OCTOBER 22,2017

Written by Benjamin Gurule,

Stephen James Taylor and Jesús Salvador Treviño

Previously, we have discussed how an original system of order, discovered and elaborated upon by Benjamin Gurule, might serve as a metaphor for understanding the link between polyhedra and quantum mechanics. Exploring this concept further, Gurule discovered that his system might also provide clues to understanding the nature of the quantum world beyond the standard model, insights beyond the quantum metaphor.

Gurule makes an important distinction between what we are calling “Woven Chirality” and the apparent “spin” generated by we will call “Directional Chirality.” “Woven Chirality” is a STATIC property that resides permanently at all surface convergences. Its left/right-handed identity is determined solely by the order in which the equators overlap each other. It is a fixed property resulting from the way the rings are woven. The woven chirality identity of the shell can be changed only by completely disassembling and then reassembling the rings in opposite order.

Directional chirality, on the other hand, arises when static convergences are imagined in motion. It is a DYNAMIC property that results from the collective orbital movement along the surface of each ring. It comes into existence only when all the “legs” of a convergence find themselves flowing around a periphery of the convergence in the same continuous direction, either clockwise or counter-clockwise. One can visualize the flow of directional chirality as the continuously renewed collective motion of imagined “particles” moving through the legs of each convergence.

Once the shell convergences are visualized as being in motion, that is, as being vortices, certain attributes of active and inactive polarity become evident. All these surface vortices can be seen to be “floating in place” on the interwoven surface. Even though the two vortices actually serve as opposite ends of the same pole, the two vortices are entangled. That is, directly connected to each other only through the outside membrane of the shell, with nothing but captive empty space in the center.

Even though some of the shells can support several active poles at the same time, every shell will always have at least one active pole. No exceptions. The topology of the system also tells us that the simple act of deactivating one active pole will always physically activate another active pole at another location that will take its place.

For example, in this four-way vortex, the secondary current flow is clockwise and is “active.” The neighboring three-way vortex is “inactive,” because all the equators are not flowing in the same direction. What happens when we reverse the current on one of the bands of shell?

Now the four way vortex is no longer “active” but the adjacent three-way vortex has now become “active.”

Another aspect of shell topology that Gurule explored was that of slicing the bands on a Gurule shell into parallel strips. Theoretically the rings can be sliced into any number of parallel bands creating a near infinite number of 2-way crossings in any Gurule shell. Each adjacent parallel band is woven in the opposite way, over instead of under and under instead of over. Hence each 2-way crossing represents a unique physical address on the shell. The implications and applications of this are yet to be tapped.

Gurule’s shells also offer clues to molecular and atomic bonding.

The Gurule Shells, on their own, are able to differentiate between acceptable and unacceptable building blocks by a natural form of selection. They bond via a series of ring linkages, one ring at a time by a simple yes/no process.

Yes, two rings in space have a better chance of engaging if they are perpendicular to each other.

And no, two rings in space have less chance of engagement if they are parallel to one other.

In his famous paper on chemical bonding, Linus Pauling suggested that atoms assemble themselves into molecules as if they had polyhedral shapes. Bonding can take the form of a single or Van Der Waals bond, a double bond or a triple bond, each with differing bond properties.

We know that when two atoms are bonded together the two atoms involved have less collective mass than they do when they are not bonded together. This tells us that in a single bond, the substance of one atom is somehow able to interpenetrate the substance of the other. We also know that in a single bond, the two single bonded atoms still have the freedom to rotate about each other, but if the rotation exceeds 60 degrees, the two atoms are known to fall part.

Single and double bonds can form at random between any two colliding shells. And given enough pressure, a simple link can be flattened into a double, triple or even higher linkage when the initial point of contact is flattened so that it encompasses an entire vortex.

But this is just the beginning of the story. Several conditions must be satisfied before any of these higher level bonds can form.

The first two conditions that must be met before a vortex bond can form are fairly obvious. The two colliding convergences must be of identical shape and size simply because a small triangle cannot physically bond to a larger triangle and a triangle cannot bond to a square of whatever size.

Once natural selection has located the first two faces that are similar in size and shape, the final condition for bonding comes to us in the form of a law that tells us that two left-handed convergences can bond and two right-handed convergences can bond, but two opposing left and right-handed convergences cannot bond with one another.

Also contributing to conditions necessary for bonding to occur is directional chirality. These two identical Q 4 shells have different directional chirality. The vortex on the right is right-handed with the directional chirality flowing clockwise. The Q 4 shell on the left is also right-handed with the directional chirality moving counter-clockwise. But in addition to the “topological” bonding requirements where both vortices must have the same woven chirality in order to bond, the directional chirality flow of the two vortices must be opposite to one another in order for bonding to occur. Somewhat like the attraction between positive and negative electrical currents.

Here we can see how two Q 4 shells with opposing directional chirality will mesh with one another. When we examine the bonding interaction through the eyes of the system, we can see that perhaps the atom, is less of a thing and more of a process, or more accurately, a network of occurrences.

If there were a unified field theory based on a very different “story” of the atom, what might it look like? If there were a simple but detailed metaphor consistent with major elements of String Theory that could not only accurately describe much of the “micro” quantum world but also the “macro” molecular-electro-chemical world, what might it look like?

Gurule’s shell system does not offer a definitive answer to this question but his system does suggest avenues for further explorations to this end. The woven and directional chirality of Gurule’s structures provide a dynamic metaphor through which to view atomic bonding in a new way.

These woven ring structures also propose new perspective on the wave nature of matter. Changes in wave, phase and amplitude create and alter polyhedral units that point to a new geometry-driven reframing of the basic units of matter. Gurule’s approach also offers quantifiable density functions suggesting a redefinition of what mass is and the nature of spin.

Most importantly, these areas of inquiry suggest a need for a reworking of the very terminology that describes the subatomic world–something beyond the scope of Gurule’s explorations at the time of his death.

In summation, it is our hope that the work of Benjamin Gurule will spark the interest of a math or physics graduate student looking for an intriguing area of inquiry, an individual who has a deep enough curiosity to explore the wonders of this particular topological realm, and to spend the time needed to find out how these structures relate to existing data in particle physics and chemistry. We believe we have taken it as far as we can and look forward to encountering the people with more expertise who can take this fascinating journey further.


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