## Deriving E8 from Cl(8) Through Pairing up Elementary Cellular Automata Bits

**Authors:** John C. Gonsowski

Tony Smith relates the 256 dimensions of the Cl(8) Clifford Algebra to the 256 rules of Elementary Cellular Automata. The graded dimensions of Cl(8) correspond to graded dimensions of the E8 Lie Algebra used in Smith’s physics model. Six Cellular Automata (CA) rules with four one-bits are related to Smith’s 8-dim Primitive Idempotent bookended by the single rule with no one-bits and the single rule with all eight bits as ones. The 64 other four one-bit rules are related to E8’s 64-dim vector representation used by Smith for a spacetime 8-dim position by 8-dim momentum. The two 28-dim D4 subalgebras of E8 are used for bosons and their ghosts and relate to the CA rules with two one-bits and six one-bits. Paired up CA bits are related to the Cartan subalgebras of these D4s. The two remaining 64-dim spinor representations for E8 are used for eight component fermions/antifermions and relate to the CA rules with one, three, five and seven one-bits.

**Comments:** 18 pages

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### Submission history

[v1] 2016-11-02 11:20:14

[v2] 2016-11-11 13:57:49

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