Always a pleasure to hear from you Steve..

This time, I do feature spheres of various dimensions, in my essay. I think it is a very useful construction that nature views as fundamental.

All the Best,

Jonathan

For those visiting here..

I thank you for your interest in my work and I'll try to reply to all comments eventually, to most as soon as there is time. I will also attempt to read as many as possible of the other essays in the time allotted.

I will be systematically working from the earlier submissions to the present, while trying to honor those who visit my essay with an earlier reading and feedback. I'll be trying to also look for topics of my own special interest and authors whose work I respect. Lastly; I will look to the community and public ratings to find essays to read, during the final run up.

While I don't often give out a rating of 10, I have not given a score lower than 5 so far this contest. I will give out a decent rating if an essay is either well-written or makes a powerful point, with extra points for essays that do both. Mostly; I will be looking for quality of writing, strength of premises, and compelling logic. Essay that have all of that will be rated highly.

Good Luck to Everyone!

Jonathan

Hi, Jonathan. This is a great essay and I agree on the role of the octonions etc. It's good that you concentrated on that theme.

You mentioned consciousness a few times but did not go into much detail. What is your view on consciousness? Is it an illusion, some new physics or what?

    Thanks greatly Phil,

    I could have written a very different essay, emphasizing the progression of consciousness angle. But I wanted to show that those Maths shape Physics in a definite way. The octonions generate a hierarchy in levels of abstraction, though, such that a pattern like what Young describes can be spelled out in many different ways to form sentences. I've written out several dozen at this point.

    One, open, as multiplicity and formless nothingness, finds peace in true relation, and knows all as self. Oneness, leads to openness, as-ifness, multiplicity, and so on. The rest reflect the theme of a book by Briggs and Peat 'Turbulent Mirror' that there is a far shore to chaos where order re-emerges, and life exploits that border region greatly. This one is a sort of personal credo. But you could also put it in religious terms.

    One being, Goddess and God, begat manyness, then complexity beyond reckoning, to find the missing pieces of themselves, and become as one again. So then it becomes a love story featuring the male and female persona of the divine, arising from the order found in the octonions. But it's a bit controversial that the divine feminine emerges first; don't you think?

    I know that sounds pretty wild, but I think the stages in the progression within octonion algebra have moods, so that the octonions could be used to craft a fully subjective and qualitative relational database, as a counterpart to the powerful objective and quantitative data classification systems we have today. But this only works because it is also something emergent in the properties of non-associative Maths.

    All the Best,

    Jonathan

    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.