Conspiracy Theories confront Mathematics

These days there’s no shortage of conspiracy theories. Many people still believe that the moon landings were faked, that climate change is a hoax, nuclear power is available at low temperatures or that the 9/11 attacks were staged by the US military. While some conspiracy theories do end up being true — the Prism project revealed by Edward Snowden is one, what is one to think of a large murky subset that might be true, but maybe not?

A recent study by Dr. David Grimes of the University of Oxford, published in PLOS suggests that most conspiracies have a high probability of coming to light in a finite time. That no conspiracy can remain hidden indefinitely. However Grimes does not dismiss conspiracy theories out right. He said,

It is common to dismiss conspiracy theories and their proponents out of hand but I wanted to take the opposite approach, to see how these conspiracies might be possible. To do that, I looked at the vital requirement for a viable conspiracy — secrecy.

Grimes developed a series of equations, using real examples such as the Snowden revelations, the Tuskegee syphilis experiment of 1932, and the FBI forensics scandal exposed in 1998. . He estimated the probability of someone revealing the conspiracy, either intentionally or by accident. He suggested 4 in one million. The effect of people in the know of dying. Not surprisingly, the more people are involved, the shorter the time it will take before a whistleblower exposes the conspiracy.

Typical results are:

Conspiracy                       Number of People involved                 Time before Exposure

Moon landing fraud           411,000                                                3 y 8 m

Climate Change                 405,000                                                3 y 9 m

Unsafe Vaccines                736,000                                                3 y  2 m

Cure for cancer withheld    714,000                                               3 y  3 m

He then considered the maximum number of people who could be admitted to a secret for the secret to last a certain time. For a conspiracy to last for over 5 years, no more than 2,500 could be in the know. To last 100 years, only 125 people could know.

While Grimes’s results certainly offer guidance as to the truth behind a particular conspiracy, no doubt die hard conspiracy theorists will dismiss the study as another conspiracy.