Whenever something changes our lives (for example a historical event, or a technological innovation), the most bizarre conspiracy theories take place. Surveys conducted on the U.S. population revealed that 7% of people believe that the moon landing was fictitious and around 20% believe in a correlation between vaccines and autism (despite having been scientifically proven wrong). While some plots are not dangerous (such as the one about the moon landing), others have serious consequences, because they are responsible, for example, for the decreased vaccination coverage or for the fact that cancer patients abandon scientifically validated treatments for pseudoscientific theories without any proven effect.

In this article I present a predictive model that demonstrates the impossibility of keeping a large-scale conspiracy secret. In 2016, Dr. David Robert Grimes of the University of Oxford published a study in which he verified whether plots involving a large number of people are actually feasible. To do this, he developed an equation to establish the probability that someone among the people involved deliberately or inadvertently revealed the plot. This equation is valid for conspiracies that do not require maintenance and is influenced by the number of conspirators, the duration of the conspiracy and even the eventual death of conspirators.

Grimes estimated (in excess) the number of people required to organize different plots: the moon landing (411,000 people involved); climate change (405,000); the theory about the danger of vaccines (22,000, assuming that only the World Health Organization and the US Center for Disease Control are involved; 736,000 including also vaccine manufacturers); the theory according to which the cure for cancer is kept hidden by pharmaceutical companies (714,000).

Applying the equation, Dr. Grimes calculated that the eventual hoax of the moon landing would be revealed after 3 years and 8 months, a climate change fraud after 3 years and 9 months, a conspiracy about vaccines after 3 years and 2 months and a conspiracy to cure cancer would last 3 years and 3 months. Clearly, if these plots were real, they would all have been publicly exposed years ago.

Dr. Grimes then calculated how many people would be needed to keep a conspiracy secret for a certain amount of time: for 5-year secrecy, a maximum of 2521 people should be involved, less than 1000 conspirators for 10 years of confidentiality and less than 125 for a century-long conspiracy. Furthermore, any plot that requires nothing more than keeping the mouth shut would be discovered if more than 650 people were involved.

Clearly, this study will not convince the conspiracy theorists to think rationally, since their position is more ideological than logical, but it gives everyone else an idea of ​​the difficulty in carrying out these plots.