1. A method for providing a differential diagnosis of a patient with progressive supranuclear palsy (PSP) from a patient with Parkinson's disease (PD) that comprises the steps of: a) identifying in a patient to be diagnosed with one or the other of PSP or PD a plurality of at least partially repetitive eye movements that over time define square wave jerks within a sequence of eye movements, each square wave jerk of the plurality of square wave jerks being defined by a first horizontal saccadic movement that moves the eye away from a fixation target that is followed by a corrective saccadic movement towards the target shortly thereafter; b) measuring a vertical component associated with the plurality of square wave jerks; c) comparing the vertical component with a threshold value for normal healthy subjects or other patients with PSP or other patients with PD; d) identifying the presence of PSP or PD in the patient to be diagnosed based upon the comparison of the vertical component with the threshold value whereby a vertical component statistically different from the threshold value of normal subjects or PD patients identifies the patient to be diagnosed as having PSP, whereas a vertical component that is (a) not statistically different from the threshold value of normal subject or (b) is statistically different from the threshold value of PSP patients identifies the patient as having PD.