quote

Every possibility is assigned a probability. These are derived from the squared norm of a component

in a wave function. Observables become operators, states become vectors, sets become functions,

objects become morphisms. In physics we call this process "quantisation." It is closely related to the

mathematical notions of exponentiation, abstraction and categorification. Even probabilities

themselves may be uncertain, so they too are given a probability distribution. The process can be

repeated to give us iterated quantisation, higher abstractions and n-categories. To understand the

origins of physics we must define this recursion more precisely in algebraic terms and see how the

physics of space, time and particles can emerge from it with specific features of our universe

understood as processes of information collection. The fundamental laws of the universe are then

uniquely determined by invariance under quantisation [4]

end of quote

Very interesting point. What I tried to do was to find , using Klauders enhanced quantization, a way to bound the behavior of classical physics, via a quantum analogue, as to the emergence of of the cosmological constant.

My essay is of December 21st. As a favor to me, could you critique my essay as given in FQXI, in terms of your above mentioned procedure?

Thanks

Andrew

    Dear Philip,

    some water into the wine of positive comments. In the following quote: "I expect to find this symmetry in a pre-geometric meta-law that transcends spacetime,taking a purely algebraic form, only beyond that point will it be emergent, rising from immutable relationships between systems of information" there feature at least six to eight terms that either are entirely undefined (e.g. pre-geometric meta-law) or at least have multiple, varied and even opposing meanings. I have roughly 'calculated' the number of possible meanings of just this sentence to be of the order of millions. The number of possible meanings of your essay is of course magnitudes bigger.

    So, your essay appears to me much like a box full up with words marketed as a novel.

    Hence your conclusion: "From there [the above] our understanding returns full circle to the nature of our experience and our personal life stories" reads something like: believe me that no less than six angles can dance on the top of a pin.

    Heinrich

      Many theorists agree that space-time geometry could be emerge from something else. That structure is often therefore described as "pregeometric." I.e. It is a common generic term in physics used to describe any hypothetical theory in which space and time is emergent. Wikipedia is always a good place to turn to when you don't understand a term and in this case it gives several good examples of mainstream pregeometric theories http://en.wikipedia.org/wiki/Pregeometry_(physics)

      "The meta-laws" here just mean the theory of this pregeometry. They are meta-laws in the sense that the laws of physics we know are just one possibility of what could emerge from the meta-laws. They exist at a deeper level. I am talking here about theory whose exact form is unknown so in that sense it does have multiple meaning, but what I am saying applies generically to whatever those meta-laws are. Again the term "meta-laws" is in common use although it is less common than "pregeometry"

      I think the meaning of my statement that it takes a purely algebraic form should be clear enough. If it is pregeometric is should not be a theory of geometry so it could be algebraic or combinatorial or something else. Quantum mechanics is very much algebraic so once the geometry has been transcended it seems reasonable to expect that what underlies the theory from which it emerges will be algebraic.

      I don't think "relationships between systems of information" is very ambiguous even though I do not describe those systems in general. Also I think the words "symmetry" and "immutable" are unambiguous.

      Possibly the problem here is not that this can mean different things, but rather that I am referring to generic concepts where the detailed implementation of the ideas is not yet worked out. I don't see how this can be avoided given the essay topic which forces us to consider questions of what fundamental means when we don't yet have a complete fundamental theory of physics to work from. I am pleased that others seem to have understood some of what I say in that context and sorry that you have not.

      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.