The mathematical thingy Larry was writing on the board in the classroom dream sequence is just the common, how-could-I-forget, well-known standard deviation. Heisenberg’s uncertainty principle in position-momentum language says that the product of the standard deviation of position and the standard deviation of momentum cannot be smaller than Planck’s constant divided by 4π.
My favorite reference on this subject is David J. Griffiths book Introduction to Quantum Mechanics, 2nd edition, which shows a drawing of a live cat on the front and a dead cat on the back. Although if you didn’t know better you could think the back cat was sleeping. It’s proposed as a mere thought experiment only, so no need to worry about the cat. And, as Griffiths mentions in his book, the problem is not considered a paradox by most physicists.
