Yes, the Pythagoreans might have been on to something, though I think they went a little overboard. They were horrified by the notion of irrational numbers, for instance, that is, quantities that can't be expressed as a ratio of two integers, and tried to keep their existence a secret. No less an intellect than Albert Einstein once wrote, "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." A very Pythagorean sentiment.
I'm inclined to think that science is not where we're going to find an answer to s_lone's question about the reality (or otherwise) of free will, it doesn't appear to be amenable to science's methods. Frankly I doubt we can come up with a precise enough definition of free will to make empirical tests of it possible. It's simple enough to describe it as the ability to make an uncoerced choice between two or more options, but presumably some process happened that led to the choice, it wasn't just quantum randomness. I can see how a discussion along those lines would rapidly lead to an infinite regress of possible causes and effects that ends up with determinism somewhere and the conclusion that there cannot be free will.
While I was pondering the difference between things that are knowable in principle and knowable in practice after my previous post, I got to thinking about chess games and computability. Chess is a finite game, which means in principle it is entirely calculable. It's possible to make a list of all possible chess games and at any point in a game look up the best move to make, with no thought or knowledge of the game at all. How many possible chess games are there? I made some simplifying assumptions and did a little arithmetic. Suppose an average chess game lasts about 50 moves and at any point in a game there are about 20 possible moves for each player. If we set a computer to calculate all possible move sequences after one player's opening move, it would have to go through about 20^50 of them to decide how best to respond. The universe is about 13.7 billion years old, about 4.3x 10^17 seconds. Simple division tells us that computer would have had to consider around 2.3x10^47 board configurations per second to be ready to respond now to an opening move made when the universe was born. Since there are 20 possible opening moves, the number of possible chess games is 20 times more than that, about 4.6x10^48. Clearly, while such calculations may indeed be possible in principle (assume a quantum computer the size of the universe... ) they are way beyond being feasible and there's no prospect that they ever will be feasible.
A distinction between something that's knowable in principle and knowable in practice seems a little lame in the context of numbers like that. Maybe the indeterminacy we seem close to agreeing lies at the heart of free will is really just a reflection of the staggeringly, incalculably huge number of possible events there are.