Colin,

There are 8 ordered terms ... that makes an octonion:-)

What this essay presents is a 5-D subset of the octonions ... I state that in the essay. The 5'th dimension for me is the complex i with the scalar an vector terms being from the quaternion. I also specify what the various scalar coefficients must be in order to satisfy the geometry that I present.

Dr. Crowell also referred to what I have presented as a bi-quaternion although the term is new to me. It does make sense though since I add a real quaternion to a complex quaternion.

Best Regards and Good Luck,

Gary Simpson

PS - I have scored your essay.

Colin,

One other thing ... if I describe the physical universe with 5 terms from the full set of octonions, then there are still 3 terms left to describe the physicality of you an me ... the observers. This is why I titled my essay "Five Part Harmony" and it is why I refer to the structure as a pentuple.

Best Regards and Good Luck,

Gary Simpson

Phillip,

Many thanks for reading my essay and commenting.

The short answer to your question is that I think the mass ratio is dependent upon the Earth's motion around the Sun.

Here's the long answer. The Earth's motion is the sum of its motion around the Sun, the Sun's motion in our galaxy, and our galaxy's motion through space. There might even be another structure to consider. I think that the major velocity component is the motion of our galaxy through space. I think the motion of the galaxy is parallel to the axis of the galaxy. The Earth's motion around the Sun is in the ecliptic which is perpendicular to the axis of the Sun. Therefore, if the axis of our Sun is parallel to the axis of the galaxy, then the Earth's motion around the Sun will not affect the mass ratio. On the other hand, if the Sun's axis is not parallel to the axis of the galaxy, then the Earth's motion around the Sun should be a factor. My guess is that stars that are clos to the galactic core have rotational axes that are parallel with the galaxy's axis of rotation. Stars - like ours - that are out on an arm could have any orientation. They might even be more stable if their axes are in their plane of motion through the galaxy.

Keep in mind that Equation 2 was necessitated to explain the difference between the observed Mp/Me ratio and 6*pi^5. There could be alternative hypotheses. At least this thinking is TESTABLE:-)

Also, thanks again for viXra.org. I continue to use your website.

Best Regards and Good Luck,

Gary Simpson

Yes, the quaternion is fascinating, a lot of promises and makes you wander before you come to a path leading to the goal. This goal - the recognition of your merits by most mathematicians and getting your name in the books, at least for the fact that you are using the quaternions of his own invention, calculated the size of the proton.

I wish you success on this path, at least in this contest!

Because you went deep and put a lot of work to that branch of mathematics which looks to be a dead end, I'll put your essay the highest score.

New Cartesian Physic, which is based on the equivalence of space-matter, needs the theory of complex numbers not only on the plane, but mostly in space. After all, Descartes himself believed that the basis of physics must lie geometry.

From New Cartesian Physic great potential in understanding the world. To show this potential in his essay I gave materialistic explanations of the paranormal and supernatural. Probably, I made a mistake that has bound New Cartesian physics with the paranormal and supernatural, because it does not attract the attention of others. Visit my essay and you will find something in it about New Cartesian Physic. Note the drawing of geometric relationships in the atom.

Sincerely, Boris Dizhechko. (Note that I did not know English and use online translator)

    Boris,

    Many thanks for reading and commenting upon my essay. I lack proper academic credentials. Therefore, I have no expectation of recognition. I simply hope to make a few people ask themselves a few questions ... is my calculation also a coincidence? Is there an alternative interpretation to the wave function other than the Copenhagen Convention?

    I'm not so sure that I would dismiss quaternions and octonions as a dead end. The Maxwell Equations can be formulated using the quaternions. Therefore, the paradoxes that occur with Relativity might simply be the result of Einstein attempting to preserve Euclidian geometry when it is more appropriate to use a Geometric Algebra.

    I will read and score your essay soon.

    Best Regards and Good Luck,

    Gary Simpson

    Thanks Karoly,

    I don't think the site is overloaded ... it probably does not get a lot of traffic compared to most sites. I wonder if there is a problem with your hardware or connection. If I have a problem accessing something, I usually close all my windows and re-open them. Sometimes I also reboot my computer and/or my internet hub.

    Best Regards and Good Luck,

    Gary Simpson

    6 days later

    Dear Simpson

    I loved the way you closed out the essay, "It is certainly possible - perhaps even likely - that these conclusions are false. However, if that is the case then the reader is left to explain the proton diameter calculation." I would have used a similar closing for my essay as well, had I been able to come up with an exacting calculation similar to what you have done.

    Having only recently discovered octonions via Yanofsky's and Dickau's essays, I cannot pretend to have suddenly gained the capacity to validate the calculations you have presented in the essay. But I can recognize simplicity and elegance when I see it, and your work has it. While I can appreciate Dickau's patience with regard to voting (he has more experience with this contest), I would much rather vote right now for an essay that I like and you are certainly one of them. All the best!

    Warm Regards, Willy

      Willy,

      Many thanks for reading and commenting upon my essay.

      Physics is very demanding. You must get the right answer and you must do so for the right reason. You are correct to focus upon the proton diameter calculation. As I see it, either a coincidence has led me to a calculation that is also a coincidence, or the Mp/Me ratio and my calculation are not coincidences. I can believe a single coincidence, but two coincidences that are linked seems too much to believe.

      You have begun a new journey. Quaternions, Octonions, and the Division Algebras are very interesting indeed. I have been studying them for a few years now and have barely begun to understand and appreciate them. There is also a related field known as Geometric Algebra. David Hestenes has written several books in this field.

      Essentially, the question that I ask is "What does it mean to move in 5-D space if time is not a dimension?". I'm not certain that Euclid type thinking is applicable. Much of the controversy of Einstein's work was because he imposed Euclid's Geometry onto Relativity ... but what if Euclid is just a subset of the geometry of space? I think this is the path that we now need to follow.

      I will read and comment upon your essay soon.

      Best Regards and Good Luck,

      Gary Simpson

      Gary,

      Suggest you take a look at the work of David Hestenes on geometric Clifford algebra, if you haven't already. Appears to me much of what you are doing is a subset of that algebra, to pick up on the rest of it might be very helpful to you.

      Several of the contributions to our contest are in that geometric language, including those of Michael Manthey Manthey FQXi essay and Michaele Suisse Suisse FQXi essay.

      Pete

        Gary,

        Yes, I have an essay in the contest. Michaele Suisse is my co-author, it is submitted in her name.

        "Aims and Intention from Mindful Mathematics: The Encompassing Physicality of Geometric Clifford Algebra"

        Surprised by your comment of earlier today on my thread, that even tho I steered you in the right direction, here it is two days later you still don't get it.

        The only thing i can conclude from that comment is that you didn't understand what you read. The algebra of the physicist's S-matrix of figure 3 of our essay is GA. The wavefunction is comprised of the fundamental geometric objects of the geometric Clifford algebra of 3D space - one scalar, three vectors, three bivectors, and one trivector. This is pure Hestenes from his 1966 book, Spacetime Algebra, very basic stuff.

        Similarly, if one models interactions by taking the geometric products of wavefunctions, that yields a 4D Dirac algebra of flat Minkowski spacetime. Again this is basic spacetime algebra.

        If you take a look at this paper co-authored with Michaele

        "Geometry and Fields: Illuminating the Standard Model from Within"

        you might find it a little easier to see the connection between the math and the physics. It is deep, diverse, and incredibly precise - at the ppb limit of experimental accuracy on many calculations.

        Haven't rated your essay yet, hope to get to that soon.

        Pete

        Gary,

        Just a quick note. I promised comprehensive commentary -- working on it. Meanwhile, you might want to look into the work of this author:

        https://www.researchgate.net/publication/280499966_The_imaginary_unit_i_as_the_temporal_directional_component_of_the_complex_position_vector

        All best,

        Tom

        Hi Gary,

        The mathematician in you has brewed another lovely essay, but I personally still prefer 'Calculus 2.0'. I will not claim expertise on quaternions so I will pick my comments.

        Yes, I agree time is scalar. This is in keeping with the physics of Galileo and Newton.

        But calling the complex i, a dimension may be okay mathematically, but physically it will be a hard sell to me who have become wary of the wares that mathematical physicists peddle these days.

        What is the 'v' in your equation 2 and how is the value to be determined? You say it represents motion, motion with respect to what?

        Then, you give a role to the observer in the determination of mass in your 'prediction' segment. This looks like a Special relativity effect and must share in the flaws of SR theory.

        Finally, when you say that the Earth is moving at 0.006136c with respect to a true rest frame, is this a new prediction? The value is so much higher than the 370km/s speed relative to CMBR.

        Best regards and all the best in the competition,

        Akinbo

          Akinbo,

          Thanks for reading and commenting and hopefully for voting. The one-bombers have been significant in this contest.

          The previous essay actually led to this one. I tried to evaluate some problems in mechanics and found the results unsatisfactory. So I revisited the problem and multiplied by Euler's Equation one more time. That gave me this subset of octonions.

          Your skepticism regarding the complex i as a dimension is wise. I don't know if it is or is not. The only evidence I can provide is that the proton size calculation is accurate and that is only circumstantial evidence. Perhaps it is simply another coincidence or perhaps it actually means something else.

          The v in Equation 2 is absolute motion with respect to a fixed background. It is a variation on the abandoned aether concept. However, relative motion is more complex that what was previously considered and the motion of A with respect to B is not the same as B with respect to A. They are more like inverses ... by that I mean they are more akin to division ... 1 divided by 2 vs 2 divided by 1 as an example. So this puts SR into the hypothesis but in a different form than what we usually have. Maybe it is better, maybe it is worse. But it does contain a fixed reference frame.

          You are correct regarding the value of the velocity. Colin Walker also pointed this out. The value I present is almost exactly 5 times the CMBR value. My best guess here is something that I remember from statistics. There is a certain type of average where you divide a value by its degrees of freedom. In this case, that would be 5. I have not found the statistical reference that I am looking for regarding this yet but I am certain I have read it before. That will provide another clue as to the correct form of the math.

          Best Regards and Good Luck,

          Gary Simpson