We want some operation that maps the point 1 to the point x, while holding the origin constant. I agree that scale and rotate is not the only such function, but

We want some operation that maps the point 1 to the point x, while holding the origin constant. I agree that scale and rotate is not the only such function, but when I personally visualize taking a grid and moving one point while keeping another constant, that is what I visualize. Additionally, this has the added property of maintaining the grid structure. It is not immediately obvious to me how skewing could define such an operation in the general case; or how flipping could define such an operation in most cases. In any case, the system of adders and multipliers in 2-dimension he describes, even if not the only reasonable 2D generalization, is certainly a reasonable generalizaion, and one that has proved useful. >It's actually at the heart of why rotation (and not some other geometric operation) is key to e^iπ. In this video, e^x is defined as a mapping between multipliers and adders. Multipliers are defined to be a combination of rotation and scaling. Any relationship between exponential, calculus, infinite sums, etc is purely a result of these definitions (except, perhaps, the motivation for choicing i * pi to be the principle multiplier mapping that gets mapped to -1 under e.)