Möbius Strips and Differential Equations

I enjoyed reading this. I have been making my way through Needham's Visual Complex Analysis (https://global.oup.com/academic/product/visual-complex-analy...) book which takes a similar visual-focused view of teaching all of complex analysis. Chapter 2 in particular covers multivalue functions and branch points to make a similar point about how some paths will yield different values at same points.

Here's the reason you need enginners in the universe. Yes, the strip has non-orientability. Howwever, just introduce spin about the center, as you would a wheel, and you get all the same benefits of orientation as long as you're not in a completely empty void in space. Upside sees constantly changing, inside sees the other side of the strip.