Nice essay. Great to see Bohm's implicate order mentioned.

Just a little point, on the attribution to Sontag of Time is nature's way of stopping everything happening at once. From John Wheeler's wikipedia page: "Time is nature's way to keep everything from happening all at once. Wheeler quoted this saying in Complexity, Entropy, and the Physics of Information (1990), p. 10, with a footnote attributing it to "graffiti in the men's room of the Pecan Street Cafe, Austin, Texas". Later publications, such as Paul Davies' 1995 book About Time (p. 236), credited Wheeler with variations of this saying, but the quip is actually much older. The earliest known source is Ray Cummings' 1922 science fiction novel The Girl in the Golden Atom, Ch. V: " 'Time,' he said, 'is what keeps everything from happening at once.' " It also appears in his 1929 novel The Man Who Mastered Time. The earliest known occurrence other than Cummings is from 1962 in Film Facts: Volume 5, p. 48".

    Dear Dean Rickles,

    Thank you very much for the comment! And for the information about the quotation about time, I didn't know about this, it's very interesting to see that it goes back to 1922! I'm happy to see that both Cummings' books are freely available online The Girl in the Golden Atom, The Man Who Mastered Time.

    Best regards,

    Cristi

    Hi Cristi,

    Fascinating general essay.I liked your questions about how to unify this gravitation with the geometry and Clifford algebras, like Hestnes you make a beautiful work.The indra net also corrélations are interesting, good luck.Best regards

      Hi Cristi:

      Congratulations. Excellent paper, well-written, concise, and thoughtful. Really enjoyed reading and agree with most of it. I have given you the highest grade it deserves. Below are some of my thoughts on and beyond what you have presented.

      I agree with your statement: "The relativity of fundamentalness implied by different axiomatizations and formulations is just epistemological fundamentalness. ......... Or maybe it is possible that something more fundamental than these exists?" Hence, the fundamental ontological reality must be beyond the selected frame of reference (axiomatizations and formulations) that biases the relative reality or ontology.

      What is fundamental is not a theory but the end state or physical reality it is supposed to depict or predict. A theory should be considered "fundamental" if the end state predicted by it is fundamental. Hence, we must define the most fundamental reality first, which in my view is the absolute Zero Point State (ZPS) that is invariant in space-time i.e. fully dilated with zero space-time. Since, a finite mass has a finite non-zero space-time, mass should also be zero in the ZPS. Such a fundamental state or reality would be immeasurable since it is absolute and not relative. A theory that predicts and bridges this absolute ZPS state with the relative (non-zero mass-energy-space-time) states of the comprehensible universe should be defined as the "Fundamental" theory. Remember, "Fundamental" refers to the predicted end state and not to the theory itself. You rightly state that quantum theories (QFT, EFT) predict arbitrarily large vacuum energy and hence are not fundamental.

      In my paper- "What is Fundamental - Is C the Speed of Light", I propose the missing physics of spontaneous mass-energy conversion (as observed in wave-particle behavior) that bridges the observed relative mass-energy-space-time states to the ZPS while resolving the paradox of the missing dark energy that is revealed as the relativistic kinetic energy, the paradox of the collapse of the wave function that is explained via transition to the classical space-time from the fully dilated space-time when a measurement is made, the black hole singularity of GR eliminated via mass dilation at small R, and solution to other current inconsistencies as well as weirdness of mainstream theories as described in my book.

      It is intriguing that in harmony with your described Indra's net, my model also depicts the universal reality as an ensemble of coexisting, complimentary (to the absolute, fundamental ZPS), parallel relativistic states corresponding to varying germs of mass-energy-space-time states of One Universe.

      I would greatly appreciate your time and feedback on my paper as to which of your criteria it satisfies?

      Thanking you in advance,

      Best Regards

      Avtar Singh

        Thank you Cristi...

        For your gracious attention and detailed thoughtful replies, you have my appreciation. I hope this excellent essay is among those awarded a prize. At this point; it appears certain you will be in the finals. You are more rigorous or thorough than I can be, your points make good sense, and they are well explicated. That would be three thumbs up, if I had an extra thumb.

        All the Best,

        Jonathan

        Hi Avtar,

        Thank you for the comments!

        You said "Hence, the fundamental ontological reality must be beyond the selected frame of reference (axiomatizations and formulations) that biases the relative reality or ontology.". Well said!

        Your other comments contain very interesting ideas as well, which I want to understand more, by reading your essay. Good luck with the contest!

        Best regards,

        Cristi

        Dear Cristinel Stoica, fundamental is what has Foundation. Physical space, which according to Descartes matter is the Foundation for fundamental physical theories. I'm here to urge researchers to develop theory everything of Descartes in the light of modern science. Look at my essay, FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich Where I showed how radically the physics can change if it follows the principle of identity of space and matter of Descartes. Evaluate and leave your comment there. Do not allow New Cartesian Physics go away into nothingness, which wants to be the theory of everything OO.

        Sincerely, Dizhechko Boris Semyonovich.

          Dear Cristi,

          Wow! (or maybe, as Neo would say in "The Matrix", Whoa!) What a densely packed, ambitious essay!

          As always, your present a lot of fascinating topics in interesting and insightful ways. I like how you state right away that it is hard to define "fundamental", and that, anyway, "reality tends to ignore our definitions"...

          Your analysis of the relevance of isomorphism to fundamentality is thought-provoking. By the way, nice illustration of isomorphism with the Sum 15/Tic-Tac-Toe example.

          I like how you frame the astounding weirdness of wavefunction "collapse": "the wavefunction spreads and interferes, but if you catch it, you catch the entire particle, not only that part of its wavefunction you thought was there."

          Nice discussion also of the relativity of fundamentalness, with the example of points vs lines.

          And now, for the main idea: the germ/seed that can unfold into an entire universe, or even a whole set of multiverses... Intriguing! In the same way that a holomorphic function car be recovered just by knowing the derivatives of all orders at a single point, the entire universe could be recovered from knowing everything there is to know at a given point... That's non-locality with a vengeance! :)

          I have to confess that, from the bottom of page 5 to the bottom of page 8, the density, complexity, and unfamiliarity (for me) of many concepts made it hard to follow your argument. I have downloaded your 2017 paper, "The Standard Model Algebra", and will certainly study it to get a better idea... I am fascinated by potential deeper-level explanations of the Standard Model, so I am looking forward to it.

          In your ambitious footnote 8 (on free will), you write:

          "If we want to turn the picture upside-down and consider that our choices also determine the germ, then would it be possible that our local actions determine the germ here, and by this the state of the universe everywhere?"

          I find this intriguing, since it resonates somehow with my ideas about "co-emergence" that I presented in my essay in the last FQXi contest. You also write:

          "Or maybe each agent is free, but if their choices conflict with each other, then the germs of the two agents turn out to unfold in distinct universes, so again their choices don't conflict with each other."

          I also find this interesting, as it reminds me of the Q-Bism like idea that the Universe only makes sense one observer at a time (the theme of Amanda Gefter's fascinating book, "Tresspassing on Einstein's Lawn").

          In closing this already quite long comment(!), I have two questions concerning the last part of your article, "Indra's net" (lovely analogy, by the way!).

          1) You say that the information about the whole universe could be encoded at each point, in higher derivatives of the field at that point. By information, do you mean the laws, or the initial conditions as well? Or is it that the initial conditions are irrelevant because you are thinking of the whole universe as infinite, so every possible initial "local" condition happens infinitely often, so everything averages out to zero information overall in initial conditions?

          2) You say there is no need for a mechanism to unfold the state of the universe out of the germ, since the germ already contains everything that happens in the universe... Is it a similar claim than when someone who believes that the universe is a simulation says that there is no need for an actual computer to run the simulation, since the "consequences" of the simulation exist whether or not it is run?

          Congratulations once again for a strong entry. I am glad your essay is doing so well in the community vote, and I wish you good luck in the "finals"!

          Marc

            Hi Steve,

            Thank you very much! yes, Clifford algebras deserve more attention! Maybe next time you will join us with an essay.

            Best regards,

            Cristi

            Dear Dizhechko Boris Semyonovich,

            Thank you for the comments, this is very interesting.

            Best regards,

            Cristi

            Cristi,

            Three generations are ensured by topological combinatorics. {I was glad when the 4th-gen theorists were excluded years ago.} I tried to illustrate this with a trecoil band in three 'flavor' states. Of course it is massive (knew that back in 1992 when I first published the idea) and oscillates, too! A massive oscillating neutrino is VERY fundamental in the model constructed.

            Wayne

            Dear Marc,

            I appreciate very much your comments. Very insightful observations!

            Now your questions.

            > 1) You say that the information about the whole universe could be encoded at each point, in higher derivatives of the field at that point. By information, do you mean the laws, or the initial conditions as well? Or is it that the initial conditions are irrelevant because you are thinking of the whole universe as infinite, so every possible initial "local" condition happens infinitely often, so everything averages out to zero information overall in initial conditions?

            I expect the laws to be encoded in some generalization of the Cauchy-Riemann equations, and the particular solution (hence including the initial conditions) in the germ. This if the analogy with complex holomorphic functions will be proved to hold for the unified theory.

            > 2) You say there is no need for a mechanism to unfold the state of the universe out of the germ, since the germ already contains everything that happens in the universe... Is it a similar claim than when someone who believes that the universe is a simulation says that there is no need for an actual computer to run the simulation, since the "consequences" of the simulation exist whether or not it is run?

            I think there is a similarity between the two. Or rather with the block world view which contains the time flow in the frozen 4D universe. But I think there is also a major difference. I think that there is one thing, which we unfold when analyzing it say in terms of axioms and proofs, or initial conditions and time evolution, or program and simulation. The unfolding exists because we analyze this whole in a dichotomic way. This is what I mean by the relativity of fundamentalness, that there is something, which I could describe as the equivalence class of various isomorphic description, or more, as the mathematical structure underlying the description (you know the description is limited by the limits of provability and computability, but the mathematical structure itself, which we try to describe, is not. However, even the mathematical structure is in fact an equivalence class of more isomorphic structures). But who are "we"? We are just part of the whole too, so the whole is an implicate order, and at once it is numerous explicate orders which are perceived as such by the relative perspective encoded in each of the possible explications. So I think this goes way beyond having the output of a program encoded in the code in a file whether we run it or not, and doesn't require computability as in the case of simulations (which require computability even if we don't need to run them, that's why Tegmark asks these structures to be computable). Now the question is of course why do I claim I get rid of this requirement? Well, because I talk about automorphisms of the whole. Think for example at a vector space, and two distinct frames. Computation is involved only when we try to translate from one frame to another. Otherwise both frames simply see the same order in different perspectives, there is no need of computation if we don't compare them.

            Best regards,

            Cristi

            You are welcome,

            Yes perhaps I will do the next essay contest.At this moment I have serious problems in belgium and my mind is weak,best regards and good luck for this cntest, you merit a prize.Always relevant to read your works and ideas .Take care.

            • [deleted]

            Cristinel,

            It is a very ambitious essay, but I would like to offer a few counter arguments in defense of space.

            It is the nature of thought to distill signal from the noise, but might something be left out that is important, but not obvious? For instance, math overlooked zero for a long time, as it seemed to serve no function, so is physics possibly doing something similar with space?

            Supposedly space arises from geometry, but could it be in fact that geometry is mapping properties of space?

            For instance, the dimensionless point is the essential geometric concept, yet it is explicitly a multiple of zero, being dimensionless and consequently, mathematically doesn't exist. Would a dimensionless apple have any existence? Yet insisting on some minuscule dimensionality would make it a fuzzy concept, so it seems to be more intellectually pretty to make it a tiny bit mathematically contradictory, than to make it fuzzy.

            Yet what is being zeroed out, with no dimensionality, but space? What is a dimensionless point in the first place, if not an ideal of location? Which is spatial subjectivity.

            Consider that three dimensions are really just the xyz coordinate system, which is located by the 0,0,0 center point. As a subjective location, couldn't more than one center point exist in the same space? Much as billions of people, the originators of this system, are all the center points of their own space, but exist in the same space as all others. (Think how much political conflict is about applying different coordinate systems to the same space.)

            How about longitude, latitude and altitude? Are they really a perfect foundational framework for the surface of this planet, or just a very useful mapping device?

            Often it is assumed math exists as some platonic realm of order, but if it isn't and all order arose with the physical reality it describes and defines, would it be any different? If not, then wouldn't it be against Occam's razor to assume it does pre-exist the manifestation? Does the void need mathematical order, lacking any structure?

            So if we are looking for what's fundamental, wouldn't space be worth considering?

            Just a thought, but remember zero is between 1 and -1.

            Regards,

            John B Merryman

              John,

              Thank you for the comments!

              > "I would like to offer a few counter arguments in defense of space."

              I don't deny space, but I am interested in your arguments anyway.

              > "is physics possibly [overlooking] space?"

              I am not aware of physics overlooking space. I am aware of theories which claim that space is emergent, but for the moment I don't have any reason to endorse this position (and no definite reasons to refute it).

              > "Supposedly space arises from geometry, but could it be in fact that geometry is mapping properties of space?"

              Here I take the position of mathematicians, that geometry is space, or at least that it is about space.

              > "For instance, the dimensionless point is the essential geometric concept, yet it is explicitly a multiple of zero, being dimensionless and consequently, mathematically doesn't exist."

              I think that statements like "dimensionless point [...] is explicitly a multiple of zero" and that from this follows that it doesn't exist mathematically are uncommon among mathematicians. Mathematicians tend to believe that if something is a multiple of zero, then it is zero, and that zero (and its multiples) exist mathematically. Maybe you want to say that the measure of a point is zero, but even this is not true for all measures. And even if it is true, it doesn't follow from this that the point doesn't exist mathematically. This would mean that no region of space can exist, being collections of points. Or it would mean at most that all subsets of space are empty sets.

              > "Would a dimensionless apple have any existence?"

              You are mixing apples and oranges. First you talked about mathematical existence, then you illustrate that it doesn't make sense by giving as example dimensionless apples. In mathematics you can only talk about things you defined, or at least you defined them implicitly by axioms. Explicit definitions are of the form "genus-differentia", or by construction. Implicit definitions are based only on properties, on relations between things. For example, Modern formulations Euclidean geometry define points and lines by their relations (although Euclidus said things like "A point is that which has no part"). The question is, how do you define a "dimensionless apple"? It seems that the genus is "apple", and the differentia is "dimensionless". But the "differentia" reffers to how you distinguish an object from a particular genus, from the others from the same genus. The "differentia" has to be a property that some of the objects of the genus have. If none of them has that "differentia", the set of objects satisfying your definition is empty. So it doesn't make sense. It is as if you define "strictly positive negative numbers", there is no such thing. Then you say you proved a contradiction, but your proof is based on nonexisting (logically inconsistent) concepts.

              > "Consider that three dimensions are really just the xyz coordinate system, which is located by the 0,0,0 center point. As a subjective location, couldn't more than one center point exist in the same space? Much as billions of people, the originators of this system, are all the center points of their own space, but exist in the same space as all others. "

              Right, I agree. "Think how much political conflict is about applying different coordinate systems to the same space" this is true :)))

              > "How about longitude, latitude and altitude? Are they really a perfect foundational framework for the surface of this planet, or just a very useful mapping device?"

              They are a mapping device. Here's how mathematicians think about differentiable manifolds. They define them using charts. Charts are mappings of pieces of the manifold on some n-dimensional space R^n. These mappings are one-to-one between a region of the manifold and an open subset of R^n. The first rule is that the manifold is covered by these charts. The second rule is that on a region covered by two charts, the composition of one of them with the inverse of the other (which is therefore a mapping of an open region in R^n to another open region of R^n) are differentiable. We call such a collection of charts an atlas of our manifold. Then, we add all such charts which satisfy the rules to the atlas, and the result is called a complete atlas. Now, think at a region of the manifold, and all the charts on that region. Mathematicians say these charts are just mappings, we used them to define the manifold, but we don't take them as the region of the manifold. They consider as "real" what is invariant, so charts are just perspectives, not reality. What is real is the result. The composed charts which give a mapping between open sets of R^n are called transition functions, and they allow us to change the perspective. And they define isomorphisms between those open regions of R^n. So what is real to mathematician is the equivalence class defined by these isomorphisms. Mathematicians use charts to define the manifold, then they throw away the charts as being just some props to obtain the definition. They continue to use the charts for example to make calculations, they translate the properties of the manifold into statements about R^n, hence about numbers.

              So we see that the mathematicians agree that the charts are just mapping devices, but they disagree that the resulting manifold is a mapping device. An applied mathematician may use such a manifold to model some phenomena from another are of knowledge, and in this case the manifold is a tool too. But to geometers who don't apply geometry to something else, the manifold is not a tool, it is the ultimate object of their interest. So while even the hardcore mathematical Platonists will agree with you that charts are mapping devices, they would say that the manifold itself is real. They wouldn't say that they can prove it to you, but also you can't disprove them. So they are free to consider it real, and you are free to not consider it real.

              > "Often it is assumed math exists as some platonic realm of order, but if it isn't and all order arose with the physical reality it describes and defines, would it be any different? If not, then wouldn't it be against Occam's razor to assume it does pre-exist the manifestation? Does the void need mathematical order, lacking any structure?"

              Ockham's razor has two edges. The side you pick is that there is a physical reality, and there is a mathematical description of it. And if somebody believes both to be real, he has to explain a lot of things. Like why the behave the same, and then if they do the same things, why maintaining that the mathematical description is real and not a mere mapping device. (the same problem face Cartesian dualists with the mind-body problem) So you say let's use Ockham's razor to cut and separate the physical reality from the mathematical description, then discard the mathematical description as being something more than a mapping device. Someone who considers that the mathematical description is in fact the reality will agree with you to cut them exactly in the same place with Ockham's razor. The only difference is that she will discard the "physical reality". Your choice is motivated by your experience that physical reality is always there, while mathematics is in books. And you don't have to explain why the mathematics describing the physical world is isomorphic to the physical world, it is so by design, duh! But the "platonist" (this is not in fact what platonist means, but let's use it this way) would say that we have to objects doing the same thing, the physical reality and the mathematical structure. She knows very well what is a mathematical structure, but she doesn't know a definition of physical reality. So why not discarding physical reality and keeping the mathematical structure? Now the physical realist may say "but it is obvious that there is a physical world, here it is, I can experience it, I can taste an apple, qed". The mathematical realist may say "we only know about physical reality by our interactions, so what we know are not the physical objects as things-in-themselves, but our relations with them. So all there is experienced is relation. And a mathematical structure is nothing more than a collection of relations (see Universal algebra). We can't probe anything beyond the relations, hence the world is a mathematical structure. One may say though that we can keep as real the physical world and discard the mathematical structure as being a mere representation. But this is not a representation as the usual mathematical models. If you want to makea mathematical model of an apple, you will have to do a lot of complicate mathematics, and the result will be approximate. But a mathematical description of the physical laws makes our knowledge redundant. All phenomena are contained in the principles. Hence, the mathematical formulation of principles is not a mere model, because it is much more compact than the thing it models. This is why I choose to discard anything outside that mathematical structure." She may believe or not that the other mathematical structures exist physically too, but if we apply again Ockham's razor to keep the simplest option, which one you think is the simplest, the principle "all mathematical structures have physical existence", or "only the mathematical structure defined by [insert the mathematical formulation of the final theory of physics] has physical existence"?

              > "So if we are looking for what's fundamental, wouldn't space be worth considering?"

              Sure, and this is what I do (more precisely spacetime). If you look at my research papers you will see that they are about spacetime. Understanding singularities in general relativity, researching the possibility to make collapse consistent with the symmetries of spacetime, these were my main themes, and the other ones where I published less are also about spacetime. Yes, I know I said everything, including spacetime, is contained in the germ. So is this denying spacetime? I would say not. Holomorphic functions don't deny the domain on which they are defined. The domain is encoded in the germ at any of its points, but this doesn't mean that that domain doesn't exist. It only means that one of them is as real as the other.

              > "Just a thought, but remember zero is between 1 and -1"

              I can't. Zero is between -1 and 1.

              Best regards,

              Cristi

              Dear Cristi,

              You have written a very attractive introduction to your research while highlighting its solid connections to the contest topic.

              A few specific comments:

              1. I really enjoyed the playful example at the beginning. While the importance of isomorphisms between seemingly different structures is well recognized by physicists, mathematicians, and philosophers of physics, I believe there is still plenty of room for it to be recognized by people in general, and your example nicely serves that end.

              2. Although I had heard of Klein's Erlangen programme, I did not really know what it was about. Knowing that it was based on the recognition of the importance of invariants has caused me to revise one of my beliefs, namely that the general recognition of their importance occurred largely as a result of their importance in relativity (Evidently, Klein anticipated Einstein in this regard by over 30 years). So your essay did change at least one belief, ha!

              3. It is interesting to consider whether the notion of fundamentality is purely epistemological or can also be framed ontologically. While I perceive it as a former, I am open to arguments that it can be the latter as well. However, here is a challenge for any ontological fundamentalist: At bottom we might consider the fundamental difference in physics to be between being and non-being. Which is more fundamental? It seems to me, either answer one chooses is open to a counterargument: If one chooses being, then it could be argued that being can be reframed in terms of the absence of non-being, and if one chooses non-being, then it could be argued that it can be reframed in terms of the absence of being. My point is that either choice seems to me to represent a particular worldview, or paradigm, and that makes it inextricably epistemological.

              4. The phrase at the end of page 6 "Also they [the GUTs] didn't explain why these particular representations out of infinitely many possible for each group", resonates with me especially. So much of contemporary high-energy theory seems to me like a sophisticated game of pattern-fitting without trying to understand what the patterns really represent. I am often reminded of Feynman's example of the ancient Mayans, who had a sophisticated framework for predicting eclipses and the positions of Venus, but not even a basic concept of planets and the solar system. To me, that is not a secondary but a primary problem with many contemporary approaches to understand nature more deeply. I laud your efforts to try to look behind formalisms and patterns to understand the "why".

              5. I admit that I did not follow the math in the latter part of your paper but I would like to raise at least one potential concern: It seems to me not sufficiently broadly appreciated that at different scales, the ratios of different powers of the scale changes, and when considered together with any kind of density, this results in different physical behavior at different scales. In short, to paraphrase Philip Anderson, in my view, bigger is different. Would your Indra's net model be able to account for that?

              All in all, a very attractive essay.

                Cristi,

                "This would mean that no region of space can exist, being collections of points."

                This illustrates my point, in that if all those points have no dimensionality, i.e. some modicum of space in the first place, then they are all multiples of zero.

                "Ockham's razor has two edges."

                If I may describe my own view of physical reality, it is a dichotomy of energy and form(information). Energy necessarily manifests all form, or it would collapse into a black hole and form is the definition of all energy. For example, waves are defined by their frequency and amplitude. Try to imagine one otherwise.

                Now I see a good proof of this dichotomy is that after a few billion years of evolution, we developed a central nervous system to process information and digestive, respiratory and circulatory systems to process energy.

                Consider the properties of both. Energy is dynamic and conserved. This means it is always and only present, but necessarily constantly changing configurations, some at faster rates than other changes.

                Form, on the other hand, is stable. If it is unstable, it loses its form. The constituent energy breaks apart, drains away, etc.

                So energy goes from prior to succeeding forms, while the forms coalesce and dissolve. The result is the effect of time. As fairly stable entities, whose consciousness functions as flashes of cognitive forms, we proceed from past forms (and units of time), to future ones, yet these forms go the other direction, future to past. Tomorrow becomes yesterday.

                Think in terms of a factory; The product goes start to finish, being in the future to being in the past. While the production line points the other direction, consuming material and expelling product. Prior to succeeding.

                Life is similar. The individual goes from birth to death, being in the future to being in the past, while the species goes the other direction, onto new generations, shedding old. As our consciousness moves from prior to succeeding thoughts.

                So I would argue time is not an underlaying dimension, measured as duration, but an effect of this activity, much like temperature. Time is the individual frequency, while temperature is masses of frequencies and amplitudes.

                Duration is the state of the present, as events coalesce and dissolve.

                Different clocks can run at different rates because they are separate actions. All being equal, a faster clock uses more energy, like metabolism.

                Time is asymmetric because it is a measure of action and action is inertial. The earth turns one direction, not both.

                The simultaneity of the present was dismissed by arguing different events would be observed in different order from different locations, but this is no more consequential than seeing the moon as it was a moment ago, simultaneous with seeing stars as they were years ago. It is the energy that is conserved, not the information carried by it. That the energy manifesting an event is radiated away is both why we observe it and why it no longer exists.

                So this distinguishes between space and time. We could use ideal gas laws to correlate measures of temperature and volume, but temperature is only foundational to our emotions, bodily functions and environment, not our thought process, so we can presume to be more objective about it.

                Given our nervous system is designed to process the information our environment provides, we do like to study it in detail and math is the most distilled and stable expression of form, but without the energy to manifest it, form does go to zero.

                So, yes, Occam's razor does have two edges and it does cut both ways.

                I would note Edwin Klingman, among others, is also disputing the blocktime aspect of spacetime.

                One more thought, events have to occur, in order to calculate the total input, consequentially the future is not pre-determined, as that would require information traveling faster than the energy carrying it.

                Regards,

                John

                Hello Cristi,

                Much appreciate the number scrabble. We have a 5yo great-grandson in the care of his great-grandmother, who loves games and puzzles, will be delighted with this.

                Glad to see so much interest in Clifford algebras in this year's competition, and particularly the geometric interpretation. Much agree with your statement

                "If there are fundamental geometric structures in physics, we expect them to bring not only a unification of the formalism, but also of principles and of

                entities like particles and fields. If we expect that the holomorphic fundamentalness plays a role in physics, probably the way is by geometric algebras."

                If one takes the vacuum wavefunction to be comprised of the fundamental geometric structures of 3D Pauli algebra - one scalar, three vectors, three bivectors, and one trivector - then wavefunction interactions can be modeled by the geometric product.

                This yields a 4D Dirac algebra of flat Minkowski spacetime, an 8x8 matrix that is the geometric structure of the S-matrix. Time emerges from the interactions in the form of relative phases of the interacting geometric structures that comprise the wavefunctions. It is encoded in the 4D pseudoscalars. Seems like there is no need for complex numbers in this Hestenes formulation of STA. Would much appreciate your opinion on this.

                It seems there is much commonality between what you are doing and the approach Michaele and I have been taking with geometric wavefunctions. What you call Indra's net can be thought analogous to the quantized electromagnetic impedance networks that couple fundamental geometric structures in our model. We are working with Cl(1,3), tho the manner in which we assign quantized EM fields to the 8 component Pauli wavefunction seems to require three or four copies. Our group theory grasp is minimal. Have more questions, would much appreciate some help if you're interested.

                and your hexagrams have me reaching for the I Ching.

                Best regards,

                Peter

                  Dear Cristi,

                  You get off to a great start showing the isomorphism between 'number scrabble' and 'tic-tac-toe'. You note that "in mathematics, isomorphism's are ubiquitous", mentioning that Euclidian geometry ~ axiomatics ~ symmetries ~ numbers/equations, for example.

                  This supports very nicely my thesis that physicists project mathematical structure onto physical reality, and then come to believe that physical reality has that structure. While it is relatively simple for competent mathematicians to 'switch' from one formulation to another isomorphic formulation, the physicist who "freezes" the projected mathematical structure onto physical reality has a tendency to "see" reality is having that structure.

                  For example, spins tend to align in fields such that statistically they are aligned or anti-aligned with each other in neighborhood/domains. Based on an over-simplistic interpretation of Stern-Gerlach data, Pauli projected a 'qubit' structure, O|+> = +|+>, O|-> = -|-> onto spin, despite that the SG data is distributed almost exactly as predicted by calculations of 3D spin traversing an inhomogeneous magnetic field. Based on Pauli's 'qubit'-based Hamiltonian, Bell 'believed' the qubit to be real and thus required qubit results: A = +/-1, B = +/-1 rather than variable deflection as seen in the data. The variable data satisfies Bell's relation which he claims is impossible to satisfy.

                  In a comment above you state: "Because Bell's theorem is a theorem. Trying to refute it is like trying to find in Euclidean geometry a right triangle which violates Pythagoras's theorem. It is simply impossible." Of course Bell's theorem is a foregone conclusion, from his first equation, in which he forces the only allowed data to be +1 or -1. No physics involved in this, simply an initial condition that is 'projected' onto the reality of spin.

                  Thus Bell's 'belief' in Pauli's mathematical projection, causes him to reject 3D spin, which does satisfy ABcos(A,B), and to claim this impossible, leading to "entanglement" as a new mystery, on which thousands of papers can be written. This is compounded by "proofs" of Bell's theorem being conducted with valid two-state experiments, where the states are detection or not of photons.

                  Finally, as Bell was forcing 'qubits' on spin, Feynman, who was in love with the two-slit photon experiments, realized that he could apply Pauli's 'qubit wave function' for spin in a manner analogous to the two-slit experiments and he applied this to SG, thus projecting "superposition" on the spin. Although Feynman's gedanken experiments have never been tested, several QM texts now begin with Feynman's two-slit-spin analogy. Thus Feynman and Bell forced a 'mystical' view on spin and Aspect "confirmed" it with photon analogs.

                  Once these giants froze the qubit projection onto reality, your isomorphisms go to hell. Isomorphisms are formalisms, qubit spin is (believed to be) physical reality! To seriously question this "reality" can be dangerous to one's career.

                  I discuss qubits because the genealogy is so clear cut. I could've discussed iso-spin, in which Heisenberg replaced two real fundamental particles with an imagined particle with 'qubit-like' projections onto reality, etc.

                  In my essay I treat another projection onto reality. Einstein, while basing his treatment on Hertz, projected a 4D-coordinate system with a new universal time dimension onto each moving object. The addition of new time dimensions (the physical 'reality' corresponding to the math structure) of course demolished time as universal symmetry and replaced it with "the relativity of simultaneity". This 'freezing' of the 4D-projection on the moving objects has lasted 100 years, despite the fact that the 'energy-time' conjugation in one inertial frame is isomorphic to Einstein's 'space-time symmetry' in two inertial frames, and agrees with all relativistic particle physics data.

                  In similar fashion, one can derive Bekenstein's "holographic principle" in terms of energy alone, without ever conceiving of information. But the 'information' projection is now 'believed' by physicists, and the door is closed to isomorphisms.

                  In summary, as long as the isomorphisms are mathematical, they are easily seen to morph into one another. But as soon as a mathematical structure is projected onto physical reality, it becomes "frozen" in the mind of the (consensus) physicist, and the fact that other isomorphic interpretations (such as 'classical' versus 'quantum') are equally possible or dismissed or rejected with almost religious fervor.

                  You wrote on Jan. 27, 2018 @ 11:32 GMT, that while it is natural to question non-intuitive physics, one has to move on in his career. Nevertheless, you say:

                  "But I still think it is necessary to start by questioning everything, and you should never stop."

                  I believe that if one projection that leads to non-intuitive 'nonsense' can be replaced by another isomorphism that is compatible with the real data, and yet makes intuitive sense, this change of isomorphisms should be made.

                  So thank you, Cristi, for focusing on 'isomorphism' and 'fundamentality' as you have done. Your essay is well written and enlightening. Of course I agree with your proposition that geometric algebra is the tool we should be using. I hope you will read my essay in terms of the above isomorphism's, and I hope you enjoy it.

                  My best regards,

                  Edwin Eugene Klingman

                    John,

                    Let's take them one by one. You said "the dimensionless point is the essential geometric concept, yet it is explicitly a multiple of zero, being dimensionless and consequently, mathematically doesn't exist"

                    Please start by proving your statement that dimensionless points are multiples of zero. Zero is a number, a multiple of zero means zero times another number, and this is zero. And you equate the number zero with a point, which doesn't seem to be a number.

                    Then, assuming that you will be able to prove the previous statement, prove that if something is zero, then "mathematically doesn't exist". Do you mean zero doesn't exist mathematically?

                    Here is what I mean by "proof".

                    Best regards,

                    Cristi