When I first came across William James’ dictum that “ … this sense of sameness is the very keel and backbone of our thinking,” I thought he had foreseen the importance of cross-correlation in the brain, and told myself to find out how he had reached this conclusion. When I finally did this a year or two ago, I slowly came to realize that I had completely misunderstood him; from the full quote it is absolutely clear that his dictum cannot be referring to the process by which a cortical simple cell responds selectively to the orientation of features in a visual image, as I had originally supposed. If one translates the original dictum into two more prosaic modern versions, his version would say: “Our minds could not think at all without neural circuits in our brains that compute auto-correlations,” but in my mistaken interpretation the last word would be “cross-correlations.” Others may have made the same mistake, but the difference is profound, and finding what he really meant has been a revelation to me. This essay explains the revelation, describes how to determine experimentally whether the brain does auto- or cross-correlation, and gives the result of preliminary experiments showing clearly that it does both. A revised view of the visual cortex as autocorrelator as well as cross-correlator claims to tell us what complex cells in the visual cortex do, and it assigns a role to its columnar structure that is as important to fulfilling that role as the concept of the receptive field has been to understanding the simple cells’ fulfillment of theirs. The new view has compelling features, broad implications, and suggests a plausible model of how neural circuits in the cortex achieve thought, but it needs further testing.