Imagine an astronaut in free space. He (or she) has zero angular or linear momentum with respect to a fixed intertial frame of an outside observer. The astronaut is intially standing up (sic) with his arms by his sides and his legs together, with zero degree offset between the top half of his torso and his bottom half. He twists 90 degrees, his bottom half torso moves clockwise and the top half anticlockwise. While he's in the 90 degree offset position he raises his arms, and then twists back. Because the top half now has larger moment of interta it won't turn back as much as the bottom half. When he's back in the zero degree offset position he lowers his arms and he's back to his intitial starting position, except he has now rotated a little as measured by the observer. Imagine we could construct a machine to do that, very quickly and with very small changes each time. In reality the net angular momentum of course is zero, the 'other half' always has equal and opposite angular momentum to the first half. However because the machine always resets itself back to its original position the external observer could measure an average angular momentum that appears to come from nowhere without having applied an external torque. This implies to me that we need to know exactly what is going on deep inside a system, even on the atomic or even sub-atomic level, before we can be sure our macrosopic measurements have any meaning at all.