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Great!
Q2: a single complex number can be represented as a point on the surface of a sphere, but often spinors (i.e 2 complex numbers) are represented as an arrow pointing on the surface of a sphere. Shouldn't I need 2? How is it possible that one is enough?
@johncarlosbaez
I've never seen a spinor represented as an arrow pointing on a sphere. That wouldn't make much sense unless you did some weird stuff with the arrows. You can however "think" of a spinor as living on a mobius strip. This at least gives an intuition of the 2:1 naturepic.twitter.com/YcXgRrt96D
I was thinking about the Bloch sphere.
(Did I say that all my question on the topic would be naive and potentially silly? 
)
"I was thinking about the Bloch sphere." The Bloch sphere is exactly what I was talking about in my reply to Q2 when I said that unit spinors modulo phase can be seen as points on a sphere in 3d space. So, everything you know about the Bloch sphere is helpful!
He is probably thinking about CP^1? The Hopf map in this case requires two complex numbers and it is possible to use them to represent a vector on the sphere S^2
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