Hello yet again Rick,

While looking for something else; I happened upon these papers by a researcher I mentioned above, which should be of great interest to you, given the subject matter. I hope it adds something, rather than detracts, and I have not read these for detail enough to know. From Merab Gogberashvili

Octonionic Electrodynamics and

Octonionic Version of Dirac Equations

Enjoy, JJD

Jonathan,

Added a new class to my scripting called NUMBERS, for doing Octonion math on 8D arrays of numeric values. Methods are so far add, subtract, multiply with Algebra choice and selective conjugation, return the norm, multiply and divide all by real number, output to console/text file. You should be able to create your own complex number, Quaternion number or Octonion number Mandelbrot sets with it. Tried something as a test, iteration Z_n+1 = Z_n ^2 + c, bailing on stationary norm with assigned value of 0, else iteration loop count to have the norm go past 1000000, staying in Quaternions. We all minutes to do a 1000 x 1000 grid of 2 Quaternion non-scalar starting points with increments .00001 with the starting points fixed for other 2 and c being fixed same non grid elements. Got some kind of pattern, have not plotted. What do you use to plot colored plots?

Rick

    Wow, autocorrect sucks, need to read first. Within a few minutes, like 10 to do 1000 x 1000 grid

    Far Out!

    I've used a purpose-built program written in Pascal for years to convert arrays of integers into 24-bit color values (3 5-bit values for R,G,&B). It's pretty cumbersome, and I have it making files in an obsolete format then converting that to TIFF, but I can deconstruct and re-construct that code to modern specs in fairly short order. It breaks the number palette into ranges, separates odd and even values, and then uses an algorithm to produce color gradients within each range. Your progress gives me a good reason to get back into the programming end of things.

    All the Best,

    Jonathan

    Hi Rick,

    I just sent you an e-mail with a snippet of code which is the subroutine for color assignment using a 24-bit palette. The choices for colors and ranges created by that code looks like this image for the standard Mandelbrot Set plot.

    Good Luck!

    JonathanAttachment #1: MandelCrop.jpg

    Dear Rick

    If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.

    Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?

    My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.

    Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

    For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

    My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.

    By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.

    To steal a phrase from my essay "A world product of evolved optimization".

    Best of luck for the conclusion of the contest

    Kind regards

    Steven Andresen

    Darwinian Universal Fundamental Origin

      As advertised attached is my JavaScript symbolic algebra tool, along with my verification script for my derivation of the Octonion conservation of energy and momentum equations. Also just for fun is a Mandelbrot set script that can do complex, Quaternion and Octonion iteration loops.

      It requires you to download the free Node.js runtime and has only been used on a Windows 7 machine by me. Expand the attached zip file (hopefully it will be there), read the pdf, have fun.

      RickAttachment #1: OctonionScripting.zip

        Not saying the Leech lattice is not important, just that it has not been important enough to me to put it in front of other things on a list too long for me to possibly get through. I still have a full time job consulting right now having nothing to do with physics or Octonion Algebra which I do on my time, my dime. Sadly this has severely limited my time to participate in reviewing other essays.

        So, maybe it can, can't say with any authority.

        Rick

        Unfortunately I am still working full time doing consulting. This has prevented me from reading many essays in enough detail to reasonably respond or grade, so I haven't.

        Rick

        Thanks for reading my essay. My "truth" was meant to imply truth that exists independent of us or our limited knowledge opinions. It is out there for us to learn, if we listen.

        As I have said a number of times and apologized for, I am working full time and have had time just to scan a number of essays here. Hopefully people will not hold this against me.

        Rick

        Georgina,

        Thanks for reading my essay. I did scan through yours, not with enough detail to comment. As in other posts here I am apologizing profusely for not having time to study the many wonderful essays in this contest.

        I have always appreciated the defense of your positions in your blog participation here. You have more patience than I for a certain individual who will remain nameless. Keep up the good fight.

        Rick

        Thanks Rick...

        I have downloaded the ZIP file from the second link and will report back after a while. I also got the e-mail before, and I will try to process or utilize soon. I have been working on my proceedings submission for FFP15. I'm also trying to read the max # of essays before the end.

        All the Best,

        JJD

        Anonymous votes with no comments to back them up is an obvious deficiency of the "community" rating.

        Going to be cowards?

        Solution to this problem would be for FQXi to publish all votes each participant made, by name.

        "Anonymous votes ..." According to Pavel Kroupa, "Science is not a democracy."

        What are the 4 most important mathematical structures? Could the answer be the real numbers, the complex numbers, the quaternions, and the octonions?

        The octonions Author: John C. Baez Journal: Bull. Amer. Math. Soc. 39 (2002)

        "Division algebras and quantum theory" by John C. Baez, arXiv.org, 2011

        9 copies of the octonions = 64 dimension of virtual particle paths 3 dimensions of linear momentum 3 dimensions of angular momentum 2 dimensions of quantum spin ???