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THE 3-SIMPLEX; THE TETRAHEDRON

View a video snippet here on the tetrahedron & Emergence Theory.

The simpliest building block in geometry is always the simplex. For example, the two dimensional simplex is the equilateral triangle.

2 dimensional simplex

Reality seems to be three dimensional. So if one wondered what would be the simplest building block of a three dimensional reality—what’s the simplest 3D bit of information—that would be the 3-simplex, known as the tetrahedron.

The tetrahedron

The more we looked at it, the more we realized that you can model spacetime and particle physics with just regular tetrahedra, if you discover a code which you can get from projecting a higher dimensional crystal down to a lower dimensional space, you can get a construct made of tetrahedra where it’s highly ordered, but it’s not ordered like a checkerboard where it’s deterministic.

A Periodic pattern

It’s ordered with syntactical freedom, where you have to put pieces together this way and that way, but then with the third piece you have an option of turning the shape right or left—that’s a geometric code or language.

geometric code

Did you invent this language?

did you invent this language

So, you don’t invent the language. It’s given to you by geometric first principles. When you take a wire frame of a cube, and you hold it up to the sun and you project it down as a shadow, you don’t invent the way that those edges, the twelve edges of the cubes, shrink and fit together in the shadow—it’s given to you by geometric first principles such as the Pythagorean Theorem relating to the angle by which you projected it to the shadow.

E8 crystal to 3D

You can take a higher dimensional crystal and project it to three dimensions and get a 3 dimensional “shadow”, if you want to call it that. We project a slice of E8 crystal down to 3D, which produces a quasicrystal code or language, and that allows these geometric symbols to build up to the ordinary world of particles and forces that we see around us.

E8 to 3D

That’s our program at Quantum Gravity Research. To model physics with a quasicrystal code made of the simplest bit of 3 dimensional information, the regular tetrahedron.

Cheers!

~ Klee