Dr Josephson,
By "trinary cancellation" I mean the red-green-blue color charge cancellation of the strong force. This particular type of cancellation is particularly powerful due to color confinement, which makes color invisible anywhere in the universe outside of nucleons and mesons. Structures (scaffolding) that emerge from this striking partial cancellation include electric charge, mass, and spin.
Thank you for the excellent (I was not clear at all) question and helpful link advice! I must also apologize for my slow response. I seem not to get notifications about responses from other essay threads, so I had to manually search to find responses.
A bit more elaboration about "fundamental circles" is provided below. My apologies for the length, but the relevance of your annihilation-emergence concept, especially with some easy generalizations, seems to have engaged my interest more than I anticipated. I think it is very relevant in particular to the anthropic probability issue.
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Assuming I understood your concepts rightly -- I do not presume this, but hope so -- then the three-part mutual cancellation of the color or strong force would seem very much to fit with your idea that persistence emerges from mutual... opposition? cancellation? Even if it is not an exact fit your ideas, your essay has convinced me that this type of almost-complete-cancellation is a deep and vital component of how our universe manages to meet the astonishing anthropic probabilities.
I would like to suggest an important and I think complementary addition, which is this: Your concept (along with your major reference; I acknowledge that it is primarily her idea) not only creates scaffolding, but also creates flatness. By flatness I mean the ability for persistent entities to spread out without penalty or excessive cost over large spaces. Within those spaces, which are just as much a creation of the incomplete cancellation as are the scaffolding structures, the emergent structures are able to exist independently and subsequently to interact in very interesting ways.
I would suggest that this emergence of flatness from your circle scenario is every bit as important as the emergence of the scaffolding itself, and that there are in fact complementary to each other. The "mutual consumption" of the entities (two or more) is what clears the field and creates a flat, expansive space possible, while the incomplete part of the cancellation creates the relatively isolate entities (e.g., atoms) that reside within that "burned out" space.
I can think of no more literal of emergent flatness than the formation of hydrogen atoms at the end of the long dark era after the big bang, which cleared space for photons and enabled the formation of far more interesting entities, such as galaxies and stars and planets. Space itself was already flat, but in terms of electromagnetic forces, which are incredibly powerful and contrary at large scales to chemistry or anything else resembling our world, this event also mostly cleared out the powerful fields and enabled entities made of atoms -- the emergent scaffolding -- to exist in relative isolation and with far greater persistence over time of their states. In short, plasma became memory, some of the earliest fabric of classical, information-rich history.
(SIDE NOTE: If you believe in space itself as emergent, which I do incidentally, then at some deeper level not covered by the Standard Model there must exist yet another circle of annihilation-emergence that quite literally creates the flat xyz space that makes our entire expansive universe possible. There is lively physics dialog going on these days about quantum entanglement as a possible path to that emergence. Alas, that dialog is sadly encumbered by a completely unnecessary historical insistence on pushing the argument down to the astronomically energetic Planck level, nominally in order to include gravity, even though that approach that has for 40 years failed to yield a meaningful theory. Since entanglement works very well indeed at the ordinary particle level, insisting that entanglement be pushed down to the astronomical energy levels of Planck space violates Occam's razor about as emphatically as any proposal of which I am aware. So: Entanglement as a possibility for emergent space is intriguing. Entanglement when forced down to the astronomically energetic Planck level is... not persuasive at all.)
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On a separate point, there is an easy way to unify oppositions of two or more as part of a single model. Here's how:
If you take your circle and imagine charge as two points on opposite side of the circle, you have the binary cancellation case.
If you instead take three equal charges and distribute them in an equilateral triangle around the same circle, you have the trinary cancellation case.
However, there is no reason to stop there. Placing the points of any regular polygon with 4, 5, etc points also works fine. That those do not seem to occur in fundamental physics does not preclude them from occurring in your higher levels of organization. I would argue for example that the benzene ring, which is to me one of the most delightful and important stabilizing structures in all of biochemistry, is an example of a six-point mutual cancellation yielding a new form of scaffolding. For biochemistry, the idea of the stable benzene ring as "scaffolding" is about as literal as it gets. We would not exist without it, because without the stabilizing effect of partial implementations of this ring, there would be no amino acids at a minimum and no strong, persistent way to make "interesting" molecules (ones more complex than, say, polyethylene).
Finally, your circle charges ("entities in conflict") need not even be regular polygons. You could have two pairs of nearby charges on opposite sides, for example.
The full generalization, including unequal charges and even distribution over three dimensional space (!), is to treat the charges like angular momentum vectors that collectively cancel out to zero angular momentum. The angular momentum model is really inherently 3D, with the 2D (circle) case just a subset, since there is a very special relationship between angular momentum and 3-space due the 3D space's unique interchangeability of rotations and vectors. The model conspicuously does not generalize in any simple way to any dimensionality other than 3D and its subsets of 2D and 1D.
Incidentally, I should note that your original circle model, if presented in terms of angular momentum vectors, is really the 1-space (1D) case; the circle is... well... not really necessary? You just have two entities at opposite end of a line, after all.
The deeply fundamental trinary color force example does, however, require an actual circle or 2-space subset. So arguably, the circle begins not at the 2-charge electromagnetic level, but at the smaller scale in which nucleons emerge. One could thus say the circle is more fundamental... but only for three opposing forces, rather than for just two.
I do not know what the potential of the full 3-space model is. However, I once again I would point to biochemistry for a very interesting high-number 3-space example of mutual cancellation leading to stability: C60, also known as buckminsterfullerene. These marvelous little geodesic spheres have no less than 60 fully symmetric vertices (the carbon atoms) that collectively form one of the most stable (scaffolding again) overall molecules known in chemistry.
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Enough. Thank you for your excellent question. I was in retrospect very far from being clear when I casually dropped in the term "trinary".
Cheers,
Terry Bollinger (Essay 3099)