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.

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.

    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.

    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ﾃ--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ﾃ--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.

      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.

      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.

      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.

      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 ".

      The ratio of nuclear to electrostatic strength of interaction between protons (the latter being essentially given by the fine structure constant), gives the approximate weight of the most stable element (iron)

      As for chemistry with given elements, only 2 physical constants seem involved:

      The fine structure constant gives the average speed of electrons compared to the speed of light, which may result in relativistic effects but as far as I know the consequences on chemistry are quite small. One of the main effects I heard of is that it gives the color of gold, due to the properties in the excitation of innermost orbitals, that of electrons having higher speed, closer to the speed of light because they come close to the nucleus. Generally, the fine structure constant determines the intensity of the photon emission/absorption processes, and also the wavelengths of photons, in case that matters.

      More importantly, the electron-to-proton mass ratio determines the width of the Heisenberg uncertainty on the distance between atoms with a given bond in its ground state. Namely, this distance uncertainty is proportional to (k.m)-1/4 where k is the rigidity of the bond and m is the ratio of the mass of the atom to that of the electron.

      In the case of covalent bonds (k close to 1) this uncertainty is quite small anyway (such as 0.1 邃ｫ), since m is so big, despite being put to the power (-1/4).

      The sensitivity, then, may come for weaker bonds (small k), especially the inter-molecular bonds (including the lateral degrees of freedom) packing small molecules into solids or liquids, however I'm not sure how much it stands as compared to the role of temperature, which should be the main factor in many cases (letting the ground state of the bond unlikely and thus irrelevant). This latter uncertainty on position is proportional to sqr(T/k). Where temperature happens to produce a significantly bigger position uncertainty of a given bond than the Heisenberg uncertainty of the ground state (even twice bigger may suffice), the sensitivity to the mass ratio becomes insignificant.

      For details and explanations, I gathered in my site some relations of dimensional analysis that give the orders of magnitude of a number of phenomena out of the fundamental constants of physics.

      But I do not see there a point to consider fine-tuning done for a specific biochemistry that would exclude other forms of biochemistry. Instead, I see the possibility of biochemistry as a very general property of chemistry, that is its ability to develop complex molecules with complex reactions. As soon as complex chemistry is possible in general, I do not see a point why the specific efficient combinations should be unique. Just take an example : without leaving this Earth, Arsenic in significant amounts is toxic for most organisms, however a few species of bacteria have a different biochemistry that tolerates it, and even uses it, to thrive where it is abundant.

      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

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

        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.

        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

          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

          7 days later

          "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.

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

          Sincerely,

          Miss. Sujatha Jagannathan

          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

          "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.