Dear Alexey and Lev
I read with great interest your beautiful essay. It was a real pleasure, there is a kind of luminosity that emerges from it - I think you understand what I mean.
The res cogitans of Descartes corresponds to mind but now we know that most of mind functions depend on matter - for instance, memory: a damage in the brain can cause a lost of memory. If we compare what can be achieved by Artificial Intelligence with ourselves, it seems that our sole characteristic that we cannot, by now, consider that depends on matter is consciousness. It may depend but by now, we do not know how.
In my essay, I exclude consciousness from my analysis; but I give a contribution to explain everything else, i.e., how, from the simple properties of matter, can the universe evolves as if guided by an intelligence towards a goal (a surprising contribution of my essay is to explain "intelligence" from matter properties).
Note that in the above phrase I excluded "mathematics"; because mathematics is just a tool, a language. When I was young, I was marveled with mathematics, but along my life I learned to consider it as a tool - a powerful one, essential, but a tool; like language is a tool for communication. Of course that it can be a source of the feeling of beauty - like it happens with language. And, like language, it can be it in two ways, the formal one and through the ideas it represents. Nowadays, I don't use an equation that I cannot replace by plain text (excluding the quantifying aspect). The reason is that mathematics has no goal, we cannot let be driven by it, we have to always understand the road in which we are because mathematics can follow any road. Like language.
As you seem to have an open mind, I dare to say that along my life I had a set of personal experiences that I cannot explain by coincidences or hazard; although I try to explain everything from matter properties, and to some extend I feel that I do it better than anyone else (my essay is just a minimum demonstration of it), I know that there is a level on the universe that in no way can be explained by our present conception of it at the Physical level.
All the best!
Alfredo Gouveia Oliveira