File 03 — Beliefs
The Leak
Add one more person who has to stay quiet. Watch the years fall off.
A physicist put a number on Franklin’s joke about three people keeping a secret. Assume one person talking ends it, and that people talk rarely and independently, and how long a conspiracy survives stops being a question about character: it is Poisson arithmetic on how many are in on it and how often any one of them talks. Drag the headcount and watch the whole curve slide across the chart — four hundred thousand people cannot hold a secret for four years, and the same arithmetic says a hundred and twenty-five can hold one for a century. Calibrated on three conspiracies that really happened, plotted at the year each one actually broke, with the catch on screen: the leak rate was measured only on the ones that leaked.
Assume one person talking is enough to end it, and that people talk rarely and independently. Then how long a secret survives is not a question about character. It is Poisson arithmetic on two numbers: how many people are in on it, and how often any one of them talks.
solid: 411,000 people. dotted: the same secret held by 4,110 — a hundredth as many. vertical mark: the 57 years you need it to hold.
conspiracies that really happened — the model is fitted on these
conspiracies people believe in
even odds it has broken
10 months
after which the secret is more likely out than in
as good as public (95%)
3.7 years
the point the paper calls imminent failure
still quiet after 57 years
<0.1%
the chance nobody has said anything yet
Moon landings faked
Peak NASA employment in 1965. This is the assumption doing most of the work: it says every single employee would have had to know.
the same arithmetic, read the other way
At this leak rate, the largest group that can hold a secret for 57 years — with a 95% chance of getting away with it — is 220 people.
You have 411,000. That is about 1,867× too many, which is why the red line is already flat against the ceiling. Drag the headcount down and watch the curve walk right off the chart — the model does not say secrets are impossible. It says they are small.
Where the numbers come from. The model and every default here are from David Robert Grimes, On the Viability of Conspiratorial Beliefs, PLOS ONE (2016). The default leak rate of 1 in 244,000 per person per year is fitted to the NSA/PRISM case; the FBI forensics case gives 1 in 4,080, sixty times looser. Both are on the slider, and the distance between them is roughly the distance between blown by Christmas and held for a century.
The honest catch. That leak rate was measured on three conspiracies that all leaked. There is no sample of the ones that held, because holding is what makes them invisible — so the one number the answer is most sensitive to is the one number the method cannot observe. Grimes says so himself in the discussion. Read the output as a way of sizing a claim, not as a verdict on it.