Dear Alexey and Lev,

Thank you for your thoughtful comments on my essay. As you indicated, I agree with your view that chaosogenesis (to use your term) must be rejected. Let me try to advance the discussion by mentioning three points.

First, about the argument (on page 7 left column): "Because the logical structure of our universe cannot be explained by chaos, and because it cannot explain itself, we are left with only one possible explanation remaining, that it was conceived and realized by a mind." What about another alternative, namely, that the logical structure and indeed the existence of our universe cannot be explained at all? On this alternative, the universe simply is, and nothing more can be said. In recent years a number of writers have advanced theories which amount to chaosogenesis in one form or another. As the weaknesses of such theories become more and more obvious, many of these people will probably retreat to this position of fundamental inexplicability. The conclusion that you present (i.e., "that it was conceived and realized by a mind") is, I think, preferable to the alternative of no explanation at all, but the interesting question is how to formulate the arguments.

Second, the argument on page 3, left column, is important, and I believe it deserves to be elaborated. I refer to the argument from the forms to their unity and then to absolute mind. As you point out, Tegmark does not bring up the matter, and when I read some of Tegmark's writings, I never thought of anything like what you say here. I think you are saying something like this: The mathematical forms are real. If a form is real, then it must be self-consistent. But self-consistency of each individual form is insufficient to guarantee the reality of the total realm of forms. If there is a mathematical universe, then all the forms in that universe must be mutually consistent. But what constitutes that over-all consistency of the mathematical universe, and for what reasons do we believe the mathematical universe to be consistent? (In my view, these are two separate questions, although related.) The ground of the self-consistency of the mathematical universe cannot itself be a formal proof or other mathematical structure. We can see why that will not work. So, the ground and guarantee of mathematical consistency has to be something outside the network of mathematical structures. Considerable additional argument is required to show that the external something is a mind or at least mind-like. You state that the logical terminus of the argument is absolute mind. As I said, your ideas on this point are new to me, but I am inclined to agree with you. I am sure that we should not simply take mathematical structures as the unproblematic starting point.

Third, in this same place on page 3 you assert that Tegmark's mathematical absolute has "total indifference to the forms it contains." This contrasts with your position that Ultimate Mind (or Absolute Mind) grants to each of its constituents "its own special significance", as you say in a comment above. I think this contrast is important. I believe you would also maintain that, from the actual contents and order of nature, we can infer something about the primal valuations which are intrinsic to what you call "the inexpressible potentiality of being". Here I am inclined to agree more with you than with Tegmark. In any event, you have brought forward an issue that has been too much neglected. Perhaps in the future you will say more about it.

Best wishes,

Laurence Hitterdale

    Dear Laurence,

    Without any exaggeration, you gave us one of the most profound responses we ever had for this text. Thank you so much for your deep attention, and, of course, for your high rating of the essay. Below I am giving our response to your points.

    1. "What about another alternative, namely, that the logical structure and indeed the existence of our universe cannot be explained at all?"

    We fully agree that this option must be properly considered. I think though that in fact we reflected this way of reasoning just after the citation of Wittgenstein:

    "Here Wittgenstein criticizes a silent acceptance of a composite and special mathematical structure as the ultimate explanation of the world. Such explanation barred from further questioning and not subject to reasonable ground of its own existence is an affirmation of unreasonableness of this ground. In other words, it is an acceptance of absurdity as the ultimate foundation of existence. Such superstition destroys the meaning of fundamental science by undermining the importance of reason, subjected by this superstition to the absurd."

    Your comment shows us that this option has to be outlined one more time on p.7.

    2. "the ground and guarantee of mathematical consistency has to be something outside the network of mathematical structures. Considerable additional argument is required to show that the external something is a mind or at least mind-like."

    I like that you are stressing this point, Laurence, and we would be happy to see any additional argument in this direction. However, I think our argument, why this "something" can be only mind, is solid (same p.3):

    "This unity must not only somehow bind every one of them [i.e. the mathematical forms] together but it has to guarantee their self-consistency. The forms though are mental entities. They are not thinkable without a mind which contains them as truly self-consistent [and so guarantees their self-consistency]. Thus, we have to conclude that this unity, the terminus of Tegmark's being, is an absolute mind, even if it is not mentioned at all. "

    3. "Third, in this same place on page 3 you assert that Tegmark's mathematical absolute has "total indifference to the forms it contains." This contrasts with your position that Ultimate Mind (or Absolute Mind) grants to each of its constituents "its own special significance", as you say in a comment above."

    It is the implicit transcendental mind of Tegmark's multiverse, which is indifferent, Laurence. As we wrote:

    "the terminus of Tegmark's being is an absolute mind, even if it is not mentioned at all. What makes this mind special and distinctive from its various platonic versions is its total indifference to the forms it contains. That is what Tegmark calls "the mathematical democracy". "

    The absolute mind of Tegmark cares about one and only one thing: mathematical consistency. After that, all forms are "democratically equal" for that mind. We are showing that this hypothesis is inconsistent with physics. To be consistent with that, we have to conclude that the absolute mind is not that indifferent; at least it cares about mathematical elegance as well.

    Finally you say, "In any event, you have brought forward an issue that has been too much neglected. Perhaps in the future you will say more about it."

    I fully agree. We think that this essay, among a few other works, sheds light onto that new field of philosophy where physics meets none other than theology in a very rigorous way. The people who are capable of such a level of discussion are rare, which makes your current and, hopefully, future thoughts on this subject most desirable.

    Cheers,

    Alexey Burov.

    Dear Alexey and Lev,

    Very good essay. To repeat my reactions for the sake of readers here: The writing was excellent, in the sense of being both technically apt as well as readable to a general literate audience (it reminds me of Penrose's writings, and in outlook as well.) I think you have an acute grasp of conceptual foundations and issues (like, the problem of existential asymmetry for specially-selected possible worlds.) Well put. First, I agree with you that physics is more than math, and that our world is not a math structure. Math by itself cannot tell us more than about its own contents (like, why there "are" five Platonic solids in that sense). However, as you well argue, the math we find in the universe can tell us much more. You correctly note the flaw in the argument that observed fine-tuning can be adequately explained (in Bayesian terms) as no more than a self-selection effect. True, if that were so, then the precision and elegance of the world would probably be less. (However, let's all admit that with continua we do have a measure problem. Still, even without enumerable sets to compare, the relative "areas" of numerical ranges give us a rough idea of what we should expect.)

    Actually I think the problem is even worse. If we really consider the full range of math structures, then we have to include inconsistent ones like e.g. the splicing together of y = x2 with y = x4. In that case, rules would not even be consistent over time etc. There are many more possible messy worlds than orderly ones, a problem noted about David Lewis' modal realism.

    These foundational arguments are fascinating and important, but I am particularly proud of my novel (in its broad execution at least) argument for why space had to be three-dimensional. It constrains possible worlds more than previously realized, although as I noted: only to the extent that we expect lawful consistency in "worlds" in the first place. And what really makes "worlds" different from mere structures of math? I basically agree with the sentiments pleaded by Roger Penrose (whose diagram is borrowed for your essay). Quote:

    "One can argue that a universe governed by laws that do not allow consciousness is no universe at all. I would even say that all the mathematical descriptions of a universe that have been given so far must fail this criterion. It is only the phenomenon of consciousness that can conjure a putative 'theoretical' universe into actual existence! ... Yet beneath all this technicality is the feeling that it is indeed 'obvious' that the conscious mind cannot work like a computer, even though much of what is actually involved in mental activity might do so. This is the kind of obviousness that a child can see--though that child may, in later life, become browbeaten into believing that the obvious problems are 'non-problems', to be argued into non-existence ... ."

    - Roger Penrose, in The Emperor's New Mind (1988), pp. 447-448.

    Finally, I invite readers to look at my own essay. It is one of a few that directly presents specific new physical insights (in this case, for why space has three large dimensions.)

      Dear Neil,

      Thanks again for your thought-provoking and multi-dimensional comment. Your comparison of our text to Penrose' is deeply flattering. Your note that "there are many more possible messy worlds than orderly ones, a problem noted about David Lewis' modal realism." invites me to underline that our essay, refuting Tegmark's multiverse, refutes Lewis' one even more. We write:

      "Our universe is special not only because it is populated by living and conscious beings but also because it is theoretizable by means of elegant mathematical forms, both rather simple in presentation and extremely rich in consequences. To allow life and consciousness, the mathematical structure of laws has to be complex enough so as to be able to generate rich families of material structures. From the other side, the laws have to be simple enough to be discoverable by the appearing conscious beings. To satisfy both conditions, the laws must be just right. The laws of nature are fine-tuned not only with respect to the anthropic principle but to be discoverable as well. In other words, the Universe is fine-tuned with respect to what can be called as the Cosmic Anthropic Principle: its laws are purposefully chosen for the universe to be cosmically observed."

      Cheers,

      Alexey.

      Dear Alexey and Lev,

      It was a great feeling when I discovered that you share the same ideas on metaphysics. I enjoyed reading your essay and gave it a high grade. I have a couple of comments, which can be thought of as suggestions for a further research.

      The Godel theorems in logic imply that there is no a TOE, which has a profound implications for a platonic metaphysics. This fact is also consistent with the fact that beside the mathematical ideas (concepts and structures) exist non-mathematical ideas (also called by Tegmark as non-computable structures). As I described in my first FQXi essay, "Temporal Platonic Metaphysics", one needs the idea of passage of time, as well as of consciousness (observer) in order to obtain a more realistic metaphysics than the one proposed by Tegmark. In your essay you raise a very interesting question concerning the multiverse, i.e. which universe is realised and why is it realised. From my point of view, an abstract Universe is realised if it is temporal. It is clear that our universe is temporal and it contains cosmic observers, i.e. us. You also raise a deeper question, which is which abstract universe is realised, and you use the arguments related with fine tuning to justify the existence of universes with observers. I think that the deeper question is why our universe is temporal, i.e. real, since there is an infinity of abstract mathematical universes. You correctly identify that there are two logical possibilities: it is God who decides or all mathematical universes are temporal.

      I also liked that you mentioned the 3 worlds: platonic, mental and material. I would like to point out that in my aforementioned essay, I described a relationship between them: the mental and the material worlds are subsets of the platonic world of ideas. The material world consists of mathematical ideas immersed in time, while the mental world consists of nonmathematical and mathematical ideas bundled together in our brain.

      Best regards,

      Aleksandar

        Dear Alexey,

        I cannot find your email adress in your author bio; perhaps it had been suppressed by organisators.

        Here is my own personnal adress:

        peter.punin@wanadoo.fr

        Please could you just return a blanc mail to this adress to establish contact?

        On the other hand I have consulted the home page of the Fermi Society of Philosophy. Is there a possibility to join it not only on forum discussions but as an active member?

        Best regards

        Peter

          Dear Aleksandar,

          Thank you for your very interesting comments and the high grade. However, something has gone wrong with your vote, and instead of a high rating, we've received from you a very low one, a 1. We've documented our ratings and vote counts before and after your vote, so this discrepancy is definitely the case. Perhaps the easiest way to correct it would be for you to contact administration, or if you want I can do that for you. For that you can send me an email to levburov@gmail.com, which I can then forward on with the request.

          Kind Regards,

          Lev

          The Burovs asked me also, to write to their email. Note to them and all: my email address is at the top of my essay.

          I think the same thing might have happened to me. I admit I didn't check that carefully, but my score surprisingly went down after a compliment, so it might have. Is FQXi Admin checking on this?

          BTW, I usually don't say much about particular ratings, or even if I already rated an essay or not, just to stay out of those concerns. I don't mind hearing from others, I just want to keep my own talk of it to a minimum. I do think, that anyone giving a low rating (3 or less) should explain or discuss first and not just take a drive-by potshot.

          Alexey and Lev,

          This is a very impressive essay. Your analysis of "order-from-chaos -- explanations is quite incisive with a laser focus. For example, Tegmark's "totality of mathematical forms," you immediately focus on deficiencies and logic of the view, questioning the unity of "these forms."

          I avoid the profundities of explaining the why and how of thinking and try to connect the mind, math and physics in the stellar achievements of science showing their successful connections in quantum biology, mapping DNA and trying to simulate the BB: http://fqxi.org/community/forum/topic/2345

          Thanks for your clear and crisp writing and an erudite analysis of important scientific thinkers.

          Jim

            Dear Peter, dear Neil,

            I just sent an email to the both of you from my personal account fi******t@gmail.com

            Thanks and cheers,

            Alexey.

            Dear Jim,

            Many thanks for your generous compliments! You are catching the very core of our approach, when pointing to our "questioning the unity of "these forms."" To give some reasonable comments on your essay, I have to read it with sufficient attendance and think a bit after that :). I'll try.

            Cheers,

            Alexey.

            I just thought of something that may cause confusion about voting, if it's based on looking at comment times (may or may not be relevant to the above worries in particular.) The comment times are shown in GMT, which someone looking may forget to take into account (like, when trying to compare favorable comment with rating change.) Just passing it on FWIW. Actually, I want to see some kind of post-verification so voters can be more sure, and that's something political voters need more of too.

            After an exchange of emails with Aleksandar, thanks to his patience, I realized that my interpretation of my rating jumps was not correct. It is too easy to be confused by the time delay between the voting and the related comment, and by accidental coincidences between the comment and unrelated rating. Everything appears to be right in my case. I apologize to all whom I confused. As a result, I am concluding do not bother any more to check anything and trust the system. To comment on Neil's reasonable idea "to see some kind of post-verification", I would suggest a bit more: it would be helpful to see for every essay not only its average rating, but the entire list of its ratings. I do not see any reason why this should be unavailable.

            Dear Alexey and Lev,

            I found great depth in your essay and good argumentation. It's a very interesting idea that the source of order in the universe cannot be limited to the fine tuning of the constants but must be extended to a "right choice of the fundamental principles of physical laws". Another striking point that you make is the distinction between the types of observers and the theoretizability of the world. My main take away from your essay is the uniqueness of the laws. Another very interesting exercise you make is the deduction of the consequences of noise in a universe with semi-stable laws of nature.

            Cheers,

            Cristi

              Dear Alexey and Lev,

              An absolutely brilliant essay. I agree with you in many points such as your opinion on Tegmark's hypothesis. I especially liked the section "The condition of Elegance". Your essay deserves the highest rating. I would be glad to take your opinion in my essay.

              Best regards and good luck in the contest.

              Mohammed

                Dear Cristi,

                Thank you so much! It is a true pleasure to be highly appreciated by one of the experts!

                You underline that your "main take away from your essay is the uniqueness of the laws." I cannot help but quote our related conclusion:

                "Our universe is special not only because it is populated by living and conscious beings but also because it is theoretizable by means of elegant mathematical forms, both rather simple in presentation and extremely rich in consequences. To allow life and consciousness, the mathematical structure of laws has to be complex enough so as to be able to generate rich families of material structures. From the other side, the laws have to be simple enough to be discoverable by the appearing conscious beings. To satisfy both conditions, the laws must be just right. The laws of nature are fine-tuned not only with respect to the anthropic principle but to be discoverable as well. In other words, the Universe is fine-tuned with respect to what can be called as the Cosmic Anthropic Principle: its laws are purposefully chosen for the universe to be cosmically observed."

                Maybe, our laws are not unique, but they definitely belong to a very special and narrow set of mathematical structures, much more narrow than Tegmark's multiverse suggests. In other words, our laws are truly beautiful in that deep meaning of mathematical beauty which was professed by Pythagoreans of all times, from Pythagoras and Euclid to Kepler and Newton and to Einstein and Dirac.

                In that light your statement that, "Mathematics is already there, eternal and unchanging. What we invent is the discovery of mathematics," is revealed as having an even deeper meaning than it may at first seem.

                Cheers and good luck,

                Alexey and Lev

                Dear Cristi,

                Thank you so much! It is a true pleasure to be highly appreciated by one of the experts!

                You underline that your "main take away from your essay is the uniqueness of the laws." I cannot help but quote our related conclusion:

                "Our universe is special not only because it is populated by living and conscious beings but also because it is theoretizable by means of elegant mathematical forms, both rather simple in presentation and extremely rich in consequences. To allow life and consciousness, the mathematical structure of laws has to be complex enough so as to be able to generate rich families of material structures. From the other side, the laws have to be simple enough to be discoverable by the appearing conscious beings. To satisfy both conditions, the laws must be just right. The laws of nature are fine-tuned not only with respect to the anthropic principle but to be discoverable as well. In other words, the Universe is fine-tuned with respect to what can be called as the Cosmic Anthropic Principle: its laws are purposefully chosen for the universe to be cosmically observed."

                Maybe, our laws are not unique, but they definitely belong to a very special and narrow set of mathematical structures, much more narrow than Tegmark's multiverse suggests. In other words, our laws are truly beautiful in that deep meaning of mathematical beauty which was professed by Pythagoreans of all times, from Pythagoras and Euclid to Kepler and Newton and to Einstein and Dirac.

                In that light your statement that, "Mathematics is already there, eternal and unchanging. What we invent is the discovery of mathematics," is revealed as having an even deeper meaning than it may at first seem.

                Cheers and good luck,

                Alexey and Lev

                Dear Mohammed,

                My apologies for a mis-post. I'm working on my answer to you.

                Cheers,

                Alexey

                Dear Mohammed,

                Your compliments are especially important for me, since we disagree in our answers to the Wigner's question. Your high rating shows a valuable and rare ability to estimate an approach contradictory to your own. Thank you so much! As you stress in your abstract, you "try to explain the reason for this effectiveness based on the view that mathematics is invented." Our point is that such invention would not be possible without very special objective properties of our universe:

                "Such a special universe deserves a proper term, and we do not see a better choice than to call it Cosmos or to qualify it as Pythagorean, in honor of the first prophet of theoretical cognition, who coined such important words as cosmos (order), philosophy (love of wisdom), and theory (contemplation)."

                Gratefully accepting your compliments, I still wish to mention that we do not think that we just expressed an "opinion on Tegmark's hypothesis". I think we clearly refuted it on the scientific ground.

                In the time remaining, I'll try to read your essay attentively and let you know what else will come in my mind.

                Good luck in the contest and cheers,

                Alexey.