The Triality in Geometry

Adding a new spin to Buckminster Fuller's vector based symmetry breaking

by Frank van den Bovenkamp, TrigunaMedia / TGMResearch,
Theo Lohman, Collin B.V,

When Einstein rejected the probability theorem of quantum physics with the remark "God doesn't play dice", many thought he meant that quantum physics is mistaken. That's not true - Einstein didn't say it was wrong, rather he was (intuitionally) convinced that it was incomplete.

In modern quantum physics, Einstein's life long vexation has been addressed to some extend, in that the hidden scalar field was introduced, complementary to the measurable vector- or gauge fields, which is crucial for symmetry breaking in quantum field theory.

Einstein could just as well have said: "God doesn't play with vectors only". Along the same line, B. Fuller's vector based symmetry breaking, no matter how self-consistent it is, can and should be made more complete, and therefore more convincing and satisfactory, by adding scalar field related geometry.

The way to do that is through the triality (universal operative principle) underlying all symmetry operations.

Synopsis of how the Triality, through its inner permutations, generates a sequential wave

Fuller obviously didn't realize that the hidden creation space might just as well be geometrized, and instead appears to refer to a realm complementary to Euler / vector space using Gibbs' terminology.

Thus the tetra is the central figure and mediator of the functionally distinct, convergent and divergent geometrical media. The vertices of the circumscribed octahedron each identify the edges of the central tetra, that is, the interactions between the original trialities' permutations initiating what will ultimately become the extroversial, sequential state in real space. Fuller showed how symmetry break can be modeled based on the octahedral geometry, which (also) in tetralogic is a vector construct:

Click to view interactive animation

Fuller's original concept is viewed in a more complete way through tetralogic, based on the triality of creative principles resp. its permutations, and the dual (invisible and visible) creation spaces. It reveils the different levels of manifestation or materialization prior to the complete symmetry break, and their resp. behaviors:


The inner octahedron represents the tetralogic of a matter wave, still embedded and (semi-) bound within the causal media, but on the verge of symmetry breaking. After the symmetry break, a prototype tetrahelix forms out of the "octahedral sub-tetra's" which is no longer geometrically embedded. This obviously represents a lightwave - massless (no scalar / Higgs impact), completely free and unbound.

The Four Causes geometrized. The octa drives the symmetry break, the dodec restores the symmetry.
The subjective-objective annotations, as well as the synthesis and reduction phases are from Sarkar.
Especially the direct reduction from final cause to the material cause is a novelty. Its quantized
form was introduced by Sarkar as "microvita" - arguably a sort of scalar (magnetic?) potential.

Tetralogical symmetry breaking and quantum field theory. The intermediation of (3+1) synergetic
and (3) orthogonal spins forms the mixed cycle or torus. This becomes the objective "behavior"
of the interacting causal media.

Unlike tetralogic, the "Cycle of Creation" is a philosophical and therefore dualistic concept. From a personal viewpoint, or for
didactical reasons, one could differentiate between two "separate" tetra's. In the extroversial phase, during symmetry break, the
"objective" trend is leading, and thus one could assign an "objective" tetra. In the internal phase, when higher competences are
formed, there is a "subjective" tetra. In reality it is one unbroken process of the triality influenced by its inborn operative principle.


Ref. main article on Tetralogic:

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