A very interesting find related to my journey if He-4 over 10 years and still going on in a sense since 2017 off and on.

Think that so many constraints, 7 known and 3 more discovered, have series of magics going on.

When you project a higher dimension to lower dimension there is a loss of factor of 2.

Like Hemisphere becomes a circle and the area is 2 times circle’s area. For sphere there is a double cover projection. 2 Hemispheres become 1 circle.

When you project a cube it looks like Hexagon in 2D.

In over simplified view of SU(3) I took 3 sides of a corner of 3D cube cut at mid points.

You have in projection an Equilateral Triangle in 2D with 3 diagonals meeting at center.

And the  cube becomes Cuboctahedron and that projected has a bigger hexagon over laid with one small one in 2D. Total 12 points. The CCP packing with highest density covers that.

3D Cube 8 points become 6 points in Hexagon in 2D and 2 in center.

3D  Cuboctahedron has 12 points and they become 2 Hexagons with 2 points in center in 2D Projection. Small Hexagon is made of N pointing Equilateral T above big Hexagonal and S pointing E T.  This is CCP Packing of 12 plus 1 sphere.

Diving deep into Cartan Alegbra, after Lie Algebra, and Roots, in last 6 months, I found to my amazement that all that over simplified intuition was correct! The Cartan A is a semester course needing many revisions. This is more abstract than Tensor Calculus.

There are two kinds of learning - one is taught and another one is like what Rishis did and reflected in Einstein and Bruce Lee. Yes both were Yogis. I do both.

But now I find that the solution to (x^3-2) = 0. It has 3 roots which are part of SU(3) and Hexagon. The first 3 roots are (1,0), (1/2, “3^1/2”/ 2 and (1/2,  -“3^1/2”/ 2). Rest of 3 are with negative signs and reflections of 3 positive Root vectors.

The Cube of volume Size 2 becomes Hexagon with diagonal size of 1!

Galileo tried to unify the Group Theory of Symmetries, which whole Physics is about, with Polynomial Theory.

Think of Polynomial as products of a series of “vector operator minus eigen values” as part of diagonal matrices which form many kinds of algebra such as Lie snd Cartan A and Lie, Weyl, Coxeter, etc. group theory. Coxeter I communicated in 90s and known as the Last Geometrician and his one puzzle I could solve, mentioned in my blog, but forgot. Need to revisit. But I think it is connected here.  🙏

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#quantummechanics

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#liealgebra

#su(3)

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