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Fuck geometry (lemm.ee)

submitted 3 weeks ago by [email protected] to c/[email protected]

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[–] [email protected] 15 points 3 weeks ago (1 children)

They're about as imaginary as numbers are in general.

Complex numbers have real application in harmonics like electronics, acoustics, structural dynamics, damping, regulating systems, optronics, lasers, interferometry, etc.

In all the above it's used to express relative phase, depending on your need for precision you can see it as a time component. And time is definitely a direction.

[–] kogasa 0 points 3 weeks ago (1 children)

That's not relevant to what they said, which is that distances can't be imaginary. They're correct. A metric takes nonnegative real values by definition

[–] [email protected] 1 points 3 weeks ago (1 children)

Why can't a complex number be described in a Banach-Tarsky space?

In such a case the difference between any two complex numbers would be a distance. And sure, formally a distance would need be a scalar, but for most practical use anyone would understand a vector as a distance with a direction.

[–] kogasa 0 points 3 weeks ago

The distance between two complex numbers is the modulus or their difference, a real number