Archimedes, Evolved (Somehow)

If you ever observe an owl watching its prey, you'll notice that its neck is extremely flexible. While eying its prey, it will turn its head 180 degrees upside down or even 360 degrees around like a corkscrew- all without moving its body. I was told that this is because owls can't move their eyes- they have to move their whole head if they want to keep their prey in sight. Dunno how true that is, I mean what kind of animal survives Darwinian selection if they can't even move their eyes?