[simpaticoder]

The author asserts vectors are functions, specifically a function that takes an index and returns a value. He notes that as you increase the number of indices, a vector can contain an arbitary function (he focuses on continuous, real-valued functions).

It's fun to simulate one thing with another, but there is a deeper and more profound sense in which vectors are functions in Clifford Algebra, or Geometric Algebra. In that system, vectors (and bi-vectors...k-vectors) are themselves meaningful operators on other k-vectors. Even better, the entire system generalizes to n-dimensions, and decribes complex numbers, 2-d vectors, quaternions, and more, essentially for free. (Interestingly, the primary operation in GA is "reflection", the same operation you get in quantum computing with the Hadamard gate)

[elbear]

Thanks for mentioning this. I think I encountered Geometric Algebra in a video related to making video games. It's this one (Why you can't multiply vectors): https://www.youtube.com/watch?v=htYh-Tq7ZBI