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

Hi Israel,

Very happy to see you back. Even happier that we have no points of disagreement. Having just read your essay I found nothing to disagree with either. In fact, your final argument about the vacuum as 'material substance' is the major physical fact underlying my model. I don't recall this particular argument. Is it new with you? It is very effective.

Your requests are reasonable and I address them here. Recall that I do not claim my Master equation for the evolution of the vacuum 'is' GR or QM but that it 'reduces to' GR and QM in appropriate cases. I have showed that my equation reduces to Einstein's weak field equations in 'Gene Man's World' (on Amazon) and, in abbreviated form, in an earlier FQXi essay. This is done in terms of vector algebra. I'm developing a more generalized derivation using Geometric Algebra. These of course derive only the weak field equations of GR. But Vishwakarma's current essay points out that the stress-energy tensor cannot handle self-gravitation or angular momentum of the gravitational field and has inspired me to investigate a tensor-based derivation of the full field equation.

As for QM, I follow an approach by Sakurai (in 'Modern Quantum Mechanics') to derive Schroedinger's equation from the C-field equation (which is derived from the Master equation). This is presented in my last FQXi essay, 'The Nature of the Wave Function'. It has since been pointed out to me that this is an idealization, treating the C-field as constant, and I have extended this to the case of a variable C-field induced by the particle motion. I've not yet published this generalization.

Since my previous essay I have developed some proficiency using Mathematica. This is reflected in the n-GEM non-linearization technique described in my current essay.

Finally you ask about predictions. I've made a number of predictions in the past, in essays and books, but all of these were based on the assumption of a constant scale factor associated with the C-field, with the value as measured by Martin Tajmar. My n-GEM approach seems to indicate that this is actually a variable factor obtained from the inherent nonlinearity of the field. Therefore I am in the process of reconfirming the results obtained based on the assumption of a constant factor. Additionally, some of my intuitions failed based on the use of the constant, but it looks like they may succeed on the basis of a nonlinear approach. So I'm cautious about predictions until I feel that I fully understand all of the implications of moving from a constant C-field scale factor to a variable strength field. I'm very optimistic about the new approach.

I will make further comments on your essay page.

Thanks again for reading my essay and agreeing with it.

Edwin Eugene Klingman

Hi Edwin,

I really enjoyed reading your essay. It is lucid, well argued and relevant.I thought it was an interesting approach to the question. I liked your introduction referring to the illustration of the two pointing men and how easy it was to just keep reading to the end. Good luck, Georgina

    Jonathan,

    You say "let me speak mathematically", then discuss smooth, topological, and measurable objects and spaces, - and relations between same." I could say "let me speak physically, then discuss smooth, topological, and measurable objects - and relations between same."

    That is my point. Yes "waves and fields require spaces that admit smooth relations", but that's physical reality! And to say it is "a looser condition than topological or measurable" is simply to impose abstractions on physical reality. And you do this with your physically real brain, and, if I'm correct, your consciousness which is integral with physical reality. I have no objection to the creation or derivation of arbitrarily complex mathematical relations from physical reality. Only to the assumption that these have real existence apart from physical reality.

    You note that the unbroken space [or field] has the not-two quality, which is divided when symmetry breaks and more complex forms emerge. This is exactly my point, that all this emerges from an initial unity [or not-two-ness]. Yes, the whole of mathematics emerges as the field evolves. But it emerges from the inherent logic of the physical field, which as far as I can tell, demands self-consistency and forbids contradiction. This alone leads to math. It leads to endless logical physical structures, one of the simplest of which is the counter, which physically implements the Peano axioms, leading to the natural numbers, which Kronecker said leads to all the rest of math.

    Yes, the key is the self-interaction, which, as you note, can lead to a torus [and does so in my theory]. All abstract questions of topology and dimension, and what have you, are consequent creations of mind, not inherent "FORMs" existing in Plato-land.

    The question is, can one start with real objects and actions, and logical combinations thereof and, first, form a language map that accurately reflects the reality that served as the basis for the evolution of the language, and, second, can one use this language to spin tales that are not physically possible, such as, for example, the sun rising and setting at the same time? Math is the evolved language that emerges from a conscious physical world, such that it can map physical reality, and then go beyond physical reality, just as language allows fairy-tales to go beyond historical novels. But the natural language does not exist in another realm. It evolved from physical reality. And so does math, which is just a 'purer, formal' language.

    I think the only point we don't agree on is the supernatural existence of math outside the natural physical realm.

    We seem to agree on everything else.

    Edwin Eugene Klingman

    Edwin,

    Perhaps you haven't noticed my post of 25 June. Though I'm aware that you are having many discussions with other contestants, I do hope that you'll find some time to formulate a reply.

    Regards, Anton

      Hi Anton, I'll study these and reply. Thanks for pointing this out!

      Hello again,

      That should have been Christoph Schiller in the above comment, who also pointed out that a lower or upper bound (depending on how described) exists. But I think Kauffmann's insight that there can be a maximum concentration of energy is the cleanest conceptual formulation, or most useful to Cosmology.

      Have Fun,

      Jonathan

      Thanks for your replies above Ed,

      FYI, professor Vishwakarma is now responding to comments. And in private correspondence, he noted that the current work is indeed an outgrowth of the research in the lecture I attended.

      Please note that I have no wish to debate here further the relative value or Platonism or lack thereof. It it pleasant that we can debate and explore the edges of the subject in an academic way, without locking horns.

      Perhaps, though I took the attitude in my new essay that Math is integral, the same principles apply if it is emergent instead. You noted after reading my draft, that most of my points stood without that connection. Didn't I say the same about your paper above?

      Have Fun,

      Jonathan

        Jonathan,

        If it's emergent, then we agree on almost every thing. And if not, we still agree on almost everything. It's not necessary for friends to agree on everything. It would get boring. So you are right, let's focus on the things we both find exciting, such as Kauffmann's, Schiller's and Vishwakarma's work, and how it relates to ours.

        Best,

        Edwin Eugene Klingman

        Georgina,

        Thanks for reading my essay and for your kind words. I've read yours and will comment on your page. Good luck to you also! Edwin Eugene Klingman

        Dear Eugene,

        Thank you for asking me to give my opinion about your essay. I will do it in the coming days.

        As an invited editor at the journal Neuroquantology I have some interest in this kind of topics although, as many sientists, I do not have a clear opinion about the deep nature of gravity and the information it contains.

        Approaching the subject probably needs quite sophisticated mathematics. I just tried to think about the perception of time

        http://xxx.lanl.gov/abs/quant-ph/0403020

        and found afterwards that the formalism relates to Riemmann hypothesis as well

        http://xxx.lanl.gov/abs/1012.4665

        You received many comments on your essay, and I will try to contribute.

        Best regards,

        Michel

          Dear Michel,

          I am pleased that you found something of interest, and look forward to your comments. I have printed out the two papers you reference and will study them.

          Best regards,

          Edwin Eugene Klingman

          In a conversation with Gerard 't Hooft during FFP10, when I inquired about the calculational mechanism for a computing universe (Planck sized space atoms perhaps?) he said it wasn't necessary, because the laws of nature do the calculating for us. Perhaps by calling them that, any dispute between us is avoided, because the same 'natural law' can have its expression in either Math or Physics - depending on what kind of knowledge we seek, concrete or abstract.

          All the Best,

          Jonathan

          Hi Edwin

          Thanks for your reply. I'm sorry, I misunderstood then. You are talking about the linear approximation of GR. Ok, I'll be looking forward to seeing the results of your nonlinear treatment as well as the predictions. I can see that there is a lot of work to do. Good luck with this.

          You: I don't recall this particular argument. Is it new with you? It is very effective.

          Well, it is not new with me, but it is new in the sense that I invoke it as an argument in my essay. Most physicists are aware of this but it seems that the majority overlook its relevance.

          Best regards

          Israel

          Dear Edwin (or Eugene),

          I have now red your stimulating essay and tried to get some hints on your reasoning, especially about the 'awareness" of gravity, for a possible coupling to my own research. The challenge would be to put mass on diagrams decribing the wholeness of quantum observables (such as the dessins d'enfants created in my essay). May be at a further stage it will be possible to convert the bits attached to the measurement space (there the Riemmann sphere rigidified at three points) into invariants having the meanig of mass. I still don't know.

          Thanks for reading my essay and good luck.

          Michel

            Dr.E.E.Klingman,

            I'm yet a bit slower to enter lately into your marvelous essay. So far I'm yet realize, I think, there is same left and right or mirror image questions to resolve the 'It from bit' or 'bit from it', we have almost similar opinion. In my submitted essay, "It from bit' equally 'bit fro it", is nothing but a same statement written on a mirror and it depends on stands of observer.

            Best wishes

            Dipak Kumar Bhunia

              Dear Michel,

              I have had a chance to review the two papers you referenced. The Riemann paper discusses the details of a specific partition function, which I find interesting as I base the applicability of the Born probability to my wave function model on the partition function. The other paper, on time perception is also interesting. I had not seen the Poincare discussion of the Continuum, and found that fascinating, as well as your connection. I am somewhat confused as to whether you are proposing the phase locking as the 'mechanism' of time perception or of the 'scaling' of time perception? I can understand how this could relate to scaling, but not perception as I understand it.

              Thank you for reading my essay and commenting. I hope it stimulates some ideas for you.

              Best,

              Edwin Eugene Klingman

              Dear Dipak Kumar Bhunia,

              Thank you for your gracious comment. I have read your paper and believe we overlap as follows: you support that nature is not (or cannot be proven to be) analog, and consider observers (us) to be digital: "then nature that perceives through such digits or quantum must appear as a digital." [and] "the digital observers (like us) have a natural limit to detect the nature non-digitally, even if it would be non-digital anywhere in its deeper levels beyond that digital limit. "

              This is a well-thought-out proposition, and the locus of our agreement seems to be here. I tend to believe that the deeper levels are non-digital, but, as you may recall, I view the transfer of information as energy transfer, that does, or does not cross a threshold. This is the digitization you refer to. If the threshold is crossed, then the digit is '1', else '0'. This sets the digital limit of observation. The details of the observed world are so rich that we cannot expect any two essays in this contest to agree upon all of them, but the basic mechanism seems to be in agreement.

              Thanks again for reading and commenting.

              Edwin Eugene Klingman