Edwin, very nice essay. I think we are in solid agreement on the approach to physics - one grounded in the idea that there is something real, an "It", from which we derive information, "Bit".

You do a good job of exploring why we believe a theory is good. The graphic of the n-parameter elephant, combined with the Jaynes quote in your conclusion "the proper question is not "How well do data D support hypothesis?" [but] "Are there alternatives which data D would support relative to H, and how much support is possible?" puts its all together. Just because one hypothesis yields a nice elephant does not mean it is correct, and we always need to explore other hypotheses which might draw better elephants.

In my essay, I put forward an argument for an interpretation of quantum theory which associates wavefunctions with experiments, not things. By rejecting assertions that QM is a theory of things, thus is not a physical theory, we are free to pursue theories that are physical. We can now explore what sort of physical things and physical theories might then explain the predictions made by the predictions of QM - other hypotheses which might fit the data. After reading your essay, and re-reading your essay of last time, I understand that you seek a locally realistic theory underlying QM, as I do.

Your proposal is that we begin with a single field ("But rather than postulate hundreds of fields as Susskind does for his Multiverse, we can assume that only one real field existed initially.") and I agree this is an excellent beginning. I am a little unsure whether you a proposing that we now have multiple fields, and I am a little unsure where particles fit in your scheme. Here we may diverge somewhat, as I would suggest exploring the hypothesis that the one real field is what existed initially and is still all there is, thus no particles (in the sense of Democritus or Newton) and no other fields (except perhaps as components of one field). Certainly, as you argue in your last essay on the nature of the wavefunction, we must also distinguish between the real field and our probabilistic estimates of what we might expect should we perform experiments on the real field.

You took some pains to distinguish between the field and geometry in your essay, but I think that if you adopt the idea that there is only one real field, then the distinction between the field and geometry is not problematic: the geometry and the field are equivalent. As you quote from MTW, "any physical theory originally written in a special coordinates system can be recast in geometric, coordinate free language." We encounter many more problems if we try to describe geometry as multiple fields and particles.

I think your final discussion regarding awareness and the consciousness field is daring, in that it may venture a little beyond the conventional realm of physics, but you argue very logically and come to a sound conclusion. You make a sensible assertion that, for example, there is a sense in which we can say gravity is "aware" and proceed very carefully from there. If you assume there is only one real field the argument is even simpler: if there is only one field, then you (or anyone else) are a manifestation of that field, and combined with the apparent evidence that you are aware, you are quite logically led to a conclusion that the field is in some way aware. As I said, this is logical but also daring.

Nice job on the essay. Thanks for recommending that others read mine. I think that it fits very nicely with yours, and discussing how ideas can be fit together - arranging the jigsaw puzzle of ideas - is the most valuable part of this contest.

Regards, Mark

    Mark,

    Thanks for reading my essays and commenting. Just as I managed to pick out the key point of your essay, that "an observable is a name for a type of experiment, not a property of some physical thing", you have discerned the key point that data fitting should discriminate between theories.

    We both prefer to start with a real field. In my essay the field can produce a self-interacting vortex which shrinks to a finite soliton-like toroidal particle, which is simply a very stable "concentration of field". So it is still field, but probably is more localized than your view of the field, although this local 'particle' has sufficient mass density to produce a secondary disturbance or circulation that corresponds to de Broglie's 'pilot wave' (but not an exact correspondence). Since the local energy is stable, particles endure, but sufficiently high-energy collisions produce new vortices which yield particle jets spitting out new particles. The process is too complex for a comment, but I hope you get the idea. The process also leads to integral charge, including quark charges, and quark confinement also falls out of the single field.

    I am certainly not opposed to geometry, but was addressing what I see as a problematic view: that physics is "nothing but" geometry. That seems to abstract away physical reality, replacing it with math.

    I am extremely pleased that you see the logic in my hypothesis. It is logical and seems to match my experience, so I put it forth at the risk all 'daring ideas' run. As I am independent and cannot be fired, I can afford to pursue probable truth.

    Mark you have a real ability to cut through the fog. I hope you continue to produce works the quality of your current essay!

    With my best regards,

    Edwin Eugene Klingman

    Hi Anton,

    As I noted in my comment on your blog, we agree on a number of points, and I'm confused on different points. I still fail to see that a BBU exists "inside" anything any more than an SCU does. In fact I see the BBU as a self-creating entity, and, I see it as conserving momentum and energy. So either we have different definitions or I am missing some fine point.

    I also find it reasonable, in fact preferable, to interpret c is a property of the material that fills, and essentially defines, space-time.

    Your description of virtual particles is excellent. In fact, as I noted in my essay, data fitting should be used to discriminate between theories. As most of QED is based on virtual particles, then that means my theory would have to fit the data as well as or better than the virtual particles to be taken seriously (unless it had other extreme advantages...).

    I'm certain that I do not understand some of your points, for example that "in an SCU it is not the same time everywhere."

    You mentioned that in a BBU particles keep existing even when isolated from interactions ... and so can't have awareness. But in my view the particles are stable concentrations of the field, which has the awareness, and so are unseparated from this (infinitesimal level of) awareness.

    Again, you mentioned that "everything is inside of an SCU" while I see a BBU the same way. I do not believe in a multiverse where multiple BBU's exist. Perhaps that is what you attribute to me that would constitute the difference in BBU and SCU. In that sense the "eternal inflation" of the multiverse picture would seem to describe a (system of) self-creating universe(s). In any case, there is some distinction here that I am missing which keeps me from understanding the fine points of your argument.

    You clearly have a theory with details worked out that fit together in your mind, and I do also. There's enough confusion between us that may be partly based in terminology and partly based on incompatibility of ideas. That leads to a situation where "data fitting" comes to the forefront, and for this reason I'm focusing my efforts on quantitative results as my qualitative aspects seem to work well. From what I can determine your qualitative aspects work well also.

    You misconstrued "we don't have access to reality". I am quoting others. I do believe there is a reality, and I listed number of ways in which I do have direct access to it in my closing paragraph. But we again are out of sync in terms of definition, as I do not see reality as something we could step outside of.

    I will have to give more thought to your comments and your essay to try to discern where this confusion arises, aside from different definitions.

    Thank you for the detailed comparison of our ideas and the effort you put into the comments.

    Best regards,

    Edwin Eugene Klingman

    Dear Edwin,

    I have down loaded your essay and soon post my comments on it. Mean while, please, go through my essay and post your comments.

    Regards and good luck in the contest.

    Sreenath BN.

    http://fqxi.org/community/forum/topic/1827

    Hi Edwin,

    A Big Bang Universe (BBU) is not a self-creating entity. This is extremely hard to explain and comprehend, yet crucial if we are to comprehend quantum mechanics (which to me seems a prerequisite to develop quantum gravity), to understand our universe. Though like you ''I do not see reality as something we could step outside of'', we actually do so in Big Bang Cosmology (BBC) as the entire 'theory' is drafted from an imaginary observation post outside of it. The psychological barrier we have to overcome seems to be that even the hard core atheists among us, tend to think about ourselves as having an absolute existence, transcending the universe, as if there's Someone outside of it with respect to which we exist, Who is witness to our existence, a habit from times when we believed to be at the center of God's attention, the idea which caused Galilei so much trouble when he questioned it.

    If there would be only a single charged particle in the entire universe, then it wouldn't be able to express its charge in interactions. Since it in that case it cannot be charged itself, charge, or any property, for that matter, must be something which is shared by particles, something which only exists, is expressed and preserved within their interactions: the 'its' indeed are as much the cause as the effect of the (exchange of) bits so you cannot have one without the other.

    Similarly, in the seemingly innocent assumption that we can regard the universe as an ordinary object which has particular properties as a whole, which change IN time, we actually assume there's something outside of it it interacts with, owes its properties to, and, implicitly, that it has been created by something outside of it. This is why I say that a BBU lives in a time (and space) realm not of its own making, that it is not a self-creating (or self-contained) entity. BBC, in looking at the universe like we may imagine God to look at His creation, in fact paints a religious picture of the universe. Evidently, this attitude can be justified only if and when the inside objects only are the cause of interactions, not when we have to concede that particles they are built out of, ultimately must be as much the cause as the effect of their interactions. Indeed, the fact that the meter, second, gram and joule are not defined outside the universe already takes any significance out of any statement about the universe BBC cares to make. If it does not make any sense to speak about its properties as 'seen' from without, then we also cannot speak about its properties, as a whole, as seen from within. This is what I mean when I say that, unlike a BBU, a Self-Creating Universe (SCU) does not live in a time realm not of its own making. While a BBU is thought to be quite homogenous and isotropic, about the same everywhere (but not at all times: a BBC obeys the Cosmological Principle (CP)), as if it 'contains' a single, unique reality, in a SCU where we can only make statements from within, any observer, no matter when he lives and where he looks from, sees objects in all possible phases of their evolution, and, unlike in a BBU, not as they were in ''the'' past. Though a SCU obeys the Perfect Cosmological Principle (PCP), it shouldn't be confused with Hoyle's Steady State Universe as this suffers the same conceptual flaw as a BBU, as it is thought about from an imaginary observation post outside of it. Indeed, if to avoid having an outside Creator, we must discard causality, and hence the concept of cosmic time, then we can no longer determine what in an absolute sense precedes what and say that the emission of a photon by A causally precedes its absorption by B. In a SCU an observer doesn't see a distant galaxy as it was in a distant past but as it is at present to him.

    In the 'virtual particle' description in my previous post I proposed that the energy a particle has according to a nearby observer contains contributions from all particles within its interaction horizon. While in a BBU it is the same cosmic time everywhere (ignoring the effect of gravitational fields on clock paces) so a photon has to travel at finite velocity so its contribution to the energy of the observed particle originate in a distant past, in a SCU they contribute in real time to its energy, no matter their spacetime distance to the particle. If you agree that particles only exist to each other if and for as long as they interact, exchange energy (so they in some sense can be said to exist 'out of each other') and have no physical reality to an observer who doesn't physically interact with them, who finds himself outside their interaction horizon, their universe, then in this sense to him everything inside of it cancels, is unobservable so he cannot make any statement about that universe. So my objection to BBC isn't just that as we cannot step outside of it to actually observe what happens inside of it, we cannot say anything about it; it is because in a universe which obeys the law which says that what comes out of nothing must add to nothing, everything inside of it must cancel so there's nothing 'left' for an imaginary outside observer to observe, unlike a BBU where the observer would find things to look at.

    To be continued in the next post

    Though at macroscopic scale a property of an object indeed is what the dictionary says it is, something it privately owns, only the cause of its interactions, independent from interactions, here the observer doesn't affect the observed in a perceptible manner. If, as classical mechanics, big bang cosmology and general relativity assumes that the properties of objects are eternally unchangeable, they obviously can, in principle, be observed without being affected by the observation, so in this, outdated, view, there indeed exists an objectively observable reality at the origin of our observations: as Einstein said: ''We all, more or less in the same way, say that a rose is red, smells like perfume, and feels like velvet. In other words, there is an objective reality which is conceived by the senses, and behind this objective reality are natural laws which are the privilege of the scientist to discover.'' However, things are entirely different at quantum level: if particles are both cause and effect of their interactions so the particles of the rose and those of the observer contribute to each other's energy, each other's properties, then he cannot observe the rose as it is since without his own existence it wouldn't be the exact same rose. Though as a rose is a macroscopic object, the effect of the observer on the rose is negligible, at quantum level an observing particle does affect the observed particle to the extent they are 'made out of each other', exchange energy. Einstein continues: ''Nature doesn't know chance, it operates on mathematical principles. As I have said so many times, God doesn't play dice with the world.'' Though despite this statement, he said that he didn't believe in God, in insisting on causality, on determinism (which made him reject quantum mechanics), he actually did, the result of which is that general relativity in its adaptation to big bang cosmology became corrupted.

    I am well aware that what I propose constitutes a completely different paradigm so cannot be understood very well in the terms of the present one: ''To adopt a new theory or paradigm means to accept a completely novel conceptual scheme that has so little in common with that of the older; now rejected, theory that the two theories are "incommensurable," for no objective yardstick exists that makes it possible to compare them. Furthermore, as the meaning of every scientific term in a given theory depends upon the theoretical context in which it occurs, even the individual scientific terms of the new theory are incommensurable with the terms of the old one, despite the fact that the same terminology is often retained.'' (''Concepts of Mass in Physics and Philosophy'' M. Jammer, p 57)

    Regards, Anton

    Eckhard Blumschein, on his thread, asked me questions that are relevant here, so I repeat portions of my answer below. I made the decision to write an extremely high level overview of my theory in 9 pages, guaranteeing that those unfamiliar with it will find it confusing, or at least incomplete. The list of references are intended to "fill in the holes". But of course many will not have time or interest to explore these. I am, in effect, drawing a high level map of my theory and staking a few claims.

    You ask how gravity relates to information. My theory of gravity produces particles, the particles create structures, and local energy transfers cross thresholds, restructuring or "in-form"-ing the structure, and creating and storing information. There exists a long chain of details stretching from the gravity field to the information stored in the local structure. I merely sketch the chain.

    The scenes from the Chinese tapestries simply illustrate that humans have always been presented with contradictory information since antiquity. The contradictory information referred to here is "it from bit" versus "bit from it". An 'artistic' illustration, nothing more.

    I do agree with most of Schlafly's essay, but I think the best essay in the contest currently is Mark Feeley's.

    My master equation for self-evolution of the universe yields solutions G = 1/r, C = 1/t. And it leads to a Newton-like equation suggesting G = gravity. If my G is multiplied by c-squared, it assumes the dimensions of acceleration, as required for Newtons gravity. The C solution already has the dimension (1/t) of Maxwell's and Einstein's gravito-magnetic field (the gravitational analog of the magnetic field).

    So, from the simplest and most universal equation I can imagine, I obtain solutions that are easily interpreted as the two aspects of gravity, just as E and B are two aspects of the electromagnetic field. The G field is radial and relates to local mass, whereas the C field is induced by mass density in motion, i.e., momentum density. Therefore the picture relates to moving mass such as relativistic particles, as the problems I am interested in are dominated by C so I ignore G for simplicity.

    As for your astute question about the possibility that my asymmetric time can be considered 'now', that is how I interpret it, however the inverse time refers to local 'frequency' associated with the de Broglie-like wave function induced by particle momentum.

    Best regards,

    Edwin Eugene Klingman

    Edwin, make no mistake, I meant "logical and daring" as a high compliment. Logical is fairly easy, and daring is even easier, but it is often very hard to combine them. Keep it up. Mark

    Dear

    Thank you for presenting your nice essay. I saw the abstract and will post my comments soon.

    So you can produce material from your thinking. . . .

    I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on experimental results.

    I failed mainly because I worked against the main stream. The main stream community people want magic from science instead of realty especially in the subject of cosmology. We all know well that cosmology is a subject where speculations rule.

    Hope to get your comments even directly to my mail ID also. . . .

    Best

    =snp

    snp.gupta@gmail.com

    http://vaksdynamicuniversemodel.blogspot.com/

    Pdf download:

    http://fqxi.org/community/forum/topic/essay-download/1607/__details/Gupta_Vak_FQXi_TABLE_REF_Fi.pdf

    Part of abstract:

    - -Material objects are more fundamental- - is being proposed in this paper; It is well known that there is no mental experiment, which produced material. . . Similarly creation of matter from empty space as required in Steady State theory or in Bigbang is another such problem in the Cosmological counterpart. . . . In this paper we will see about CMB, how it is generated from stars and Galaxies around us. And here we show that NO Microwave background radiation was detected till now after excluding radiation from Stars and Galaxies. . . .

    Some complements from FQXi community. . . . .

    A

    Anton Lorenz Vrba wrote on May. 4, 2013 @ 13:43 GMT

    ....... I do love your last two sentences - that is why I am coming back.

    Author Satyavarapu Naga Parameswara Gupta replied on May. 6, 2013 @ 09:24 GMT

    . . . . We should use our minds to down to earth realistic thinking. There is no point in wasting our brains in total imagination which are never realities. It is something like showing, mixing of cartoon characters with normal people in movies or people entering into Game-space in virtual reality games or Firing antimatter into a black hole!!!. It is sheer a madness of such concepts going on in many fields like science, mathematics, computer IT etc. . . .

    B.

    Francis V wrote on May. 11, 2013 @ 02:05 GMT

    Well-presented argument about the absence of any explosion for a relic frequency to occur and the detail on collection of temperature data......

    C

    Robert Bennett wrote on May. 14, 2013 @ 18:26 GMT

    "Material objects are more fundamental"..... in other words "IT from Bit" is true.

    Author Satyavarapu Naga Parameswara Gupta replied on May. 14, 2013 @ 22:53 GMT

    1. It is well known that there is no mental experiment, which produced material.

    2. John Wheeler did not produce material from information.

    3. Information describes material properties. But a mere description of material properties does not produce material.

    4. There are Gods, Wizards, and Magicians, allegedly produced material from nowhere. But will that be a scientific experiment?

    D

    Hoang cao Hai wrote on Jun. 16, 2013 @ 16:22 GMT

    It from bit - where are bit come from?

    Author Satyavarapu Naga Parameswara Gupta replied on Jun. 17, 2013 @ 06:10 GMT

    ....And your question is like asking, -- which is first? Egg or Hen?-- in other words Matter is first or Information is first? Is that so? In reality there is no way that Matter comes from information.

    Matter is another form of Energy. Matter cannot be created from nothing. Any type of vacuum cannot produce matter. Matter is another form of energy. Energy is having many forms: Mechanical, Electrical, Heat, Magnetic and so on..

    E

    Antony Ryan wrote on Jun. 23, 2013 @ 22:08 GMT

    .....Either way your abstract argument based empirical evidence is strong given that "a mere description of material properties does not produce material". While of course materials do give information.

    I think you deserve a place in the final based on this alone. Concise - simple - but undeniable.

    Hello Ed,

    I greatly enjoyed reading your paper. It was well-reasoned and you make a great case for your main point. I find a lot to agree with, but as you know I find the Platonic view appealing. Why can't we all just get along?

    It is my opinion that your main point is well supported by the logic and evidence you cite, and that your Plato bashing is a side trip - wholly unnecessary to your point or its establishment. So I'll treat that separately later, once my own essay has posted.

    All in all, yours is an excellent paper. I got mine in early on the final day, so I imagine it will appear by Tuesday or Wednesday, but that my paper is one of many in a queue.

    All the Best,

    Jonathan

      On Platonism,

      It's interesting Ed; I think our stance on the archetypal aspect of Math has a lot to say about the way we got to our present view. What kept me in the Physics game for many years was my investigation of the Mandelbrot Set and how the progression of form at the periphery relates to Cosmology.

      So I've spent a lot of time wondering about why a purely mathematical object might influence or shape the evolution of the Cosmos - because I already had the absolute conviction that such a connection exists. I was scheduled to give a talk on this at FFP12, but never made it to Udine - and it has sat on my shelf.

      But I am not ready to totally give up on the MUH or other types of mathematical Platonism, as that is what brought me to the table, or is the horse I rode in on. Who knows? I might need a way to get home. And I'll say more when my essay posts. In the meanwhile; I think I see a way our ideas can coexist.

      Regards,

      Jonathan

      Hello again,

      I wanted to comment that I especially liked your comments on linearizing equations. My take is that it is not so much a trick of abstract geometry, nor a matter of conflating a mathematical reality with the physical, as it is a tendency to ignore the fact a simplifying assumption was made.

      It is common, for example, to replace Cos (theta) with 1 for a small angular displacement. But this breaks down, once there is more than a tiny excursion. As you point out; the behavior of the system is not linearized at all, but the key point is that the assumption that allows linearization of a non-linear equation has a limited range of applicability.

      Regards,

      Jonathan

        Jonathan,

        I'm glad that you enjoyed the paper, and feel bad that you think I bashed Plato too hard. I have another friend who likes the physical aspects of my theory but wishes I had left out any mention of 'awareness'. He feels like you that it is "wholly unnecessary to your point or its establishment".

        Of course I point out that one can omit the 'awareness' aspect and the physics still holds. But then one must explain awareness, which no one has done (satisfactorily). You are probably correct that I could omit any mention of Plato and the physics of my model would still hold. But the essay is not just about my model of physics, but about the main question of whether physical reality is fundamental, and it seems to me that if one believes that math lives, and particularly in Tegmark's MUH, then one can believe somehow that 'information' is real, and 'It from Bit' is possible, which I decidedly do not. So at the very least my whole argument is weakened, and much of the rational for assuming only 'ONE' field disappears. If there are TWO fundamentals there may as well be Susskind's hundreds of fields.

        So I'm not so sure that it is wholly unnecessary to my point. As you know, we both agree on very many things, and I have expressed my surprise that you are so in tune with Eastern process thinking and Taoism, yet do not seem to accept the 'Not-two' basis of reality. Yet you and I actually do get along rather well.

        I am sure that you came to Platonism through a path that was meaningful to you, such as the Mandelbrot Set. But it is incompatible with the way I make sense of things, which is outlined (far too briefly) in my essay. So I particularly look forward to hearing your idea about how our ideas can coexist.

        Best wishes and I look forward to reading your paper.

        Best Regards,

        Edwin Eugene Klingman

        Jonathan,

        Thanks for commenting on my point about linearization. I agree about "a tendency to ignore the fact a simplifying assumption was made." Your example of cos(theta) = 1 as an approximation that works in a limited range is appropriate. I am suggesting that it is misleading to assume that there is even a limited range where a non-linear field behaves linearly. There are only ranges where the available energy is exhausted before non-linear effects become dominant. The effect may look 'linear', but the mechanism is never so.

        By the way, I have you to thank for my development of my n-GEM non-linearization scheme, as it was Kauffmann's paper which you brought to our attention that made me realize that gravity can dominate other forces. Then the East and Pretorius paper in Phys Rev Letters the next week sealed the deal!

        Thus I'm pleased to point out to you the existence of a current essay that I believe is very significant, and supports my C-field theory.

        However, I just looked at Professor Vishwakarma's page and see that you have already discovered it! It's hard to keep ahead of you, Jonathan. I agree with you that "The ideas presented in this essay are indeed worthy of note." I have read it twice and his arXiv paper, and find it very exciting. In case you haven't realized it, the 'angular momentum of the gravitational field' that he speaks of is just the C-field! And I have, in previous essays, proposed this model, and the associated energy of the field, as the source of dark matter, dark energy, and the WMAP anisotropy, as he seems to be doing. My non-linearization supports these claims even more strongly, as does his paper. I am trying to relate my model to the Kasner solution and finding interesting results. So if you feel his essay is worth a high score, I hope you don't decide to punish me for 'Plato-bashing'!

        These FQXi essays are more valuable than most seem to believe. Every year very significant ideas are published here.

        Thanks again for the comments,

        Edwin Eugene Klingman

        Thanks, Edwin. It's a delightful essay full of pearls of wisdom, seemingly simple concepts but steeped in meaning and nuance. I'm impressed.

        Perhaps in my simple way I touch upon some of your concepts, probably because you open so many boxes.

        Jim

          Jim,

          Thank you. I appreciate your comments at face value, but after reading your essay I treasure your comment. You've obviously put much thought into the topic at hand with emphasis on the role of consciousness and its nature. I enjoyed your entire essay. Your discussion of the number of neurons (100 billion) and connections (1000 trillion) "channeling countless sub-atomic particles in a consciously assembled reality" was excellent! As was collapsing the electron into one state when observed, versus all states when not observed! And the "unimaginable assemblage of trillions upon trillions of ... particles from the superposition state" into a cat! In short, you put the "It from Bit" picture into clear perspective. It helps to bring all scales into view, as opposed to focusing on one particle.

          Your summary of various current beliefs about consciousness was masterful. As was your discussion of the Anthropic era. Although your previous essays have focused on gravity and the flow of time and space, this topic seems to tie it all together for you. You succeed in shining a light on some of the fuzzy thinking that resulted in It from Bit. This is not your first essay, but it is your best. Both your writing style and content are superb.

          Thanks again for reading my essay and commenting so graciously.

          Edwin Eugene Klingman

          Hi Edwin

          It's nice to read you again. You did such an excellent job that I'm afraid I have no points of disagreement. I'm interested in your work because I think we have many points of common, specially, we are suggesting simplicity in theories.

          I only have a request. In your work you claim that GR (and perhaps QM) can be derived from your formulation. Of course, the space in this essay is so short that one cannot put all the information. So I'd be glad, if it's not much to ask, if you could show me the derivation of Einstein's equations (and QM if you have it) according to your formulation. Do you have any publication about the derivation?

          As well, I wonder if your approach make some new predictions. do you have any comments?

          You also say: Gravity is a field, not abstract geometry.

          I definitely agree. I'd like to invite you to read my essay and leave some comments. There I discuss about Wheeler's dream and propose a potential way to get out of the present crisis assuming also that space is not geometry.

          I'll be looking forward to hearing any comments you may have.

          Regards

          Israel

            Let me answer mathematically.

            One can speak of smooth, topological, and measurable objects and spaces - and relations between same. Waves and fields require spaces that admit smooth relations, and this is considered a looser condition than topological or measurable, which are respectively more strictly defined. I first saw this hierarchy spelled out in a 2000 paper by Connes, but I understand it forms the basis for differential geometry and topology.

            However; this all comes into play more or less automatically, when considering how some of the very simplest forms arise. An unbroken space possesses the quality of oneness, or not-two, but the presence of an observer (of whatever form) induces a sense of toward and away from some center. But consider a loop in the C-field and the induced geometry - as it is analogous. A circle is a topological object, having an inside and outside, and a 1-dimensional face, but the space is no longer unbroken - oneness is now divided.

            Somehow; even though you have but one field, the whole of Mathematics comes into play as it evolves and complex form emerges.

            More later,

            Jonathan

            Ah so My Friend,

            I had the pleasure to share a meal with and hear a lecture from Ram Gopal Vishwakarma a few years back, when in Port Angeles for CCC-2. As I recall; he was a student and later colleague of Narlikar, and presented a cyclical universe model at that conference. I think that work may have been related to his essay offering, focusing on one of the solutions mentioned.

            And I am very happy to have inspired you by promoting Kauffmann's paper on an upper bound for concentrations of energy. It is interesting that the point of how energy and even gravity are self gravitating is missed. But the subtle point that this leads to an upper bound for energy concentrations is all too easy to miss entirely, so we owe bold thinkers like Steven Kenneth Kauffmann, Christoph, and Gibbons a vote of thanks.

            All the Best,

            Jonathan

            Let me expound further here;

            You speak of one thing acting upon itself, and it is notable that the one free standing form which can arise and propagate in a single medium (physical systems in nature) is the torus, as is the case with smoke rings. Now of course; the loop or circle constructed above is actually a special case of a torus. If, as in String Theory, we consider the curved field line to be a flux tube - this analogy is made explicit.

            But the question of the dimensionality of the space inhabited by such a loop is not a trivial one. I am coming to favor a bi-metric view of the early universe, where one must keep track of both an upper bound and a lower bound upon the array of dimensions that has evolved at a particular stage of the universe's evolution. If the space in which we reside has a non-trivial topology, at this point, that has some interesting consequences we have discussed elsewhere, but its relevance rests upon the very nature of topology.

            So the question of whether such Maths are pre-existing is moot.

            Regards,

            Jonathan