Dear Sylvain,
Thank you for your detailed analysis of my essay. It is very welcome!
I have read your essay, the more complete version on your website ("Specifications for a Mind Makes Collapse interpretation of quantum physics", that you suggested to Tommaso Bolognesi) and your very interesting description of the Many-worlds interpretation that you suggested in your post above.
You certainly have many interesting and provocative ideas, and some of them do correspond to the way I (currently) see things. Like you, I think it makes a lot of sense to say that a mathematical structure becomes "physical" (whatever that means) when it is consciously observed. I really like the way you put in in your analysis of Laurence Hitterdale's essay:
"But what do you think it might mean for a universe to "physically exist" when considered independently of the presence of consciousness? How would such an "independent existence" differ from purely mathematical existence? In my view, that is what it is: the physical aspects of the universe, insofar as we examine what "exists independently of minds", turn out to be mathematical because the mathematical nature is exactly what remains of the physical universe when the role of consciousness is removed."
Where our views differ, is that your system is essentially dualistic, with consciousness existing in a separate realm, being NON-mathematical and NOT being subject to physical laws. I agree that our world does seem dualistic, with consciousness residing in a separate plane, but I believe that an Ultimate theory of Existence should reconcile all aspects of existence in a single category (so ultimately it would be monistic instead of dualistic). In keeping with the theme of this year's FQXi essay, I argued in my essay that everything that exists (including consciousness) can be understood in terms of mathematical structures, but I think one could also make an interesting case that everything can be understood in terms of mental structures. So in my view, Existence is monistic, but this monism can be interpreted, from one point of view, as "all is math", and from another point of view, as "all is mind".
In your comment above, you make very interesting remarks about what gives "quality" to a theory: compressing the observed data, or, equivalently, minimizing the "entropy" of the explanation. You go on to say that the position I argue for in my essay, by avoiding "the issue of specifying probabilities by admitting the existence of all possibilities and qualifying the whole probability issue as a kind of mystery waiting for future elucidation", does not constitute a "very good theoretical job". I am fully aware of this, but what can I do? Suppose it is true that capital-E Existence ("All that exists") does indeed follow from the most simple rule imaginable, "Everything Exists", but that we are not advanced (or intelligent) enough to solve the riddle of the measure problem. Should we just refrain to make that hypothesis?
As an historical analogy, suppose a philosopher in the time of Kepler was skeptical of Kepler's attempt to explain the fact there were 6 planets by linking the geometry of the solar system with the 5 regular solids, and said instead that the simplest possibility was that every possible solar system exists, but that the hypothesis was, of course, unverifiable with 17th century technology. If you had lived at that time, you would probably have said that the philosopher's idea did not make a "very good theoretical job". Yet, we now know that his idea was closer to reality than Kepler's hopeless attempt to explain "from first principles" the contingent details of our solar system!
You claim that qualia (sensations and feelings) are an example of something that is not mathematical, and in your essay you also claim that the flow of time (the distinction that consciousness makes between past and future) cannot possibly be described by mathematics. But if mathematics is the general study of structures, that would mean that qualia and the flow of time are not structures. What are they then? I will address this issue when I review your essay on your forum (hopefully, within the next few days).
About the observed regularity of our universe... you criticize Moravec's explanation (that our universe stays lawful and predictable, even if there are many scenarios where it doesn't, because in these scenarios, our consciousness immediately ceases to exist) with the analogy of the lottery ("If I won at Lotto first, why would it make me more likely to win again another time?"). But suppose that the lottery's prize is Existence itself. Then, you never become aware of the scenarios where you lose, and you always keep winning, against all odds. This is, of course, the main reasoning behind the "Maxiverse Immortality Hypothesis" that I describe in my essay.
As I said, I read your webpage on the Many-worlds interpretation, and I agree with you that there is no such thing as a number of possibilities, and that there are better ways to describe the thorny issue of the "amount of existence" of the different possibilities within a Many-worlds or Maxiverse model. I will try to be more precise next time when I discuss these issues! :) By the way, I really like the way you describe the Many-worlds worldview, especially when you deal with the issue of how the past evolutionary history of the universe, relative to a given individual, is largely undetermined (a view that is similar to how I view things, and that I have seldom seen so explicitely and clearly stated).
More to come on your own forum!
Marc