Human Super EEG entails measuring ongoing activity from every cell in a living human brain at millisecond-scale temporal resolutions. Although direct cell-by-cell Super EEG recordings are impossible using existing methods, here we present a technique for inferring neural activity at arbitrarily high spatial resolutions using human intracranial electrophysiological recordings. Our approach, based on Gaussian process regression, relies on two assumptions. First, we assume that some of the correlational structure of people's brain activity is similar across individuals. Second, we resolve ambiguities in the data by assuming that neural activity from nearby sources will tend to be similar, all else being equal. One can then ask, for an arbitrary individual's brain: given what we know about the correlational structure of other people's brains, and given the recordings we made from electrodes implanted in this person's brain, how would those recordings most likely have looked at other locations throughout this person's brain?