Dear Sylvain,
Following the conversation we already had on my essay's page, I am now going to comment your essay in detail.
The way I understand it, your system is based on the twin entries at the bottom of your table on page 7: Mathematics and "The Matrix", which encompasses all relevant aspects of "reality" that are not mathematical. That's why you begin your essay by arguing for the existence of laws that are not mathematical. You give the example of "artistic laws" and "psychological laws" as being impossible to define in an algorithmic fashion. I agree that those type of laws can certainly seem non-algorithmic and un-mathematical, but could it be that it is just due to our failure to be able to consider complex enough algorithms and mathematical entities? You claim that the behaviors that result from these laws would require algorithms that are "too big to be stored in a computer", but do we really know what is the theoretical limit that a computer can achieve? Even if we could show that the physics of our universe prohibits such a computer, how can we be sure that our universe is not being "run" on a computer in a higher-level reality where the physical laws do allow for such complex algorithms? I know, from reading your website, that you firmly believe that artificial intelligence will forever remain impossible, because of the classic "computers have no soul" argument. We certainly do not agree on this issue: I think we will see true general artificial intelligence within the next 20 or 30 years, and I am convinced that this technological breakthrough will have a profound impact on philosophy and on the way we see reality. I guess we will just have to wait and see!
On page 2, your discussion of "Time and unpredictability in mathematics" is very intriguing. I will have to dig deeper and explore what you wrote on your website about the "time order" of mathematical reality. Since, in my view, there is a way to understand the totality of what exists as a a mathematical structure, I believe that, although mathematics as a whole is "atemporal" and "eternal", it is possible to define mathematical structures that evolve and change relative to other mathematical structures that play the role of "time counters".
On the issue of the relationship between mathematical and conscious existence, I agree with you that "the conscious perception of mathematical structures can explain and constitute their physical existence". In my view, mathematical structures that do not contain "self-aware substructures" are not physical, since there is no one to "feel" their "physicality". Where our views diverge (but maybe not that much), is on the question of the need to "add" something to brain computation (what you call an "immaterial soul") to explain consciousness and feelings (qualia). I think that the mathematical computation, the biophysical reactions, and the conscious experience are three different levels of description of the same structure --- a structure that can be seen, from one point of view, as purely mathematical (all is computation), but at the same time, from another point of view, as purely mental (all is thought). Of course, I think most physicists, and most authors in this contest, would say that it is the middle ground, the biophysical reactions, that is the true fundamental level... which make essays such as ours terribly counter-intuitive and almost nonsensical to many!
Let's assume for a moment that you're right and that there is a non-mathematical Matrix, a set of minds united in a coherent whole, that uses the mathematical (and sometimes physical) Maxiverse as a "playground". You claim it is the Matrix that "selects" which universes truly exist: as you say on page 4,
"To create the Universe, Consciousness first chose a mathematical law as "theory of everything" of physics [...] The physical Universe is the trajectory of this exploration of the Hilbert space by consciousness."
It is an intriguing hypothesis, but to entertain it, we need to postulate an entire, separate level of reality, "The Matrix", that has remarkable capabilities and complex behavior, such as the ability to "choose" and "explore". Everything that current scientific understanding has trouble with (the hard problem of consciousness, the flow of time) gets conveniently explained and taken care of by The Matrix. The Matrix even allows us to have "real" free will, while making sure that we do not have too much liberty to individually select which part of the Hilbert space gets explored, by enforcing global coherence across all physical perceptions... But the fundamental nature of the Matrix remains a mystery, and it seems to me that we are back to square one: instead of having no idea what the fundamental nature of the Universe is, we've separated the Universe in two: one part is what we understand (math/physics), and all the rest is The Matrix, but we have no idea what it truly is, where it comes from... As Morpheus says in the movie, "No one can be told what the Matrix is... You have to see it for yourself!"
Although we do not agree on many issues, I find your essay and your website fascinating, and I will certainly be going back to what you wrote (and continue to write, as I see your process as a work in progress) when I have the time. Meanwhile, I've given your essay a boost that, I hope, will make it more visible: with so many essays, the essays at the top of the community ratings have a better chance to get more attention and more votes, while many good essays remain buried and forgotten in the middle of the heap...
Oh, I almost forgot one specific question I have: in your essay's abstract, you talk about the mathematical world being a "Platonic mathematical realm slightly less than infinite". Why "slightly less than infinite"? To avoid the paradoxes associated with infinity and incompleteness? I find the concept of "slightly less than infinite" intriguing, so I would like to know more about how you think about this.
Best regards,
Marc