DAMNIT you beat me to Zeno!
The arrow one is my favorite of his:
The arrow paradox
“ If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. ”
—Aristotle, Physics VI:9, 239b5
In the arrow paradox (also known as the fletcher's paradox), Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. However, it cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible.
Whereas the first two paradoxes presented divide space, this paradox starts by dividing time—and not into segments, but into points.[11]
That staircase was developed by Roger Penrose and his Father Lionel Penrose. Escher used it in one of his paintings. I love it.
From wikipedia:
The Penrose stairs is an impossible object created by Lionel Penrose and his son Roger Penrose. It can be seen as a variation on the Penrose triangle. It is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three dimensions; the two-dimensional figure achieves this paradox by distorting perspective.
