Hi Cristi,
I very much enjoyed your essay, and I have a couple of questions.
The first is that you mention free will as being possibly "compatible with the determinism of the Schrödinger equation". This is an issue that I wish I had touched on more than the short paragraph it got in my essay, so I can't resist expanding a little bit here. Simply: I wonder if looking at free will in terms of determinism isn't by necessity an impasse, but if (as you seem to be leading towards as well) it would not be more fruitful to define it in terms of the specific nature of the determinism that is involved.
If we accept that individuality can be characterised by information-theoretic relations (that make it possible to establish a clear but porous boundary between an organism and its environment), then an array of measurements for different aspects of this individualised organism's relationship with its environment becomes available. This provides a framework within which to define how and to what degree an organism's behaviour is controlled by its environment. Autonomy, openness, etc. could then lead to a satisfying description of free will.
I wonder how you would see this view as relating to yours on this topic?
The other is the classic question you bring up of "What breathes fire into the equations?" I wonder -- and this is way more speculative even than the previous part -- if mathematics doesn't admit a lower level of description that is entirely processual/functional, and that the static, timeless relations we have extracted above that are not "simply" special cases that happen to lend themselves to such static-oriented analysis. Notably I have been wondering how many paradoxes vanish if mathematical statements are taken to be transformative operations in which the output cannot conflict with the input since the world has changed by that very operation (eg. the barber shaves those who did not shave themselves in the current time step -- in the next step they will have shaved themselves and therefore will not do so again, etc.). In other words, the fire has always been there, we just took it out.
Admittedly this notion is barely in its infancy and might require just a little bit more work ;-)
Thanks a lot for sharing your essay!