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How did the Rabbit get into the Hat?

The question of my title is asked every time someone witnesses a certain feat of stage magic, no matter how young or old the witness. Statistical versions of essentially the same question are becoming increasingly rare in the Big Data era, where magical results can make headlines without such questions being raised. Issues arising from this phenomenon will be discussed, including susceptibility to zombie data, whether post-selection inference is really a "thing", and what some of Persi's earliest work has to tell us related to this issue.