For some, rejection of the human role in climate change reduces to a conspiracy: the world’s climate scientists are part of a socialist cabal falsifying research to justify energy regulations. Someone who has never met a climate scientist or looked closely at published studies can simply hold onto this idea rather than deal with the mountain of scientific evidence. Of course, it is patently ridiculous. The conspiracy would include an incredible number of scientists around the world, perfectly coordinating for decades, with nary a leak to give the game away—and that's before getting into all the socialists who would have to be involved.

In a recent paper, Oxford physicist and cancer researcher David Robert Grimes decided to try to create a mathematical measure for just how stupidly implausible that idea is—a sort of conspiracy probability equation. (Isn’t that exactly the kind of thing the cabal would use to throw the sheeple off the scent? Grimes must be in on it!)

The equation calculates the probability of a conspiracy-busting leak as 1-e-tφ, where φ includes the (potentially changing) number of conspirators over time and the odds that one of those people leaks information in a given year. To estimate the odds that your average conspirator spills the beans, Grimes turned to some historical examples of events fitting the academic definition of “conspiracy”: the NSA’s PRISM program, the Tuskegee syphilis experiment, and the FBI’s shoddy forensics uncovered by Frederic Whitehurst in the late 1990s.

In each case, Grimes used a very generous estimate of the number of people in the know and how long it had taken for the group to spring a leak. The resulting conservative estimate was 0.00000409 leaks per conspirator per year. Call it Snitch’s Constant.

Grimes applied the equation to several science-related conspiracy theories, including climate change, vaccines, and the suppression of cancer cures. For the vaccination conspiracy, he added up the number of people at the Center for Disease Control and the World Health Organization, which would form a group 22,000 strong. For climate change, he tried both the number of published climate scientists (about 29,000) and a larger tally that included another 376,000 members of relevant scientific organizations. The secret cancer cure was estimated to involve about 714,000 people from the eight largest pharmaceutical companies.

Grimes then calculated how long it would take each of those groups to reach a 95 percent chance of secret leakage. If it was just the CDC and WHO keeping a lid on the vaccine conspiracy, they’d last almost 35 years before reaching 95 percent. Add in the pharmaceutical companies, however, and that number drops to a measly three years—the same amount of time they could keep the cancer cure under wraps.

The span of the Great Climate Change Hoax comes in at four to 27 years, depending on the number of scientists in the know. Even the most conspiracy-friendly of these numbers fall well short of what would be necessary for the world to still be in the dark.

Obviously, these spit-balled numbers are a bit of a lark to make a point, but Grimes hopes that some people will get that point. Even if you ignore the thin premises underlying these conspiracies, as well as the logistical challenge of fudging every measurement and study ever, the odds of maintaining the illusion are not kind. But conspiracy theories survive partly because they are completely invulnerable to argument, after all. So if you really think we faked the Moon landings, crunching a few numbers probably won’t pin down mental gymnasts and get them to say “uncle." The X-Files would have had a pretty short run if Mulder were that easily dissuaded.

On a practical note for you henchmen hirers out there, Grimes’ equation suggests that if you want your conspiracy to last at least 10 years, you should definitely limit yourself to no more than 1,257 conspirators.

PLOS ONE, 2016. DOI: 10.1371/journal.pone.0147905 (About DOIs).