Trick or Truth: The Mysterious Connection Between Numbers and Motion and Geometry by Doug Bundy

Errata: Several errors in the paper went undetected in the rush to beat the deadline. The three most serious are:

1) Page numbers were omitted.

2) Figure 2 is incorrect as shown.

3) There is a textual error on page 8.

Number 1 cannot be helped at this point. Number 2 can be addressed by attachment to this comment, while number 3 can be pointed out.

Error number 3 is found in the third paragraph of the eighth page, in the sentence "This means that the unit space volume goes from zero to unit value and back to zero, in two picoseconds, but the number corresponding to the cubic value of the three-dimensional interval motion (2^3=8) is incompatible with the numerical equation for the volume of a ball;"

The prepositional phrase, "in two picoseconds," should be deleted, and the sentence should read: "This means that the unit space volume goes from zero to unit value and back to zero, but the number corresponding to the cubic value of the three-dimensional interval motion (2^3=8) is incompatible with the numerical equation for the volume of a ball;"

Error number 2 is found in the incorrect labels of the exponents of the number "1" of the tetraktys, which shows them as all zeros. The exponent labels are corrected in the attached figure.Attachment #1: Tetraktys.jpg

An Expanded version of Figure 4 might help to understand how one cycle of the expanding/contracting motion of a ball is equivalent to 4π radians of rotation.

Therefore, the expanded version is included here, as two attachments.Attachment #1: 3DOscillation1a.jpgAttachment #2: 3D_Oscillation2a.jpg

Clarification: On page 7, paragraph 4, the statement is made: "However, now we know that particles themselves ultimately have dimensions of space and time, or motion, and force is just a quantity of motion."

The last clause should read "and force is just a changing quantity of motion, or acceleration."

A corrected and Expanded version of the paper, with 10 more pages and 7 figures in total, is now available at the LRCphysics website.

POLL: This essay is only a few days old, so I want to try to jump start the discussion of it, by taking a poll:

Given that the "novel" concept of pulsating space and time, represented by rational numbers defined herein, logically leads to the graph of figure 4 and the chart of figure 6, in the expanded version of this paper, which in turn leads to a natural and easy understanding of the 4π rotation of the quantum "spin" concept, as illustrated in figure 7, which has never been physically explained before, would you like to see how the algebra of these numbers works, and leads to a model of the first family of the standard model, as shown in the attachments to this post?

Please reply to this post with "Yes" or "No" as the title of your reply.Attachment #1: STBosons.pngAttachment #2: ST3Grps.png

The fact that we are able to provide a physical, as well as a mathematical basis for the concept of quantum "spin," for the first time ever, deserves some notice, I believe.

So, as a further elaboration on the happy fact that π/2 radians of rotation is equivalent to 1/8 of unit volume, enabling the full expansion from 0 to unit volume and back to 0 volume, in the equivalent of 4π radians of rotation, I have a new graphic to illustrate it very simply.

I hope it helps.Attachment #1: Unit_Volume_Cycle.jpg

Judging from the increased traffic to my website, I believe people are reading this paper and these comments, at least in part.

There are so many papers to read, so it does not surprise me that one so unorthodox as this one is, is not getting a lot of attention.

I would dearly love to get some feedback on it though. Can an error be detected in the physical concepts or the mathematical development? I know the clock escapement analogy is faulty, because the escapement wheel advances one cog with every full cycle of the escapement mechanism. It would be more accurate if it advanced once every half-cycle.

But regardless, the analogy should be clear that the motion of figure 1, consists of a combination of bi-directional and uni-directional motion. Maybe I should have used the example of a pendulum, where each swing is timed, so that there are two units of increasing time, for each full cycle of the pendulum.

Nevertheless, the simple explanation of space and time, as the reciprocal aspects of a universal motion, is exceptionally sound philosophically, as first proposed by Dewey B. Larson.

And who can reasonably argue that what we measure and call distance, or space, is just the past history of motion, the space aspect of it? Clearly, to measure space, requires time. When we measure the time aspect of the motion, or the space aspect of the motion, between two locations, we must include both aspects of the motion that separates them. The magnitude of the motion is irrelevant. We can take years to move a measuring rod into place, over time, or we can time the travel of a light beam or a sound wave between them, but regardless, space is meaningless, without time and vice-versa. The only known relationship between them is motion, v=deltaS/deltaT.

So, going from physical motion, having two, reciprocal aspects, to a mathematical expression, having two, reciprocal aspects, we find a perfect analog of the motion in our rational numbers, when we simply recognize that all numbers are rational numbers, whether or not expressed as integers, just as Kronecker insisted.

We cannot escape the fact that a moving point must transit the last subdivision of a current unit, and the first subdivision of a subsequent unit, not withstanding Zeno's argument. This means that infinite sets do not apply, after we choose a divisor, which we must do, to construct a clock, no matter how small.

I would love someone to engage me on any of these points, but if everyone agrees, we can move on.

What about challenging me on the Chart of Motion? Surely, someone here will take issue with that proposal. For crying out loud, I'm asserting that rotational motion, the foundation of Newton's program of research, is not even a fundamental motion! Don't the readers of my paper want to challenge me on that?

It could be that the prevailing opinion of my readers places the paper in the "Not Even Wrong" category, dismissing it outright, preferring to spend the time on more orthodox reads.

However, the fact that it can explain quantum "spin" physically and mathematically, for the first time ever in the history of quantum physics, should merit at least a comment, if not a reasonable rebuttal, I do believe.

Well, there is still a lot of time left for the community to stumble upon it and to discuss it, so I'll keep checking back. I hope to have at least as much interaction as we have had in previous contests. I enjoyed it then, and I know I will enjoy it this time, if and when it comes.