Right, now that my essay is up to illustrate where I'm coming from, some more comments.

I like how you characterized your approach over in my thread---as 'pushing back' the fundamentals. This somehow seems very intuitive: the more general the mathematical structure, the less assumptions have to be made, and the less attack surface for 'But why this?'-type questions exist.

But does this process have an end? In some sense, you can always generalize further---throw away some more axioms, to put it starkly. When are we general enough? Is there some endpoint that does not contain any assumptions that can be rationally doubted---and even if so, does this say something about the world, or about the boundaries of our reason?

Exceptional structures seem to be good candidates for endpoints, in particular because they lend themselves to chains that actually do seem to terminate. Octonions are the division algebra with the highest dimension, things stop there---but then, why division algebras? E8 is the largest exceptional simple Lie group, but why any of that?

That said, I can certainly relate to the intuition that there's got to be some mathematical object of maximal symmetry, something ideally self-justifying, which---one might hope---gives rise to observed phenomena through some process of iterated emergence, be that symmetry breaking or multiple quantization. So this is kind of a point where I have my doubts whether the whole thing works---but would love to be proven wrong.

The "Why this?" question is an important driver in my thinking. I should perhaps have mentioned it more as you have. Of course it is nothing new. Wheeler asked what gave the equations wings to fly? Hawking asked what breathes fire into the equations?

I know some people see exceptional structures like E8 or the octonions as something that can answer this question. These things do seem to turn up, but for me they don't answer the "Why this?" question. I feel a bit like the annoying who just keeps asking why? every time something is explained to them. If any information is needed at all to specify the way things are then there is still a question to answer.

One candidate for a solution is that you just keep pushing back through layers of emergence until you arrive at a system with no information, where everything is possible. This is like Tegmark's MUH. This has problems. Firstly you need to define some measure or weight on the space of all mathematical possibilities and that introduces an unsourced system of information. Again I would ask Why this? Secondly, it does not explain why there is order and symmetry in the universe. If anything can happen we should live in a world where anything is possible. We might as well be living in a Disney cartoon.

Emergence is usually something approximate. The Navier Stokes equations emerge from inter-molecular forces in a fluid, but if you look closely enough you can see the molecules. I think the emergence of space and time is like that too. If we look closely enough we can in principle see the underlying structures from which it emerges. However, I think there is a layer beyond which we can't see, even in principle. A system that emerges from a universality principle on the ensemble of all possibilities without any input of information. I know I keep saying this, but the important point that responds to your comment is why I think that it must be that way. It's because that provides the only possible answer I can think of to the "Why this?" question that fits with our experience of a rational structured universe without any external source of information.

What is the difference between a necklace and a mouse? The mouse, or maybe it was moose, is a chain of Lie algebras. The vector spaces in the representations of these algebras form a sort of quiver. It would seem to me that in some setting if the group is a quotient H = G/K, then This algebra corresponds to a Hermitian symmetric space. An elementary example are the Grassmannian manifolds. This is an interesting development, where the local charts on the manifold are made of vectors that locally are a Lie group, and the atlas construction is a moose or what appears to be a necklace.

My essay have finally showed up. I can now vote and gave your essay a boost.

https://fqxi.org/community/forum/topic/2981

LC

    Hans. I agree that theorists have always looked at too high a level for fundamentals. This even goes back to Plato when he named the elements as earth, water, air and fire. We now realize how wrong that was because we have penetrated several levels of structure further down, and yet many physicists still think that elementary particles will be fundamental. I am saying that if it requires information to specify how it works then a theory can't be fundamental. there is still some way to go before we reach that point.

    I will read your essay to better understand your point of view.

    Lawrence, I have not heard this mouse/moose terminology before. Is there a reference?

    I am looking at your essay, but may take a few days to comment.

    Nainan, What you say seems to make perfect sense.

    I have your essay on my list to read.

    I see your point regarding the approximate nature of emergence---although we often try to do so, one can't really stratify the world into neatly separated layers and expect them to stand on their own. Your notion of the 'layer beyond which we can't see', however, is somewhat opaque to me. What makes it so that we can't see beyond? Is is a limitation of human nature, or of the world as such? Could perhaps some alien scientist see beyond, only to be stumped at another layer, or perhaps, not at all?

    I think that possibly the main difference between our approaches may be that you keep on asking the 'Why this?'-question, while I, on the other hand, think that it's ultimately not the right question to ask, and might only seem to make sense to us thanks to the way our own thinking is structured.

    These are the ideas I am struggling with so I don't have clear answers, but here is how my thinking goes. Imagine you were able to run some simulation of a small world on a very powerful computer, so that within that simulation there is an intelligent entity that can examine its world. The entity could observe the artificial laws of physics that you were simulating, but it could never see what programming language you used or the hardware details of the computer you were using. I think this last layer must be similar in a way. We can't see the details of the ensemble of mathematical possibilities from which the bottom layer is emergent. We don't get to see the mathematical symbols or the choice of axioms.

    There are also examples of this from physics. Near a critical point in some system of statistical physics you can get scaling behavior. If you take the limit at the critical point and rescale than the details of the statistical physics system shrinks to zero and vanish. A quick google search brings up this talk on the subject.

    Both these examples are based around types of universality. In the first case it is the universality of computer languages that gives a definition of computability that is language independent. In the second case it is universality in critical systems. I think that something like this is happening at the bottom layer of physics. It's a form of emergence but it is different from the approximate forms that we can unpack.

    I think symmetry emerges at that bottom level and is then spontaneously broken or partly hidden as space and time emerge higher up.

    I do agree that there is a danger of being misled by the way our thinking is structured. I am quick to criticize when I see people thinking in terms of temporal causality. The same may apply to reductionism in the form that I am using. The "how" may be more important than the "why." However, there is also a danger of throwing out too much so that we find ourselves lost and unable to do anything. Perhaps it is necessary to keep some philosophical principles as scaffolding to build on. They can be removed later.

    There is this paper

    Strings from Quivers, Membranes from Moose

    Sunil Mukhi, Mukund Rangamani, Erik Verlinde

    A moose sounds very similar to a necklace. Both are in effect chains of Lie algebras.

    Cheers LC

    Ah, yes, I see what you mean. I think David Deutsch mentions such worries somewhere. On the other hand, I once had the idea that this means we're already at the end of our search for a fundamental theory, and it's electromagnetism (or any other theory capable of describing universal computers): because whatever the fundamental theory happens to be, if it is computational, you can write a program simulating it and run it on a computer. This computer can then be described via Maxwell's equations, thus showing that we need nothing else to describe the world. (I sometimes wonder if the dualities between various theories could not fruitfully be understood as a kind of reduction, in the sense the term is used in computer science, but that's another discussion.)

    Of course, this really just means offloading all the work to the initial conditions---essentially, the configuration of electromagnetic fields describing the way the computer is programmed. But this highlights another facet of the 'Why this?'-problem: it seems that any fundamental theory, in order to describe a given universe, is going to need some initial conditions. But well, why those? Is there really a set of initial conditions such that they are self-justifying?

    And then there's the question of why the simulation starts at some pretty deep down level. Why simulate nature at (say) the Planck scale? In principle, it should be possible to simulate higher-level physics just as well---the way Newtonian physics is simulated in modern computer games, for instance. I mean, one could probably mount a simplicity argument here, but again, if there still is some finite complexity, one could always go more simple, and if there isn't, well, it seems difficult to even think about what the 'program' would be like---in a sense, it would be (again) no program at all...

    Hi Philip,

    It was a real pleasure to read your contribution to this contest.

    The first half is like I could have written it myself, but each of us have a different way of explaining our perceptions.

    The second half of your essay is a witness of your dedication to mathematics, but your end conclusion NOTHING IS EVERYTHING is the same as mine, only I add "INITIATIVE" as a property of Consciousness.

    I hope you will also have some time to read and rate my essay : "Foundational Quantum Reality Loops.

    Thank you for making me think again.

    best regards

    Wilhelmus

      Dear Philip Gibbs,

      You wrote: ""Fundamental" is an adjective to describe a level of reality that is not derived from anything else." My research has concluded that reality does not have any levels. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single dimension that am always illuminated mostly by finite non-surface light.

      Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

      Dear Philip Gibbs,

      You wrote: ""Fundamental" is an adjective to describe a level of reality that is not derived from anything else." My research has concluded that reality does not have any finite levels. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single dimension that am always illuminated mostly by finite non-surface light.

      Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

        Hello Philip...

        With regard to "guessing correctly the answer to questions like 'what is "fundamental?'", the "stories" are ancient... REF: TOPIC Indra's Net - Holomorphic Fundamentalness by Cristinel Stoica ... and although such "stories" are prolific, multi-epoch, and multi-cultural, requirement for a logic reduction is a common element.

        However, cognitive abilities to resolve a math model of a logic reduction of "fundamental" are apparently emergent...REF: TOPIC: How to Empirically Confirm a Rational Theory of Fundamentals by Jack H. James ... and application of Math semantics to an invalid logic reduction of "fundamental" have often muddied the cognitive waters.

        The Spatial quantization is fundamental to all derived Spatial relationships/logic.

        In that evolution is driven by the "What is fundamental? quest, then technology is also, and development of digital tools has been reciprocated with a cognitive enhancement, in the form of a more precise Mathematical model of Indra's net "cast in all directions"... i.e. resolve of an Origin Spherical Singularity Geometry, which supports infinite minimum unified volume unit shell closure expansion as a valid CAD environment/field quantization... has now been added to the "stories", and a pulsed Emission of minimum quanta of Energy (QE), is being digitally simulated/animated within the virtual environment.

        REF: UQS Origin Singularity Geometry http://www.uqsmatrixmechanix.com/UQST-TVNH.php

        It is not a theory, it is a digital CAD/SIM virtual reality constructed on a logic reduction... i.e. an Origin Emission equal in all Spatial directions from a single point.

        Better than a guess?

        Thanks Philip, for sharing your insights and thus making an opportunity for comment... I would read with attention your comments on my essay entry Title: Knowledge Base (KB) Access as Fundamental to Info Processor Intelligence.

        Will return to rate after I read as many essays as I have time.

        S. Lingo

        UQS Author/Logician

        www.uqsmatrixmechanix.com

          Thanks, I will read your essay. I have a lot to go through and want to give each one a good read but will get to it.

          Joe, thanks for your comment. These competitions would not be same without you.

          I am glad to here we have some conclusions in common. I will put your essay on my list to read.

          The "moose" seems to go back to Herman Georgi in 1986 as a tool for model building. I don't think its the same as necklace Lie algebras but can't rule out a connection.