Sorry, conspiracy theorists. If the moon landing were faked, someone would have spilled the beans long ago. In fact, so many people worked at NASA at the time that the jig would have been up in 1973, less than four years after the Eagle landed, according to a new paper published in PLOS One.

David Grimes, a physicist and postdoc at the University of Oxford, calculated how long conspiracies—like the supposed moon landing hoax—could last based on the number of conspirators and the time since the inception of the conspiracy. Unlike most conspiracy theorists, Grimes didn’t just pull his ideas out of thin air. “Historical examples show that even in incredibly secretive organizations, there is always some possibility of an accidental or intentional intrinsic leak whether by whistle-blowing or ineptitude,” he wrote.

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Using data from real-world affairs, including the NSA PRISM project, the Tuskegee syphilis experiments, and the FBI’s 20-year-long forensics scandal that was exposed earlier this year, Grimes created an algorithm that calculated the probability of a cover-up being revealed. He then applied that algorithm to four prominent conspiracy theories—the moon landing hoax, climate change fraud, vaccination conspiracy, and a suppressed cancer cure. To carry out each of these conspiracies successfully, hundreds of thousands of people would have to coordinate with each other. That shortened the timelines considerably. For each of the four, the lid would have been blown off in as few as four years after the supposed plan was first hatched. That shouldn’t come as a surprise given that real-world scandals involving orders of magnitude fewer people were revealed relatively quickly. Still, some people will probably insist that this latest research—and maybe all of mathematics, too—is a fraud.

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Photo credit: NASA