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I am not sure the question makes sense… how exactly are we defining “free will”? It’s just our neural network, with its biases, neural weights, synapses, inhibitory and excitatory neurotransmitters etc – all these things work up to give our behavior. And all these things are physical things, obeying the laws of physics. So I think the onus is on the people that say we have the “libertarian” kind of free will to show what the mechanism through which that could arise is, not the other way around. And I’m not sure how you’d devise an experiment for that – it happens in consciousness, in a subjective world, in an abstract realm – you have to show that that abstract realm has causal power on the physical world without an underlying physical, neural correlate. Pretty hard to do, if not impossible.
I think the question of free will looks good but it’s not – you wouldn’t be you if you wouldn’t take the decisions that you will take or you did take, you’d be someone else. Neither determinism nor probabilism is compatible with true, libertarian free will. The only way to have true free will would be if the “software”, abstract realm of thoughts, feelings, emotions etc would have causative powers on the physical world through some undiscovered mechanism. Otherwise, it’s just an illusion. There’s also the compatibilist view in which the computational irreducibility of the universe kind of creates the impression of free will and the only way to find out what will happen is to run the universe computationally – no Laplace’s demon is possible that gets and input and produces an output in a computationally reducible way.
Fraser said it pretty well. Other than what he said, I don’t know what you could do, the immune system is a really complex (and fascinating) system and it is definitely the key for the cure for cancer, since it’s distributed in the entire body and could in principle kill every cancerous cell if trained correctly.
I would say “yes”, although I think using voice in my head. Some people use images to think, for example they count not with voice but imagining slides with numbers in their head, visually. This makes a big difference depending on what you’re trying to solve – it’s much easier to do math if you can represent the symbols visually in your head than just saying “two plus two equals four” as spoken words in your head. Few people understand this and think that you’re a moron simply because you have a different representation in your head and you appear “slow” in math precisely because of that representation.
It would be a little weird, because SUSY helps with a bunch of stuff. The mystery of why the dark energy has its current value would deepen, for example, because one possible explanation is that we have a SUSY and because of it the value of the cosmological constant is so close to zero (because the contributions of all the fields, including the supersymmetric ones, almost cancels perfectly). The forces of nature wouldn’t add up to a single, unified force at the Planck energy, either. SUSY simply makes a lot of sense.