cranial nerve IV
Trochlear nerve palsy affects torsion. Torsion is a normal response to tilting the head sideways. The eyes automatically rotate in an equal and opposite direction, so that the orientation of the environment remains unchanged - vertical things remain vertical.
Weakness of intorsion results in torsional diplopia, in which two different visual fields, tilted with respect to each other, are seen at the same time. To compensate for this, patients with trochlear nerve palsies tilt their heads to the opposite side, in order to fuse the two images into a single visual field.