three is a magic number

[Albers]

I have modelled the electron as an electrodynamic field of essentially <m=0>, saying there is no azimuthal variation. This is a field of frozen phase where asymptotically intense rotation cancels intrinsic helicity of light. Now I offer a study I did a few years ago as a simple geometric investigation on three-vertex rings, or possible <m=3> structures of circulating light energy of free rotation with helicity. I imagine possible vertex transformations of either phase or spin. The game is to construct a positively reinforcing ring structure that lays consistently with itself. I set the distance between vertices at one-half wavelength so the wave has gone through that change. Then each vertex is an operator which does, or does not, change phase by pi radians, and/or spin by flipping. Given that a helical wave proceeds between vertices, what combinations make possible a standing wave? SPIN is a binary quantity here and must go through zero or two flips to match itself. PHASE goes through three flips because we set up a three-sided model. Therefore, among the three vertex operators, either one or three of them must flip phase. It turns out there are twenty or so combinations and fascinatingly, there are two pairs of the form: <a,b,b> , <a,a,b> . GO FIGURE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tell me all about quark theory while I tear apart my player piano pneumatics.

[Albers]

When I started my electron theory a few lifetimes ago I figured I could either look up coordinate transforms of spherical fields, or spend time recreating them myself because I needed to become thoroughly comfortable here, and I needed practice with matrices. In that spirit here is an interesting simple study in attraction/repulsion/geometry whose results surprise me. Consider one attracting center. How many oppositely charged 'particles' can be held by the one? Place a <+> between two <->'s. Repulsion is only one-fourth of the attraction so one can hold two opposites. Nature here is bigamist. Now consider three <-> for which the highest symmetry is clearly a triangle. I calculate components such that there is still net attraction. With four the answer is more interesting. Arranged in a planar square, repulsion wins. Given the higher separation and symmetry of the tetragon, there is net attraction still, small but positive. Unabashed polygamy!

[Epsilon=One]

Originally Posted by Albers

...here is an interesting simple study in attraction/repulsion/geometry whose results surprise me. Consider one attracting center. How many oppositely charged 'particles' can be held by the one? Place a <+> between two <->'s. Repulsion is only one-fourth of the attraction so one can hold two opposites. Nature here is bigamist. Now consider three <-> for which the highest symmetry is clearly a triangle.

Your insight is truly amazing.

Take a close look at the last (bottom of page) Tini Circle group. (This image was done more than ten years ago and requires some minor tweaking.) Where you see three inscribed tangent circles suppose that the the three circles are pulsing with each adjacent circle (and group of three circles) spinning and pulsing opposingly. Then, imagine that the action of each "pulsing spinner" determines what is referred to as "charge" and "spin."

Also note: The curvature of the largest circle ("A") can be any Natural integer and that all the other inscribed tangent circles will also have integer curvatures.

Originally Posted by Albers

With four the answer is more interesting.

Four times three gives us twelve . . . the mysterious number of quarks. Four has to do with cycles; three has to do with variation.

Originally Posted by Albers

Arranged in a planar square…

How ‘bout resonating spheres arranged in tetrahedron form. Suppose three tennis balls are tightly grouped on a plane; then, a fourth is placed in the center on top. This tetrahedral arrangement of four resonating, interacting spheres is the structure of a photon arranged behind the wave front of its ellipsoidal envelope.

Your interest in the number three has prompted me to develop a post where an equilateral triangle (in three dimensions a tetrahedron) is related to: all elliptical shapes; all arithmetic functions including numbers from One up; the revised Fibonacci sequence, the Golden Ratio, etc.

I have started it. I will keep you informed. It may be a day or so (Never enough time in a day. Don't hesitate to nag re my promises.) until I can get to a computer with the graphics I need. I will probably post it at several threads ???

[Albers]

Among the innumerable studies of several or many pages starting from the elementary, five years ago, there is nothing in my Devil's Tower of which I am ashamed. Thank heavens, soon into the game I started numbering series, many worlds ago. Have you heard the lovely song, "Three Is A Magic Number"?

[Epsilon=One]

Originally Posted by Albers

Have you heard the lovely song, "Three Is A Magic Number"?

Three, oh, it's the magic number,
Yeah it is, it's the magic number.

Somewhere in that ancient mystic trinity
You get three.
It's the magic number.

It takes two to make three; and, one to make two.

The trick is to get your mind around what makes one.

[Albers]

ONE sucks. Innies and outties are where I begin!!! For $6.25 I get a good lunch at the China Buffet, where we do not share many words. One day, however, we got on down together as I held forth on this topic. Now hold up both hands with fists and hitch-hikers' thumbs. Consider the obvious YIN-YANG. Now connect thumbs; imagine more thumbs in; what sticks out?? Now imagine the opposite. The first presents YIN to the outside. Both are BUILT OF ONE STICK!!! Chinese culture is built on YIN-YANG. I kept exclaiming, 'One stick!' and everyone (Chinese) nodded and smiled. ONE STICK. Opposite appearances. Do not ask, where are the magnetic monopoles? Rather, rejoice that we are delivered of the concept of electric monopoles.

[Epsilon=One]

Originally Posted by Albers

ONE sucks.

Gödel would agree; I don't.

I believe that a starting "point" must be a point. And, that it is possible to get from there to Yin-Yang.

Originally Posted by Albers

Do not ask, where are the magnetic monopoles? Rather, rejoice that we are delivered of the concept of electric monopoles.

I do not believe in monopoles anymore than I believe that a big bang started it all.

By the way, what "actually" is magnetism? What is its speed? Is it hyper-relativistic like gravity? Is it voodoo action-at-a-distance? What's its medium of action?

[Albers]

Just Say No! . . . . . . . "Actually"? I tried to warn you about words like this. All seriousness aside, to me I guess it is what happens when the thumb and fist separate. To me, all of space is hitch-hiking. Currents happen. Mutual induction is an attempt to balance out the disturbance, perfectly evident in the superconductor, or electron writ large. Space evidences an elastic reaction. Available bound states are moved in reaction. Yes somehow it is basically circles.

[Epsilon=One]

Originally Posted by Albers

Currents happen. Mutual induction is an attempt to balance out the disturbance, perfectly evident in the superconductor, or electron writ large. Space evidences an elastic reaction. Available bound states are moved in reaction.

This reads more like an engineer than a theoretical physicist.

Transformers are just as "spooky" as a pair of magnets.

[Albers]

My Princeton degree was Aero Engineering, so I can take this!!! 'Tis a rollicking and excellent discussion. My instincts are saying that epistemology has to be let go. We can never hope to find terms external to this reality with which to describe it. Like many of the things I hear myself saying lately this is somewhat new just because I have not deeply thought about it. You ask a fundamental question. Even charge is still spooky then, to you. Fine if I explain dipole construction as the near field but this blends into the far field which is, to you, spooky, right? In another forum I read a similarly profound question, "What is epsilon-nought, permittivity of space?" I visualize, in my photons, an "A" field plowing a bilateral current. I'm tempted to say massless, but it is time to get beyond this mask. The only question to me is localization of energy and here the second term of my current expression bespeaks a "mass-energy" of (rho)U. In the electron model it is necessary to use a different expression, namely j-dot-A, to make sense in this different situation. I have not yet made a connection to the homogeneous permittivity and will be meditating here. I sense the presence of the laughing fox. Without both Platonists and engineers we wouldn't get far. Physics starts by induction, not deduction. We first perceive a pattern.