov self-consistency principle: Stating that “if an event exists that would give rise to a paradox, or to any ‘change’ to the past whatsoever, then the probability of that event is zero” (quote from Wikipedia).

If one were to look at the world without time, then, where every choice has “already been made” in a sense, doesn’t that make the universe deterministic? Is there still free will, if everything has already been settled and determined? Well, put mathematically, it may still turn out to be impossible to formulate a function t(S, S’) for a single individual. The fact that the two states S and S’ have already taken place, may turn out to be a mere coincidence.