I agree a rotation matrix story would fit better, but I do think it’s a fair analogy: the numbers stored are just coses and sines, aka the x and y coordinates of the hour hand.
Like, the only reason we’re calling it a “Fourier basis” is that we’re looking at a few different speeds of rotation, in order to scramble the second-place answers that almost get you a cos of 1 at the end, while preserving the actual answer.
Is this really an accurate analogy? I feel like clock arithmetic would be more like representing it as a rotation matrix, not a Fourier basis.
I agree a rotation matrix story would fit better, but I do think it’s a fair analogy: the numbers stored are just coses and sines, aka the x and y coordinates of the hour hand.
Like, the only reason we’re calling it a “Fourier basis” is that we’re looking at a few different speeds of rotation, in order to scramble the second-place answers that almost get you a cos of 1 at the end, while preserving the actual answer.