There is a reason conspiracy theories exist. As the old adage goes, "Where there is smoke, there is fire."

Conspiracy theories, however, are either fundamentally brilliant or dubious in nature.

Most people react to conspiracy theories in two ways. These theories are either scoffed upon or regarded with curious interest.

For instance, not too long ago, American rapper and recording artist B.o.B. started a thread on Twitter that explained why he believes the Earth is flat, not spherical.

The rapper tweeted several photos as evidence to back up his theory.

And because he's on the Internet, a lot of people replied to his tweets to refute his claims, including Neil DeGrasse Tyson who pointed out inconsistencies in the rapper's conspiracy.

Perhaps to set finality on the matter, DeGrasse Tyson tweeted, "Being five centuries regressed in your reasoning doesn't mean we all can't still like your music." Did it convince the rapper to stop? Probably not.

The Science Behind Conspiracy Theories

B.o.B. is not alone in his thinking, as conspiracy theories have been widespread even before the dawn of the Internet.

Neil Armstrong's "giant leap for mankind" on the moon may have been a hoax. A cure for cancer probably already exists but drug companies are hiding it from people. Vaccinations are dangerous. Climate change is not real.

The adherents of these conspiracy theories have marked their territories online. It also appears as if their ideas have basis, making it difficult to debunk them as quickly as possible.

That is what physicist and cancer researcher David Robert Grimes plans to do. He's already come up with a mathematical model to find loopholes among those conspiracy theories.

The model mainly focuses on the probability of success for different conspiracies, taking into account different factors such as the number of conspirators, the length of time, the possibility of a leak and the effects of the conspirators dying.

Grimes said conspiracy theories were commonly dismissed, but he wanted to take the opposite approach and see how these conspiracy theories might be plausible.

"To do that, I looked at the vital requirement for a viable conspiracy – secrecy," said Grimes.

The Secret Ingredient Is Literally A Secret

It is important to note the definition of the word "conspiracy." Academics define the word as an effort to explain some event or practice by reference to the machinations, or the acts of scheming, of powerful people who attempt to conceal their role, at least until their goals are executed and accomplished.

Using secrecy as the key ingredient for the success of a possible conspiracy, Grimes applied his mathematical model to four supposed conspiracy theories. He estimated the number of people required to be in on the secret, and how long it would take for these conspiracy theories to unravel.

After finishing his calculations, Grimes found that if the hoax moon landings were true, they would have involved about 410,000 NASA employees and would have been revealed in three years and eight months since its implementation.

If climate change was indeed a fraud, it would have involved 405,000 people and would have been exposed in three years and nine months.

A plot to cover up unsafe vaccinations would have involved 22,000 employees, and would have been known to the public in three years and two months.

Lastly, a suppressed cancer cure would have involved 714,000 people and would have been revealed in three years and three months.

Grimes said his findings suggest that any conspiracy with more than a few hundred people would rapidly collapse, and big science conspiracies would not be sustainable.

Maintaining The Art Of Deception

In his mathematical study, Grimes also took into account the maximum number of people who could take part in a conspiracy in order to hide it. For a conspiracy scheme to last five years, the maximum number of people needed was 2,521. For a plot to stay hidden for more than 10 years, less than a thousand people can be involved. For a conspiracy to last a century, it should include less than 125 collaborators.

Where did Grimes derive his equation and his intent to look into the possibility of conspiracies?

Grimes studied patterns and incidents from the past in order to find an answer.

He started with a statistical tool called Poisson distribution, which calculates the probability of a certain event occurring over a particular amount of time.

He looked into a surveillance program that was conducted by the U.S. National Security Agency (NSA) called PRISM, which involved 36,000 people at most. The existence of the program was revealed by Edward Snowden after six years.

Grimes also studied the Tuskegee syphilis experiment, in which penicillin, the cure for the disease, was decisively withheld from African-American patients. The experiment may have involved more than 6,700 people. After about 25 years, Dr. Peter Buxtun blew the whistle on the matter.

"Not every belief in a conspiracy is necessarily wrong," said Grimes, adding that the Snowden's revelations had confirmed theories about the activities of the NSA.

He said conspiracies, especially in the field of science, are hard to sustain because of scrutiny by other scientists. If a small devious group of "rogue" scientists decided to falsify data for climate change or attempted to cover up vaccine information, studies and investigation by other scientists would fatally undermine the false ones, he said.

And to create false data, a majority of experts in a field would need to mutually conspire, Grimes said, but it was a circumstance that the model predicts to be exceptionally unlikely.

Lastly, Grimes admits that hard-core conspiracy theorists may not be easily dissuaded by his equations, but he had written his paper as a middle ground for those who wonder whether scientists could successfully perpetuate a hoax or not.

Grimes' work, titled "On the Viability of Conspiratorial Beliefs", is featured in the journal PLOS ONE.