I've not yet watch the Horizon programme (probably this evening), but in the meantime I'll contribute a slightly amended copy of one of my posts in an earlier thread. I broadly agree with what the others have said so far:
Free will must be an illusion, unless you want to invent some completely unsuspected property of carbon.
The brain is a collection of carbon and other atoms held together in some chemical relationship, which are in turn asserablages of the fundamental building blocks of matter, all obeying the basic laws of the Universe. Or, to put it another way, a kilo or so of mushy porridge. To ascribe free will to that, you must allow it the ability to alter the behaviour of fundamental particles using some as-yet-undreamt-of physical process. In the free will scenario, this is the 'mind'; an effect of the workings of the brain which is divorced from the matter of which it's made.
In order to exist, that 'mind' must have a source of energy. But where from? It can't be from the brain, or any other known physical matter, because that would destroy its independence. And yet in order to implement its decisions, it must be able to influence the behaviour of matter in some way which does not involve physical interaction.
Suppose my arm is resting on my desk. Left to itself, it would stay there until something external happened to it. So if I now decide to lift it up, I must instruct the fundamental particles in its atoms to alter their behaviour. I do this in my brain by altering the behaviour of the components of certain neurons. But how could a non-physical 'mind' do that? It would need the ability to control matter directly, and there is simply no known mechanism in the Universe by which it could.
Okay, the pro-free-will advocates might respond: then we'll have to postulate an unknown mechanism. But that's silly: why not simply go the obvious route and assume that all the mind is is the focus of the brain's activity, analogous to the instruction mill in a CPU. That makes everything simpler and easier to understand. It does of course have the implication that not only does free will not exist, but that the Universe is totally deterministic from the moment of the Big Bang (subject to the vagaries of quantum uncertainty). But that's not a big deal: as far as we know, the DNA brain is the only object in the Universe which might, under the concept of free will, counter that determinism. In other worRAB, why should the brain be unique in the Universe, and how could it be?
And that opens up another train of thought: how far 'down' the evolutionary ladder do the advocates of free will believe it extenRAB? Do chimps have it? Dogs? BirRAB? Reptiles? Fish? Insects?
Not to mention ET?