The recognition of objects is exceedingly difficult in indirect view. This complication cannot be explained in terms of retino-cortical magnification, as size scaling fails to establish position invariance both for character recognition [Strasburger, H. & Rentschler, I. (1996) Eur. J. Neurosci., 8 1787–1791] and pattern classification [Jüttner, M. & Rentschler, I. (1996) Vision Res., 36, 1007–1021]. Thus we compared, for two tasks of discrimination learning and category learning with respect to a common set of grey-level patterns, how humans perform in foveal and extrafoveal vision. Observers learnt to discriminate (size-scaled) images equally well in foveal and extrafoveal view, whereas they displayed profound deficiencies in extrafoveal category learning for the same patterns. From the behavioural learning data, internal representations of the learning signals were reconstructed by means of computer simulations. For foveal view, these representations were found to be veridical to their physical counterparts for both learning tasks. For extrafoveal view, they were severely distorted for category learning but not for discrimination learning. A variance reduction of the pattern classes by a factor of 100 reduced the dissociation between extrafoveal categorization and discrimination but did not remove it. These observations suggest a scale-invariant superiority of foveal vision for learning object categories. This implies a high degree of space variance of visual cognition which is vastly underestimated by classical measures of visual performance, e.g. acuity, visual field and contrast sensitivity.