Tom,

Looking in from outside of your universe, you continue to present your case brilliantly.

James

    James, that is very kind of you.

    In this context, I interpret Bar-Yam's theory of multi-scale variety thus: Though we may all see the world through our own unique eyes, it doesn't make the world any different for any of us. It only means that the marvelous variety of viewpoints available is many times bigger than any one of us. Isn't it the greatest pleasure to participate in, and increase, that variety?

    Thanks, and all best to you in the essay competition!

    Tom

    Hi Thomas,

    Great essay! You provide compelling arguments for the mathematical universe hypothesis. However, my essay takes an opposing view; I would be glad to take your opinion.

    Best regards,

    Mohammed

      Tom, it's a very fascinating essay and a great contribution. Your philosophical approach on non-locality and Bell's theorem which you backed up by a thorough technical analysis, is quite inspiring. Also very enlightening is the last section on the Correspondence Principle and Popper Falsifiability. Thanks again, Steve

        Also (as I mentioned in my reply to your post)- congratulations on being published by Springer :)

        Thanks, Steve -- as I posted in your forum, we are in accord on many things, and the foundations of computability is, I think, the most important issue in frontier science.

        Beyond the scope of the essay question, the growing fields of brain science and artificial intelligence depend strongly on resolving the issues of network robustness and integrity -- i.e., the amount of information that can be effectively used at each decision point such that positive feedback doesn't overpower the computing function.

        It's a key point -- the number (1) in your concluding remarks, that twice applying the self-referential operation generates a true statement. It's the identical point I was making with the Popper example of pairwise correlations followed by a single result that may or may not be correlated with the pairwise value. Length restrictions kept me from exploring the basis of Popper's program -- which is Richard von Mises's theory of the independence of collectives -- Popper notes (p. 196) in *Realism and the Aim of Science*:

        "von Mises's 'axiom' (which postulates the existence of a limit of the relative frequency of the occurrence of a property P in any probabilistic sequence of events or 'collective') may be written as a universal-existential-universal-existential-universal statement, of the following form: '*For every* probabilistic sequence, *there exists* a real number x between 0 and 1, called the limit of the relative frequency, such that *for every* given fraction y, however small, for which y > 0 holds, *there exists* a natural number n, such that *for every* natural number n (for which n > m holds) the relative frequency of m/n, of m occurrences of the property P up to the nth event of the sequence does not deviate from x by more than y, that is to say, - y =/< x - (m/n) =/< y."

        In network terms, adding a time parameter, this implies that information lost to one decision node is not lost to the network hub at which it originated, such that continuously shifting hubs of decision activity are self-organized in the same context that you take to be self-referential.

        As I think it is pertinent to the content of both of our essays, if you don't mind, I am going to repost this in toto in your forum.

        Thanks again and all best,

        Tom

        Sure, Mohammed. As soon as I can make time. Thanks for commenting.

        Best,

        Tom

        Hi Tom,

        As I told you in my FQXi page, I have read your intriguing Essay. Here are my comments:

        1) Although I am a collector of aphorisms (particularly of Einstein's ones) I did not know the aphorism of Bronowski that "All science is the search for unity in hidden likenesses". It is very nice.

        2) I think that black hole physics and its importance in the route to quantize gravity is an example of your beautiful statement that "Mathematics research will uncover further physical regularities in nature". I also find intriguing your extending to symmetry between mathematics and physics the Tegmark's MUH.

        3) I find profound your question "What determines the objective result of a measurement - hidden variables or hidden assumptions?".

        4) Can you give details on your statement that "Hawking radiation is a theoretical example of a locally real quantum phenomenon with simultaneous past and future equality"? This could indeed have implications for the black hole information puzzle.

        5) I find very nice your Einstenian equation M=Pb^2=4P

        6) I think your pretty final sentence that "In this game of unlimited possibilities called mathematics, our bet is on human imagination" should have been appreciated by Einstein.

        In any case, the reading of your very nice Essay enjoyed me a lot. It deserves the highest score that I am going to give you.

        I wish you best luck in the Contest.

        Cheers, Ch.

          Thanks, Christian!

          The Bronowski quote is from his collection of post-war essays in the 1950s, called, *Science and Human Values.* It is a very inspiring little volume that I return to often to renew my optimism for the future of the human race and the role of science in it.

          My view on Hawking radiation is based on the Hawking-Hartle no-boundary/imaginary time proposal: "This absence of boundaries means that the laws of physics would determine the state of the universe uniquely, in imaginary time. But if one knows the state of the universe in imaginary time, one can calculate the state of the universe in real time. One would still expect some sort of Big Bang singularity in real time. So real time would still have a beginning. But one wouldn't have to appeal to something outside the universe, to determine how the universe began. Instead, the way the universe started out at the Big Bang would be determined by the state of the universe in imaginary time."

          The state of the universe in imaginary time is local -- every point of the Minkowski space-time in an expanding universe, is the origin of creation. (I'll send you something privately that explains it in more technical terms.)

          Thanks again, and all best -- looking forward to more dialogue,

          Tom

          Tom,

          Thank for taking the time to read my essay. I am not a mathematician but more another reading brought me closer to your well-thought-out vision and argument.

          Jim

          That's very kind of you, Jim. Thanks!

          Best,

          Tom

          Tom,

          You've got to be one of the most eloquent mathematical writers I have ever read. Phenomenal clarity and rigor.

          I've given you my highest mark in this contest so far.

          Best of luck!

          Rick

            That's very kind of you, Rick. Thanks!

            Best,

            Tom

            Tom,

            Its great to see your essay getting attention of serious and informed people, and free of those whom like to dance on the bar and start fights. That's probably because your approach of possible vs. probable is presented with math results that many people don't know enough about what they come from. I sure can't contribute much! I do have more a curio than a question that might be pertenent...

            Steven Sax provided an e-address for a thesis on laser experiments with Rubidium that I've waded into and think you would find interesting, and from which he launches his discourse on decidability. Here 'tis; http://www.bgu.ac.il/atomchip/Theses/Amir_Waxman_MSc_2007.pdf

            Its QM, of course, and uses the Bloch Sphere as the spin co-ordinate system. I realized that in their protocols what they specify as 'free precession' is in fact 'freely gimballed', in that the axis of precession intersects the origin at intersection of the orthogonals. To be 'free precession', the antipodal points of the axis of precession must be free to wander like the magnetic poles of the earth, the p-axis does not necessarily intersect the orthogonal. Intuitively this must fundamentally alter the landscape of co-ordinate pairs. And what seems to be already decided in QM is symmetric precession. Would that not impose an undecidable condition?

            I don't get into coin tossing, I pinch pennies like to bring a tear to Lincoln's eye. So maybe this niave observation is a standard issue. Your comment would be instructive, at your leisure, I'm just now off on errands.

            All the best, as always. jrc

            Hey, John -- I have always thought of *you* as a serious and informed person! :-)

            Give me your email address, and I'll send you something privately that addresses your question.

            Thanks for the link to Steve's research -- it's on my list.

            All best,

            Tom

            One of the advantages of being as old as I am, is that distant memories come into sharp focus with the right trigger.

            The trigger to my recollection of Jim Cowan's wonderful short story was David Hestenes's discussion of modeling in his essay forum.

            The Cowan story ("The Spade of Reason") and Jose Luis Borges's "Library of Babel" are two pieces of fiction that have had a deep impact on my intellectual life. Remarkably enough, Borges's story is referenced in Cowan's story.

            All best,

            Tom

              Thanks much Tom,

              I just posted my e-address to your 1209, sent this date 5:59pm.

              I'm getting myself a little swamped, but appreciate any help in learning 'the language'. And things just matured that are time sensitive that I have to concentrate on to finalize and make sure my ducks are in a row. I'm in for a long weekend but will acknowledge receipt of your post. If your check for receipt of my post to: 'contact' on your blog and don't find me, let me know here.

              Thanks again, I rely on the acumen of you and others whom come to converse rather than convert. Like the song goes, 'I can make my own mistakes just fine.' :-> jrc

              Tom,

              Got it! Six short pages! I gave it a quick read and its really well written. There will be questions, and once I have a list I'll try posting through my e-mail. Thanks very much and good luck with it! Later, Friend - jrc

              Dear Thomas,

              Thank for the comments on my blog and the high rate. I had your essay in my list and you write about CHSH!

              You can expect my feedback soon.

              All the best,

              Michel