Hello Michel! Thank you for your comments. And your essay is on my list to read (I noticed that you wrote a dialogue as well). I absolutely believe that the quantum world is tangible. In my opinion, if it weren't, then nothing would be tangible.

7 days later

Ian,

Very fun and imaginative dramatization. Math is a representational reality which means it must be peer reviewed by others (like BICEP2) to make sure it really represents tangible reality. Eddington's observation did help prove Einstein's theory but at the same time Eddington mistrusted mathematical derivations from relativity theory to explain "degenerate stars."

Thanks for sharing an imaginative creation that helps clarify roles of math and physics.

My "Connections" tries to show the relationships of math, the mind, and physics in new discoveries in quantum biology, LHC and DNA.

Jim

    Dear Professor Durham,

    I am just a humble student but noticed a similarity of one moral your excellent story conveys to the main thesis presented in my little opera "Map = Territory" where I ponder the possibility of an actual merger of the description and the described in fundamental physics.

    Your message "the universe is nothing more than our description of it" reminded me of my beginner's take on the subject and I would very much appreciate an opinion of an accomplished professional like you (if some time can be found for that). I would be honoured by your feedback and advice.

    With deep respect and best wishes,

    Martin

    Hi Ian,

    I hope this isn't a re-post. I thought I commented on your essay but when I checked back to today I didn't see it. (Un)Luckily I had it saved in a word document...

    I totally agree with what you were trying to say via your dialogue... or maybe I completely disagree... or... Anyway, at the very least I liked the dialogue (reminded me of Gödel-Escher-Bach) and think the thoughts you provoked with it definitely relate to my Digital Physics movie essay. I think we're still trying to reach a consensus on infinity, probabilities, and mathematics in general, so I see little hope for achieving a Grand Unified Theory in physicists before some of these fundamental ideas are better addressed.

    I also tried to have a little fun with the essay format, so hopefully it makes it an easy read. I'd love for you to comment on my thoughts regarding real numbers in my essay. I think you might also like taking a crack at a few of the questions I have at the end of my essay. Here's a sample of one that might interest you:

    How quickly could a tape be processed through a Turing machine and is this constraint physical or informational in nature?

    Thanks again for making an interesting and entertaining read.

    Jon

    8 days later

    Dear Ian,

    I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

    All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

    Joe Fisher

    Dear Ian,

    Lovely! Here is a quote from G. H Hardy in his "Mathematician's Apology":

    (p. 70) " A chair or a star is not in the least like what it seems to be; the more we think of it, the fuzzier its outlines become in the haze of sensation which surrounds it; but '2' or '317' ha nothing to do with sensation, and its properties stand out more clearly the more closely we scrutinize it. ... 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way."

    For Hardy, mathematics was more tangible than physical reality.

    Best,

    Lou Kauffman

    Ian,

    Time grows short, so I am revisiting essays I've read to assure I've rated them. I find that I rated yours on 3/28, rating it as one I could immediately relate to. I hope you get a chance to look at mine : http://fqxi.org/community/forum/topic/2345.

    Jim

    5 days later

    Dear Ian,

    I am particularly amused by and happy to have read you essay. I must say that I wanted to make mine a dialogue as well, but then reconsidered as I thought it might be deemed as not matching with the contest; I'm glad at least one person wouldn't have thought that ;) I decided in the end to just go with a light and funny writing tone.

    I like the symmetry of your essay. It begins and ends with the same action, somewhat like a Turing machine caught in an infinite loop. It must mean it's meant to be read and enjoyed by thinking beings. In this context, the eternal 6 o'clock made me consider what would happen if the March Hare would put on the table such a machine rummaging through an uncomputable calculation. I enjoyed very much how you are working your way to the argument of the representational and tangible realities and found very satisfying in this respect (and hilarious) the Hatter's remark that "A character in a dialogue has chosen tangible reality. How comforting."

    Profound and packed in dry humor. Great read! Wish you the best of luck in the competition and I'm rating your work accordingly, in the hope that it will make a difference.

    Warm regards,

    Alma

    Dear Ian,

    As others have commented, this is a wonderful choice of style. I wish you could of included one or two more topics, but this was fun and clear.

    All the best,

    Jeff

      Thank you all for the kind comments! I have been busy with work and have not been able to find the time to respond to each of you individually, but I appreciate the thoughts! I am very glad indeed that I was able to inject a bit of humor without taking away from the depth of the subject. I do wish I had had more space to elaborate on some points, but perhaps I will do so in the future elsewhere. Thank you all again!

      Ian,

      I am replying to my own thread, because I realized it was incomplete.

      In writing class (which you clearly do not need)we learned "show do not tell". This essay was showing, not telling. Is the idea of something the thing itself? Is the name of an idea the idea? Is an equation of the universe, the universe (at this point I clearly went beyond the text)? You let us make these decisions, which I do not know if I like or hate you for putting us in such a position.

      All the best,

      Jeff

      Dear Ian,

      Thank you for going to my essay. I expect that my essay will not be red as a tree but as a surface with punctures, it is non local in some sense. I also hope a big picture is emerging, some points are ongoing research (as those pointed out in the abstract), some technical aspects may not be familiar to quantum physicists (e.g. modular forms and characters).

      If you go to reference [17] just appearing in QIP, you can see that I cite a work of yours on the "order theoretic quantification of contextuality", meanwhile I also found another measure of geometrical contextuality that I am currently working on. A mathematician would say the Langlands program but I stay closer to physics.

      Best,

      Michel

        Dear Ian,

        Thanks for the very enjoyable essay. The distinction between representation and tangible realities is well articulated. One of the oddities of this dichotomy seems to be that some physical systems can characterize what may (or may not) be tangible using representation. So it seems these two modes of description are not entirely independent but that the representational influences the tangible and the tangible constrains what can be represented. You seem to suggest a starker line between the two, so I am curious on your thoughts where these two domains interact. In particular, my view is that addressing this aspect is essential to addressing why math seems to work for describing physical reality.

        Best,

        Sara

          Dear Ian,

          very nice essay. I still need to read it in full detail to appreciate all the sides of the conversation. For the moment let me say that I appreciate the choice of Lewis Carrol, which, btw, raised the famous logical paradox that proves that even the "modus ponens" must be formalized. If logic itself must be formalized, than you would agree with me that Physics must be formalized, otherwise would not be logical, whence not logical falsifiable, whence not scientific. As you know, this is the point raised in my essay.

          Hope to see you soon, and enjoy a thorough conversation about this crucial point about physical science.

          My best regards

          Mauro

            Hi Sara,

            Thanks for the comments. I think you raise a very important issue: where *is* the line between tangible and representational reality? Is the line, if it exists, well-defined or fuzzy? And if we err on the side of caution, should we err on the tangible side or the representational side?

            I'm torn on this issue, to be honest. I'm not a pure operationalist, but I'm not even sure operationalism, at least as it is practiced today, is even purely tangible. I do firmly believe that physics should be about the physical, but I also believe that well-founded theories are as broad as possible in their explanatory nature. So, to give you an example, if you've ever watched Susskind's videos on what you need to know about modern physics, he starts out talking about Newton's laws. Whenever I teach introductory material, I start with energy and momentum because Newton's laws are easily derived from conservation of momentum and energy. When I made this point to a friend of mine, he argued that introducing Newton's laws (and general laws of motion) first, made more sense from an operationalist view. So, in that sense, I am not an operationalist.

            On the other hand, as I said, I do think we need to default to physical reality. Feynman said something about this once. In fact Carl Caves said something to me once many years ago to this effect: we're physicists and we're doing physics so we should default on the side of physics.

            So, in short, I unfortunately don't have a neat and clean answer to your question. I think the line I painted in the essay is quite stark for that particular example. It may be that there is a stark line in *every* example, but that there is no single, unifying way of defining that line such that we can "know" it in a given case (if that makes any sense).

            Cheers,

            Ian

            Hi Mauro!

            Part of me completely agrees with you that physics needs to be formalized if it is built on logic (which it partially is). But another part of me says that it is ultimately built on what we can measure (see my reply to Sara above). In other words, it still has to explain what we see in a lab. It's not clear that we can formalize everything we see. Certainly people have tried ever since Hilbert's original proposal (and, to some extent, Newton and others in the 17th century tried as well, before physics took a more experimental turn). It seems telling to me that no one has fully succeeded in this endeavor yet, though of course that doesn't mean it can't be done.

            Hope to see you soon! Let me know if you will be in Boston at some point.

            Cheers,

            Ian

            Hi Michel,

            Thank you for citing that work! I look forward to hearing about your additional measure of geometrical contextuality when it is finished.

            Indeed, I am not all that familiar with modular forms and characters. But that is one of the beautiful points of your essay. It introduces some really terrific ideas to the physics community.

            Cheers,

            Ian

            11 days later

            Hi Ian

            I really enjoyed your essay!

            It was very brave as such a dialogue is extremely challenging. You have to maintain a direction to the conversation leading the reader to thoughts without explicitly stating them, and all the while make the conversation lively, engaging and natural. Its a daunting challenge, and I think that you did a great job!

            I enjoyed how the dialogue began and ended with the two attempting to shove the Doormouse into the teacup.

            I wonder, did the Doormouse actually count to infinity in the same way that Achilles caught up to and passed the Tortoise?

            Cheers

            Kevin

            a month later

            Congratulations on your prize. Yours is the most memorable of the essays I read and deserves recognition among the winners. Well done, kind regards Georgina

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