Dear Philip,

thanks for answering a not so positive comment! The fact that a term is accepted in, say, physics does not imply that it has meaning. The 'multiverse' is such an example, because it is not hypothetical but merely speculative. My point was to say that a compound of meaning-less or very vague notions is not well suited to argue anything.

In addition, by the very well defined meaning of the word 'transcendence' one points to a domain about the form and operations of which nothing can be known in principle. Your 'transcendence', however, mediates between two domains of which you claim to have or hope to gain knowledge. So, the use of 'transcendence' WITHIN physics is an oxymoron.

Heinrich

Something being 'speculative' doesn't mean that is has no meaning: one may for example speculate that someone is late because he has been held up by traffic, and it is perfectly clear what the meaning is. In regard to terms such as emergent or multiverse one has to turn to the literature to discover what precise meanings have been assigned to the term concerned, it is not a matter of there being an absolute meaning as there is for example in the case of multiplication of integers.

I agree with Brain Josephson that speculative ideas can be meaningful. FQXi forums are full of speculation.

I know that the word "transcendence" in a religious context means to go beyond what can be understood in physics, but that is only one of its meanings. I used the word "transcend" which is just a verb that also has a much more down-to-Earth meaning. It means to go beyond some kind of limits. I was using the word in the context of emergence of space and time. If space and time emerge from some physical theory then you transcend geometry by working with that theory. I don't know what that theory is but I have offered a few ideas and if space and time really are emergent then I do think the theory of how that works can be understood. There are at least well understood pregeometric models of spacetime emergence that could be part of the answer, including matrix models for example.

I accept that some of my terminology could benefit from a longer explanation, but I think part of the way this contest works is that the essays raise questions which can be discussed in the comments. I am happy to try to answer any such questions here.

I can easily accept that inexact laws have some significance. This is fine when we are in the realm of complexity theory and emergence. I think I come in at the high end of the scale when it comes to emergence. My default for anything would be that it is emergent at some level, all the way down to nothing.

I am also well strapped into the bandwagon that says information is fundamental. Information is a robust concept and it is important in biology as it is in physics, so the inexactness of biological systems could connect to physics through information processes.

I think your 'principle of universality through recursion' provides a mechanism whereby exactness can emerge, as your [math]$\sqrt{2}$[/math] example demonstrates.

Dear Philip,

I have written to you already several days ago, but you must have lost my comments among the many ones you received. I report the main points here again, because I would like to have a confrontation between our ideas, that seem to show some similarities (you find my essay here https://fqxi.org/community/forum/topic/3017):

Thank you for pointing out some long overdue problems with the intuitive reductionist approach. I am glad that you point out, for instance, that "the hypothesis has been further bolstered by the observation that the laws of particles physics are unnaturally fine-tuned". I follow a falsificationist approach, namely a deductivist methodology in science that allows (in your words) "mathematics [to] guide the way until the experimental outlook improves".

Your idea that "Reality is relative to the observer" is indeed one of the most promising directions of investigation in the modern foundations of physics. I find a particular affinity with a recent proposal by Brukner that there are "no facts of the world per se, but only relative to an observer" (If you havent seen this yet, please see https://arxiv.org/abs/1507.05255).

Best ratings.

Best wishes,

Flavio

    The late (and great) Michael Conrad also brought up the idea of representing ideas in computer language (he favoured LISP on account of its simplicity). But I believe he may have also suggested that not everything can be put into such forms.

    Information does not always come in discrete bits. If I tell you that the last digit of an unbiased number is not a seven, how many bits of information have I given you? However, quantisation in physics does seem to have discretised the information spectrum.

    It is interesting that Witten admits that he does not have much talent for philosophy. That may have been limiting for him, although it seems silly to speak of Witten's work as limited. I think he is typical of many physicists in that regard. Some physicists are able to do more with philosophy, e.g. Einstein, Wheeler and more recently Arkani-Hamed. I think they are the exceptions which is one reason why so few physicists enter this contest.

    The interesting thing about computability is that it has universality. There is not an obvious best computer language for defining computability but any choices you try can be shown to be equivalent by writing a simulator of each language in the other. I learnt this from John H Conway at his Cambridge logic course in 1980. He went to great lengths to show that a Minsky Machine is equivalent to a Turing Machine in fine detail. Universality comes in other forms, some more closely related to physics, but it may be this lesson that makes me think so much about the philosophical side of its significance. It may also be interesting to think about how uncertainty and imprecision relate to universality.

    Apologies for the delay. I am working my way through stuff.

    If we could derive physics from biology that would be truly something. I don't think I am ready for that yet, but the connection between biology and physics via information is something I can work with.

    Dear Philip Gibbs,

    Thank you for an essay with a lot of ideas. While I was intrigued by the whole essay, I was wondering if you can elaborate on one point. You write "The assimilation of information is an algebraic process of factorisation and morphisms." What do you mean by that? I look forward to your response.

    Thank you again for an interesting essay.

    If you have a chance, please take a look at my essay.

    All the best,

    Noson Yanofsky

      Flavio, thanks for your comment. I agree that we have some similarities, but in some ways this makes the differences more interesting.

      Ultimately I reject reductionism, but not in the same way as you. I think that reductionism will continue to work until we arrive at a final level where everything is possible and the whole theory is described with zero information. We will realise that actually nothing can therefore be derived from the final theory of everything and we will be forced to look back through the levels of reduction and ask ourselves where the real information about the world and how it works entered into the equations. What we will realise is that at every stage there is some extra information added when we go back up. Physicists would consider this information irrelevant until they reach the end when they will finally understand that it was all there was left.

      For example, space-time and the particle spectrum of the standard model emerge from some deeper theory. but it is likely that it will do so only with the arbitrary choice of one vacuum state out of many possibilities. That choice is then a source of information that has been disregarded. To give a better known example, biology reduces to chemistry but it also depends on the choice of environment and the accidental processes of evolution. These things add new information in addition to the theory of chemistry in order to give us biology. My view is that in the end we will realise that it is this added information that gives us everything, not the final theory that everything reduces to.

      You also reject reductionism, but the question is to what extend is your view consistent with or conflicting with mine. I have been reading your essay which is very good, but I will post my critique in your forum when I am done.

      Hi Phil,

      I enjoyed your essay immensely. At one point you suggest that "quantization as a sum over histories is more fundamental than particles or field or even time and space." What is history without time or path without space? You then ask if there is a fundamental law which is not derived from anything deeper? Yes, if we assume that a law governs something, there must exist at least one thing. Since I cannot conceive of this one (and only) thing being a particle, I assume it's a field, or at least a continuum. You then say that such law must be as it is because it could not be any other way.

      Thank you for asking "Why would those answers be incomprehensible to us?"

      And congratulations on finding computational methods that mathematicians had missed for 100 years, and advising that "... physicists should not give up...". Amen.

      Conscious experience is our contact with the universe; you say "information is everywhere" crossing the universe. I prefer "energy is everywhere" crossing the universe. When energy triggers a change in structure (absorb the photon, switch a logic gate, ...) the structure is 'in'-formed and becomes a record (~bits of information). It has no meaning absent a codebook or context: "one if by land, two if by sea." Thus it's hard for me to find meaning in the statement: "the information in a wave function is conserved." Most wave functions describe situations in which energy is conserved, so in that sense "information" might be conserved. As you note we're dealing with idealizations. If information implies energy and change of structure, where is the energy of the wavefunction and what does it change?

      You then note that such "informative" 'records' are more real than the 'past'; "Our reality is what we experience." Thanks for describing the "great hitch" inherent in multiverse and anthropomorphism. And for noting that recursion can take us places independent of the starting point. You say

      "... we must define this recursion... in algebraic terms and see how the physics of space, time, and particles can emerge..."

      You note this iteration will be algebraic without a Lagrangian, and conjecture that the holographic principle may argue for 'complete symmetry'. I believe one can formulate this principle in terms of energy, with no mention of information. Would this imply such symmetry?

      You suggest a "free algebra" generated from a vector space V and you say that "if it requires information to specify how it works then a theory can't be fundamental." and you conclude by expecting to find symmetry in a pre-geometric meta-law that transcends space-time, taking a purely algebraic form, beyond which point it will be emergent. May I suggest how this might work?

      I don't believe a 'lattice' can satisfy your requirements for 'fundamentalness', so I assume a continuum, f. "Pre-geometric" must mean there is only one such, else we would have two different things and can subtract f1 from f2 and begin geometric correlations between continuums (kind of like Einstein's inertial reference frames). So if there is only one continuum, f, it can only interact with itself, as there is nothing else to interact with! This provides a basic principle for the pre-geometric, primordial law, based on algebra only:

      The Principle of Self-interaction is that any operator O acting on the continuum f must be equivalent to the continuum f acting on itself, represented as

      Of = ff.

      This iteration is fundamental, not derived from anything deeper, and is infinitely recursive. One can solve this for characteristic features of the continuum, and the operator spectrum might determine the feature spectrum. Let one operator be the essential derivative d/dq and the second operator be the generalized derivative 'Del' = d/dp. [it's hard to find symbols that don't bring something to mind, so I've already biased you.]

      As it turns out we have two unique solutions corresponding to these two operators. For O = d/dq we find that f = 1/(-q) solves the algebraic equation, Of = ff, and for O = d/dp we find that f = 1/p solves Of = ff. We assume geometric algebra (Clifford/Hestenes) is our context. Therefore we need only interpret q and p. These may of course be anything we can get away with that agrees with our experience, but I believe the most fundamental (or at least the most useful) fundamental interpretation's are q = time t and p = spatial vector r.

      Thus our Self-interaction Principle leads to a unidirectional time and a general 3D space. One feature of the continuum is the frequency f ~ 1/t and another feature is a 1/r spatial dependence, with appropriate gradient, ~1/r.r . All of this is easy to prove (except the identification of q with time and p with space) once one adds a 'connector' c ~ r/t then ccf is an acceleration and f is a frequency. The dimensions thus associated with f and f are those of the gravito-magnetic field: G ~ cc/r, C ~ -1/t --- acceleration and frequency. When one brings rotation into the picture the self-interaction equation generates a quantum solution, and the minus sign associated with the frequency yields a fundamental left-handedness such as that characterizing neutrinos and amino acids.

      The equations that govern these fields are in my essay's equation (1). A result of iteration is figure on page 12. Of course there's much more of interest than will fit into a comment. For example, the Self-interaction Principle leads to Newton's law, Einstein's equations, and the Klein-Gordon equation, for starters, when augmented by E = mcc. I do believe "we arrive at a final level where everything is possible and the whole theory is described with zero information."

      My very best regards,

      Edwin Eugene Klingman

        Thank you for this question. Since you are a mathematician you will understand the basic idea here. I have said that I think the universe must have "complete symmetry", meaning that there should be one degree of symmetry corresponding to every physical degree of freedom. I believe this may be the only way to explain the holographic principle to resolve the information loss paradox for black holes. If symmetry was equivalent to group invariance then another way of saying this would be that the state space of the universe must be represented by a group, or a Lie algebra. In fact I think the concept of symmetry here has to be generalised, e.g. to supersymmetry and probably beyond, but for the sake of argument let's consider the hypothesis that the algebraic structure for the universe is a group.

        If you then started with no other information about the laws of physics you might say that the universe is described by a ensemble of all possible groups, a strange kind of algebraic multiverse. However, I want to go beyond that view which I think is too simplistic because it does not take into account relationships between universes. If you make some observation within the universe you get some information about it. In group theory information would take the form of some algebraic equivalence relations between group elements. Given those relations what can you then say about the group? I am sure you know the answer. To construct the largest group G satisfying any specific set of algebraic relations you start with the free group F generated by all possible group elements and then construct the normal subgroup N of elements that must be equivalent to the identity given the provided relations the group you have is then G = F/N.

        If you are then given further information you can construct a normal subgroup M of G and reduce further to a group H = G/M. Each time there is a group homomorphism mapping F onto G or G onto H taking the normal subgroup onto the identity.

        When we think of an ensemble of possible universes we would imagine that gaining information would simply select some subset from the ensemble. If we believe the universe is algebraic it is more natural to start with a free algebraic structure and form homomorphic images of it instead of selecting sub-algebras or sets of sub-algebras. That is basically my idea.

        I will give another example of how this can work. In a theory like string theory, the world is described on top of a geometric structure called spacetime. It has too many dimensions but dimensions can be reduced by compactification. Suppose that a more general underlying theory is found which is algebraic. Spacetime would then be a feature of the algebraic structure. When we compactify the spacetime we are identifying points and reducing the algebraic structure modulo those identity relationships. I think when string theory is seen as algebraic compactification will be seen as part of a more general process of factoring out some normal subgroup or whatever the equivalent of that is in the right type of algebraic structure. Being given information about what vacuum state the universe has selected will be equivalent to factoring out the corresponding algebraic structure.

        Now I must confess to how this idea fails. In quantum mechanics gaining information is equivalent to making a measurement. If you measure position and then momentum you do not get the same result as when you measure momentum and then position. The operations do not commute. The simple algebraic picture of factorisations cannot for this noncommutivity. However, I don't think all is lost. It may be possible to take a level of abstraction and replace homomorphisms with morphisms between objects having a more non-commutative structure. I've no idea how something like that can be made to work, or even whether it corresponds to something that mathematicians have already considered.

        Dear Philip:

        Your statement - "Time comes into it. Say it. Say it. The universe is made of stories,not of atoms." is vindicated by my paper -"What is Fundamental - Is C the Speed of Light" that describes the fundamental physics of antigravity missing from the widely-accepted mainstream physics and cosmology theories resolving their current inconsistencies and paradoxes. The missing physics shows that Big Bang is just a story and depicts a new spontaneous relativistic mass creation/dilation photon model that explains the yet unknown dark energy, inner workings of quantum mechanics, and bridges the gaps among relativity and Maxwell's theories. The model also provides field equations governing the spontaneous wave-particle complimentarity or mass-energy equivalence. The key significance or contribution of the proposed work is to enhance fundamental understanding of C, commonly known as the speed of light, and Cosmological Constant, commonly known as the dark energy.

        The manuscript not only provides comparisons against existing empirical observations but also forwards testable predictions for future falsification of the proposed model.

        I would like to invite you to read my paper and appreciate any feedback comments.

        Best Regards

        Avtar Singh

        Hi Philip,

        I like your open and expansive compilation of ideas on what is fundamental. A Universe Made of Stories resonates with me.

        I made an essay that explains "the speed of darkness". Take a look and let me know what you think. You may want to add it to your collection of "fundamentals".

        Thanks for introducing me to Muriel Rukeyser,

        Don Limuti

        Edwin,

        Thank you for reading my essay and thinking about it in so much detail. Your participation in this contest through your essay and your engagement with other authors is exemplary.

        The following is how I see things, if it differs from your view I may be wrong :-)

        I agree that a lattice is not a good pregeometry. Matrix models are much more interesting, but I expect some principle from algebraic geometry to provide the real answers.

        You compare energy with information. Which is more fundamental? I think the answer is that these two things are of a different nature so it is hard to set one up against another. Energy is something you find in physics. You don't encounter energy in pure mathematics. Information on the other hand is ubiquitous. Everything requires information to describe it. It is important in physics but it is important beyond physics.

        Energy is just one conserved quantity. If energy is important then it is in many ways still on a par with other conserved quantities such as momentum, charge and spin. Energy is linked to time, so if time is emergent then so is energy.

        My point of view is that anything in physics is emergent rather than fundamental. there is no fundamental structure from which everything else emerges. If we find some principles which explain the universe then they must be natural principles of logic, information etc. I think it is important to avoid the statement that mathematical structures are the fundamental elements of nature. That implies a kind of platonic realm. That is the wrong philosophy. We need to talk in terms of logical possibilities and the relativity of reality to see it the right way.

        You ask how a path integral can work without space an time. That is an interesting question. The path is the path integral is actually a path through the classical state space. For a single particle this is equivalent to a path through space, but for multiple particles or fields it is something higher dimensional. The path can easily be replaced by more abstract constructs in the absence of space. What about time? The path integral is a sum over all possible ways the universe could be. We often call these "histories" but it does not necessarily imply the existence of time. The terminology is a bit misleading in that respect. I have looked at path integrals which are sums over all configurations of random graphs or random matrices with no explicit time element. Time may emerge in such models if the parameters are just right. I don't consider time to be an essential fundamental feature of the universe. It seems much more natural to me that it would be emergent.

        Thanks again for you extensive comment and good luck in the contest.

        Dear Phil,

        Thanks for your response. We agree on so much. Not to beat a dead horse, but local energy is ubiquitous. Information requires structure and context/decoding. Description is secondary (in my opinion), not fundamental. It requires a 'model' or image of whatever is fundamental.

        You find matrix models more interesting, but didn't the Heisenberg/Schrödinger equivalence show they are different perspectives on the same thing?

        I agree that there is no fundamental structure from which everything else emerges. The continuum is not a 'structure' (I don't think.) I certainly agree that "it is important to avoid the statement that mathematical structures are the fundamental elements of nature." I formulated my comment as an attempt to address your specific requirements. The self-interaction equation does lead to momentum, spin, and charge (given the appropriate physical assumptions to interpret the math.) I don't think either energy or time emerges from the equation, but are inherent to the primordial field "described" by the equation. I think energy and time are dual and have no separate existence or meaning.

        I'm glad you find the Platonic realm the wrong philosophy. I used to think you were a Platonist. I asked the "history without time?" question to see how you would answer. I expected your answer and I agree with it. We're getting closer in our old age.

        Your comments and replies to people are a model for how this contest should operate. You have a very generous nature (probably accounts for viXra.)

        Edwin Eugene Klingman

        Dear Philip Gibbs,

        Admittedly I mistook you for a while. With stories you meant histories, not levels, and the thoughtless use of "made" doesn't necessarily imply a creation.

        The universe (in the sense of everything) consists of histories. Well, this was Shannon's and is my most fundamental point too. Therefore I rate your essay high.

        Nonetheless I would like you to respect arguments that fundamentally differ from what you correctly called your "speculative view":

        Shannon didn't speak of "past, present and future". As did he, I too exclude the fuzzy middle "present" between past and future.

        You wrote: "Reality is relative to the observer." Doesn't already this differ from Shannon's opinion that in the assumed reality, the past is unchangeable?

        Isaac Newton was born in the year when Galileo Galilei's live got history, independent from chosen point of view.

        While I respect your almost mandatory view concerning symmetries, I can also not hide my suspicions concerning this topic.

        Eckard Blumschein