The Notion of Time and the Geometric Algebra

„Only in the light of Grassmann’s outer product is it possible to understand that the careful Greek distinction between number and magnitude has real geometrical significance. It corresponds roughly to the distinction between scalar and vector. Actually the Greek magnitudes added like scalars but multiplied like vectors, so multiplication of Greek magnitudes involves the notions of direction and dimension, and Euclid was quite right in distinguishing it from multiplication of “Greek numbers” (our scalars).”
/David Hestenes, New Foundations for Classical Mechanics/

Content

1. Memo¹ about the special multiplications defined on the plane of two-element numbers

2. Differences between the definitions of multiplications defined on geometric algebra and defined on the planes of two-element numbers

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¹ See The "natural presences" of the symplectic camel, and The Geometric Algebra and the Numbers I

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