The dimensionality of face space is measured objectively in a psychophysical study. Within this framework, we obtain a measurement of the dimension for the human visual system. Using an eigenface basis, evidence is presented that talented human observers are able to identify familiar faces that lie in a space of roughly 100 dimensions and the average observer requires a space of between 100 and 200 dimensions. This is below most current estimates. It is further argued that these estimates give an upper bound for face space dimension and this might be lowered by better constructed "eigenfaces" and by talented observers.