In one study, shoppers in a blind taste test of two types of jam were asked to choose the one they preferred. They were then given a second taste from the jar they picked. Unbeknown to them, the researchers swapped the flavors before the second spoonful. The containers were two-way jars, lidded at both ends and rigged with a secret compartment that held the other jam on the opposite side — a principle that’s been used to bisect countless showgirls. This seems like the sort of thing that wouldn’t scan, yet most people failed to notice that they were tasting the wrong jam, even when the two flavors were fairly dissimilar, like grapefruit and cinnamon-apple.

In a related experiment, volunteers were shown a pair of female faces and asked which they found more attractive. Then they were given a closer look at their putative selection. In fact, the researchers swapped the selection for the “less attractive” face. Again, this bit of fraud flew by most people. Not only that, when pressed to justify their choices, the duped victims concocted remarkably detailed post hoc justifications.

Such tricks suggest that we are often blind to the results of our own decisions. Once a choice is made, our minds tend to rewrite history in a way that flatters our volition, a fact magicians have exploited for centuries. “If you are given a choice, you believe you have acted freely,” said Teller, of the duo Penn and Teller, to Smithsonian magazine. “This is one of the darkest of all psychological secrets.”

Another dark psychological secret magicians routinely take advantage of is known as change blindness — the failure to detect changes in consecutive scenes. One of the most beautiful demonstrations is an experiment conducted by the psychologist Daniel Simons in which he had an experimenter stop random strangers on the street and ask for directions.

Midway through the conversation, a pair of confederates walked between them and blocked the stranger’s view, and the experimenter switched places with one of the stooges. Moments later, the stranger was talking to a completely different person — yet strange as it may sound, most didn’t notice.