A world with four spatial dimensions, in which linear algebra students get uncomfortable about vector spaces with five or more dimensions.
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Teaching multivariable calculus is harder in that world, because ∧ cannot be composed with Hodge star to get a binary operation on ℝ^4, and exterior derivative cannot be composed with Hodge star to get an operation on vector fields.
10:38 AM - 3 Dec 2017
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