Thanks 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.)”

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.”

“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.”

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! 🙂