The brain acquires visual information from the eyes and then interprets this information to assess its significance. The resulting impressions, judgments and decisions commonly outlast the dynamic stream of visual data and are thus able to influence behavior in a time frame separate from sensation. We have begun to study the neural basis of decision formation using a combination of electrophysiology and behavioral testing in monkeys trained to discriminate the direction of motion in dynamic random dot kinematograms. I will describe data that support the following conclusions. Decisions about visual stimuli are formed by accumulating "evidence" from visual cortex as a function of time. The accumulation of evidence toward a threshold accounts for the time it takes to reach a decision. The accumulation is represented in brain structures that are involved in sensorimotor integration. Interestingly, the neural computations that underlie such a decision process were anticipated during WWII by Alan Turing who developed a methodÑBanburismusÑto crack the German Enigma cipher. I will explain how the brain might implement similar computations.