A conspiracy is at minimum, nothing more than a handful of people working together in the shadows, to accomplish a goal that benefits themselves and hurts everyone else. By that definition, there are countless conspiracies in the world. There are so many conspiracies that in all likelihood, the vast majority of them will never reach the public’s awareness.

However, that mainly applies to conspiracies committed by a small group of insiders. When you have hundreds or even thousands of people who are in on the conspiracy, there’s a much greater chance that at some point, somebody is going to spill the beans. How likely that is, would be anyone’s guess of course. Human beings are pretty unpredictable. It’s not like you can come up with a mathematical formula for predicting how long it would take for a conspiracy to unravel, right?

Dr. David Grimes from Oxford University would beg to differ. One human being may be unpredictable, but when you look at a large group of people, certain patterns emerge. So by looking at past examples of conspiracies that have since seen the light of day, how many people were involved in each conspiracy, and how long it took for someone to blow the whistle, you can predict the longevity of any given conspiracy.

Specifically, he was missing a good estimate for the intrinsic probability of a conspiracy failing. To determine this, Dr Grimes analysed data from three genuine collusions.

The first was the surveillance program conducted by the US National Security Agency (NSA), known as PRISM. This programme involved, at most, 36,000 people and was famously revealed by Edward Snowden after about six years.

The second was the Tuskegee syphilis experiment, in which the cure for syphilis (penicillin) was purposefully withheld from African-American patients.

The experiment may have involved up to 6,700 people, and Dr Peter Buxtun blew the whistle after about 25 years.

The third was an FBI scandal in which it was revealed by Dr Frederic Whitehurst that the agency’s forensic analysis was unscientific and misleading, resulting in the imprisonment and execution of innocent people.

Dr Grimes estimates that a maximum of 500 people could have been involved and that it took about six years for the scandal to be exposed.

Dr. Grimes determined that at any given time, the odds of a conspiracy being foiled by one of its own members, was four in one million. Obviously, the odds rapidly increase as time passes, and as more people get in on the conspiracy. So he came up with a formula that can take those factors into account, and produce an estimate for how long a conspiracy might last. The first thing he did then, was apply this formula to several popular conspiracy theories.

Dr Grimes’s analysis suggests that if these four conspiracies were real, most are very likely to have been revealed as such by now.

Specifically, the Moon landing “hoax” would have been revealed in 3.7 years, the climate change “fraud” in 3.7 to 26.8 years, the vaccine-autism “conspiracy” in 3.2 to 34.8 years, and the cancer “conspiracy” in 3.2 years.

So does this prove that these conspiracies are untrue? Not exactly, though that’s certainly the conclusion that Dr. Grimes wants us to reach. However, he came to these numbers based on the assumption that a certain number of people were involved in the conspiracy. But it’s impossible to really know how many people are involved in a conspiracy, if it hasn’t been conclusively proven to be real. Here’s where the formula gets really interesting in my opinion. Take a look at the numbers for the Moon landing hoax:

The Moon landing hoax, for instance, began in 1965 and would have involved about 411,000 Nasa employees. With these parameters, Dr Grimes’s equation suggests that the hoax would have been revealed after 3.7 years.

Additionally, since the Moon landing hoax is now more than 50 years old, Dr Grimes’s equation predicts that, at most, only 251 conspirators could have been involved.

So the formula doesn’t really disprove anything. What it does show is that if the Moon landing hoax were real, only 251 people were in on it. In other words, his formula is a great tool for determining whether or not a conspiracy is compartmentalized.

The Manhattan Project is a perfect example of compartmentalization. The race to build the world’s first atomic bomb employed over 120,000 people, but only a handful of them really knew what they were working on. Everyone else in the project was in the dark. They were given instructions and goals that only pertained to a very narrow segment of the project, and they didn’t really know about the other groups of scientists and engineers who were working on their own narrow goals.

Thus, they were just as surprised as everybody else in the world when the US dropped the atomic bomb on Japan. I’d wager that if the bomb wasn’t used, it would have remained a state secret for many years afterward.

All in all, I’d say this formula is helpful, but limited. Dr. Grimes thinks that he can use math to boil down human behaviors into a formula, but you can’t. It’s great for playing devil’s advocate, and helping us reach certain possibilities about conspiracies based on certain assumptions, but it doesn’t uncover the indisputable truth, as much as Dr. Grimes would like it to.