It's well known that our sense of balance depends on three things:
- vision -- better with binocular vision
- tactile senses -- e.g., the pressure on our feet -- better with bipedal pressure
- inertia (semi-circular canals in the inner ear) -- probably better if binertial (not a word; I just made it up since everything else here is better when bin- )
I've observed that there is actually a fourth component: hearing, and it's better with binaural hearing. In order to maintain balance, you need to have at least two of these four things functioning and in agreement. Lose any three and you fall over.
For example, plug your ears, close your eyes, and stand on one toe. At that point, you only have the inertial sense, and you will hit the floor before you even realize you are falling.