According to a physics professor quoted by Ann Landers, to get the toilet paper roll to turn requires a certain torque, which comes from the tension in the paper being withdrawn. The greater the distance between the plane of the paper being pulled and the axis support line, the lesser the force required and the lesser the chance of tearing the paper before you have enough.
(Yeah, I'm not sure what all that proves either.)
Which camp are you in: Should the toilet paper be hung so the paper dangles over or under the roll? This is a pet peeve of mine and I say that the paper always has to be over. I so hate when someone puts it under. I always wind up changing it to over.