- MathNotebook
- MathConcepts
- StudyMath
- Geometry
- Logic
- Bott periodicity
- CategoryTheory
- FieldWithOneElement
- MathDiscovery
- Math Connections
Epistemology
- m a t h 4 w i s d o m - g m a i l
- +370 607 27 665
- My work is in the Public Domain for all to share freely.
- 读物 书 影片 维基百科
Introduction E9F5FC
Questions FFFFC0
Software
Understand the significance of the octonions.
- Complex numbers describes rotations in two-dimensions, and quaternions can be used to describe rotations in three dimensions. Is there a connection between octonions and rotations in four dimensions?
- Compare trejybės ratas (for the quaternions) and Fano's plane (aštuonerybė) for the octonions.
- Relate the octonions to Clifford algebras. Learn how the complex, quaternions are defined in the Clifford algebras and how that would proceed further. And then compare that with the Cayley-Dickson construction. Give combinatorial interpretations of both and see how they differ.
Readings
- John Baez. Octonions and the Standard Model
- John Baez on octonions
- The Peculiar Math That Could Underlie the Laws of Nature, about Cohl Furey
- Hughes, Mia. Octonions and supergravity
Notes
- The octonions can model the nonassociativity of perspectives.
- Is there a way that the octonions get identified with the reals? The eightsome = nullsome gets understood as a onesome? And the identification of nullsome with onesome is related to the field with one element. And we are left with exceptional Lie structures.
- https://math.ucr.edu/home/baez/octonions/node7.html
- https://m.youtube.com/playlist?list=PLNxhIPHaOTRZMO1VjJcs7_3dgyJ2qU1yZ | C.Furey. Division algebras and the standard model.]] Octonions.
- https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/