Dear Neil,

Thanks for your good words and interesting remarks to our essay. I am glad to see that we agree on most important points, and there is a good potential for a productive discussion in many others. In particular, I wish to discuss your 3D arguments, but this requires different format. You can easily find my address; if you like, you may send me an email and we'll find a better way to discuss that. Meanwhile, please do not miss out on rating our essay :)

Cheers,

Alexey.

Dear Sylvain,

Thank you for noting my essay at your review site. This gem is among your top four picks:

"Genesis of a Pythagorean Universe," by Alexey and Lev Burov.

I consider this essay one of the best as well, as you might gather from my reply to their comment here. You group them in the Idealism/Dualism sector, where I put myself too. But I make clear, that stance is in terms of ultimate considerations.Operationally, I accept the practical and apparent reduction of most processes to objectively discernible laws, etc. I would compare the attitude to that of Penrose, whom the Burovs clearly admire as much as I do.

My argument about 3-D draws on contexts that just aren't part of most physics these days, because of concentration on particles, quantum and GR theory etc. Most physicists are out of touch with the relativistic dynamics of extended bodies and this sort of foundational reasoning by analogy. Yet it's straightforward application of SRT and the principles of retarded field projection. I hope that when readers have more time to work through it, the demonstration will become clear.

I'll take a look at your essay. I sometimes mull over them awhile before commenting but at least that means I didn't just skim and throw something out there without thinking much. Cheers.

PS: reminder to everyone to check if you are really still logged in and if you pick the link for the thread you want to reply to.

Well, to add more about the 3-D argument since I really shouldn't imply it's just about applying retardation of fields: a key element is the stress adjustment, which has been controversial. Few people think about it other than those with a specific interest, and it's mostly taken for granted as something in the background. IOW, few people think about the workings of it in a way that would allow insight into the generalization of that correction to n dimensions. So, the implications of it for comparative physics is neglected.

Neil,

You are not alone. Of the 34 ratings, at least 6 (I haven't kept track throughout) are a rating of 1 w/o comments

Jim

Neil,

I am revisiting essays I have read to make sure I rated them. I found that I rated your on the day of my comments 4/13/2015.

I would like to see your thoughts on mine. Mine, I must admit, is not as open-minded as yours: http://fqxi.org/community/forum/topic/2345

Thanks,

Jim

    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.