I wanted to add this..

If viewed as a generator of conceptual hierarchy; the octonions appear to spell out the entire arc of learning - from knowing only that you exist, to knowing everything about the universe and seeing it all as a part of yourself. This last stage is sort of like the experience described in T.S. Eliot's classic poem "Little Gidding" to return back home and see it anew, as if for the first time, but now in fullness with the perspective gained from exploring the world.

For the record; I don't think I am making this up, but re-discovering an ancient truth. The same message appears again and again in Mythology, where the Zen Ox fables and the Hero's Journey tell the same tale. Arthur Young expounds somewhat on this Math-Mythology connection, but I think that he never got to make the explicit connection with the octonions - which is what jumps out for me.

All the Best,

Jonathan

Jonathan,

If you get the time, I would be interested in your thoughts on my essay.

Jim

Jonathan,

You write: " ... evolution of consciousness or intelligence will be seen as a natural outgrowth of higher-order Math."

I think it's rather the other way around. Math is an artificial language. Whether invented or discovered, it remains an artifice.

You spend a lot of time on dimensionality. This, you also treat as artifice, as if spacetime is not physically real and thus not interactive.

Do you think that?

Best,

Tom

    And Jonathan, please let me remind you of the productive dialogue you launched between you, me and Steven Kenneth Kauffmann in 2013.

    http://fqxi.org/community/forum/topic/1586

    Thanks for your interest Tom..

    While it may be true that Math as we know it is an invented language; it is also a fact that certain regularities arising in mathematics display the same form, regardless the area of interest or line of reasoning that brings one to them. In the realm of pure abstraction; I can observe that the power of observation is supreme, in that the awakening of consciousness is a necessary and sufficient condition for all else to arise. There is a long history of logical and mathematical constructivism too. So one might assert that the existence of Math we have not discovered yet is evidence of a higher consciousness beyond our own, or which conscious beings like ourselves might develop in a future time.

    Why should that time not be in our past instead? The elephant-headed god in the Hindu tradition, Ganesh, is said to have a mouse for a steed - which is a paradox. But in non-commutative geometry, size is not an absolute, but instead it is relative - so the paradox goes away. But does that mean the ancients inhabiting what is now India put some higher Math into a parable? I don't think spacetime is not unreal Tom, but instead of being like an object it is more like a relation. Recent papers by Hyun Seok Yang assert that if space is NC on the microscale, then spacetime must be emergent. So its properties are not fixed.

    My conversation with Tevian at GR21 was a wake up call. At one point I expected him to chime in with a comment like "Well actually..." but instead what he said was "I agree with everything you have said to this point; what is your question?" That response was rather mind blowing, because it confirmed that some of the 'elephants in the room' are quite real, and yet it sorted out a whole lot of confusion to make a direction for progress obvious. Dr. Kauffmann is still around and still looking for feedback on recent work. His current direction involves offering corrections for unphysical assumptions that are inherited when one adopts comoving coordinates.

    More later,

    Jonathan

    If spacetime is not physically real, Jonathan, special relativity is false.

    I did not say math is invented. I said no matter whether it is invented or discovered, it is artifice.

    Good point Tom!

    Thanks for your input. I guess what I was trying to get at is that definitions change when we approach the extreme limits of scale. Below 10^-19 cm, the concepts that define relativity are themselves ill-defined. This takes nothing away from the effectiveness of Relativity over a broad range of scale, but it does suggest we need to open a different toolkit to plumb the depths of minutiae.

    The physical reality of spacetime is somewhat an indication that it is a fabric of sorts, where theories of quantum gravity are believed to be needed to discover how that fabric is woven. If not QG, then perhaps it is from some other deeper reality that both a spacetime fabric and quantum mechanics arise. But if the rules of size/distance and interiority/exteriority become invalid at the smallest scale, and must be replaced with relations; it is necessary to assume that the geometry becomes both non-commutative and non-associative at that point. That is the gist of what Tevian primarily agreed with.

    What to do from there is another question entirely.

    All the Best,

    Jonathan

    Jonathan,

    You say, " ... it is necessary to assume that the geometry becomes both non-commutative and non-associative at that point. That is the gist of what Tevian primarily agreed with."

    The geometry never becomes non-commutative or non-associative. That's impossible, because geometry (generalized to topology) is continuous. The properties are mathematical artifacts--the point I was making.

    The least (only) representation of a complete algebra is the 2 dimensional complex plane, facilitating 4 dimension analysis -- and the least physically complete representation of 4 dimension geometry is the Minkowski space-time.

    One gets a 16 point matrix from this artifact, 6 points of which are redundant with the 3-space coordinates of ordinary existence, leaving 10. So plenty of connections/relations available--with the constraint that the time parameter is included, not calculated out, nor normalized. This one extra degree of freedom compels the nonlinearity of the time metric (and accelerated relative motion) consistent with Einstein's observation that,

    "The law of heat conduction is represented as a local relation (differential equation), which embraces all special cases of the conduction of heat. The temperature is here a simple example of the concept of field. This is a quantity (or a complex of quantities), which is a function of the co-ordinates and the time."

    And the definition, also given by Einstein,

    "I think of a quantum as a singularity, surrounded by a large vector field. With a large number of quanta a vector field can be composed that differs little from the one we presume for radiation."

    All of which points to a complete field theory of quantum gravity--and by implication--to the origin of consciousness.

    How does one account for the integrated role of time in your static model?

    Thanks for the additional explanation Tom..

    It appears we are in disagreement about whether the properties of numbers are entirely static. It is certainly true for the integers, and by extension the real numbers appear perfectly static. But it may be that the appearance of a static nature for the complex and hyper-complex types is an artifact of how mathematical artificers put them to use. That is; we have become overly dependent on symbols and assert a one to one correspondence between symbolic and actual numeric quantities.

    I assert that how nature views numbers is fundamentally different, in terms of how numeric quantities help constitute physical reality and necessarily preserve order. From this view; nature preserves the higher-order aspects of numbers as a kind of variability. This of necessity induces quantum mechanical uncertainty through purely geometric means. There is no artifice involved. From nature's view, number don't just sit there, but from our view the static aspects stand out and give comfort or reassurance.

    I left a comment in your thread that explains in some measure why my model is not static (far from it!), but I guess I did not articulate some things as well as I thought, in this essay, or I have to go back to thinking some more to clearly understand it myself. By saying that the reals and complex numbers are a subset of higher-order types, I am also saying they are the end product of dynamism - not just a fixed quantity. I know that sounds wild but is true.

    More later,

    Jonathan

    Dear Jonathan,

    To say like "It seems silly to ask how aimless Math can give life and the universe a sense of

    direction, when Mathematics is anything but aimless......" is quite wrong within itself because, the mathematical terms as we derive in circular motion, v^2/r is actually mindless terms but see my essay 'Newtonian Dynamics: An explict diversion...' how big scientific breakthrough could it posses when a bit sense is applied on it. And saying like "Seeing Math as dry - as though it was mindless and lifeless - is the real problem, and the mystery of where evolution..........." is always not to be true as our mathematical framing are based on mostly in virtual or imaginary tendency whose real applicants are only observed indirectly through a different path way than it directly refers..and to observe its real presence we need to create the 'sixth sense'.

      Thanks for weighing in Bishal..

      You mention circular motion, and I am sure that you can appreciate how a wheel without friction continues spinning endlessly. A point on the wheel will move up and down, or left and right, alternately. One can model this using the imaginary unit i to generate sines and cosines using Euler's famous equation (which does not render correctly here). I guess I did not explain adequately that the quaternions and octonions are merely an extension of this principle into 3 or 7 dimensions of rotation.

      But if you believe the wheel keeps spinning, so long as there is no impeding force to slow it, then you implicitly understand the evolutive properties of Math. Higher order numbers are like wheels within wheels, in that they encode multiple axes of rotation in layers. This is why they can behave like an evolving system. I am sorry if the natural beauty of the Mathematics does not speak to you, as it does for me. However; it would appear that some of the Math you invoke in your own paper depends upon what I am saying to be true.

      All the Best,

      Jonathan

      Dear Jonathan,

      ".........and I am sure that you can appreciate how a wheel without friction continues spinning endlessly"- please note that this term directly reflect the conservation of angular-momentum which is impossible in none of frame or place in reality because, to move endlessly requires setting no friction but in real practical world it is impossible...whether you perform in empty space or here on earth surface....most of time we refer the perfect empty-space as a possible test of different thought experiments but we all forget that the extrinsic-effect interactions on any body is almost impossible there.. and so, the impeding force you say is never effective to any body extrinsically there in one aspect and in other way in gravitating surface we could not reduced the friction zero.....

      best regards from Nepal

      Hi Jonathan,

      Good to be in another contest with you and to read your excellent paper.

      I am reluctant to put a crown on language or mathematics. I consider mathematics as an evolution of language. And mathematics itself is a forever evolving ring of power. And as a ring of power it is a false god. The ring of power caused Frodo no end of trouble!

      Nevertheless this essay is one of the best.

      Put on your never ending list of things to do (it's important) to read my two papers on gravity and dark energy. These are listed in my about the author section.

      Will mathematics grow up (evolve) and solve its own problems :)

      Don Limuti

        Hi dear Jonathan,

        It is a pleasure to re-meet you here in FQXi Essay Contest.

        I have just read your nice Essay. As usual, you released a remarkable contribution. In this case, your Essay seems also a bit provocative, but I strongly appreciate people "thinking outside the box". Hence, your Essay deserves the highest score that I am going to give you. Good luck in the Contest!

        Cheers, Ch.

          Jonathan,

          I've been looking forward to reading an essay arguing the more minority view and I found you did an excellent job, though I can't say you reversed my support of physical 'causality' in the universe, which at times your language seemed to challenge; i.e. mathematics 'giving rise to processes' and 'telling the universe what to create'.

          I assume you really haven't abandoned cause and effect, i.e. an action producing an effect not the mathematics that describes it, but if that's true then appearing to do so did seem to need a little more explanation.

          I have a rudimentary understanding of non-commutativity and non-associative geometry but both seemed in need of your definition before invoking them so heavily. Similarly I never did see or fully understand your own view of what the elephant in the room actually was. I've long understood and rationalised octonians, fractals and perturbation theory (to higher orders), loved the amplituhedron, and know those in QG see it as the only way ahead, but do you felt you introduced any new argument to win over those less sold on the concepts?

          I was interested in your comments on the '2D' higher order case that some math posits, (which seems rather at odds with 10D!). What I first saw I tended to dismiss as 'unreal' understanding but for me such responses are always provisional so can you provide any good links on that?

          Nicely written and argued as usual and I think should certainly be a finalist.

          I hope you may also offer a mathematical perspective on classical momentum transfer distributions I describe in my own essay appearing to reproduce QM's predictions.

          Best wishes

          Peter

            Hi Jonathan,

            I read your submission and I am glad that you are one of the many people in this contest that choose the math aspect of the contest question to answer instead of the the mind aspect. Reading your article I find out you are a fan of string theory. That does not make me happy, but I can't count it against your article. What I do count against your article is the fault in your logic over two of your sentences that seems to be the basis of your whole article. The bold words in the quote of yours are mine to make my point. Here are your sentences.

            "The Principle of Indeterminacy could then arise in a natural fashion from relativistic considerations, making quantum theory a consequence of an underlying 8-dimensional hidden-variable process, very much in the flavor of the theories of de Broglie and Bohm." [3] So we see that octonion Math dictates emergence."

            You've taken a could and turned it into a dictates. That to me is a fault in logic.

            The other problem I seem to be having is this disease of "math predates the universe". I just wrote this post to James Stanfield on his submission page and I feel it is equally valid here. I quote the relevant parts.

            "I read your interesting submission and if I had excepted its premise (math predates universe) I would give it high marks. But I don't except its premise because I was working on the very same idea years ago and I found out where the idea fails. If you disagree on my conclusion, please tell me where I went wrong.

            The stumbling block for me concerning the idea that math predates the universe was how is this communicated to the universe. Math is no small subject in terms of quantity of information in contains. While I was trying to figure this out, I had also decided to read a book that had been on my shelf for many years "Adventures In Group Theory" by David Joyner. the book explains group theory through the puzzle of Rubik's Cube, which I learned to solve independent of books teaching how to solve. I figured my knowledge of Rubik's Cube would help me in understanding group theory. So I learned some group theory and it impressed on me the the consequences of numbers and their relationship to other numbers of the same quantity. So then I asked the very simple question; the universe started out as one object and went on to many objects, between that time it passed through six objects, those six objects instantly possessed the rules of group theory for six objects, where did it get them? My current answer is that it didn't get them from anywhere, the rules for six objects in group theory are there only if we asked them. I am not pioneering a new thing in math here. You, yourself already know that spacetime is only considered Euclidean if the rules of Euclidean geometry apply, otherwise it is non-euclidean. All I am saying is that the rules of any particular topic of math when applied to this universe only apply when asked and give an answer in the positive or the negative. To exaggerate my statement. Do the rules of topology apply to the color of my grass in my backyard? No. Do the rules of topology apply to the surface of the donut I eat this morning? Yes. Euclidean geometry only shows up where the rules of Euclidean geometry are valid. Topology only shows up where the rules of topology are valid. Group theory only shows up where the rules of group theory are valid. Set theory only shows up where the rules of set theory are valid. I could go on all day like this."

            If you also feel I have errored in some way, I would like to know.

            Jim Akerlund

              Jonathan J. Dickau,

              Evolution starts from biological virus.

              Knowledge of virology, linguistic, memes, contagion and mechanics of computer virus can help us solve this problem.

                I am compelled to respond to this..

                While I am not a great fan of String Theory; I admit its value and I think it's part of the total picture we must examine, but it is a smaller piece of the puzzle than some believe. I am a friend of Brian Greene and I have met Ed Witten, but I am more in the camp of Abhay Ashtekar, in regards to how the Strings program fits into the overall spectrum of gravitational Physics, at least. I had the pleasure to sit with him, during a few lectures at GR21, and he shows a genuine interest to make use of every advancement, regardless from what camp it comes. I figure there is something behind the fact that regularities appear, when various theories of Quantum Gravity make similar predictions, despite having a completely different theoretical basis.

                I admit the 'Math predates universe..' idea is a little hard to swallow, and the idea that it also dictates both the laws of Physics that shape the universe, and that there be an evolution of form and consciousness within that universe makes my premise ambitious indeed. But I think Max Tegmark did not go nearly far enough, in his MUH. Connes is emphatic about features of NCG that have no parallel in conventional Maths. Kainen in correspondence has endorsed my usage, and was flattered to be mentioned with Connes. I had my doubts until recently, as well. But my conversation with Tevian affirmed that these are complications that must be dealt with.

                After a discovery I made more than 30 years ago, suggesting the Mandelbrot Set could be a sort of road map for Cosmology; I have tried in vain to disprove this, and instead I have settled on the idea that the universe is maximally mathematical. While trying to understand why the universe would mimic the Mandelbrot Set, or vice versa, I came to understand it is only one piece of the puzzle - which like E8 can tell us a lot about the universe. Seeing how far Garrett Lisi was able to take it, but that more was needed, got me to thinking. But my collaboration with (now departed) Ray Munroe was the clincher for me.

                All the Best,

                Jonathan

                Thank you Peter,

                I appreciate the time taken to read the essay, and also your comments. I should indeed have defined my terms better, and failing that I needed to include some endnotes with appropriate definitions and a descriptive summary of important concepts my point hinges on. I will cue you in to other works in the queue, which will explain the 2-d relevance. Suffice it for now, to say that the Mandelbrot Set is maximally asymmetric, and so serves as a counterpart to highly symmetric objects like E8. It serves as a window into how higher-dimensional trends drive evolution - but it is a cross-section in 2-d.

                All the Best,

                Jonathan

                Thanks greatly Don!

                It is good to be in community with you as well. I think there is plenty of confusion in the Math and Physics community, where a lot of people put the symbolic reality ahead of the real world. But when I talk about Mathematics in the context of this essay; it is rather about the unchanging patterns that make Math what it is. Projective geometry is the mathematical study of perspective. I can't tell you why some of its root postulates bring us straight to the octonions, but I know it is true.

                Math is much abused by those who try to make it bend to their will. A good example of Math forged into a ring of power would be the Gaussian Copula Function, which was the basis for financial derivatives, and was itself based on formulas used in risk and failure analysis. But it was used fictitiously (as though predictable risk equals zero risk), and its broad mis-usage was one of the contributing factors of the market crash in 2008. Mandelbrot had warned us before then, but the finance gurus did not listen.

                So pure Math had the answers, but nobody wanted to hear.

                All the Best,

                Jonathan