## Trick or Truth: The Mysterious Connection Between Numbers and Motion and Geometry

Almost two years ago, now, on August 20, 2013, I wrote about a meeting I had with Bruce Peret and Gopi Krishna V, at Rainer Huck’s home. I was really happy to have had an opportunity to discuss some important ideas of the LRC’s work with these guys, but I never managed to finish the post, as my LRC work was overcome by events.

This changed, however, when I found out about a new essay contest at FQXi, and I decided to enter it, albeit in February, just before the March 4th deadline. It was very stressful, but I managed to write and submit a paper in time.

The theme of the contest is: “**Trick or Truth: the Mysterious Connection Between Physics and Mathematics.**” It was impossible to resist, but almost impossible to imagine that I could do justice to the theme, given the constraints FQXi puts on the essay entries and the little time that was left to write it.

Nevertheless, with much effort and prayer, I managed to meet the deadline with a paper I think made sense, even though there is nearly zero chance that it will be noticed much, with the hundreds of papers submitted, including one by Lee Smolin.

There are also typos and editing errors in it that I wish I could have discovered in time to correct. Yet, I hope that the readers there will overlook them. The effort was worthwhile, I think, because it gets the ideas of the LRC’s RSt, and thus Larson’s work, on the table of the judges, participants and readers of the essay contest, many of whom are professional mathematicians and physicists.

The title of my essay is: “**Trick or Truth: The Mysterious Connection Between Numbers and Motion and Geometry.**” I hope everyone will read it and comment on it at the FQXi site, when it is posted (it hasn’t appeared there yet, but should sometime next week,) but I thought I would post a corrected and expanded version of it here, as well.

And I will do that soon, but in the meantime, as a preface to the paper, I have determined to publish what I wrote nearly two years ago, after I met with Rainer, Bruce and Gopi, because, it is relevant, I think:

Yesterday I enjoyed a discussion of scalar motion fundamentals with Bruce Peret and Gopi, as we met at ISUS HQ, in SLC, UT, as guests of Rainer Huck. It was the first time that I had met Gopi, a young physics PhD student, studying in Texas, but originally from India.

It was actually a fruitful discussion, in large part due to Gopi’s interest in the LRC’s RSt, which gave me a chance to not only explain somewhat the unique development of our RSt and how it differs from Larson’s RSt, and the RS2 re-evaluation of his RSt, but also to introduce Gopi to the

newideas of scalar motion fundamentals, which we have been developing, while they have been experimenting with substituting projective geometry for Euclidean geometry in their work.I explained how the tetraktys incapsulates the concept of two “directions” in three dimensions (four including zero), and how Larson’s 2x2x2 stack of unit cubes is the geometrical equivalent of the tetraktys, which, by adding the concept of magnitude, to the tetraktys concepts of dimension and “direction,” incapsulates the totality of scalar motion fundamentals: magnitude, dimension and “direction.”

I’m not sure how impressed he was with this phenomenal connection we have found between the binomial expansion that we call the tetraktys and the 3D stack of unit cubes we call Larson’s cube, especially in the course of the disjointed give and take of a living room discussion. However, I was so pleased with his careful and thoughtful curiosity that I entertained the idea of extending the discussion into the implications for a scalar algebra fit for use in RST theory development.

In fact, we did talk about imaginary, complex, quaternion and octonion numbers, and the algebraic pathology that the use of them engenders, but I was not able to get much beyond that except to touch briefly on Hestenes’ geometric algebra and Altmann’s paper, “Hamilton, Rodrigues, and the Quaternion Scandal.”

From there we got into quadrantal versus binary rotation, and I tried to explain how that fit into our work with 3D oscillation (“pulsation” as Gopi calls it. I like that.), and its physical explanation of the 720 degree “rotation” of the LST community’s concept of quantum spin.

I was so pumped, for having the opportunity to lay out these vital discoveries we have made here at the LRC to Bruce and Gopi, that I continued the discussion in my mind as I drove home, after our meeting had ended.

It was then I felt a great desire to finish the conversation, maybe in a message to Gopi, or a presentation at ISUS HQ, or something else. I finally settled on writing this blog entry, because it is here that we document the development process of the LRC’s efforts to develop a useful RSt.

Of course, like I said, I never actually got around to writing it then, but now I have written it for the essay contest. In fact, I wrote it three times, trying to fit it into their constraints. So, in the next few days, I will take those three versions and try to combine them into one expanded article, without the constraint of the contest rules.

Wait for it!

**Update: **A few days later and here is the expanded paper!

## Reader Comments (3)

Please take a look at this.

http://reciprocalsystem.org/PDFa/Preparing%20for%20the%20Reciprocal%20System%20(V%20Krishna,%20Gopi).pdf

Hi Doug, did you write the "Reciprocal System of Mathematics - Background"? It matches so many of my unstudied intuitions on the subject.

My one question, for now, is: How does 1/2 + 1/1 + 2/1 = 4/4 = 1/1 ? Do I need to study Hestenes book? What's a good selection of books and articles to prepare me to grasp and contribute to this work?

Thanks. My e-mail is galokhaugen@gmail.com

Hi Roman,

Thanks for writing. I am sorry for taking so long to reply. Yes, I wrote the background article and all the others on this site. The mathematics part is my effort to put the LRC's Reciprocal System on a mathematical basis.

I'm not much of a mathematician, but I have enjoyed taking a stab at it and have had some amazing experiences in the process.

As far as the 1/2+1/1+2/1 = 4/4 = 1/1 equation is concerned, you can think of it in terms of space/time cycles. It accounts for the ratio of oscillating space cycles to time progression and the ratio of oscillating time cycles to space progression.

It's the mathematical equivalent of the chart of Figure 1 shown in the New Math blog entry here: http://tinyurl.com/oo938wt The s/t = 1/2 is the equation of the Space Unit Displacement Ratio (SUDR) and the s/t = 2/1 is the equation of the Time Unit Displacement Ratio (TUDR).

When these two oscillating units combine into a S|T unit, they form bosons and fermions, as explained here: http://tinyurl.com/nax7glk

The equation for the S|T unit must include the unit progression, s/t= 1/1, to account for the inward direction of the oscillation of both the SUDR and the TUDR.

I hope that makes sense.

As far as what to read, I started with Larson's

New Light on Space and Time, but the definitive work is published in the three volumes ofThe Structure of the Physical Universe.(see http://www.reciprocalsystem.com/dbl/)1) Nothing But Motion

2) Basic Properties of Matter

3) The Universe of Motion

The LRC was formed to advance a new theoretical development of fundamental physics, using Larson's system of physical theory, by incorporating a mathematical formulation in the development.

It differs from Larson's theoretical development, in that it does not treat the postulated three dimensions of space and time independently, as his theoretical development does. However, it is based on his system of theory.