Dear Edwin,
I did not raised at all the issue of consciousness in my essay. I wrote about aims and intentions, from the point of view of the definition of life I gave. So, it was about the meaning of life.
The math part, I tried to make it clear in section 1,2 and in the additional notes. Section 1 and additional, it is about that the fundamental operation life can do is an inequality operation, in the additional notes I wrote how these are accomplished and I cited the mathematical tools used to model that. Section 2, I wrote about the composition that life could make, as I defined, during early natural selection, to compose new life. That was a kind of lambda calculus, but there was not much space to talk about it. I should talk about the Chemoton theory, as what I proposed was even more fundamental, since it reduced all to a simple chemical clock.
On section about the Gaia Hypothesis, I mean that the definition of life can be extended to the stage as life as we know, if we consider it from the point of view of an entire ecosystem. In this regard, the biosphere is a life form with "arms", or "pseudopods" like and amoeba, that can reach food and redistribute for all system. I consider extended because the original Gaia Hypothesis is about regulating the Earth conditions for life, while in the essay, the biosphere is a gigantic lifeform living on earth. Perhaps I should had used extended from a restricted Gaia Hypothesis.
As you can notice, well, I tried to make noticed, the components of the biosphere, have a tendency try to reproduce the totality of the biosphere. A multi-cellular life or a society of humans or ants, try to exercise a number of independent functions to an extent would be require an ecosystem. That is, a tendency to a division of work.
Humans are becoming aware of this process, and use math to reach this totality. But, there is an ecological meaning of this, that to reach that, we must become in harmony with the rest of the biosphere. (If we reach and colonize other planets, we must be able to reproduce one very well, cue to the failure of the Biosphere 2 project).
