James, thanks, will take a look. I recall that your essay last time was rather interesting. I don't say much about rating per se for obvious reasons, other than my overall opinions.

James,

Thanks for the support. Also, there may be some mistakes going around. The Burovs (who commented here and have an excellent essay) suspect that someone meant to give them a good rating, but they calculated it having registered a "1".

Dear Alexey and Lev,

As noted by a commenter at your essay site, I don't see an email address for either of you. My own address is at the top of my essay, please use that and we can discuss things. I don't say much about ratings, but you can assume rational correlation between praise and prior or subsequent credit.

BTW I recommend the essays by George Gantz and Christine Dantas, and I'll mention some others in awhile.

  • [deleted]

Dear Neal,

Your essay conjoins two topics I would not have immediately thought of as being closely related in an interesting way. A few comments:

1.Your eqn. 2 reminded me a little of Ehrenfest's argument already over 100 years ago that one way to answer the question about the dimensionality of space is to consider that in space dimensions other than 3 orbits become unstable. Now, I realize your argument is very different, even drawing from a different theory (EM vs. CM) but it still has a similar flavor.

I tend to be skeptical of such arguments because the takeaway I get from them is not that space had to be 3D, but that for other dimensionalities, the "stuff" that would be the analog of mass in spacetime would have to have different properties and obey different laws.

2.Your discussion of the 4/3 problem reminded me that there have been over the last few years claims of having solved it. One name that comes to mind is Fritz Rohrlich. He also wrote a book "Classical charged particles" which you may enjoy, given your interest(I found it extremely readable, which in the EM literature is not always the case).

3.Regarding your discussion of whether mathematics has the capacity of formally expressing conceptually intuitive ontological distinctions I agree with you that in its present form it does not. However, I also believe that compared to what it could express, the current form is very impoverished, and that the only reason most of us don't see this is because we are too beholden to its present state. To better understand what I mean, I invite you to peruse any reference on various non-classical logics. You will find a large menagerie of species, mostly developed by philosophers for comparatively narrow purposes, many of which an offer the possibility for serving as a foundation of mathematics with expressive powers beyond what you might have thought possible. Indeed, my own main area of research is in this area, and in fact my entry in this contest is concerned precisely with introducing the distinction between actuality and potentiality into mathematics.

Overall, your paper offers several interesting ideas, I hope that some experts in the area will take the time to examine your dimensionality argument in depth. From my perspective, its correctness would be interesting not so much for the reasons you give but because it might have the potential to illuminate other foundational questions in that area.

Best wishes,

Armin

    Dear Neil,

    Please pardon the misspelling of your name, I noticed it as soon as I posted my previous comment.

    Armin

    Dear Armin,

    You ask good questions. About your #1: it isn't enough to have some kind of stuff with whatever rules would be an extrapolation to other dimensions. The change in rules has to all add up to a consistent system. I showed that if we make the expected change in exponent for basic field law and combine that with requiring electromagnetic inertia and the stress correction, things don't work together harmoniously except for D = 3 (here just referring to space dimensions.) Yes, the 4/3 problem has been a wild ride and with lots of conflicting arguments, unbelievable (?) as that may seem. Yes Rorlich's book is a great read, and many interesting articles about such issues appear in American J. of Physics, while the more glamorous cutting-edge journals have mostly left this behind as unfashionable.

    Yet a clear implication can be worked out, going back to Einstein's old argument about the effect relative simultaneity has on force-application times, and therefore momentum and energy. This in turn has specific implications for stressed bodies that are accelerated. Well I will add more later.

    Hi Neil,

    You present an interesting case for why we probably do live in a 3 dimensional universe. But I'm mainly interested in your major thesis that "math can tell us what works, but not what is real or why it is real".

    I think your argument is correct that "Math and logic don't have the tools to reach beyond their realms and characterize the status of another existential level." - "We must transcend math and logic to grasp this". I think you made a very good case.

    As you have noted, our essays address the same sort of foundational questions.

    Best wishes,

    Lorraine

      Dear Neil,

      My apologies for reading your essay so late, but each year there seem to be more and more notable pieces like yours and choosing the order is a hard thing to do. You have some delightful expressions, this one in particular reminding me of how Einstein saw the world, "the orderliness is the expression of the mind of God". You are making a very interesting point approaching the self-energy problem, allow me to add to that the whole theory maybe deserves more attention than it receives nowadays, and perhaps a careful treatment in the framework of general relativity. Another good point of yours is that of structure and essence and I appreciate your treatment. I agree with "math can tell us what works, but not what is real or why it is real", and the final words conclude well that "Mathematics cannot tell us about anything more than itself".

      My very best regards,

      Cristi Stoica

        Dear Neil,

        Great essay. It is well-written and well-argued. I agree fully with your analysis, and there are some similarities between my essay and yours. Your essay deserves the highest rating.

        Best regards and good luck in the contest.

        Mohammed

          Lorraine, thanks for writing. Please consider attending one of the Tucson interdisciplinary conferences on consciousness some day, I think you have much to contribute on the great mystery of the mind. I went to the 2000 event and gave a paper on willful choice. I've enjoyed your previous essays too. We can't really extract "worlds" from math, although Max Tegmark's heroic effort of the MUH deserves credit for audacity and creativity. It should not be dismissed casually (even though I don't agree with the thesis.)

          Dear Christinel,

          Thank you very much for your supporting comments. Many of us think that the order in the world is an expression of some deep "idea" or complex of ideas, aside from how a person wants to imagine that ultimate reality. We agree that math by itself can do the job, but ideas like MUH shouldn't be dismissed breezily. (Remember also that Max was instrumental in starting up FQXi!)

          There are solid ways to critique math. monism. One inadequacy is the failure of neodeterminist quantum interpretations to properly account for observed probabilities. The structure of the evolving parallel states just can't fairly derive the Born rule. Quantum probability therefore seems to be "intrinsic", and deterministic math cannot pick the actual outcome if they are exclusive. We need these kinds of technical issues to make headway, despite our clear intuition that the "esse" of material existence is something that transcends mere abstraction. (Penrose made similar points in his wonderful books that I admire so much.)

          I'm glad to see a few commenters appreciating the problem of electromagnetic mass (note, not to be confused with QED field problems. This is about relations for macroscopic charges and separations.) The problem can be resolved within SRT (but has implications for GRT because stress and pressure exert gravity), but later thinking obscured the mechanics of it. It became a sort of "given", taken for granted and not understood inside. That won't let you see how it works out in other kinds of space.

          Your essay gets off to a good start, I haven't time to finish just yet but will go over it and have some comments. I'm the sort who often hesitates to say my first impressions, which delays my reviews or I sadly forget sometimes. (We can comment past the voting limit, true?) You bring up that amazing and humbling case of the point on a line that can in theory encode any amount of information (actually, an infinite amount if on a perfect mathematical number line!) I also recommend the essays by George Gantz and the Burovs. The latter is so adept at framing the problems and prospects, it really should be the nucleus of one of those grand books about the nature of reality (like Penrose's works or "Our Mathematical Universe" etc.)

          My regards to you.

          Dear Mohammed,

          Thank you. I'm going to read your essay soon and leave a comment. I already see it is well-organized and presented. Good luck to you and your co-author.

          Hi Neil,

          It is nice to meet you again here in FQXi Essay Contest. Even this year, you made a very good work. I indeed found your Essay very interesting and enjoyable. In particular, I appreciate your pretty argument which explains why the Universe consists in three spatial dimensions.

          More in general, I found the reading of your nice Essay very interesting and enjoyable. Thus, I am pleasured to give you a deserved highest rate.

          I hope you will have a chance to read my Essay.

          I wish you best luck in the contest.

          Cheers, Ch.

            Christian, thanks.

            I haven't had time to read your essay in detail (and I'm neurotic about saying much unless I do), but I already appreciate that you address specific experimental results and predictions in light of particular theoretical expectations and critiques. That adds more than generalizations can do on their own. Note this curious irony: you correctly say that GR (now celebrating its 100th anniversary, so an apt time for your essay) is a geometrical theory, which constrains its form and predictions in certain ways. Yet you are boldly asserting that many physicists have missed an important insight, in their handling of clock synchronization in the rotating disk (all this I am gathering from your abstract alone.) How could this be?

            Well if you are right, it means there are subtle problems of framing issues in this area - analogous to the problems dogging quantum mechanics and relativistic dynamics (such as arguments about the right-angle lever and the "energy current", how is angular momentum conserved in Thomas Precession, etc.)

            I will go into more detail at your own essay.

            Regards.

            Neil,

            I really appreciate your incisive review, including your constructive comments.

            Best regards,

            Jim

            18 days later

            Ramin,

            Thanks for your complements. I looked over your paper. It is clearly ambitious and you put lots of hard work into it. There is a lot of rather advanced and intricate math but I get the impression you have latched onto something significant. Do keep in mind, math is so rich that it's possible to find all kinds of promising "connections" but hard to know which ones will hold up better with more knowledge, than others. How do you think that possible EM inconsistency in D > 3 affects your generalizations? (BTW I used D for space dimensions, do you think it's better to designate for space time?) I note that you didn't have an essay here, perhaps you feel too boxed in by the length requirements. BTW must someone be a Member to post to that data forum? tx

            Sherman,

            You're welcome. Sorry for the delay, I got slipped in the shuffle. Yeah, I get a kick out of calling myself "Tyrannogenius." Don't worry if I deserve the title, but it was fun to pick out and now I "own it." I should look at your essay. Cheers.

            Christinel,

            Sorry that I need to correct a statement that inadvertently misrepresented our positions. I should have written:

            "We agree that math by itself CANNOT do the job, but ideas like MUH shouldn't be dismissed breezily. (Remember also that Max was instrumental in starting up FQXi!)"

            Here the correction is in bold, I originally had "can do the job". Good luck in the finals.

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