So many eights!

number 8's puzzle

Can you draw uncountably many non-intersecting "8" shapes in the plane (they can be contained in one another however)?

No, you can't. For each "8" shape you can choose a pair of points with rational coefficients - one in its top loop and one in its bottom loop. Since no two "8" shapes can have the same corresponding pair of rational points, their number should be countable.