Padgett's cognitive transformation is real, even if the mathematically-illiterate reporting on it obscures the nature of that transformation. Berit Brogaard, who's a professor of philosophy and neuroscience at the University of Missouri St. Louis, has done a lot of studies with Padgett in the course of her work on synesthesia [1]. I haven't read any of her papers involving Padgett myself, but people looking for a more rigorous treatment of his condition might find something of interest in her writing.

[1] http://www.stlmag.com/St-Louis-Magazine/August-2013/Pieces-o...