Free will is typically defined to mean you[n+1] != classical_function(you[n]), at least sometimes or with some probability. That does not necessarily imply anything supernatural, though if the supernatural (or any kind of dualism) exists that would explain it. It could also arise due to quantum noise or any other process that violates classical determinism.

There are those who define free will a bit differently though. It's not a precise term. Another definition is that you[n+1] cannot be computed from any function other than you or something isomorphic with you -- in other words you are not coarse-grainable or predictable using any subset of your state. Someone would have to literally make a copy of you to predict your behavior, possibly down to the atomic or quantum level.

I've heard functions/processes with this property called computationally irreducible:

https://en.wikipedia.org/wiki/Computational_irreducibility

Basically the computational irreducibility definition of free will just means nothing outside of you can predict what you're going to do unless it has an exact copy of you or something functionally equivalent (uploaded mind, etc.).

Another variation on the same idea is the "arrow of time" view put forward by Ilya Prigogine:

http://www.amazon.com/The-End-Certainty-Ilya-Prigogine/dp/06...

This is IMHO very close to if not identical to Wolfram's computational irreducibility, but framed a bit differently.

Obviously humans are somewhat predictable, but somewhat predictable doesn't imply deterministic. My personal opinion is that the second theory (irreducibility/arrow of time) is almost certainly true, and the first is also probably true. So we are probably both irreducible and indeterminate. I'd say the same is likely true of any living thing and possibly other complex natural processes.

My opinion is that we are predictable and deterministic, but we choose to cling to the idea of us being more than that because we can't deal with the other option. The other option is quite simple, from what I see: we'll never manage to completely read, simulate and predict a complex system like our body, so in reality nobody will be able to predict what we'll do - and for me that's enough to feel comfortable. From what I see free will is defined by others as some kind of magic process through which our decisions are based on some random factor which is unpredictable. I'd say the randomness doesn't need to exist as long as the unpredictability holds.

If we cannot really choose, we are not really responsible of anything we do. Are you comfortable with that?

This appears to be an appeal to consequences.

That aside, however, I would say that this depends on what you mean by "responsible".

> My understand of the usual common-sense interpretation is roughly "The actions that I take are supernatural, and are not a consequence of physical laws", which seems quite absurd to me, and I'd expect that to have very little support in the physics community.

I can't speak for the physics community, but most philosophers are ok with a purely physical being having free will.

http://plato.stanford.edu/entries/compatibilism/

http://www.math.leidenuniv.nl/~gill/causality.pdf :

> Finally we need to assume that we have complete freedom to choose which of several measurements to perform - this is the third principle, also called the no-conspiracy principle.

https://en.wikipedia.org/wiki/Bell's_theorem#Overview :

> Freedom refers to the physical possibility to determine settings on measurement devices independently of the internal state of the physical system being measured.

Thanks; that clears it up.