nice intro to clifford algebra

Clifford Algebra, a.k.a. *Geometric Algebra*, is a most extraordinary synergistic confluence of a diverse range of specialized mathematical fields, each with its own methods and formalisms, all of which find a single unified formalism under Clifford Algebra. It is a unifying language for mathematics, and a revealing language for physics.

Unlike the standard vector analysis whose primitives are scalars and vectors for representing points and lines, Clifford Algebra has additional spatial primitives for representing plane and volume segments in two and three dimensions, and it can be extended to any number of higher dimensions by the same basic scheme, *and they do*, with remarkably useful properties.

Adding one extra dimension to a total of 4 produces a *projective geometry*, a concept not exclusive to Clifford Algebra, but very simply expressed in it, with some remarkable invariance properties.

Adding two additional dimensions to a total of 5…

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