Thanks for you comment. I already read your essay and made one comment, but hopefully I will find time to give it another read in the context of your comment and perhaps say more.

Numbers are always used to count things or measure them, yet in mathematics we can study the properties of numbers in their own right without reference to what is being counted or measured. This is abstraction.

Information also needs a carrier and it needs to be about something, but it has its own generic properties independently of these. The same information can be transmitted by radio waves or stored in a disk. We don't have to take that into account if we are computing the entropy of a bit stream.

I am not saying that you are wrong about the medium being more fundamental. I am just saying that because of abstraction it does not have to be.

Another interesting question is whether information can have meaning without some way of interpreting it. A compressed bitstream appears random and is impossible to extract meaning from, but uncompressed data may eb able to convey a message without an interpreter. Remember the film "Contact" where they picked up an alien communication that started with prime numbers and then moved on to other forms of information that could be understood. If the information was about pure mathematics that could even work across universes if there were some way of transferring bit streams between them. The key to making sense is to use redundancy and universal concepts like prime numbers that inevitably arise in the mind of any mathematician no matter what form of being they are.

Thanks for your comment. i will have a look at your essay.

Dear Philip,

You give very deep ontological ideas in the spirit of Cartesian doubt. I believe that this is the right way to overcome the crisis of understanding in the foundations of knowledge. I invite you to see my ideas of ontological с, where the "logos" - "metalaw" creates from the matter another alternative model of Ideality.

All the best,

Vladimir

Hi Philip,

Thank you very much for your comment. I agree with Tegmark that All mathematical structures (circles, triangles ....etc) exist in what is dubbed as PLATONIC. However I think we must find the *correct structure* that represents our reality with all of its details (like I have proposed) before dabbling in Multiverse types( his four levels) which are connected to premature interpretation and cosmology (which should be based on the newly found theory). My idea leads to possible proof that reality is a mathematical structure and reality is a proof that mathematical structures are Platonic i.e. they exist(actually the only thing that exist).

As for the cellular automata, as you know many have been proposed but no direct results that connect to physics have been shown. Some of Wolfram's NKS rules seem to come close to some aspects in my idea but I have not investigated fully. Also 't Hooft idea for example does not use CA to derive any physics as such only to use it as general argument for the interpretation part.

My system is not strictly an automata only some resemblance because I started as a design of a simple mathematical structure which is based on relations between numbers (two of them interpreted as lines). As I added some relations which lead to the concept of interaction, only then the system seem to resemble a CA, however with one major difference, that is the cells could be faraway anywhere. And so the big result in my system is that QM arises precisely because of these non local relations, so that is why EPR in my idea is so trivial and automatic(see spin). That is Entanglement (in my theory the relations between all point in space which themselves were created imperatively by the structure) is the basis of QM and hence reality. Of course, all these nonlocal effects also lead to local effects( as in standard theory) which I have not shown explicitly, also particles cannot have higher speed than light. You could see modern theories (entanglement ideas) are like rats in a maze, they can smell the cheese and get close to it but haven't fount the right road. I think they will reach the same conclusions as mine however longer road they have chosen.

you can zip through the programs by removing two zeros from Kj variable which is the number of random throws, you will get less accuracy but I think you will get the idea.

You can also see that all the programs pretty much they use the same logic.

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