When you have a process where the behavior is quite simple – like a planet orbiting around a star – we are smart enough to use math to figure out what will happen in the future without having to wait for the planet to move around. We can compute the outcome by plugging the right numbers into a formula. But many systems are irreducible after a number of steps – you really have to simulate each step to see what will happen.
The problem with human free will is that deterministic stuff is going on underneath, like the chemical processes in our brain, but that we don’t seem to act in a deterministic way. People used to think that deterministic processes must result in deterministic behavior, and that belief has underpinned much of the debate about free will. It’s the reason why the science fiction robots of the 1950s often speak very logically and behave very stupidly. The main scientific discovery is that it must not be like that. We can have simple deterministic underpinnings that result in very complex and seemingly random behavior.
Computational irreducibility is a key feature of life: We cannot grasp life through a formula, but must really simulate and observe it to see what happens. That’s how we as humans end up freeing ourselves from the deterministic rules. I tend to think that the concept of computational irreducibility is probably the answer to the philosophical debates of the past two thousand years about the relationship between free will and determinism. Philosophy is always at a certain distance to human behavior, so a lot of questions really get answered by science.