Quantum Numbers and Spin
How perceptive of you. The fourth quantum number, s, does indeed pertain to an electron's spin.
I know that each electron has either "spin up" or "spin down"...
Yes, and, correspondingly, s only has two possible values. For good
reasons that I shall not explain here, s= +1/2 means "spin up" and
s= -1/2 means "spin down."
So that's it; those four quantum numbers completely describe an electron. I
see how this fits in with Bob's visual
picture of a "quantum state":