Golden Ratio Appears in 8D to 4D Quasicrystals, Black Holes, Consciousness Theory of Everything

SciFi - wrist watch - from "What is Reality" video by Quantum Gravity ResearchThanks to geometer colleague and dream researcher, Ed Kellogg for alerting me to this very interesting (and fun) video “What Is Reality?”  from Quantum Gravity Research (check out the lovely video loop of a slowly rotating polyhedron made of tetrahedra on their website’s home page) – in addition to meshing interconnections with our faithful  omnipresent proportion, the Golden Ratio – also talks about higher dimensional geometric polytopes, Planck’s time and space constants, meaning, self-representing symbols, pixelation, geometric codes, non-local information … of course, consciousness – that ‘elephant in the room’ that mystics (not just in India) have been riding for millennia. 🙂

“The (8-dimensional) E8 Lattice … to generate that 3D quasicrystal, the substructure at the pixelated fabric of reality, we project this 8D crystal to 4D, and then we convert that to 3D. … just like the basic shape of the 3D cubic lattice is the cube, the cell shape of the E8 lattice is an 8D shape with 240 vertices. We call it the Gosset Polytope. When the Gosset Polytope is projected to 4D, it becomes two identical shapes of different sizes. The ratio of their sizes is … 0.618 (the Golden Ratio.)”

E8 (Garret Lisi) lattice 8D-to-4D - from "What is Reality" video by Quantum Gravity Research

The video – after mercilessly exploding a cubic lattice made of Zometool, tsk, tsk! 🙂 – then references the appearance of the Golden Ratio in an equilateral triangle inscribed in a circle which we have documented on this website for many years.

“The Golden Ratio may be the fundamental constant of nature. … It is weirdly ubiquitous in the universe, appearing everywhere from the quantum to celestial scales. … it appears in black holes. The golden ratio is the precise point where a black hole’s modified specific heat changes from positive to negative. Ø = (M^4) / (J^2) … and it is part of the equation for the lower bound on black hole entropy. The golden ratio even relates the loop quantum gravity parameter to black hole entropy. Ø = 2 ^ (π𝛾) … Why does this support the claim that the golden ratio is the fundamental constant of nature? Because a theory of everything must unite general relativity with quantum mechanics and a black hole is where these two theories converge at their limits.”

Golden Ratio - Black Hole Entropy Equation - from "What is Reality" video by Quantum Gravity Research

“Meaning is subjective and requires choice.” … Seems like physics is treading on metaphysical turf again. Fun! 🙂

To dive a bit deeper into the projected polyhedral shape (which evidently resolves to an icosidodecahedron), check out this cool video – featuring Klee Irwin of Quantum Gravity Research –  (“The 20-Group Twist”.)

For further detail, check out this video: “Quantum Gravity Research: an Overview Presented by Klee Irwin.”

-polyhedron made of 20 tetrahedra rotated; golden ratio proportions - from "What is Reality" video by Quantum Gravity Research
Lots more to learn and explore… Here is Ed Kellogg’s commentary (quoted below) that initiated this post … It goes without saying that there are numerous disciplines requiring massive amounts of study to understand all this that I have barely scratched the surface on, but it sure is interesting! 🙂

“I felt glad to see this model incorporates E8 theory.  I met Garrett Lisi when I attended his presentation on E8 theory (“An Exceptionally Simple Theory of Everything”) when I went to the 2010 Joint Mathematics Conference in San Francisco years back and felt quite impressed, but had heard nothing since.  (See attached paper and check out this video link: ).

I really enjoyed QGR’s ”What Is Reality” video, as it brings together a whole set of variable’s I’ve had an interest in – sacred geometry, consciousness, the golden ratio, the universe represented in a pixilated interface, derived from a non-local beyond time and space information matrix code, etc. all integrated into one congruent and entertaining presentation.

I especially found it quite cool that the golden ratio pops up as the ratio between the two sizes of the projection of the 8D Gosset polytope (from E8 theory) onto 4D – I’d never heard of that.

… check out this paper also: “Quantum Walk on a Spin Network and the

Golden Ratio as the Fundamental Constant of Nature,”

One possibly important insight that occurred to me. The narrator talked about tetrahedrons as fundamental units (“physical reality pixels”), with each of them having different states.  This reminded me of Donald Hoffman’s Conscious Agents, CAs, which he represented in a first rough approximation as triangular shapes/processes, functioning analogously in a manner somewhat similar to Turing machines:

From  “Objects of Consciousness” (,

Even this simple model of interacting hierarchies of CAs leads to the identification of “a wavefunction ψ of the free particle with a harmonic function g of a space-time Markov chain of interacting conscious agents.”As a next step, bringing in another dimension of processing for more complex CAs, one would add another point to create higher dimensional tetrahedral CAs (“TCAs”), as it would add one more fundamental point, and three more communication channels might lead to the emergence of many more equations from the interaction of hierarchies of more complex TCAs.  If so, what might that additional “point” represent, and what might the communication channels ?  Something I find quite fun to think and to speculate about!

This has already given me ideas about what an upgrade of the “Beyond the Matrix: Conscious Realism and Lucid Being” workshop that I just gave at the Anaheim IASD conference might additionally include, in version 2.0. <g>”

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