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

              Thank You greatly Christian!

              It is my pleasure to again encounter you here. As you know; I hold your work in high regard, and your praise is much valued. I think that we need to look 'outside the box' to a degree, since Physics will paint itself into a corner otherwise, but I was trying to awaken people also to part of what we have inside of the box with us.

              So many in Physics make use of the mechanisms of Math in a utilitarian way, but I think to an extent our tools have a life of their own, which deserves to be brought to light. While people in some parts of the world are eager to make elephants into beasts of burden, they are marvelous creatures in their own right, and they deserve as much appreciation as the mahout who skillfully prods them along - to do our bidding.

              All the Best,

              Jonathan

              I appreciate the insight Shaikh Raisuddin..

              It is true, as you say, that simple organisms like the virus begin the upward spiral on the ladder of evolution - forming early branches on the tree of life, while not yet living in the sense of what evolved organisms have achieved. Indeed; we are a symbiosis of co-opted pieces from earlier organisms, where bits of code have been merged to form our human genome.

              So I agree that what you suggest can be helpful.

              All the Best,

              Jonathan

              Johnathan, I am pleasantly surprised by how accessible and enjoyable your essay was considering it was primarily about mathematics.Well done. I think the point you make about complex algebras being non commutative and naturally related to geometry and sequential change very important as that is what a description of the material universe requires. Quaternions have that non commutative characteristic. They are sufficient or modelling evolving 3 dimensional objects and fractals too. I 'm not sure that higher (than 4) dimensional algebras are needed for modelling the material universe we inhabit, though I'm sure they do produce interesting models. Isn't it just that the 3 spatial dimensions unobserved don't have an orientation? we could say they are in all orientations, any orientation or no orientation as orientation is relative and without the observer viewpoint orientation doesn't apply.Could 248 dimensional E8 be an approximation of that? What is it about the higher (than 4) dimensional algebras that makes them particularly relevant. You mentioned hidden variables, and sphere packing -is there something else that in your opinion make them necessary, rather than just appealing? Kind regards Georgina

                Thanks for your kind remarks Georgina..

                I am happy you grasp my main point. Some folks learn a lot of Math, but don't have the sense of such things, possibly because they are stuck on manipulating symbols or finding equations that are easy to work with, while nature ignores our boundaries of convenience. One knowledgeable friend asserts that many scientists simply don't go far enough with the Math to do the job correctly, or stop short of a rigorous treatment with the solution in sight. Borrowing an idealized equation from a textbook, without considering its limitations, won't always allow you to capture nature as it is.

                But I agree that it is a waste of time to invoke the octonions for everyday Physics, while the quaternions have great utility - and do capture the needed dynamism to model evolutive properties. However; when one gets to some of the tough problems at the crux of fundamental Physics, as with quantum gravity where one is dealing with the extreme regions where both gravity and QM have a strong effect, is where knowing about the octonions and non-associativity becomes important. And the 8-d octonions are adequate to hold E8, even though its largest regular extent is in 248-d. One can also make a beautiful Zome model in 3-d, which is a projection of the 8-d figure. Pretty cool, huh?

                All the Best,

                Jonathan

                I don't know yet, where still higher dimensions will fit in..

                But I think there is a place for them on the spectrum of possibilities, that nature will employ and project down to three dimensions if that's where it's needed. I mainly imagine that there are important things to know about what happens in the higher heavens of Math, but I don't claim to be able to explain their import. There appears to be a telescoping property that I think is inherited from Bott periodicity, where higher order quantities are extensible, but can be reflected down to lower order forms. So some of what happens there can be shown relevant to what happens here.

                All the Best,

                Jonathan

                Thanks Jonathan.

                Yes, I completely agree with you that awakening people to part of what we have inside of the box with us is important in the same way that thinking outside the box. What is important in both of the cases is starting from plausible hypotheses and proceeding with mathematical rigor. Your aphorism on elephants is very nice.

                I hope that you will have a chance to read our Essay.

                Dear Jonathan Dickau

                I saw your comments on the essay of K. Willy and I become curious about both essays.

                There are different ways of "decoding" the universe; yours and mine are quite different. I read your essay, which is very well written, and you present well your point. I think that you have a promising approach but it is not my line of reasoning, I can only be a curious spectator of your work.

                I read that you are part of viXra team; well, I want to congratulate and thank you. I have a paper in viXra with more then 900 downloads in spite of my almost null divulgation of it (vixra.org/abs/1107.0016) ; I receive emails from cosmologists confirming that I found the solution to the cosmological problem, some urging me to publish it in whatever "citable" place. However, as I am not "affiliated" and that solution implies a change of paradigm, hardly could I ever publish it in a relevant scientific journal. I hope that one day you will see viXra entering the history of science because of that paper that could not be published anywhere else.

                From the above, you may assume that I am an "amateur". If you are so kind to take a look at my essay, you will understand that I am something else - in spite of our different approaches. And I have something to ask you: a piece of advice.

                All the best

                Alfredo Gouveia de Oliveira