To me their purpose only came clearly recently. They're just a way to rotate smoothly one dimension into another. And control the speed of the rotation.
x into y. Potential energy to kinetic energy. Charge into current.
Keeping this definition but going higher in the dimensions: x into y, y into z and z into x. Going meta, the x into y rotation defines a plane; And a plane going into another direction is a volume. (x into y) into z.
What made it click, what made it beautiful is Geometric Algebra:
x into y. Potential energy to kinetic energy. Charge into current.
Keeping this definition but going higher in the dimensions: x into y, y into z and z into x. Going meta, the x into y rotation defines a plane; And a plane going into another direction is a volume. (x into y) into z.
What made it click, what made it beautiful is Geometric Algebra:
https://youtu.be/60z_hpEAtD8?is=e3GxYU4J1SdpsumW