Exactly. No need to propose a "supernatural" origin for the 2 choices, if that was ever needed. They occur as physical processes within the brain. This lays the foundation for the possibility for free will, since free will requires the existence of choices.
No... it does not... I can freely will anything I want... whether I get to freely actually do it or get it or even to choose it... has no effect on the fact that I freely willed.
Wishful thinking to soar like an eagle is as much free will as choosing to eat an apple or an apple pie.
The fact that I do not choose to eat the apple pie because my sugar meter was beeping is as much of a restraint on my free will as not having feathers.
So then the two choices are evaluated by the "decision engine" within the brain. Standing at the end of time, we would be able to look back and see the physical processes within the brain working to evaluate those two choices, coming to a conclusion.
Why this need to stand at the end of time (whatever that is).... can't one evaluate the decision 1 minute after it was done???
And... as you said... the choice was the result of the one's
BRAIN... which is as unfreely unwilled as not having feathers or a bad pancreas.
Is there a need for a "supernatural" component there in the decision engine? No, it's superfluous. The playing out of physical processes within the brain is enough.
There is no such thing as "supernatural"... and everything is "playing out physical processes"... whether in the brain or out of the brain... and just
like the balls in the video pointed out several times already... just like those balls which had a "choice" to go left or right at every juncture... so do the brain synapses... and if the balls or the device can't be said to have had free will... so neither does the brain.
Is this an "illusion of free will"? No. We can see the physical processes involved in creating the choices and we can see the decision to choose one of them occurring. The fact that this is deterministic, that physical processes are involved all down the chain, is completely irrelevant. Two choices, one decision. That's free will.
I think the whole problem is that you are not actually clear on what "free will" is ... your above definition is utterly wrong.
A volcano has two choices... to erupt or not ... an atom of
14C has two choices... to fissure or not.... an electron in a lightning strike had many choices... a Brownian motion particle had many choices.... a part of the Sun has a choice to flare or not.... a tree has a choice to spread roots or not..... etc. etc. etc.
If you think all those natural physical processes don't entail free will... why on earth or the end of time would you conclude that the equally natural physical processes of the brain are not the same????