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Essay Abstract

This is my vision of the relationship between mathematics and physics based on my observations on the nature of physical laws and mathematical structures. I use mainstream ideas from quantum gravity such as string theory, holography, the landscape and loop quantum gravity as a base for my reasoning. In addition I bring together more speculative ideas such as the Mathematical Universe Hypothesis, multiple quantisation, universality, iterated integration maps and complete symmetry. In my view these clues come together into a consistent whole where a structure from higher category theory is the central piece from which all else stems. The future of fundamental physics is going to be much more challenging than the past on both the experimental and theoretical sides and these meta-physical structures need to be understood to guide us towards the more specific physical laws which rule our universe. On a more philosophical level they can provide an explanation for why we exist and why the laws of physics are so steeped in mathematical abstraction.

Author Bio

I hold a PhD in theoretical physics from the University of Glasgow. I have also published a number of papers on fundamental physics as an independent researcher. In addition I love problem solving in mathematics and have made modest contributions including progress on a problem in number theory proposed by Diophantus himself and recently a new improved solution to Lebesgue's universal covering problem. The philosophical links between physics and mathematics are something that I have given much thought to over many years.

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It is good to be back for another FQXi contest and the topic this time is something that has long been of interest to me. I know there are going to be some diverse views here many of which will be strongly opposed to mine. I look forward to your criticisms and questions. I expect to defend my own view which is quite mainstream in some ways and radical in others, but hopefully some comments will also make me think in new ways. If I argue against the points you make it does not mean I do not apreciate what you said.

I am also planning to read as many of the essays as I can. I will rate them too but not so much on the basis of whether I agree with them or not. What I am looking for are points that are original, relevant, well-argued and that make me think of things I have not come across before. One thing I want to avoid doing is to drop hints to say how I rated an essay and I prefer that nobody gives me any hints about how they rated mine. I prefer to have an open and honest discussion without worrying about how it will affect my score. If it means I lose out I am not concerned. The rating and prize aspect is fun but it is not the most important thing. I think the opportunity to argue and exchange thoughts is much more valuable.

Good luck to all

Michael Rios replied on Feb. 28, 2015 @ 10:24 GMT

Philip

A very nice essay on cutting edge topics that reflect the current unreasonable effectiveness of mathematics in physics. The hidden structure behind the amplituhedron, sporadic groups, noncommutative geometry and M-theory is rapidly being revealed. I gave an overview in my essay, through the lens of motives.

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Philip,

This is an excellent read. Many thanks for sharing your thoughts. For whatever it is worth to you, I agree completely that Geometric Algebra must play an important role in the nature of reality. It is very humbling to realize that not only do we not know the answers, but we do not even know how to go about asking the right questions. Yet somehow we manage to learn and to leave whatever new truths that we discover to the next generation.

Also, allow me to thank you for the website viXra.org. Without something like it, the amateurs, dilettantes, and ... ahem ... others, would be homeless.

Best Regards,

Gary Simpson

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Author Philip Gibbs replied on Jan. 11, 2015 @ 18:37 GMT

Gary, thanks for your comments. I agree that knowing how to ask the questions is an important goal. Until we know that we are all just stabbing in the dark, but if we keep trying one of us may hit something.

Member Matthew Saul Leifer replied on Mar. 26, 2015 @ 22:53 GMT

Allow me to just point out that Geometric Algebra \neq Algebraic Geometry. I got confused about that at one point when I was a Ph.D. student and started learning some Geometric Algebra when what I really needed was Algebraic Geometry. Still, it was a very interesting diversion to see the mathematics of spinors presented in terms of GA.

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Author Philip Gibbs replied on Mar. 27, 2015 @ 12:04 GMT

Yes, good point

Philip,

You have an amazing ability to "defuse" situations. Ideas that I tend to reject rather strongly when described by others seem much more reasonable when you discuss them. That is a real talent, in my opinion. I also like that, when discussing some of the farther out ideas you note that "we should not get carried away by thinking they are less speculative or more testable than they...

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Philip,

You have an amazing ability to "defuse" situations. Ideas that I tend to reject rather strongly when described by others seem much more reasonable when you discuss them. That is a real talent, in my opinion. I also like that, when discussing some of the farther out ideas you note that "we should not get carried away by thinking they are less speculative or more testable than they really are."

You have a most impressive grasp of the modern range of math and physics, and seem very comfortable moving over this range. Thank you for doing so in your excellent essay.

Your metaphor of chess playing aliens is a very clever way of contrasting 'invent' versus 'discover' math. And you seem to have split the baby when you caution not to worry about 'exist' [Tegmark's MUH] and then describe the 'ontology' in the next paragraph. You certainly have an impressive graphical representation of a metaphorical chart of mathematical ontology. It is quite a universe, isn't it?

I also appreciated your discussion of symmetry, generally conceived as the key principle that determines laws of physics. As I doubt this, I was happy to learn that "there is a growing movement... that thinks symmetry is not so fundamental." I tend to agree with you that "the fundamental principle that determines the laws of physics is universality, not symmetry." I have significant problems with the Holographic Principle, or more specifically with the "black hole information loss puzzle", but your analysis in terms of symmetry in terms of one degree of symmetry for every field variable is interesting.

If I understand you correctly I agree that "the structure that emerges from universality is also a mathematical structure in its own right." And that it is self-referential and recursive. And I need to reflect more on your idea of recursively iterating quantization. Finally you note that Tegmark's mathematical universe hypothesis tells us that all logical possibilities are equal. This seems to imply that there is more than one completely self consistent logical possibility [for the universe]. I doubt this.

In other words, as we've come to expect from you, a first-class essay! I invite you to read and comment on my essay.

Finally, having last year posted three papers on viXra, I wish to join many others in thanking you for creating that system.

My best regards,

Edwin Eugene Klingman

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Eugene, thanks for going through my essay in such detail.

It is certainly the case that symmetry is being dissed from all sides at the moment. The importance of symmetry was drummed into me as part of my education and I have taken it too much for granted, so I am pleased that there is now some opposition to the idea. As well as the reference to string theorists in my essay you can find this in John Horgan's latest interview with Lee Smolin http://blogs.scientificamerican.com/cross-check/2015/01/04/t
roublemaker-lee-smolin-questions-if-physics-laws-are-timeles
s/

This forces me to question why I think symmetry is so important. Of course symmetry has been central to 20th century physics and is supported by experiment but that does not necessarily mean that there is more of it to be found. My main remaining justification is the argument I gave about holography, so if you have a different solution to the information loss puzzle I cannot hope to persuade you. Well we have to explore all the possibilities and each physicist will take one route, so this is good.

When I talk about different logical possibilities I think that different solutions to the laws of physics from different starting conditions are different logical pssibilities. I also think that your experience of this universe is a different logical possibility from my experience. I think that different laws of physics are no different from these different solutions. They are all different solutions of some higher meta-laws. Of course this is just one point of view.

I will be reading your essay soon

Author Philip Gibbs replied on Jan. 11, 2015 @ 12:30 GMT

I think this idea of different possibilities/solutions is the key element in the new paradigm shift. In the past people thought there would be one nice quantum field theory that would tell us everything about particle physics and GR and all the parameters of physics could be derived from first principles, then these laws would have different solutions depending on different initial conditions, perhaps there would even be just one unique possibility for the initial conditions.

Now the view has changed so that the laws of physics are not thought ot be so fixed. For string theorists there is M-theory from which all other string theories can be derived as solutions with different vacua, then our universe is also just a solution which has this vacuum state. Lee Smolin also thinks this way when he talks about cosmic evolution. I take this further because I think that even M-theory is just one solution in a more general system of meta-laws which I imagine might be something like a free weak omega category. This is just an algebraic structure, perhaps the most general possible algebraic structure so that all other algebras are images of this structure under homomorhisms. This is how "solutions" are realised. To make this idea work you need to be able to project those algebraic structures onto geometry which is where the maths of algebraic geomerty come in to play. The pay-off for this way of thinking is that if all logical possibilities are included in the laws of physics then you dont need a magic spell to decide what the laws of physics become reality.

I noted your comment to Klingman’s essay. Those are the two popular views of math and physics.

For me the math and physics emerge together and are the same physical reality. Therefore, properties of math can be used to suggest the physics of reality. The difficult things of math can also imply things that don’t exist in physical reality such as mapping math and infinity. So the quantum math (not real) of Bell is incorrect which is shown by the de Broglie-Bohm interpretation that suggests the ``hidden variables’’. There are few papers written on this, I am aware of only one that takes this issue head-on that references earlier work that have been ignored. Klingman’s paper uses this to highlight how this works.

For me the prime thing to understand is the double--slit experiment with the Afshar’s experiments of which--way and single photon interference. This experiment is the key to understanding the world of the small. That was the subject of my previous paper on photon interference and current effort on the single photon interference. Newtonian mechanics must apply to create the wave (Bohm’s weakness) and direct the particle.

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Author Philip Gibbs replied on Jan. 13, 2015 @ 22:04 GMT

John thanks for reading my essay. I am still looking at yours.

I an sure there will be many other ways of thinking about what came first in this contest besides the three you have highlighted here. My view is in sync with that of Max Tegmark who proposed that the existence of mathematics came first. I just see that as a tautological statement that there are logical possibilities for our world or experience and that these can be explored and understood using mathematics. The main idea I add is that of universality, i.e. that the uppermost meta-laws of physics come about because of a principle of universality or self-organisation within the "Ultimate Ensemble" as Tegmark calls it. Our universe is just one solution of these meta-laws which are much more general. (By the way I first wrote about these ideas in 1996 before I had read Tegmark's paper which appeared in 1997. the first piece I wrote about it can be found at http://www.karlin.mff.cuni.cz/~motl/Gibbs/tot.htm)

However, if I was cornered I would admit that the difference between starting with maths, physics or both together could just be a matter of philosophical interpretation. I just find it nicer to start from the mathematical possibilities because it leaves me with a sense that the existence of physical reality and the laws of physics are derived without a requirement for any unexplained process of design or arbitrary principle.

What really matters is how we can use these meta-physical ideas to say something about what the laws of physics are like. For you this involves an analysis of the two slit experiment and for me it is about the structure of physical law in terms of multiple quantisation, complete symmetry, algebraic geometry and the emergence of space, time, causality and the universe as we know it.

Hi Philip,

You essay was interesting. You do point out the apparent direction of physics that research usually pushes us into new areas of mathematics. Some eagerly embrace this and others have to be dragged kicking and screaming into it.

I do think there are possible trends into different mathematics. I would have to say that this is probably in the direction of category theory, motives and “magma,” and with that into HOTT, or HOmotopic Type Theory. This approach would reduce the salient mathematically based observables into topological invariants. The two slit experiment is a form of homotopy, and this further is expressable as a logic switching theory.

I don’t know if I will write an essay for this iteration. I do have a couple of ideas, but the whole business seems rather futile to me right now.

Cheers LC

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Author Philip Gibbs replied on Jan. 16, 2015 @ 12:06 GMT

Lawrence, its good to see you are looking at the essays. I hope you will decide to write one too.

I think the idea of something like a magma as a starting point is very powerful. A magma is just a very general algebra with a binary operation, by imposing other conditions you get loops, semi-groups, groups etc. I see this as a model for what I referred to as the "cascade of solutions" in my...

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Lawrence, its good to see you are looking at the essays. I hope you will decide to write one too.

I think the idea of something like a magma as a starting point is very powerful. A magma is just a very general algebra with a binary operation, by imposing other conditions you get loops, semi-groups, groups etc. I see this as a model for what I referred to as the "cascade of solutions" in my essay. You start with something like a free magma, each time you impose new conditions you are defining a homomorphism onto a more restricted structure such as a free group. Further homomorphisms give you specific groups. You can get any group this way, or any algebra if you start from something sufficiently general like an n-category.

Since I noticed that a free lie-algebra has a structure like discrete closed and open strings that can be mapped to string states in continuous spaces using iterated integrations I have been keen on this as a way to see things. Ultimately the cascade leads to something like M-theory from which known string theories can be derived by compactification. What is compactification? It is just a process of identifying points on a manifold so it is a continuation of the algebraic process of setting identities to map a free algebra to more specific examples by taking it modulo some expressions, i.e. by mapping with a homomorphism. So starting with a general algebraic structure you can see how it could lead to a specific universe through a cascade of "solutions" which are just homomorphisms. In a category the homomorphisms are already built in as morphisms so a very large general category or n-category is a natural multiverse of related universes. That is how I see it at least.

I have tried to limit the amount of mathematics in my essay because I want to reach a wide audiance and in past essays the mathematical details have not hit home. With so many essays to get through people want an easy read. Your essays have always been heavy on the maths so that may limit their appeal, although you have still done well.

I have lost interest in the prizes especially since you now need a second prize to get membership, but the essays and discussions have always helped me map out my ideas a little further each time so I keep doing them.

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Lawrence B Crowell replied on Jan. 16, 2015 @ 18:51 GMT

It would be interesting to see the foundations of mathematics necessary for physics reduced to groups, groupoids, monoids and categories such as motives in a Grothendiecke type of system. I have I think found a possible route towards this using discrete systems.

There are various entanglement schemes, and the GHZ entanglement is 1/8 supersymmetric. There are bipartite and tripartite...

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It would be interesting to see the foundations of mathematics necessary for physics reduced to groups, groupoids, monoids and categories such as motives in a Grothendiecke type of system. I have I think found a possible route towards this using discrete systems.

There are various entanglement schemes, and the GHZ entanglement is 1/8 supersymmetric. There are bipartite and tripartite entanglements that are ½ and ¼ supersymmetric. This means that on BPS black holes these entanglements of states associated with the BPS charges have this number of supersymmetric generators that are unbroken. The algebraic geometry of these entanglements involves a quotient homology of projective varieties. These are systems between the Hilbert space and a projective Hilbert space with the geometric phase as the fibration. This system is categorically the same as a quotient homology on the moduli space for quaternionic bundles, such as with SO(4), or SO(3,1) in the hyperbolic case. The isometries for the this system is SO(4,2) and the moduli is AdS_5 ~ SO(4,2)/SO(4,1).

The two quotient systems are given by discrete groups. In the case of the AdS_5 the quotients are Kleinian groups, which are quotients with a discrete group, such as an elementary Z_n ~ Z/nZ, or a more complex polytope group. For the case of projective varieties on the Hilbert space these are a system of discrete orbits that have a discrete geometric phase ~ e^{nEt}. The two orbit spaces are I think categorically equivalent.

The various quotient groups correspond to cobordants of one dimension lower.

For instance, with AdS_5 there is a boundary spacetime, and for the quotient group on the moduli AdS_5 defines two boundaries with different spacetimes that may have different topologies. The equivalency between quantum projective varieties and the Kleinian orbit space of different spacetime topologies connects topology changes with different quantum states or sets of quantum states.

I think these correspondence goes beyond one particular type of entanglement. There is a whole algebraic category of entanglements by Micheal Duff and his research partners. This algebraic system of entanglements is connected to this structure of quotient homologies and algebraic varieties. The categorical equivalency with the AdS_5 is a surprising aspect that I have suspect exists with respect to the mathematics of four manifolds as found by Atiyah, Donaldson, Freed, Singer, Uhlenbeck and others. The moduli space when reduced to a finite group is equivalent to the orbit spaces of quantum states with a discrete structure. This structure is given by the Kirwan polyhedra of holomorphic coadjoint orbits. This is categorically equivalent to the quotient of the moduli space or AdS_5 with a discrete or Kleinian group.

The theory does of course connect with Raamsdonk’s observation that entanglement can be converted to geometric content. In particular the entanglement of a quantum system with states associated with gravitation is equivalent to the entanglement of that system with the stretched horizon of a black hole or similar system. The “large N limit” means the set of states entangled with the gravitational system become entangled with a system that has a coarse grained structure, such as how an event horizon has lots of Planck area units that states can be shuffled around in.

By doing this I think we can reduce physics to certain topological invariants, and all of physics can be reduced to a homotopy theory of logic gates. I expect in time to see physics rely upon mathematics that is less motivated by concerns with infinite and infinitesimal elements or sets, and more motivated by discrete structures. For now the more traditional geometric interpretation of things is a necessary aspect to how these are derived, but in time these things may be of less importance.

LC

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Donald G Palmer replied on Mar. 11, 2015 @ 04:16 GMT

Thank you for an interesting essay, Philip Gibbs

I agree strongly with the position you take on universality being the common bond between mathematics and physics. I do wonder if a universal property is that everything is unique, if we get precise enough in our measurements.

And I am responding to this sub-thread regarding foundations of mathematics mentioned by Prof. Crowell. We might need to consider the assumptions in the foundations of mathematics- especially as mathematics is applied to physics. In particular we assume our system of representing quantities (numeric representations) are adequate for what we can measure. What about things we might be unable to measure (today)? While we might be able to accomplish much of technology today using Rational numbers (we can only approximate Real numbers), we would be completely unable to build our technology with only fractions - a representational system for Rationals. The calculational power of decimals (and like based systems) far outstrips that of fractions. Might there be a more powerful system than the single-based numeric systems we use today that could manage calculations unthinkable today? Such a system would likely apply to a larger set of numbers and encompass operations not in our current systems (more universal). Being on the boundary of theoretic and applied mathematics, it could have a major impact on science as well.

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An earlier comment sent me to your comment on Klingman's essay, in which I noted "For you the physical world comes first and is unique while mathematics emerges in its many forms. For me the mathematical world is a unique structure from which many possible physical realities emerge." Whereas I couldn't find a point in your paper on which I felt a wish to hang my hat, those two sentences lead me to ask how does mathematics emerge? What kind of detector do we use and what kind of signal processing do we use to allow "mathematics" to "emerge"? It seems that we use the same body/senses and brain/mind to discover/invent physical structure as we use to discover/invent mathematical structure. An empiricist such as myself might think that the two are names for parts of the same thing, our evolving attempts to model, describe and to control some aspects of our continued existence (and that discover/invent presents a delicate demarcation problem), at progressive levels of abstraction.

I feel unable to engage with this FQXi topic in an essay because however much I have thought about it I have far too little knowledge of the literature, which I know, however, to be voluminous. So a teeny comment is as far as I will go.

Another earlier comment leads me to discover that you are the founder of viXra, for which Kudos.

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Author Philip Gibbs replied on Jan. 16, 2015 @ 13:05 GMT

Hello Peter, I think if people allowed "too little knowledge of the literature" to stand in their way there would be a lot fewer essays written for these contests, and that includes mine.

I am not sure about how mathematics might emerge either from physics or from nothing. Klingman has some nice ideas about emergence from physics using pattern regognition of whatever. My current view is...

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Hello Peter, I think if people allowed "too little knowledge of the literature" to stand in their way there would be a lot fewer essays written for these contests, and that includes mine.

I am not sure about how mathematics might emerge either from physics or from nothing. Klingman has some nice ideas about emergence from physics using pattern regognition of whatever. My current view is that mathematics is just the structure of all logical possibilities so it does not have to emerge from something else. It is about what can be rather than what is.

I am therefore more interested in how physics can emerge from mathematics. I had another idea about how I might tackle this question which was a little different from what I eventually went with in my essay. I was going to write about what might happen if there were only mathematicians and no physicists. How many ideas from physics would they invent without any input from the real world. You can imagine that they even have no direct contact with the physical world. They could just be brains in a vat left to ponder on logical problems. It may even be possible one day to see this happen using artificial intelligence.

To be more specific we might program an AI system using Sparse Acataleptic Bayesian Inference algorithms to solve integer diophantine equations. It would try to classify solutions to as wide a range of possible equations as it could. Initially it would have just the definition of integers and polynomial equations to work with but would use heuristic methods to find new definitions to help it solve problems and find logical proofs, just as mathematicians do. Real mathematicians have of course had the benefit of knowledge about the physical universe to inspire the use of real numbers and geometry to solve this kind of problem but they have also invented new concepts such as complex numbers and quaternions from scratch which were only later known to be useful in physics. I think an isolated AI program if it is sufficiently good would do the same thing. Diophantine equations are very rich in terms of the kind of mathematical tools are required to solve even simple cases. The AI system would have to invent rationals then real numbers and even geometric ideas. It would probably also realise that to find new ideas it has to explore a wider field of mathematical concepts and would need to get a feel for what is interesting enough. I am confident that it would discover all the concepts used in mathematical physics just to use them to solve diophantine equations. If you are skeptical you should remember that string theory has already been used to solve the Monstrous Moonshine conjectures which came from problems in number theory.

If this project could be carried out in practice it would be proof that physics can emerge from just mathematics. Unfortunately I made up the term "Sparse Acataleptic Bayesian Inference" and nobody really knows how to do it yet.

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Jonathan Khanlian replied on Apr. 6, 2015 @ 20:30 GMT

Hi Philip,

I am just curious how you think an AI could invent the concept of real numbers. If everything a computer can deal with is computable, how could a computer handle uncomputable real numbers (as opposed to computable reals such as pi or e) which have an infinite amount of information and cannot be referred to in any unambiguous way? The information content of most "real" numbers cannot be compressed. How would a computer define operations such as addition on these types of numbers?

Please check out my Digital Physics movie essay if you get the chance. I'd be interested to hear your thoughts.

Thanks,

Jon

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Author Philip Gibbs replied on May. 6, 2015 @ 18:42 GMT

I think computers would understand real numbers the same way we do, through symbolic logic. You dont have to be able to understand every individual real number to be able to explore the properties of real numbers as a whole. This is the same for humans as it is for an AI. Mathematica and other symbolic logic programs can already handle real numbers in this sense.

Philip,

A very nice essay. I am also intrigued by the multiplicity of landscape solutions, and the thought that a priori we can only assume that all consistent vacuum solutions have equal probability of being correct. Such indetermination may not be an obstacle for progress though. We can certainly define the maths that use indeterminates and at some level, that might be enough. Curious as to what you think of just letting go of the idea that we will ever know the exact vacuum state.

Best,

Harlan

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Author Philip Gibbs replied on May. 6, 2015 @ 18:53 GMT

I think that once we know the rules for constructing the possible vacuum states it is going to be a huge challenge to work out exactly what it is.

It may turn out not to be so hard or it may be so hard that we can never work it out completely, either because the necessary experiments are out of reach or because the computation is too complex.

The most interesting scenario would be that it is possible but only after some very clever experimentation and computation, but we will have to accept whatever nature has in store for us.

Dear Sir,

You have raised some very important questions that can be answered only if we think out of the box. The problem is that we collect lots of data and without proper examination, reject most (like at LHC) that could have given us equally plausible ideas about the natural laws. Secondly, we follow the beaten path without reviewing it and reconciling the apparent contradictions that...

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Dear Sir,

You have raised some very important questions that can be answered only if we think out of the box. The problem is that we collect lots of data and without proper examination, reject most (like at LHC) that could have given us equally plausible ideas about the natural laws. Secondly, we follow the beaten path without reviewing it and reconciling the apparent contradictions that are being increasingly observed. However, your essay provoked us to expand a few thoughts.

Even though the viability of the loop quantum gravity is questionable, one of its predicted scenarios is the big bounce. If we replace the big bang with the big bounce, add to it the laws of thermodynamics and some ancient ideas about time, we get a totally different picture.

Let us start from the last. Time is the ordered interval of events, which are measurement of observables at various coordinates. There is a fixed pattern of all events. These are: being (situation leading to its creation), becoming (its creation itself), (growth due to addition of other particles/events), transformation (as a result), transmutation (due to the same effect – incompatible/excess addition), destruction (change of form as a consequence) to start a new chain. Since galactic blue-shift has been observed putting a question mark to dark energy concepts, let us assume a steady state universe, where everything follows this pattern. Everything is measured/perceived through the radiation it emits – thus, through thermodynamic processes. Condition of maximum entropy is the final stage of the cycle. Then, in the Universal scale, big bounce will be the beginning of a cycle. At that stage, it will be only creation through redistribution. There is the universal space and universal energy, but no one to perceive or measure. The one energy is all pervasive. The emergent energies can be different, local or unknown. Structure formation being an event, must have followed the beginning of the cycle. Since space is the base and interval of structures, space as we know it, must be an emergent property after time. But how did it all start?

If you look at motion and action, you will find that action is momentary, but it creates a pair of equal and oppositely directed inertia that create local disturbances to create composite and differential inertia that tends to restore equilibrium in a multiple reaction mode. On the other hand, motion is mechanical – it perpetually responds to density fluctuation in all sorts of manners: energy, material density, air density, charge density, etc, created by all sorts of manners including heat (electric), cold (magnetic), etc. Anything subject to strong interaction has the capacity of confining motion. It generates inertia that also acts mechanically till local equilibrium is restored (weak interaction). This is followed by redistribution (electromagnetic). But action is different. It is induced by a conscious agent that breaks the stability or equilibrium. Thus, at the creation event, inherent instability of the conscious system of the universal observer starts the process by creating a perturbation. Some may question this as religious belief. But can quantum theory survive without observer?

We have a fully developed theory that explains many things. In our essay, we have discussed the Wigner’s view of unreasonable effectiveness of mathematics and Gödel’s incompleteness theorems as well as Einstein’s formulations.

Regards,

basudeba

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Philip,

Thanks, for sharing your ideas. It is nice to see so many different points of views regarding this topic.

Best Regards,

-D.C.Adams

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Professor Gibbs,

The new paradigm shift (from one Universe to multiple Universes) is hard even on Western thought. At first I was reticent but then... . It is actually amazing when one thinks about it compared to the concept of the one singular Universe our egocentric minds have somewhat logically been led to believe in (hard to let go). There are hints to the Meta-Laws. Frank Wilczsek...

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Professor Gibbs,

The new paradigm shift (from one Universe to multiple Universes) is hard even on Western thought. At first I was reticent but then... . It is actually amazing when one thinks about it compared to the concept of the one singular Universe our egocentric minds have somewhat logically been led to believe in (hard to let go). There are hints to the Meta-Laws. Frank Wilczsek stated something to the order that why are the gauge coupling forces unifying (GUT except gravity) at one point in our Universe (I am assuming SUSY makes the unification more exact)? Thinking about this, is it probable that most successful Universes has this form of unification of gauge forces more or less in some tolerant area near a unifying energy (Planck energy type) with gravity? This cannot be attributed to coincidence. You stated in your essay, "It is known that the combination of quantum theory and general relativity imposes tough constraints on the possible range of consistent space-time models." Also, the GUT point being (how much?)variable with other Universe formations this does rule out 'fine tuning" and maybe one should not look at just one number (say the Higgs boson mass) and say it has some 'unnaturalness' because it looks random and especially 'fine tuned'. It is best just to look at the GUT points in any formed successful Universe that has a 4D space-time. It may be hard to trust just a few numbers whereas the GUT points are more of a gestalt of what is going on. Why 4D? It is well know that 4D manifolds are the most interesting manifolds/topologies in mathematics. Even more so than higher dimension topologies. Recently, the Triangulation Conjecture was disproven. Coverings of simplices (triangles or tetrahedrons) cannot completely cover higher dimension topologies (past the 4D) based on some simple rules. This leaves higher dimension coverings 'foamy' or full of holes. Makes one wonder whether this means that higher dimensional Universes can exist in a 'physical' sense. I am not sure that 'all solutions exists'. It is bound to be super variegated (though with 57 varieties ;)). I am thinking that one should not even consider 'fine tuning' anymore but to look at the tolerance or range of solutions in the hierarchal space as a mathematical structure that can eventually be computed in a Scientific framework. All other Universe that have the 4D space-times would somehow have a computational relation to each other (a dictionary?). The GUT point would also be a measure of how fast nuclear rates (and chemistries) and gravity combine to create the Universe. In some Universes (even if 4D) that stars would burn too fast or gravitational collapse only produces black holes where life could not have enough time to form or exist. Or the GUT point is such that stars cannot ignite and that Universe is a cold dead world with not much going on. Where there is no GUT point for a Universe it perhaps collapses to nothing. I think a lot of people misunderstand the Multiverse especially when it is hyped to the point that suggests 'all outcomes are possible' somewhere in a Universe we will never know. And there is no parallel person that is me somewhere else with a different set of beliefs or lifestyle as that is hogwash. I think that the other Universes have some sort of 4D path integral sensibility which produces some similar outcomes but not the same or nearly the same outcomes found in the other Universes. Finally, here is a direct quote from a white paper "Higher-Order Intersections in Low-Dimensional Topology" by Conant, Schneiderman and Teichner, "The Whitney move, sometimes also called the Whitney trick, remains a primary tool for turning algebraic information (counting double points)into geometric information (existence of embeddings). It was successfully used in classification of manifolds of dimension > 4 specifically in Smale's celebrated h-cobordism theorem (implying the Poincare conjecture) and the surgery theory of Kervaire-Milnor-Browder-Novikov-Wall. The failure of the Whitney move in dimension 4 is the main cause that, even today , there is no classification of 4-dimensional manifolds in sight." I quoted this to make the point that there is a lot of work to be done and that perhaps the unreasonable effectiveness of math in physics is really related to the 4D space-time issue of physical-ness.

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Philip,

Your mathematical description of doing frontier theoretical physics is noted. However I believe that there is a need to change our emphasis from the mathematical development to the physical model development.

In the past 100 years theoretical physics and cosmology developments have been conducted almost exclusively on a mathematical basis, leading to non-physical objects or processes such as fields, space-time, curvature in space-time, time dilation, length contraction, virtual particles, action at a distance, curled-up dimensions, Entanglement, Dark Energy, Dark Matter....etc. I believe that these abstract mathematical objects are different aspects of one physical model of our universe. Therefore I urge that we devote more efforts on the physical model development.

Regards,

Ken Seto

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Sorry for not responding to comments for a while. I will get back to it at some point soon.

I am what you call an amateur scientist. In 2001 I discovered what I thought something significant. I submitted a paper to the “American Physical Society, Physical Review D”, put up a web site, published a book: nothing. I discovered FQXi and thought it great. I have submitted contest entries with the simple hope that someone would review my material. Now, I have found viXra. The purpose of this note is to express extreme thanks for your involvement in that device. Now, I will continue to read your essay.

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Hi Philip,

multiplicity of the vacuum is the most promising idea of physics

see more www.fopi.info

attachments: standard_model.png

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Thank you for your well written essay.

I like your idea showing the symmetry between the complexity of mathematics and physics, going hand by hand. I am not sure they are attracted towards a point of universality. It is an interesting subject.

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Christophe Tournayre replied on Jan. 29, 2015 @ 18:31 GMT

Philip,

In my previous response, I said that I am sceptical about the universality.

The reason is not found in arguments, but in our position. We humans are close from our evolutionary relatives (for example chimpanzee). How can we pretend that our differences with them make us more susceptible of reaching “universality” more than they are?

In my view, understanding can be compared to a sense. From an evolutionary perspective, we humans may have developed this ability to perceive nature/our environment through another way. At first, our understandings were weak, fuzzy, black or white, but as this sense developed, our ability to perceive our environment became richer, varied and even colorful though it is still a long way to the deepness of visual perception.

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Author Philip Gibbs replied on Feb. 5, 2015 @ 18:05 GMT

Christophe, the attraction towards universality is a feature of complexity theory and self organisation. Think about the theory of strange attractors in chaos theory for example. I dont think we fully understand why it works that way but it does.

I don't think a chimpanzee is qualitatively different from us. he is just a little less intelligent. It is not us that reach universailty, it is a feature of mathematics that arises independently of us. The only role we play is in establishing a selection criteria in that the solution to the equations of universality which is actually realised has to be able to support us. This is the anthropic principle and it applies to some extent to chimpanzees too.

Hi Philip,

It is interesting that we have partly similar opinions on the links between math and physics, that is, a mathematical Platonism carrying all possibilities, and the idea that the physical universe comes as a particular case of deep mathematical theories. Here are my remarks:

"It has been observed for years that the nature of physical laws appears fine-tuned for the convenience of life (...) Almost every natural occurring element of the periodic table plays some essential role in the making of multicellular life form."

Sorry, while a case for fine-tuning can be made indeed, I don't see it well expressed in this specific way. If I saw well, only few of the physical constants really matter in all crucial processes of the evolution of stars and nucleosynthesis, and they already need to be tuned to fulfill the vital requirements. This does not let many available degrees of freedom to also fine-tune the details of chemical composition, which is actually not so fine-tuned but more guided by its own rigid necessities (mathematically necessary list of nuclear orbitals).

To make water, hydrogen came first and did not need to be produced; oxygen is much needed but its abundance is no mystery, as 8 protons is a magic number for nucleus stability, not much sensitive to physical constants.

After oxygen, the next 3 most abundant elements in the Earth's crust are silicon, aluminum and iron. Silicon is only 2×10^-5 of mass in the human body, and "very few organisms have a use for it" (wikipedia). Aluminum "has no known function in biology". Iron is useful but in very small proportion only. Phosphorus is needed as 1% of mass of human body but it is only 0.1% of continental crust and 6×10^-8 the mass of sea water (as it better stays in rocks).

"Some physicists have speculated that there is an eternal process of inflation with vacua decaying to different solutions so that our own universe is just one bubble inside a larger arena. "

Hum, if I understand well it requires 2 inflation periods, one before and one after decay ; inflation before decay is natural, since, by definition, the void had higher energy, but then the problem is that for different possible lower levels the inflation needs to still go on for some time and then stop in a synchronized manner (but what would happen otherwise ?). Hard stuff.

"I think it is more parsimonious to accept that all solutions exist in some higher sense, whether inside or outside our universe (...) I take it as self-evident that logical possibilities exist even if only in some metaphorical sense that we don’t understand. It is just a way of saying that some things are possible"

I agree that, according to the nature of mathematics, all logical possibilities exist. However I see this as very clearly, formally defined and not mysterious at all, only subject to the well-understood limit of undecidability. As you should know, existence is a mathematical concept, expressed by a specific symbol, that only needs an axiomatic theory to describe the shape of a universe where it is interpreted. The typically suitable framework to state the existence of all mathematical possibilities, is set theory, which admits itself many possible variants to specify the details (due to the undecidability of existence of many kinds of infinite systems we cannot construct).

"What then would happen if we treat the whole of mathematics as a statistical physics system or as a path integral over the moduli space of all possible theories ? Would some universal behavior emerge that could describe the meta-laws of physics?"

A big problem to define an integral over a range of "all possibilities", is that it requires some kind of measure to compare their weights. Such a measure usually requires, at least, a kind of fixed size of a local part of body whose variations are considered at a time. However no such comparison is possible between infinite systems that cannot be precisely described by a common specific theoretical framework.

I think that before flying to such highly speculative, ill-defined generalizations (that I would consider not really mathematical anymore, since I see mathematics as the science of definiteness), you need to consider the obvious first step and particular case of application of such ideas of "admitting the coexistence of all possibilities" that combines the advantages of being very well-known and well-defined, a natural direct consequence of the known laws of physics, with a well-defined measure of the weight of the many possibilities that is very directly and massively verified by observations, and for which, at the same time, this idea of coexistence of all possibilities has the amazing advantage of being still highly controversial. You see what I mean ? Answer below.

You wrote "I was going to write about what might happen if there were only mathematicians and no physicists. How many ideas from physics would they invent without any input from the real world. You can imagine that they even have no direct contact with the physical world. They could just be brains in a vat left to ponder on logical problems. It may even be possible one day to see this happen using artificial intelligence. To be more specific we might program an AI system using Sparse Acataleptic Bayesian Inference algorithms to solve integer diophantine equations.(...) Diophantine equations are very rich in terms of the kind of mathematical tools are required to solve even simple cases."

This is quite interesting as I have a similar project of rebuilding mathematics from scratch, starting with purely logical concepts before reaching physics. I use my own intelligence instead of an AI system, and of course I do know much physics at the start but I care to put things into an optimal logical order so as to make every step appear sufficiently motivated by purely logical concerns without any feeling of arbitrariness nor external (physical) source of motivation or inspiration.

Though the properties, and proofs of properties, of integer diophantine equations may potentially involve lots of mathematics indeed, I'm afraid they would be a quite inefficient way of rebuilding maths from scratch. In fact, I guess the power of development of high mathematics is much less a matter of what problem is supposed to be tackled, than a matter of what kind of intelligence or algorithm is tackling it. Indeed, this AI needs to know from the start what is a proof and what is a definition that can be used to make shorter proofs... finally you need to give it a huge a priori knowledge of mathematics beyond diophantine equations, before it starts searching. But the worst point in my opinion is that, even considering deep mathematics as an intrinsic necessary reality to be discovered, I guess the act of discovering them may require a conscious mind (not AI) to be efficiently done. The concepts of elegance and universality in mathematics may be themselves diversely interpreted and not always in mathematically well-defined manners. Insofar as they would be mathematically definite, I would compare discovering deep maths to a problem of breaking a cryptographic key, for which the solution may indeed be mathematically unique and well-verifiable, but purely mathematical systems could not efficiently discover the solution themselves if it is not revealed from the outside.

Of course I was referring above to the many-worlds interpretation of quantum physics. The most famous difficulty with this interpretation is how to make sense of probabilities. You wrote "The Mathematical Universe Hypotheses tells us that all logical possibilities are equal". Consider the simple example of a polarized photon that is measured in another direction with an arbitrary angle. Both possible observed states are well-defined elementary states, not any variably large numbers of possible states, and have no intrinsic difference of quality having anything to do with the entropy of the measurement apparatus or whatever. Still the theory says one is more likely than the other, with a probability that can take any value depending on the angle of measurement. How to make sense of their difference of likeliness if they are equally real ? See my longer analysis of the paradoxes in this interpretation. Finally I invite you to read my essay where I defend another interpretation.

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Author Philip Gibbs replied on Feb. 3, 2015 @ 18:29 GMT

Sylvian, thank you for your detailed points. These are all interesting things and I will give my responses one at a time. Overall I would say that these are things where different people have very different opinions and have been the subject of interesting debates. I recognise that my opinion is not likely to be the right one on everything but for the purposes of argument I will put my best case...

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Sylvian, thank you for your detailed points. These are all interesting things and I will give my responses one at a time. Overall I would say that these are things where different people have very different opinions and have been the subject of interesting debates. I recognise that my opinion is not likely to be the right one on everything but for the purposes of argument I will put my best case in defense of how I see them.

On fine-tuning in chemistry: First let me correct a few misunderstandings. When I said that "Almost every natural occurring element of the periodic table plays some essential role in the making of multicellular life form." I did not only mean that every element is incorporated into biochemistry. Silicon has only minor roles to play in biology itself but it forms rocky planets without which life as we know it would not exist. I also did not mean to imply that every element is used in proportion to its abundance. Some elements are used in only very trace amounts but the role they play is still very important.

Now it is true that there are not enough free parameters in the standard model to fine-tune every element to a specific role. That is not how it works. The coupling constants are however fine tuned to control the richness of chemistry. Small differences would mean different numbers of elements with different properties and we can expect chemistry and abundances to vary quite dramatically and perhaps even chaotically as the parameters change. It is very difficult to work out what chemostry would really be like with different values of constants and even harder to try to work out what forms of biochemistry may be possible based on different sets of chemical elements. Perhaps science and computation will make that possible one day but another thing that will happen (hopefully) is that we will get an idea of what other lifeforms exist in the universe. If the fine-ytuning idea is right then there should be exactly one major form of biochemistry on which complex life can be based. If we find that there are two different types of biochemistry that lead to sophisticated lifeforms then the fine tuning argument is wrong. I don't think we will.

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Sylvain Poirier replied on Feb. 6, 2015 @ 18:48 GMT

Of course the details of modifications of chemistry would be very hard to find out but the main principles of dependence with respect to the fundamental constants are clear.

As for nucleosynthesis, we have this:

A fine-tuning of constants is needed for the Triple-alpha process: " ⁸Be + ⁴He has almost exactly the energy of an excited state of ¹²C...

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Author Philip Gibbs replied on Feb. 8, 2015 @ 18:48 GMT

Sylvian, thank you for these detailed and interesting points. The only thing I would add at this point is that the fine structure constant does not just affect the chemical bonds. It also affects nuclear stability because the electrostatic repulsion is balanced against the strong force. A small change would have a profound affect on which elements are stable.

I think it would be interesting nut hard exercise to work out the chemistry and nuclear properties of elements as constants vary. Until someone does that I am not sure what the real situation is.

Hurry back. I gave your essay a high score. Yours is one of the better of the lot here.

LC

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Author Philip Gibbs replied on Feb. 3, 2015 @ 16:41 GMT

Thanks Lawrence, I hope to find some more time now. I see you have an essay up, that's great. In fact quite a lot of essays already.

Dear Phillip,

I thought your essay was well done and very interesting. I am not sure that I understood it all, but I agree that the concept of universality is critically important (no pun intended) to understanding the underlying *process*, which I think we perceive as dualistic aspects of reality. I emphasize process because my life experience (my “lazy process” that includes graduate...

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Dear Phillip,

I thought your essay was well done and very interesting. I am not sure that I understood it all, but I agree that the concept of universality is critically important (no pun intended) to understanding the underlying *process*, which I think we perceive as dualistic aspects of reality. I emphasize process because my life experience (my “lazy process” that includes graduate education (physics, math, electrical and nuclear engineering, medical physics, and national security/ strategic studies) and as a nuclear submariner and clinical medical physicist) has given me a perspective that is more focused on process (especially the unity of space and time as opposed to the differences). I don’t recall learning about universality in my statistical mechanics class, so I have to look it up, but from what I just read on line, it seems to be an excellent direction for continued research.

Scientific writing has never been one of my strong points, and I’ve struggled with putting my ideas in a format acceptable to scientific journals, so allow me to express my sincere gratitude to you for vixra. If I never succeed in getting it published in a journal, at least I now have a chance to share my philosophy about the unity of space and time, especially my space-time-motion model (see http://vixra.org/abs/1402.0045) with people who are much smarter and knowledgeable than I. My only hope is that it will be useful in the quest for understanding the importance of unity (the metaphorical center of the ring) as a foundational concept. I believe that the entire world (not just physics) is in crisis because science has proven the utility and power of reductionism yet failed to recognize the importance of concepts such as unity and universality (except physicists like David Bohm and Fritjof Capra).

I took a very different approach to presenting space-time-motion unity in this essay contest, because the guidelines emphasized "Original and Creative” ways of pushing forward understanding “in a fresh way or with new perspective". So I invite you to read and comment on “Doctors of the Ring - The Power of Merlin the Mathematician to Transform Chaos into Consciousness.”

Best regards,

Ted St. John

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Author Philip Gibbs replied on Feb. 8, 2015 @ 18:37 GMT

Thank you for your comments. I am glad you like the central idea of universality. I look forward to reading your essay

The free weak Omega-category is one of the most abstract objects in math.

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Author Philip Gibbs replied on May. 7, 2015 @ 16:45 GMT

It was the most abstract, complete and general algebraic object I could think of.

Hello Philip,

I got what I expected. A nice and interesting submission. Looked to me more of a review of the topic. Although your Bio says you are a theoretical physicist, my understanding of your essay seems to make you look more like a 'physical mathematician' than a 'mathematical physicist'.

I have need for some clarification and to learn more...

You talk of Space as being 'emergent'. What does this mean in simple terms?

You also talk of vacua, are you taking vacua and space as synonymous or different?

Then, I challenge you with the question: Since you say the elephant is not to be envisaged as something that existed before the big bang and also ask “How do we exist?”, can what exists perish? If not, why not? If yes, can you make out a list of what exists, so we can apply the doctrine of perishability on them?

Best regards,

Akinbo

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Author Philip Gibbs replied on Feb. 16, 2015 @ 08:03 GMT

"You talk of Space as being 'emergent'. What does this mean in simple terms?"

If you were to write down a full mathematical model for the standard models of physics as we knoe them at the present time the first thing you would do is define a 4D spacetime geometry, then you add the particles and their dynamics. When we say spacetime is emergent we mean that at a deeper level that is not how it is done. Instead we would start with some mathematical structure that is not defined in space time, like a network of connected nodes or a matrix. These objects are then subject to some kind of mathematical rules that tell us what weight is given to each configuration. When we study the complex system this provides we would find emergent phenomena which look like the laws of physics we are familiar with including spacetime. This is what we mean when we say that spacetime is emergent. It would only have an aproximate existance that fades away of we examine it very closely.

An good analogy to this is the surface of a liquid such as the sea. We know that at a microscopic level the sea is just a collection of molecules that interact and when we right down a mathematical mode for this we do not define a surface, just the properties of the molecules, but under the right conditions a liquid surface is formed. The surface is an emergent geometrical phenomena with its own macroscopic dynamics. This does not mean that spacetime is made of something like molecules or that it has to exist within some other geometry. The way it emerges is probably very different but the principle of emergence is the same.

Akinbo Ojo replied on Feb. 16, 2015 @ 15:10 GMT

Thanks Philip,

That analogy was very helpful in understanding the mysterious adjective "emergent". Unfortunately you point out that the analogy does not go all the way down by saying, "This does not mean that spacetime is made of something like molecules or that it has to exist within some other geometry". If you had not put up this red flag, I would have wanted to interrogate your position to see or bring out any illogicalities therein, if present.

Nevertheless, if I may use the opportunity to do some 'dialectic':

- is it only space-time that can be entitled to the adjective "emergent" or can space itself before being wedded to time by Minkowski also have a claim to the title "emergent"?

- In your model, is a length infinitely divisible into positions or is there a finite limit to the number of positions available on a given length?

- When gravitational waves travel, it is said that spacetime is distorted with alternate lengthening and shortening of a given length orthogonal to the direction of wave travel. If I am right, can something that is not made of anything discrete vibrate? Don't you think that the coincidence of gravitational waves and light travelling at c , may suggest that perhaps they are similarly propagated and share a spectrum, just as the finding that light travel at same velocity as the electro-magnetic waves predicted by Maxwell and verified by Hertz resulted in the classification of light as belonging to the spectrum of electromagnetic waves.

You may not like my essay being a hard-core physicist but please take a look when you can spare the time. The ideas are directly opposite to your viewpoint. Also you probably find confusing my other questions about what exists subsequently perishing so I spare you the agony, worrying what I mean.

All the best in the competition. And God bless your idea of setting up your non-discriminatory vixra.

Regards,

Akinbo

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Author Philip Gibbs replied on Feb. 16, 2015 @ 20:31 GMT

"is it only space-time that can be entitled to the adjective "emergent" or can space itself before being wedded to time by Minkowski also have a claim to the title "emergent"?"

Either or neither or both could be correct. I favour the view that space and time are both emergent as one unified space-time structure. If you want to read about a different point of view you could look at Lee Smolin's essay. His idea is that time is fundamental but space is emergent. I dont like that idea for numerous reasons but we dont know yet how it works so it is good that there are people exploring different possibilities.

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Hello Philip,

I very much enjoyed reading your essay and I am very much in agreement with your view that we are ready for a paradigm shift in fundamental physics.

My own feeling is that the unification will not come from trying to extend existing models to include gravity but rather by understanding how gravity provides the right model for understanding all fundamental forces.

I hope you will take the time to read my essay which is titled Solving the Mystery and give me your comments.

With best regards

Richard Lewis

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The ordering of meta-physical aspects is more imposing subject of talk.

Sincerely,

Miss. Sujatha Jagannathan

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Dear Philip,

a central point in your essay is universality. A mathematical structure is more universal - more discovered than invented - when it is instantiated in more structures that superficially appear different from one another; and a physical law is more universal when it describes more physical systems that appear different from one another in some aspects (e.g. different particle...

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Dear Philip,

a central point in your essay is universality. A mathematical structure is more universal - more discovered than invented - when it is instantiated in more structures that superficially appear different from one another; and a physical law is more universal when it describes more physical systems that appear different from one another in some aspects (e.g. different particle types in systems that obey the same thermodynamical laws).

A dense spectrum of universality degrees is envisaged, for which we still lack formal treatment and measure. And yet, the idea to navigate the mathematical universe guided by this compass and reach the top of the hill (or the bottom of the valley), with the idea that the most universal mathematical structure coincide with the meta-laws of physics, is very appealing.

We have another interesting notion of universality, however, more advanced in terms of possibilities of formal treatment, and simply of a True/False type (no spectrum of degrees): that’s of course computational universality (Turing universality) - the ability of a model of computation to reproduce any computation of any other conceivable model of computation.

To those who attribute a fundamentally algorithmic nature to the universe (thus justifying its mix of order and disorder better, in my opinion, than any other approach) this would be the first choice for a notion of universality. Then, the democratic idea that all vacua, or all mathematical structures, enjoy some form of existence, could perhaps also apply to the multiplicity of universal models of computation.

There seems to be a very large gap between the idea of an algorithmic uni/multiverse and the scenario that you describe. You place ‘algorithms’ in your picture below ‘games’, but still far from the ‘point of universality’. I agree that individual algorithms are more invented than discovered, but what about the Universal Turing machine?

Thanks and best regards

Tommaso

P.S. In case the algorithmic paradigm gained credibility in the future, I suggest to replace the elephant with an ant, for its ‘minimality’, as a metaphor for the head of a Turing machine, and as a reminder of the variety of properties that emerge from the computations of ‘turmites’ (2D Turing machines), including Langton ant.

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Author Philip Gibbs replied on Feb. 18, 2015 @ 17:09 GMT

Tommaso, thank you for your comment. It is good to see you in the contest again.

You have made a very astute point which is not lost on me although space constraints meant I did not say much about it in the essay. If you look at the paper by Seth Lloyd "The universal path integral" which I have cited you will see that he concentrates on algorithms. This may be very close to the kind of approach you are thinking of.

There are a couple of reasons why I did not want to focus on algorithms myself even though the universaltiy of computing is certainly very relevant here. One thing is that computers tend to run calculations forward in one direction. A normal sequential program has a time ordering in its calculations. This may be relaxed in a parallel programming architecture but there is still a partial ordering which people will inevitably try to link to temporal causality. As I said in my essay I dont think this kind of causality is important. I aknowledge that you could work with algroithms without making this connection.

The other thing is that path integrals are not just sums over configurations. When you have fermions the sum is replaced with an algebraic integral over grassman varuables. I suspect that the universality we see in maths and physics is also more general in this way. It is an algebraic principle that we do not understand and the kind of universality you get in statistical ensembles is just a good metaphor for that. The universality in computing is a little different again and it fits in somewhere, but here I tried to convey the idea of some other kind of self-referntial, self-organising universality that we understand very little about.

I look forward to reading your essay a little later

Dear Philip,

I read your essay with great interest. I totally agree with you: we need a new paradigm in basic science. To do this, need to consider the "universal point" as ontological "proto- existential - extremum". But not "meta-laws", only one "law of laws" - "Logos". My high score.I think that we must first to consider the proto-structure of the Universum (matter) from the point of view of eternity ("sub specie aeternitatis"), that is, to carry out the ontological structure of matter in the proto-era, "time before times began". When we "grab" (understand) the primordial (ontological) structure of space, then we will understand the nature of time. Therefore, we must move from the concept of "space-time" to the concept of "space-matter-time", which represents the ontological unity of the Universum. The primordial structure of matter determines the structure of the language in which Nature speaks to us, single language for mathematicians, physicists and poets , ie, language that contains all the meanings of the "LifeWorld" (E.Husserl).I invite you to read my essay .

Kind regards,

Vladimir

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Author Philip Gibbs replied on Feb. 21, 2015 @ 13:36 GMT

Thank you Vladimir, I will read your essay, sounds intriguing.

Dear Dr. Gibbs,

I read your essay with great interest.

I note your citing of the parable of the blind men and the elephant, as a metaphor for incomplete knowledge. However, I think that abstract theories inferred from incomplete knowledge can be more pernicious than the lack of knowledge itself. Such mathematical theories can act to narrow the mind and blind the vision.

You might be interested in reading my own essay, "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory". I argue that premature adoption of an abstract mathematical framework prevented consideration of a simple, consistent, realistic model of quantum mechanics, avoiding paradoxes of indeterminacy, entanglement, and non-locality. What’s more, this realistic model is directly testable using little more than Stern-Gerlach magnets.

But questioning the foundations in this way is considered heretical, and is unpublishable in physics journals.

Alan Kadin

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Interesting essay. You frame a hypothesis of the existence of meta-laws. You write:

"At the same time technological progress will enable new empirical observations to help us understand inflation, dark matter, proton decay and other subtle phenomena that help to chart our course through the ontological realm to where we stand in it. They will enable us to pick out the universe’s particular solution to the algebraic meta-laws."

AFAIK< and I may be wrong, so far science works the other way around (Higgs particle for example):our models make a prediction and we try to falsify in or verify it.

You allude to a procedure in which experiments will determine the selection of meta-laws. How can we look for something we do not know what it is? (Knowledge Paradox). Besides, we are far from making experiments at the Planck scale. If meta-laws exist, you think we will find them by experimentation without a formal framework of what we are looking for? Thanks.

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Author Philip Gibbs replied on May. 7, 2015 @ 16:59 GMT

Science works both ways. Sometimes theorists make predictions that are then verified by scinece, but sometimes experienters find things that were not predicted and theorists have to find the right theory for them. There are plenty of examples of the latter e.g. the muon, law of black body radiation, constancy of the speed of light etc.

Particle accelerators search for predicted particles but they can also find things that were not predicted. This is done by continually measuring every quatity at higher and higher energies and checking to see whether they match predictions from accepted theory.

While accelerators are limited in energy scale, the other experiments I mentioned are not. proton decay could give us information about the GUT scale for example.

You dont need a formal framework to find something new. As soon as something does not match the existing framwork you can start looking for what might explain it.

Dear Dr. Gibbs,

I think the meadow of physics is marred by mathematical demons. So I was happy when FQXI announced the subject for this year's essay competition. The first essay I read was yours. Instantly, I identified you as a 'mathematicalist' trying to impose the rule of mathematics in the domain of physics.

The way you have written, however, is impressive that any one reluctant...

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Dear Dr. Gibbs,

I think the meadow of physics is marred by mathematical demons. So I was happy when FQXI announced the subject for this year's essay competition. The first essay I read was yours. Instantly, I identified you as a 'mathematicalist' trying to impose the rule of mathematics in the domain of physics.

The way you have written, however, is impressive that any one reluctant will jump into the 'mathematicalist' wagon. That I think is the beauty of the mathematics-oriented thinking coming from somebody who knows the intricacies of both mathematics and physics.

Your statement “geometry is an angel and algebra is a demon …....... the signs are that the devil rules at the deepest levels of existence” is thought provoking. Can I say that the rules of mathematics are essentially algebraic, and geometry just represents its emergent structures. Then the universality of mathematics is in its rules, not in its structures. Regarding the question, whether mathematics is invented or discovered, I think the rules are discovered, but the structures are invented. For example, in chess the properties of the pieces are invented, but the emergence follows mathematical rules and the overall structure of the game is thus invented. Starting with another set of arbitrary properties, you will obtain a different structure.

Again I would like to quote another statement “the theory you get by recursively iterating quantisation should be unique” . Without referring to existing Quantum Mechanics, your statement can be construed to be implying that fundamental particles, just because they are quanta, may be obeying a unique law, which is universal. Does it simply mean that starting from qunatised entities, you cannot have an infinite number of emergent structures?

The 'physicalist' idea that I propose in my essay is this: physics decides the properties, mathematics decides the rules. For the given properties, mathematics decides the emergent structures; for that emergent structures, physics again decides the emergent properties, and so on. Thus, the equations are mathematical, but the variables are physical. Starting from a finite number of variables having finite properties, the number of variables will soon come to the minimum that further emergent structures are impossible. That final structure is the physical world that we observe.

Somewhere above, you have stated that 'physics emerges from mathematics'. This I think tantamount to saying that 'the physical world emerges from mathematics'. Or, given the basic properties of matter, mathematics decides the final emergent structure. That way, I will have to call you a physicalist. So I am just confused. I have just submitted my essay, and expect it to be available within a few days. I would be awaiting for your comments.

I claim myself to be an independent researcher. And I find solace in the free-for-all 'VIXRA'. I take this opportunity to express my sincere thanks to you for providing an asylum for people like me.

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susanne kayser-schillegger replied on Mar. 2, 2015 @ 00:28 GMT

Dear Dr. Gibbs,

after a second try I still have to admit not to understand most of your certainly excellent statements. It is a fact that mathematical constructs are difficult to translate into comprehensible physical meaning. Or, is it a trick to confuse those with a desire to understan?

Anyway, the theoreticians have an easy life. Nobody can refute your theories such as multiverses since there are no empirical facts. It sounds to me more like philosophy or clairvoyance.

I wish you good luck with your further work

Best

Lutz

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Author Philip Gibbs replied on Mar. 2, 2015 @ 14:24 GMT

Susanne, the audience here has a wide range of levels of expertise so it is difficult to get it right for everyone. I have never seen these essays as an exercise in science popularization, but I have not included any equations as some people do here. That is my best compromise. I want to say something substantive to people who are familiar with the subject. If I did not mention the specific concepts I am referring to everything would be too vague, and if I attempted to explain them for those less familiar the essay would be ten times as long. Any of the terms used can be skipped and just accepted as something you don't know about, or they can be looked up. I hope you managed to get something out of it.

The topic for this essay is deeply philosophical so I make no apologies for the fact that my essay is philosophical and meta-physical. This kind of thinking is very important at the frontiers of theoretical physics where strongly help assumptions sometimes need to be given up to make progress. It is not testable in its own right but the idea is that it should guide thinking towards new ideas that would be testable. The route from foundational thinking to experimental checking is very long these days and will take many steps and many years. To complain that each step cannot be empirically tested or refuted misses the point of how science is being done. Note that my essay does not use the word multiverse which has been used to describe too many different things.

The other thing that philosophical thinking does is to provide an interpretation of physical theories. I think that is important too if we want to understand where we fit in the grand scheme of things, rather than merely finding practical uses for science.

Dear Philip,

A very interesting approach of the ontology of math indeed.

As an architect I fully support the idea that it is the geomtrical aspects of the universe we should focuss more.

Then more thinkig out of the box seem to be possible, which even could lead to our understanding of the golden mean of the penta dodecahedron multiverse

attachments: Big_Bang_MWI_1.jpg

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Dear Sir,

Thank you for the essay but for someone like me who is trained in another field of science is was quite incomprehensible. I thought that FQXi essays target a general audience. Someone once said that if a scientist cannot explain what he means in a few sentences then he probably lack understanding of what he means. I get the impressions you are trying to impress people more than to educate them. With all respect of course...

Alex Newman

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Author Philip Gibbs replied on May. 7, 2015 @ 17:11 GMT

Sorry, but I dont see this contest as an exercise in popularisation. If we had to write for people who dont know any fundamental physics we could not explain very much in nine pages.

Dear Philip,

You wrote:

“Thus we learn finally that there is no mysterious force that defines our consciousness.

We have no existence beyond our journey in this material world.”

However, No extra mysterious force is needed to understand local or universal entanglement between mirror symmetric particles at large distances right?

So if the universe has mirror symmetry, from the start, then we live in one of the two ( or even more) instant entangled symmetric universes.

Then Max Tegmark is right if he suggest that there is a copy person over there who also read these letters ! at the same moment.

See: Democratic Free Will in the Instant Entangled Multiverse.

http://vixra.org/pdf/1401.0071v2.pdf

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Author Philip Gibbs replied on Mar. 3, 2015 @ 21:03 GMT

Hi leo, good to see you here. Are you doing an essay this year?

Leo Vuyk replied on Mar. 4, 2015 @ 18:09 GMT

Hi Philip,

Sorry I was not able to cope with the subject.

Perhaps an other time or perhaps ablog post

However indeed the relation between Math and physics for me is sort of a problem.

Pehaps you remember that Gerard 't Hooft my topological string model declined because my model did not fit into known math sustems.

I believe that OUR COMPLEX WORLD can not be described by FORMULAS ALONE. WHY? Because we don't know why the universe is as it is. An example: “Finetuning”: Why are the "fundamental constants" constant? My suggestion: because the sub-quantum FORM of particles and the Higgs vacuum lattice have a certain form and play a game with us.. So I designed simple convertible shapes for real QUANTUM particle information use. At the same time I realized that black holes should also have some nuclear form and as a result I found that dark matter is related to black holes and Higgs particles have only energetic mass inside an oscillating Higgs vacuum lattice. Multiverse based mirror symmetric consciousness (entanglement) is assumed to be the base for all particle- wave -and human guidance or wavefunction collapse. SEE: https://www.flickr.com/photos/93308747@N05/?details=1and: http://vixra.org/author/leo_vuyk

I am an architect who is interested in the possible sub-quantum particle FORM as information medium and building blocks in nature. I also focus on the possible dynamical FORM transformation aspects in micro- and macro physics as a base for dark matter black holes, the Higgs field vacuum and the Big bang. see also:

attachments: STEPHEN_HAWKING_1.jpg, YELLOW_BALLS_2.jpg

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Dear Sir,

Dimension is the perception of differentiation between the internal structural space and external relational space of objects. Since we perceive through electromagnetic interaction, where the electric and magnetic fields are perpendicular to each other and both move perpendicularly, we have three mutually perpendicular dimensions. These are invariant under mutual transformation...

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Dear Sir,

Dimension is the perception of differentiation between the internal structural space and external relational space of objects. Since we perceive through electromagnetic interaction, where the electric and magnetic fields are perpendicular to each other and both move perpendicularly, we have three mutually perpendicular dimensions. These are invariant under mutual transformation (if we treat length as breadth or height, the object is not affected) and can be resolved into 10 different combinations. But even after more than a century of failures to find extra-large or compact dimensions; you still subscribe to such fiction perpetuated by the novel FLAT LANDS!

There are many unexplained questions relating to the strings. For example, given the measurement problem of quantum mechanics, what happens when a string is measured? Does the uncertainty principle apply to the whole string? Or does it apply only to some section of the string being measured? Does string theory modify the uncertainty principle? If we measure its position, do we get only the average position of the string? If the position of a string is measured with arbitrarily high accuracy, what happens to the momentum of the string? Does the momentum become undefined as opposed to simply unknown? What about the location of an end-point? If the measurement returns an end-point, then which end-point? Does the measurement return the position of some point along the string? (The string is said to be a Two dimensional object extended in space. Hence its position cannot be described by a finite set of numbers and thus, cannot be described by a finite set of measurements.) How do the Bell’s inequalities apply to string theory? We must get answers to these questions first before we probe more and spend (waste!) more money in such research.

We have discussed Wigner’s paper in our essay “REASONABLE EFFECTIVENESS OF MATHEMATICS” to point out the fallacy. In conformity with the second law of thermodynamics, arrow of time is well established - Past, Present and future are segments of sequences of intervals between events that are strictly ordered – all of future always follows present. The same sequence is not true for past, because any past event can be linked to the present bypassing the specific sequence of its occurrence but you cannot move from past to future violating the sequence. Further, we can remember events of the past and not of future. Thus positrons travelling backwards in time, is fiction. True, time and space are emergent properties, but not because of M theory or LQG. There are simpler explanations based on empirical principles that explain these.

Obviously, this new way of thinking is “giving up” on fundamental physics!

Regards,

basudeba

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Author Philip Gibbs replied on May. 7, 2015 @ 17:21 GMT

basudeba, the "unexplained" questions you ask about string theory are very ordinary questions whose answers are well understood by string theorists. I am afraid you will just have to accept that it is only to you that they are not explained or understood.

The "new way of thinking" is not "giving up" . That is just the opinion of the old guard who does not understand the unexpected truths that new discoveries are telling us. That has always been the way science has progressed.

Dear Pilip,

I like your statement: "layers of speculations" are needed etc. because I also think that this out of the box thinking could be productive.

IMHO:

I think that Stephen Hawking did not calculate with the possibility of a chiral oscillating Higgs field vacuum lattice combined with propeller shaped Fermions. Then, Electrons and positrons could both pushed away from...

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I am not sure if comments are working here. I had two notifications of comments but nothing has appeared.

Excellent paper Phil,

I like the way you would re-frame our treatment of the vacuum, and I agree that a multiplicity or landscape of vacuum state solutions is a feature of a large class of quantum gravity candidate theories, not only Strings. I like the way you informed us about how the concept of an algebra can be generalized, and about the free Lie algebra - which is new to me, but obviously significant. Also; I like that you weave in higher category theory, as I savvy that the category theoretic framework can subsume a lot of other Maths.

Well done!

Jonathan

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Author Philip Gibbs replied on Mar. 12, 2015 @ 07:33 GMT

Thanks Jonathan and good to see you in the contest again. I will be looking at your essay soon.

Phil

Dear Philip,

In Grothendieck's 'dessins d'enfants' all is about a two-generator free group, as I am rediscovering step by step with Magma, motivated by the application to quantum observables and contextuality. Reading your wide range excellent essay, I start to be convinced that playing with free algebra over the appropriate rings, new territories of understanding may be reached.

As you refer to topics also investigated in my essay, e.g. Moonshine, modularity and groups, I suspect you may be interested to read me. I would love to have some comments from your side.

Best,

Michel

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Author Philip Gibbs replied on Mar. 13, 2015 @ 19:47 GMT

Michel, thanks for your feedback. I am glad to see you back here. Your areas of maths are very closely linked to my ideas although I do not knoe them as well as you do. If my talk of free algebras gels with your thinking then I am encouraged by that.

I will of course be reading your essay shortly

Dear Philip Gibbs,

"You talked about nature of physical laws and mathematical structures and then metaphysical structures to guide us in the development of physical theories. why we exist and why laws of physics are so steeped in mathematical abstraction.Uncovering the meta-laws is now the most important goal in our quest to understand the universe.

You also talked about referring...

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attachments: vivekanada_universe.pdf

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Dear Pankaj Mani, thank you for your detailed analysis.

I agree that the question about conciousness is very relevant to this topic. There is a lot to say about it and I could not possibly have fitted the subject into the space for this essay. What I hope is that a future essay topic will ask that question so that I can write about it at length. Meanwhile I am always glad to see other people bringing it up.

regards

Phil

Hi Philip,

Last essay contest I had a system that created QM from just pure random numbers" reality is a mathematical structure". This year's essay has much more astonishing results and I have put in the links (at the end of the sections) to the JavaScripts program, which I am sure you have no problem with. Although I know you are a busy man.

Philip, I am relying on you since I don't seem to have too many customers here. It is ironic that often people say "show me the math" and cut the word salad, and now when I show it, they don't want to bother and it seems like they are saying "bring on the word salad"!

Essay

Thanks and good luck.

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Dear Philip,

Your statement, ‘SUSY is a natural consequence of string theory and would account for fine-tuning of the Higgs mechanism’, indicates the imperativeness for the string theory to be modified. Thus we may think of another set of principles with strings, in that, field with matter is ascribed as single unit of eigen-rotational string-segment. Thus the Univacuum and the Multiplicity of the vacuum, that are descriptive with Space time foam and Spin-foams by String Vaccuua, is differently interpreted with an alternative paradigm of Universe; that is used for a comparative analysis in my essay, ‘ Before the Primordial Geometric origin: The Mysterious connection between Physics and Mathematics’. Hope you may enjoy in reading that.

With best wishes,

Jayakar

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Dear Philip,

Thank you for your essay, excellent as always, stimulating reflection. But it is not about praising. Let us start a discussion.

I do not agree with your interpretation of Tegmark’s Mathematical Universe Hypothesis… You argue that “such ideas are about concepts beyond our ordinary experience for which we do not have predefined words. To think about them we can only...

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Author Philip Gibbs replied on Mar. 18, 2015 @ 15:20 GMT

Jacel, thanks for your interesting points. We aeem to take different philosophical views. You prefer geometry and I prefer algebra for one thing. Of course I cannot say that I am right and you are wrong. That remains to be seen, or perhaps the truth will be neither or both. All we can do is each take our ideas to their conclusions and see which result fits nature.

"Is there any possibility to get an experimental confirmation of the statement that space and time are emergent? "

That could only be done directly by an experiment so cataclismic that it tears space and time apart. However, indirectly we can find the right TOE and use other more doable experiments to check it. The answer will then come indirectly from that TOE. We will never be totally sure that the TOE is completely correct unless we tests everything it can predict including things like the emergence of space and time, but I hope that once we have the answer it will be something sufficiently convincing.

Jacek Safuta replied on Mar. 18, 2015 @ 17:40 GMT

Thank you Philip for the response.

I agree that we will never be totally sure that the theory is completely correct unless we test everything it can predict. However I would not include the emergence of space and time (this just seems to me too speculative). I guess that if we uncovered in nature these five exotic Riemannian manifolds: S2 × R, H2 × R, SL(2, R), Nil and Solv geometry, it would be convincing enough that the geometrization conjecture is the first physical theorem. And the theorem we cannot falsify. But, apparently, at the moment we have to wait. But not so long. As I have mentioned, Torsten Asselmayer-Maluga’s works are my hope to show the direction for future experiments. He now works on NIL, SOLV and SL2.

Best,

Jacek

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Hello Philip

I was able to read your essay despite the fact that most of the concepts you deal with either in physics or mathematics were too technical or specialized for me to understand the points you are making. Is it possible to describe what you mean by universality in a simple way or by analogy?

Nevertheless the essay is lucid and well-written and I read it through. It left me with the hope or rather belief that beyond all the disparate phenomena and complicated theories there is a breathtakingly simple unity.

That is what I have argued in this year's essay, and this time did not have the aid of the elephant as I too did in a past essay, but of the amazingly 'smart' slime mold that can solve mazes. Amazing world!

Best wishes

Vladimir

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Author Philip Gibbs replied on Mar. 18, 2015 @ 12:38 GMT

Vladimir, these issues are technically difficult for everybody and we can only move forward by pulling together and throwing in good ideas. I am glad to see you back to do that again. I too find the subjects difficult so I pick out the bits I understand and try to see some of the picture take shape from those.

Thanks for your comments, I will probably be nicking your slime mould idea next time.

Dear Dr. Gibbs,

I think my earlier post has gone unnoticed because somebody inadvertently posted a new comment as a reply to my post. So excuse me, I am posting it again, especially because I claim myself to be an independent researcher and find solace in the free-for-all 'VIXRA'. I express my sincere thanks to you for providing an asylum for people like me.

The first essay I read...

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Dear Dr. Gibbs,

I think my earlier post has gone unnoticed because somebody inadvertently posted a new comment as a reply to my post. So excuse me, I am posting it again, especially because I claim myself to be an independent researcher and find solace in the free-for-all 'VIXRA'. I express my sincere thanks to you for providing an asylum for people like me.

The first essay I read was yours. Instantly, I identified you as a 'mathematicalist' trying to impose the rule of mathematics in the domain of physics. The way you have written, however, is impressive that any one reluctant will jump into the 'mathematicalist' wagon. That I think is the beauty of the mathematics-oriented thinking coming from somebody who knows the intricacies of both mathematics and physics.

Your statement “geometry is an angel and algebra is a demon …....... the signs are that the devil rules at the deepest levels of existence” is thought provoking. Can I say that the rules of mathematics are essentially algebraic, and geometry just represents its emergent structures. Then the universality of mathematics is in its rules, not in its structures. Regarding the question, whether mathematics is invented or discovered, I think the rules are discovered, but the structures are invented. For example, in chess the properties of the pieces are invented, but the emergence follows mathematical rules and the overall structure of the game is thus invented. Starting with another set of arbitrary properties, you will obtain a different structure.

Again I would like to quote another statement “the theory you get by recursively iterating quantisation should be unique” . Without referring to existing Quantum Mechanics, your statement can be construed to be implying that fundamental particles, just because they are quanta, may be obeying a unique law, which is universal. Does it simply mean that starting from qunatised entities, you cannot have an infinite number of emergent structures?

The 'physicalist' idea that I propose in my essay is this: physics decides the properties, mathematics decides the rules. For the given properties, mathematics decides the emergent structures; for that emergent structures, physics again decides the emergent properties, and so on. Thus, the equations are mathematical, but the variables are physical. Starting from a finite number of variables having finite properties, the number of variables will soon come to the minimum that further emergent structures are impossible. That final structure is the physical world that we observe.

Somewhere above, you have stated that 'physics emerges from mathematics'. This I think tantamount to saying that 'the physical world emerges from mathematics'. Or, given the basic properties of matter, mathematics decides the final emergent structure. That way, I will have to call you a physicalist. Kindly go through my essay: A physicalist interpretation of the relation between Physics and Mathematics. I would be awaiting for your comments.

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Author Philip Gibbs replied on Mar. 19, 2015 @ 14:23 GMT

Ho Jose, I am sorry for not replying earlier. I was busy due to unrelated events and am now back.

I think your assessment of my position is fair and correct. I see mathematics as the realm of logical possibilities and physics as the realisation of those possibilties. From this point of view it obviously makes sense to start with the possibilities and then move on to the realisation.

However, this is just one philosophical position of many and I always recognise that other ways of looking at it can be equally valid. The test of meta-physical ideas is how they lead to more physical theories and from there to experiment. I have described in my essay how I related my philosophy to physics via multiple quantisation, algebraic geometry etc. It will be a long time before we know how it all pans out.

The multiple quantisation idea has been around for a while. I speculatd about the uniqueness of iterated quantisation a few years back at http://arxiv.org/abs/hep-th/9603165 My view of that has not changed but it has developed. I now think that the structure this gives us has to be seen as a system of meta-laws rather than a specific physical theory inside a particular geometry like our spacetime that we can relate to directly through experiment. Physics as we know it is just one solution of these meta-laws. In act you have to go through a cascade of refined solutions to get to the end. So in one sense the end-result of iterated quantisation is unique but the physical theory is not. Perhaps you can realate this to your way of seeing things.

I look forward to reading your essay

Hi Philip,

I still wait for your next replies to my previous message, especially about the Many-worlds interpretation.

Recently I wrote this general overview of how I see things going in this contest, with a list of essays I found best. I also included there a list of essays criticizing the mathematical universe hypothesis which you defend. So I look forward to your comments on these essays.

I also included some not so rejoicing stuff there. I am sorry for this and I wish I did not have to do that, but when I see a nonsense growing too big I cannot go on very long as if it did not exist. So I am also curious to have your view on that. Thanks for your understanding.

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Author Philip Gibbs replied on Mar. 19, 2015 @ 20:58 GMT

Hi Sylvain, it is a nice idea to try and label all the essays with different isms (as on your linked page) so long as you do not take it too seriously.

I think you may also be trying to take the rating too seriously. In my post at the top I say the rating and prizes don't matter to me. What I have found each time is that I start near the top, then later I drop down. You see there are just as many people who hate viXra as people who love it but they arrive later :-)

The reason I keep coming back to the contest is that it is good to formulate thoughts and get some feedback. The FQXi essay contests are very good for that.

I want to respond to some of the unanswered questions here as follows.

I see mathematics as something that comes before physics but I don’t see mathematics as a platonic realm. Mathematics is just the study of logical possibilities and our physical experience is just a stream of those logical possibilities being played out. We don’t need to explain existence and reality any more than...

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I want to respond to some of the unanswered questions here as follows.

I see mathematics as something that comes before physics but I don’t see mathematics as a platonic realm. Mathematics is just the study of logical possibilities and our physical experience is just a stream of those logical possibilities being played out. We don’t need to explain existence and reality any more than that. Our intuition may demand a causal and structural explanation for why it all happens but that is just part of our psychological makeup and has no answer. However, we do need to explain why the laws of physics follow certain mathematical rules.

When people started doing mathematics they were interested in counting and measurement. There was no mystery about why the mathematics was effective in physics, because it was derived from it. But then mathematicians saw interesting logical structures that did not have obvious applications, such as prime numbers. Mathematics took on a life of its own.

Logical possibilities include stuff that is very interesting to mathematicians and stuff that is less interesting. The interesting stuff is characterised by its universality. It is applicable to a range of problems. Mathematicians are delighted when something they formulated for one problem turns out to be useful for another. They get a sense that those logical structures are discovered while others are merely invented. This is what distinguishes pure mathematics from other intellectual endeavours such as art and literature where we consider things to be created rather than discovered. All these things are logical possibilities but the mathematically interesting structures are more universal. They would probably be discovered by an alien race of mathematicians no matter what point they started from.

Already there seems to be some mysteriousness about this universality. Why is it there? Some people are not convinced. They see no mystery yet, so let’s look further.

As pure mathematicians continued to study these objects for their own sake without any remaining interest in physics they went beyond the naturally occurring logical structures. They discovered the mathematics of complex numbers, non-Euclidean geometry and higher dimensional spaces. They did not expect these things to be useful to physicists but later they were. Already the unreasonable effectiveness of mathematics seemed mysterious to Wigner, but some people still shrugged their shoulders. They can say that these things were still inspired by physical ideas originally or that the universe is obviously going to be mathematical so of course these things are going to be useful.

For me the real clincher came when string theory was used to prove the monstrous moonshine conjectures. These were mysterious problems connecting areas of number theory and algebraic geometry that nobody would have expected to be connected to the real world. String theory has not yet been shown to be real physics but it was certainly discovered by physicists generalising the framework of quantum field theory with the goal of forming new physical theories. The distance across mathematics spanned by string theory and monstrous moonshine could not have been greater, and yet they turned out to be deeply connected in an unavoidable way.

This is no longer just a simple matter of the unreasonable effectiveness of mathematics in physics. It is also about the unreasonable effectiveness of physics in mathematics. The mystery is deep and cannot be shrugged off. It demands an explanation.

In my opinion, that explanation will come from a better understanding of universality and how it emerges in complex systems. It must be a self-organised structure embedded in the complex system of logical possibilities and their interrelations. It may be characterised by scale-free networks, self-similar fractal structures, path integrals over the grand ensemble of algorithms, iterated quantisation, n-category theory, symmetries etc. Our experience then unfolds according to laws of physics that form as a hierarchy of solutions derived from these universal systems. That is how our universe is put together and it explains the mysterious links that bind mathematics and physics together because this universality is ultimately what both mathematicians and physicists are drawn towards for different reasons.

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Hi Philip,

I agree with Ken Seto about the need for concentrating more on physical models. I have witnessed their potential in my own research and theory (TOEBI). Also, don't be too judgemental towards people who think that the contemporary physics has gone into woods for a long time ;-) I'm one of those people.

Anyway, you are a solid performer as usually, thanks for your essay! Check out my essay, it's a good example of a more physical theory.

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Author Philip Gibbs replied on Mar. 23, 2015 @ 19:45 GMT

Thank you Kimmo, glad to see you here again.

Kimmo Rouvari replied on Mar. 24, 2015 @ 08:05 GMT

Do you think that there is an underlying physical, concrete, entities which are the building blocks of our universe? For example photons, electrons... concrete or not? Lets forget our contemporary theories about them, clean table view and your opinion.

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Anonymous replied on Mar. 24, 2015 @ 12:02 GMT

Kimmo, that's an interesting question from the point of view of universality which I did not have space to cover in the essay, so thanks for asking it.

The idea of universality is that the laws of physics emerge from an ensemble of different complex systems. Because of this they dont tend to have unique best descriptions. Take as an example the concept of universal computing as defined by Turing. He used a Turing machine but he could equally well have used something else like any programming language. You can show that the different possible definitions are equivalent. The concept of universal computing is unique and would be classed as something that mathematicians discovered, yet the Turing machine is invented and not special or unique.

If the laws of physics emerge from a principle of universality I expect the same thing to happen. I dont think reductionism will lead to a unique end point with a fundamental set of building blocks such as parrticles or strings. Instead there will be multiple ways of ariving at the laws of physics via definitions, none of which will be obviously the best or simplest or right way to go.

We already see this in some (still speculative) theories of physics such as elecromagnetic duality. In this case you can regard electrically particles particles and fields as fundamental and particles with magnetic charges are derived or composite, but you can also start from a descritpion where the magentic fields are fundamental and the electric fields are derived

Perhaps you are trying to amke a distinction between theories based on abstract mathematical ideas and theories based on concrete physical ideas? I dont see how there can be such a disinction. How do you define concrete?

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Hi Philip,

Sorry for my last post ,it was cryptic and done in a hurry. In this one I will elaborate .

I was trying to dig up some concrete material on your random graphs and random matrices and how they lead to Necklace algebra and symmetries. That is because as I explained very very briefly that my system which is based on simulation is indeed nothing but a Buffon's needle type, something like two needles which are larger than the gap(the space between the needles).

As you well know Buffon's needle is a geometric probability problem which is well connected to integral geometry which is the theory of measures on a geometrical space invariant under the symmetry group of that space.

So my theory and your theory and the theory of particles in standard physics are connected.

Can you post some links to your materials, and what do you think about my way of thinking of linking all these ideas. I know I am asking for too much effort on your part, but I need some clear help in the direction which I will be taking to put my system in a more formal incarnation. But of course I understand if you cannot oblige.

Essay

P.S. Some info about the setup of distance in the program

Thanks and good luck.

attachments: 1_dist.png

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adel sadeq replied on Mar. 25, 2015 @ 16:34 GMT

Just a note

I can't find any mathematical write ups on you material , they are too general, so DO you have more concrete material. Thanks

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Author Philip Gibbs replied on Mar. 26, 2015 @ 09:11 GMT

Adel, thank you for the questions. Since you ask I will give you a potted history of how my work developed and you can compare with your own path.

As a PhD student I worked on Lattice Gauge Theories and wrote programs to do Monte Carlo calculations, much like the Buffon's needle trick except there are many more variables in the calculation.

I left academia but was still interested in...

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Dear Philip Gibbs,

In your essay you wrote, "If there is indeed a class of many possible solutions for the vacuum, is only one of these real? I think it is more parsimonious to accept that all solutions exist in some higher sense, whether inside or outside our universe. Some physicists have speculated that there is an eternal process of inflation with vacua decaying to different solutions so that our own universe is just one bubble inside a larger arena. Others have looked at evolving universes where the laws of physics evolve in leaps where new universes are born from old. We can learn a lot from thinking about such possibilities whether they are eventually testable or not but we should not get carried away by thinking they are less speculative or more testable than they really are."

If the foundations of physics are mathematical equations that restrict energy and spacetime then there might two basic possibilities: (1) the restrictions cause spacetime to curl up according to energy-density based upon generalized quantum information, or (2) the restrictions cause approximations to energy and spacetime to build up from Fredkin-Wolfram information below the Planck scale. How many fundamental particles need to be added to the roster of the Standard Model of particle physics? My guess is that there 2 basic possibilities: (1) if the Heisenberg uncertainty principle should be generalized to use both hbar and alpha-prime, then some form of supersymmetry is empirically valid, or (2) if Einstein's equivalence principle fails for dark matter then the finite nature hypothesis is empirically valid (because the multiverse has a boundary and an interior). Google "witten milgrom" for more information. What is your opinion of the space roar and the photon underproduction crisis?

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Author Philip Gibbs replied on Mar. 27, 2015 @ 12:21 GMT

David, thanks for these points. I feel they go beyond the subject of my essay which does not have much to say about details in cosmology. The anomalies (dark roar and photon underproduction) you mention are very interesting and not ones that I am familiar with. I fear that the resolutions will be rather mundane but I hope there will turn out to be something fundamental at work and I will keep an open mind on it until more compelling data is available either way.

I follow the digital physic and finite nature ideas which are very interesting to someone like me who sees information and qubits as fundamental but I dont agree with some of the stronger claims or theories about cellular automata. This is because I steer away from the idea that simplicity has nay part in determining the laws of physics and use universality instead. Nevertheless digital physics is also interesting from the point of view of universality.

David Brown replied on Mar. 29, 2015 @ 12:46 GMT

Dear Philip Gibbs,

In your essay you wrote, "Today the more progressive physicists take a different view. Space and time are seen as emergent from a yet unknown new way of looking at the universe that must go beyond the bounds of standard quantum field theory, but that much is widely accepted and therefore is not the defining feature of the new paradigm. What is harder to accept is the...

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Dear Philip Gibbs,

In your essay you wrote, "Today the more progressive physicists take a different view. Space and time are seen as emergent from a yet unknown new way of looking at the universe that must go beyond the bounds of standard quantum field theory, but that much is widely accepted and therefore is not the defining feature of the new paradigm. What is harder to accept is the multiplicity of the vacuum – the idea that there may be more than one stable solution for cold empty space and that the one we know is nothing special or unique." If spacetime needs to be replaced, there might be 2 basic possibilities: (1) there exists a continuous, non-commutative geometry for the string landscape with different Lagrangian formulations of quantum field theory; (2) quantum field theory is an approximation generated by Wolfram's automaton via approximations to string vibrations on a finite lattice. Could there be a third alternative? According to Jacob Bekenstein, "The present paper introduces TeVeS, a new relativistic gravitational theory devoid of a priori fields, whose nonrelativistic weak acceleration limit accords with MOND while its nonrelativistic strong acceleration regime is Newtonian. TeVeS is based on a metric, and dynamic scalar and 4-vector fields (one each); it naturally involves one free function, a length scale, and two positive dimensionless parameters, k and K. TeVeS passes the usual solar system tests of GR, predicts gravitational lensing in agreement with the observations (without requiring dark matter), does not exhibit superluminal propagation, and provides a specific formalism for constructing cosmological models." — J. Bekenstein, "Relativistic gravitation for the MOND paradigm", 2004, arxiv.org

What is my fundamental objection to TeVeS? I doubt that it makes sense in terms of string vibrations. Digital physics might, or might not, be empirically valid. In any case, MOND is empirically valid — on the basis of the work of Milgrom, McGaugh, Kroupa, and Pawlowski. MOND might suggest 2 basic possibilities: (1) the equivalence principle is 100% correct but the concepts of gravitational mass and inertial mass need to be slightly changed by a complicated modification of Einstein's field equations; (2) the equivalence principle is 100% correct for particles that are measured but fails for dark matter. Why do I think that the first alternative in the preceding statement is wrong? If you modify GR by adding two or more new mathematical mechanisms then you need to explain the modifications in terms that make sense to most physicists. You also need to explain what went wrong in Einstein's original derivation. I say that the -1/2 in the standard form of Einstein's field equations should be replaced by -1/2 + dark-matter-compensation-constant. This means that the multiverse has a boundary and an interior and that gravitational energy is lost from the boundary; the process eventually results in an instantaneous collapse of each matter universe and each antimatter universe into a synchronized big bang that occurs every 81.6 ± 1.7 billion year. Let us suppose that the fundamental string domain really is 10-dimensional in empirical reality. If nature is infinite, the 10 dimensions somehow curl-up into 4 spacetime dimensions. If nature is finite, the 10 dimensions DO NOT curl-up. There are 4 dimensions of spacetime in a universe composed primarily of matter, 1 dimension of Wolframian time that determines the nonmeasurable clock speed of Wolfram's automaton in a matter universe, 4 dimensions of spacetime in a universe composed primarily of antimatter, and 1 dimension of Wolframian time that determines the nonmeasurable clock speed of Wolfram's automaton in an antimatter universe. The Wolframian time is needed to explain the discrepancy between astronomical time and atomic time. Here "astronomical time" and "atomic time" are as described by Fernández-Rañada and Tiemblo-Ramos.

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Hi Philip,

Your central thesis that mathematics and physics converge due to universality is very intriguing to me. However, it still leaves open the question of why the meta-laws should exhibit such universality. We still have a "miracle" to deal with, but just at one higher level than Wigner's miracle of the effectiveness of mathematics. Of course, all answers to Wigner's question will open their own new questions, so I do not see this as a defect of your view. However, I think that maybe if we take into account that human knowledge is developed by a social network of individuals, that might help to explain why universality should inevitably emerge in our fundamental laws. It is perhaps a bit controversial to bring social factors into the analysis of fundamental physics, but I think we can safely admit that knowledge is partly shaped by the society that generates it without descending into full-scale social constructivism.

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Anonymous replied on Mar. 27, 2015 @ 13:26 GMT

Interesting points. I dont claim to have all the answers. These are the Marianas Trench of philosphical questions and the bottom is still a long way down. However, I am guided by the idea that there cant be any miracles. There must eventually be some way to understand our experience without harking back to something more fundamental, even something like simplicity is too much of a human construction.

I am able to accept that the range of logical possibilities is an acceptable starting point which does not require any miracle. Mathematics is just the analysis of these logical possibilities. We can start from there and try to find a bridge that takes us to physics without putting in any miracles. Universality is just that bridge. It must be there because we got here somehow.

I dont know exaclty how the bridge is constructed but I use metaphors from complexity theory to try and get some ideas. Most of the things we know about universality in complexity theory exist within some bigger context. Everything has to be intrinsic rather than extrinsic. We have to avoid the need for some measure on the moduli space of possible theories because that measure would need an explanation itself. I think some forms of universality such as the universality of computability do not need such a measure. I think there is a similar universality principle at work in category theory but it is harder to find.

I dont think social constructs are involved in forming these meta-laws. I do think that social constructs such as anthropomorphic selection is relevant in selecting the solution to the meta-laws that forms our experience of reality. So there can be no fine-tuning in the meta-laws. They must be perfectly natural.

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Phil,

Count me among your admirers. Though I haven't always understood what you're saying, I find this essay crisp, clear and abundantly meaningful.

"What then would happen if we treat the whole of mathematics as a statistical physics system or as a path integral over the moduli space of all possible theories [4]? Would some universal behaviour emerge that could describe the meta-laws of physics?"

I think so! Taking your reference to chess-playing aliens, one finds that that every chess game, as complex as the game is, has a critical point where the game can go either way, or to the equilibrium state of a draw. I agree also with your view of vacua -- my conclusion is that nature cannot respect any vacuum state without respecting all vacuum states.

Years ago I suggested that even mathematics (at the level of analysis) is a self organized system. You get my highest score, and I hope you can read my essay when you get a chance.

All best,

Tom

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Dear Philip,

Thank you for the comments you left on my essay's page. About a week ago, following a reference at the end of Jonathan Dickau's essay, I came upon your almost twenty-year-old essay Theory of Theories, and I found your extension of the idea behind Feynman's path integral to the space of all possible theories absolutely fascinating. Quoting from that essay:

"We might well...

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Dear Philip,

Thank you for the comments you left on my essay's page. About a week ago, following a reference at the end of Jonathan Dickau's essay, I came upon your almost twenty-year-old essay Theory of Theories, and I found your extension of the idea behind Feynman's path integral to the space of all possible theories absolutely fascinating. Quoting from that essay:

"We might well ask if the same can be applied to mathematical systems in general to reveal the laws of physics as a universal behavior which dominates the space of all possible theories and which transcends details of the construction of individual theories."

I then reread your entry in this year's contest, where you expand upon this idea, whose significance I had missed on first reading, and followed your reference to the recent paper by Seth Lloyd and Olaf Dreyer, The universal path integral.

If I were to rewrite my essay today, I would certainly mention these ideas. I totally agree with you that, if all possible mathematical/physical universes have potentially the same existence as ours, the anthropic principle is not enough by itself to explain why we find ourselves living in a universe that is so regular and relatively simple. Something like your Theory of Theories could "collapse" the chaotic ensemble of all mathematical possibilities, via something like a path integral, to a reduced set of relatively well behaved "coherent" scenarios, on which the anthropic principle would then act. The principle of stationary action has always been my favorite idea in all of physics, and to think that something similar could play a role in "regularizing" the "smorgasbord" of the multi/Maxiverse is very appealing to me!

I agree with you that a future FQXi contest on the relationship between consciousness and physics would be absolutely fascinating! In this year's contest, we have splits between mathematical platonists and anti-platonists, as well as the usual split between the "let's evolve physics from the current accepted theories" crowd and the "bring back local realism and/or absolute space-time" crowd. Imagine if we add a split between "consciousness-first" and "matter-first" views, and between the "free-willers" and the "free will is an illusion" camp... Oh what a wonderful, delicious and mad cacophony this would be! :)

Marc

P.S. I have also posted this on my essay's page, and I will be back with a proper review of your essay, hopefully within the next few days!

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Member Marc Séguin replied on Apr. 10, 2015 @ 05:00 GMT

Dear Philip,

Following our previous conversations, I just reread your essay. Indeed, we share a lot of the same views.

I like the way you begin your essay by considering the shortcomings of the “univacuum assumption”. I googled “univacuum” and I think you are the first to use the term in this context. I would say that I am clearly in the camp of the “multivacuers”… but...

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Dear Philip,

Following our previous conversations, I just reread your essay. Indeed, we share a lot of the same views.

I like the way you begin your essay by considering the shortcomings of the “univacuum assumption”. I googled “univacuum” and I think you are the first to use the term in this context. I would say that I am clearly in the camp of the “multivacuers”… but I think there are many “univacuers” out there! You say that the idea of the multiplicity of the vacuum “bruises the egos of particle physicists who thought that the laws of physics they were unveiling were special in a very fundamental sense.” This echoes the final sequence in the third of my "This Is Physics" videos (submitted to the recent FQXi video contest) where I claim that “Most physicists don’t like the idea of the Multiverse, because if it is true, it means that they have devoted their lives to master only ONE physics of ONE universe instead of THE physics of THE universe.”

I agree with you when you explain that it is more “parsimonious” to accept that “all solutions exist in some higher sense, whether inside or outside our universe.” I claim essentially the same thing in my essay when I discuss the issue of Occam’s razor (the “law of parsimony”) in the context of the multi/Maxiverse.

Like I said in the most recent reply to my conversation with you and “En Passant” on my essay’s page, maybe we are obscuring the issues by insisting in labelling as "mathematical" or "physical" the fundamental structures that make up reality. In your essay, you take a safe and wise approach when you simply talk about the “timeless and spaceless” ensemble of “all things that are logically possible”.

For me, the highlight of your essay is when you say that “Universality brings together all the logical possibilities of mathematics under one metaphorical path integral”. Indeed, emergent universal behavior, as expressed by the Meta-Laws of physics, is what we need to understand better if we are to explain why, in the space of all possible worlds, we find ourselves living in a universe that obeys stable and relatively simple laws. I like how you use the concepts of path integrals and critical points in the context of finding out the Meta-Laws of physics.

Finally, you nicely address the subject of this year’s essay directly when you explain that “mathematicians and physicists are attracted towards the same critical point of universality”.

Great job!

Marc

P.S. As you say, the fact that the Monstrous Moonshine Conjectures have been studied by using the methods of string theory is an astounding demonstration that “there are deep relations between ideas from physics and mathematics”. I have to confess that I’m having some difficulty understanding clearly the complicated concepts behind the Monstrous Moonshine Conjectures and Borcherds’ approach. Do you know of any (relatively) accessible sources that deal with this fascinating topic?

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Author Philip Gibbs replied on Apr. 10, 2015 @ 08:31 GMT

My use of the word "metaphorical" when talking about the path integral is deliberate. We get an intuitive idea feel for universality when we think of it as a sector of the path integral that dominates or where phases do not cancel out, as in maximum entropy or the classical limit. But even in quantum mechanics that is not the whole story. The path integral for fermions works differently through some less intuitive algebraic mechanism.

Universality of the concept of computability is another example that is less intuitive. Some people do not even recognise it as the same use of the word universality, but I think it is. The universailty that I am looking for in this essay may also be more subtle than just a path integral dominated by some kind of comonality, but it is a good metaphor and possibly a source of toy models that might be instructive.

The monstrous moonshine conjectures are quite deep and a bit beyond my expertise, but you can get an idea by learning a little about the Golay code and the Leech Lattice and the related groups. There are a lot of mathematical ideas mysteriously connected by the number 24 which are also connected to the number of dimensions in bosonic string theory. John Baez wrote some easily understandable articles about that.

Dear Phillip,

There are opinions that Euler's identity is of particular importance for physics. In this competition is very rarely mentioned. I have no idea about it, but I see the possibility of complementarily exp(i*pi), (from Euler's identity) and exp(2*pi), which I use in my essay, under the name cycle. I ask: what you think about the possible progress in using Euler identity in physics?

Regards,

Branko

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Author Philip Gibbs replied on Apr. 18, 2015 @ 09:46 GMT

Dear Brabko,

Euler's identity was an early example of the surprising connectedness of ideas in mathematics and physics. It linked

$e$

and

$\pi$

in a surprisingly direct way where previously they seemed unconnected. Now we take it for granted because it is part of complex analysis that is common place in maths and physics, for example it is used in Fourier analysis. However it is a good idea to use it in this contest.

Hi Phil,

It is a pleasure to meet you again in FQXi Essay Contest. Even this year, you made an excellent work as I found your Essay very interesting and enjoyable. I must confess that I have read your Essay after reading a nice sentence of yours reported in the Essay of our friend Jonathan J. Dickau which claims that “the laws of physics are a universal behaviour to be found in the class of all possible mathematical systems". In any case, here is a couple of comments on your nice Essay:

1) Some years ago I discussed in San Marino with two great physicists, i.e. Hagen Kleinert and Alexander Burinski, on the new paradigm that is emerging in fundamental physics concerning the new way of looking at the universe. All of us three agreed that gravity is the key. We think that gravity goes beyond string theory and quantum field theory.

2) I disagree on the issue that the holographic principle is required to resolve the black hole information loss puzzle. This assumption by Susskind is based on the Maldacena conjecture. But I agree with Mathur's criticisms, see here and here. The key point is that the AdS/CFT duality works only for low energy processes, where black holes do not form. In other words, if we force the gravity theory to be the dual of a given CFT, then we cannot assume that black holes will form in the theory. Thus, the duality seems to break down in presence of black holes.

In any case, I still remark that I find your Essay very intriguing. Thus, I give you a deserved highest score.

I hope you will have a chance to read my Essay .

I wish you best luck in the Contest.

Cheers, Ch.

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Author Philip Gibbs replied on Apr. 19, 2015 @ 11:54 GMT

Christian, It is good to see you here again.

I agree that gravity and spacetime is an important key. For me it is about how to understand that the geometry of gravity emerges from somthing more algebraic and abstract, but there are other ways to see it.

I dont think the holographic principle is really based on AdS/CFT. The principle was formulated by 't Hooft and Susskind before the Maldacena conjecture and is independent of that or string theory. The problem is to know the general context in which the conjecture could be true. For that I have suggested that "complete symmetry" is the required element. Of course it is not unreasonable to be skeptical of the principle. It is speculative, as is string theory. I am sure it will be many years and there will be many interesting discussions and revelations before any consensus is formed.

Philip,

Heavy stuff. As some politicians would say, "I am not a scientist specializing in quantum gravity, so ..." Well, what they say is simpler.

"All is possible in the quantum realm but there is a hierarchy of classical limits ... these limits define worlds in which math rules are played out according to the law of quantum averages."

Can we simply start with trying to explain a mystery in the classical world, for example, how European robins navigate N and S seasonally. A theoretical physicist and a molecular genetics professor did this. They combined a receptor for the avian chemical compass with a protein capable of generating entangled electrons that interacted with the Earth's magnetic field. Does their study impose a classical limit which utilizes what they know about quantum mechanics?

I know I am cherry-picking your quotes but I am struggling to understand.

Incidentally what does a successful BICEP2 discovery of a primordial B-mode cosmic inflation caused by gravitational waves do for quantum gravity?

Like to see your thoughts on my essay: http://fqxi.org/community/forum/topic/2345.

Jim

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Author Philip Gibbs replied on Apr. 21, 2015 @ 21:40 GMT

James, the world seems classical but that is only superficial. Quantum mechanics plays many roles in life.

If the BICEP2 discovery had stood up it could indeed have allowed us to explore the effects of quantum gravity in the early universe. Sadly that seems not to be unless we can find a clear enough window through the dust. Other opportunities to see similar effects may come from direct observation of primordial gravitational waves or low frequency radio waves.

Phil,

Well up to you usual high standard and with signs of greater maturity of view. I hope my score helps keep you at the top. I particularly like your identification that the question can be just as well reversed (why is it that physics...). I do however have a couple of questions;

1) Do you really believe there must be a greater or 'super' symmetry hiding away behind the 'dipole' symmetry considered 'breaking' by Green and most particle physicists? ..and what would it bring. Do you think of the concept that the dipole may perhaps be the very quiescence of 'matter' (inc anti) as opposed to (maybe dark?) 'energy' alone?

2) This may be semantic, but suggesting a 'map of all things logically possible" would seem to many to be excluding QM and non-locality. Do you suggest QM; a) CAN have a 'logical' explanation. Or b) ??

Re 2; I hypothesise a 'quasi classical' mechanism that seems to reproduce it and reveal the mathematical 'sock switch' trick that hides it in my essay, so prefer a).

I hope you get to read mine. I feel that in 'stabbing in the dark' I've felt something, but how can we then expose what it really is when each of us has a different vision? Perhaps the value of reading these a essays is in converging those vision.

Well done, and very best of luck with the definitive judging.

Peter

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Author Philip Gibbs replied on Apr. 21, 2015 @ 21:49 GMT

Peter, supersymmetry was first conceived as a component of quantum gravity where it may be very hard to detect. If is important in making perturbative quantum gravity more consistent. In my idea of "complete symmetry" where there is a degree of symmetry for every degree of freedom supersymmetry is essential simply because there are fermions. All this is specualtive of course. I dont think there is any good evidence even in dipole measurements.

So called quantum logic can be described using ordinary ideas in logic. We can pretend that it is something more general but I dont see it that way. Of course there are some mysteries in quamtum mechanics but I dont see them as questions beyond logic. Perhaps I am wrong.

Dear Philip,

Because universality is the central concept in your ontology, I wonder whether it would be appropriate to put logic at the point of universality. We usually think of universal concepts as the concepts which apply to everything. Similarly, universal principles are defined as those principles which apply to everything. The common view seems to be that the concepts and principles of logic are universal in this sense. Your chart includes all logical possibilities. If we try to organize and understand the realm of all logical possibilities, then I think we would begin by using the concepts and principles of logic. In a sense a very basic part of the meta-laws are the laws of logic. Of course, there are more specific meta-laws as well, including meta-laws for physics. But maybe I am misunderstanding the role of universality here. In any event, thank you for a stimulating essay.

Best wishes,

Laurence Hitterdale

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Author Philip Gibbs replied on Apr. 21, 2015 @ 21:51 GMT

Laurence, I dont think you have misunderstood it. You have expressed it very nicely.

Philip,

Shark time when some are pulled under, so I am revisiting essays I’ve read to assure I’ve rated them. I find that I rated yours on 4/20, rating it as one I could immediately relate to. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345 as the hours tick down.

Thanks,

Jim

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Philip,

I am uploading an Excel spreadsheet with the contest results. This might be useful if you decide to do a comparison between viXra authors and FQXI authors in general.

Thanks again,

Gary Simpson

attachments: FQXI_2015_Results.xlsx

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Dear Philip,

This is very well written essay, and an enjoyable read.

I read quite a long time ago, and I think I am now on my third read. I guess that I really have a different perspective.

You have a logically-ordered ontology of mathematics which you present metaphorically. And central to this is the idea that there is some sort of universality around which the mathematics...

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Author Philip Gibbs replied on May. 6, 2015 @ 09:43 GMT

Kevin

Thank you for your insightful comments

I don’t think there are really different types of mathematical theories. There is just one self-referential logical whole. We see it from the inside as participants and like children who rep4eatedly follow every answer with the question “why?” we are never satisfied with a final answer. Yet I think that the class of logical...

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Kevin

Thank you for your insightful comments

I don’t think there are really different types of mathematical theories. There is just one self-referential logical whole. We see it from the inside as participants and like children who rep4eatedly follow every answer with the question “why?” we are never satisfied with a final answer. Yet I think that the class of logical possibilities is as far back as you can go. We have to accept that it is consistent because we know that cannot be proven from within the system other than by the fact of our own being.

I may overstate the metaphorical aspects of my ideas but I do so to try and keep things separate from the physical models and ideas that our minds are programmed to look for. Sometimes we seek explanations for things that are not there. Inspired by the words of Marc Seguin I would put it like this , consciousness is biology plus noithing else, biology is physics plus nothing else, physics is maths plus nothing else, maths is logical plus nothing else and logical is just nothing else. We look for more in our minds by trying to decide what exists and why and where it came from. We can only express these questions by analogies from our physical experiences. This is a good way to gain some philosophical understanding but we should not lose sight of the fact that they are just metaphors

I agree on te importance of symmetries is algebra but I think that gauge symmetries are the same thing. That is where they come from. In fact the meta-laws have much more algebraic symmetry and the symmetry we know of in physics must be part of a much greater whole. This is the only way to explain the holographic principle for example. The algebraic symmetries are more fundamental but the physical gauge symmetries are what remains of them when the solutions of the algebraic equations are mapped to emergent space and time. I hope one day people will understand in detail how this works using the principles of category theory, algebraic geometry and the like.

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Thanks to everyone who commented and rated my essay. This was a subject that I started thinking about 25 years ago so I was very happy to have the chance to write about it here. I dont take the final placements seriously. I used to wish for a prize place in these contests but now I realise that the winners tend to be those who take the safer options. If I win I will feel that I was not sufficiently controversial. I like to imagine that in a hundred years time someone will revisit the essays to rate them in the light of future discoveries. I aim to write for that rather than the present judging. Perhaps it is a good thing I wont be here to see the result.

Questions I would like to see for future contests are:

- Can we explain consciousness?

- Is there merit in the multiverse?

- Why is there symmetry?

- Why the quantum?

- Where are the aliens?

- What is the long-term future for humanity?

Author Philip Gibbs replied on Jun. 11, 2015 @ 08:10 GMT

I am very honoured to receive a prize in this years contest. Congratulations to all the winners. To those who did not make it I say dont be disheartened. These contests are a bit like mother and baby contests and we all think our baby is the most beautiful. It is hard not to feel offended when someone elses baby is judged to be better but the judges are only human and following their own opinions. My guess is that the unknown judges are not always the high level experts we imagine them to be so the result is just one set of opinions and not necessarily the most important one. The truth is that all the babies are beautiful in their own way and we will have to wait for them to grow up before we have the hindsight to judge their real ptoential.

I suppose that I should now follow my words prior to the announcement and say that my essay was not radical enough because it won a prize. However I have to point out that they had to invent a new lowest ever fifth level of prizes and a special category of non-academic author to get me in :-) Some people are going to think that I dont fit the non-academic label bacause I have a PhD and have published in academic journals, but all of my work on this topic has been carried out independently of any academic institution over 28 years so I think it is right. I dont think I am the only prize winner that fits this description. It is good to see that top places are going to some non-FQXi members this year.

A lot of the prizes went to people who argued against the mysterious nature of mathematics in physics. Most notably the first prize to Wenmakers who argued that mathemaricians are just following the influence of the physical world. Most pure mathematicians would strongly dispute this and they are right. They are very capable of exploring abstract ideas independently of any kind of real world application yet such applications frequently appear later. The manner in which ideas from physics are unexpectedly applied to problems in pure mathematics is even more striking. The moonshine conjecture is just the most obvious example of this.

Looking forward to the next essay or video contest. Thanks to the people at FQXi who worked hard behind the scenes to make this work.