In two experiments, electric brain waves of 14 subjects were recorded under several different conditions to study the invariance of brain-wave representations of simple patches of colors and simple visual shapes and their names, the words blue, circle, etc. As in our earlier work, the analysis consisted of averaging over trials to create prototypes and test samples, to both of which Fourier transforms were applied, followed by filtering and an inverse transformation to the time domain. A least-squares criterion of fit between prototypes and test samples was used for classification. The most significant results were these. By averaging over different subjects, as well as trials, we created prototypes from brain waves evoked by simple visual images and test samples from brain waves evoked by auditory or visual words naming the visual images. We correctly recognized from 60% to 75% of the test-sample brain waves. The general conclusion is that simple shapes such as circles and single-color displays generate brain waves surprisingly similar to those generated by their verbal names. These results, taken together with extensive psychological studies of auditory and visual memory, strongly support the solution proposed for visual shapes, by Bishop Berkeley and David Hume in the 18th century, to the long-standing problem of how the mind represents simple abstract ideas.