Putting the Elephants to Work by Jonathan J. Dickau

I am happy you enjoyed it Willy..

Even some hardcore Math folks shy away from the octonions, but they are worth the effort for those with the skills. My main point is that if you go high enough up the chain, evolutive properties in Math are easy to observe.

All the Best,

Jonathan

I thank you Lawrence,

I am not worried about you being a vote rigger. It does appear there must be folks who enter the contest on a pretense, then vote for their friends, while casting down those who might be serious competition. It is discouraging to see such childish behavior.

Sorry to hear about the flu. I have had lingering cold symptoms myself. I think it might be worth elaborating on the hairy ball theorem, as an explanation of the above. The conventional sphere S2 has hair that can't all flow one way, so is non-trivial, while S3 can be combed all the way around - because it is parallelizable.

More later,

Jonathan

Thanks for this follow-up Jim..

The Mandelbrot formula is very compact, compared to the complexity of the object. And it elegantly displays the replication of similar forms at different levels of scale. I think it is the progression of form, which is the most relevant, but the regularity of its repetitive form is impressive.

I am glad I gave you something to chew on.

All the Best,

Jonathan

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

This is not my concern..

JJD

The music of the spheres!

Let's play!

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

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

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

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

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