Great explanatory writing, thanks.

> In mathematics, we say that the length diverges. If you were measuring a smooth curve, the length would converge on a single value -- incorporating more detail would change the length, but only by tinier and tinier amounts.

Can you say something bout the exponential curve in this context? IIRC whatever level we zoom to we see the same curve, neither converging nor diverging. Is there something special we should take note of here?