I think that there is a complete analogy between gravitational field and electromagnetic field, because of the gravitoelectromagnetism formulation, that it is deeper for me because of:

[math]

R_{\mu \nu}-\frac{1}{2} g_{\mu \nu} R = -\frac{8 \pi k}{c^4} T_{\mu \nu}

[/math]

so that, when I read your essay some weeks ago, I saw a possible gravity inertia application; that I had forgotten to consider, because of I had not taken notes because I read dozens of essay at a time (each essay is worth reading)..

I prefer not to comment on the essays, because they affect the votes, but in any case I would have informed you after the vote; I break the rule just because I consider polite to reply to my posts.

I am thinking that if it is true that the dimension of the space is constrained by an interaction, then there is a problem with elementary particles like quark, or electron, that don't give the right dimension (following your demonstration); so that the solution is that the elementary particles must have a real probability distribution, a quantum diffusion in the space, that constrains the space dimension: an interaction between the parts of the single elementary particle

Greetings Tyranno,

I certainly agree with the 3 dimensions of reality and arrive there from a different direction. A totally worthwhile essay, thank you.

Sherman Jenkins

    Dear Neil,

    I appreciate the depth of your essay and its level; to my mind, it is among the top ones here. Although I disagree with some of your points, I give your essay very high rating. Your conclusions that

    "math cannot either describe what "concreteness" is, nor which if any model worlds should be manifested as "actual worlds." It cannot explain why any such transcendently "more real" world should be mathematically elegant or "simple," instead of messy and not effectively accessible through math"

    are extremely important and correct. However, physics is more than math, and its success with elegant mathematics tells something very important about the universe. I am inviting you to read our essay where we refute Tegmark's MUH on the ground of fundamental physics.

      Dear Alexey/Lev,

      Thank you. I read your essay at your request and was very impressed at the writing as well as the 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 the fine-tuning we observe 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.

      Dear Akinbo,

      First of all, I'm sorry for the delay in answering your question or in looking at your essay or commenting there (indeed, in general to everyone - I have been too busy.) The electron: no, I'm not suggesting a difference between its inertia and other effective definitions of "mass" such as energy equivalent, basis for deBroglie matter wavelength, etc. However, it has long been controversial as to how MUCH of the electron's mass-inertia is electromagnetic in origin (see for example Feynman's wonderful discussion in V. II of his Lectures). Much of this is due to issues of QED, but there has still long been a problem in general: the direct interactions, even for extended charge distributions, give the wrong answer ("4/3 problem") unless there is some correction due to stress.

      That correction has been somewhat controversial because of arguments over von Laue's "energy current" (as per attempted solutions of the paradox of the right-angle lever, etc.) In any case, we make the problem simpler by consider only the CHANGE in EM inertia due to changes in charge configuration. Then we don't have to wonder, how much of the total is from EMI to start with.

      In my essay, I explain how to derive that correction properly, and in a space of any number of dimensions. This only gives the correct answer (correct EM inertia) for three macro dimensions.

      Dear Neil,

      I found your essay quite interesting, so I added it to the list of quality essays in my review. Unfortunately I did not have the time to analyze in details your arguments about dimensions. But I found that we completely agree on the metaphysics which you expressed in your last 2 pages. I expressed the same idea in very short on the bottom of page 2 of my own essay. I also explained there how quantum physics is naturally interpreted in this way.

        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 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]

          • Post #51

          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