hifrote

> Or are you arguing that you should always try and teach complex numbers and the Euler identity to avoid strained analogies?

I think it’s okay to be explain complex numbers. I think it’s just best to additionally explain why. That is, show why (real, imaginary) is a better numerical system than the more broadly taught (x,y) of the 2 dimensional space being explored.

As for the Euler identity I suppose you could include that when explaining why we use the exp() function, which is because it plays nicer with integration and derivation than other numerical representations.

I want the analogies to be representative of the work rather than my own mental model of it.

> What do you not like about Feynman's "little arrows" / rotating clock hands in the QED book?

It’s difficult to articulate, but two aspects are:

The amount of times I have only confused people more by trying to explain even modular arithmetic by calling on the clock analogy.

And the fact that the little “clock hands” are a complete abstraction from both the physics being described and the mathematical models that describe that physics. ~“Quantum physics is just about adding clocks?”

> I can't think of a more simple metaphor for the exponential of a complex phase, exp(i omega t).

As I noted in the gp I think code implementations or numerical methods should be the goal.

The solution to the confusion about referencing clocks when talking about modular arithmetic was just to write down a complete numerical example, ie all natural numbers mod 6 up to 10, and use that as the abstraction for further discussion: negatives, reals, periodicity, infinities, applications, et al.