The Math Behind Conspiracies: Why Secrets Always Leak
An Oxford researcher proved that large conspiracies are mathematically doomed to fail. We integrated his formula into every claim on They Knew.
In 2016, physicist David Robert Grimes published a paper in PLOS ONE that did something nobody had done before: he applied mathematics to conspiracy theories. Not to prove or disprove any specific theory, but to answer a fundamental question: how long can a secret involving many people actually last?
The Formula
L(t) = 1 − e−tNp
L(t) = probability the conspiracy has been exposed by time t
t = time in years
N = number of conspirators
p= intrinsic leak probability per person per year (~4×10−6)
Grimes calibrated the leak probability (p) using real-world conspiracies that were eventually exposed: the NSA's PRISM program (exposed by Edward Snowden), the Tuskegee syphilis experiment, and the FBI forensics scandal. These real failures gave him the data to estimate how quickly secrets unravel.
What the Numbers Say
Grimes ran his model against four popular conspiracy theories. The results are striking:
| Conspiracy | People | Time to 95% leak |
|---|---|---|
| Faked Moon landing | 411,000 | 3.7 years |
| Climate change hoax | 405,000 | 3.7 years |
| Vaccine conspiracy | 288,000 | 3.2 years |
| Suppressed cancer cure | 714,000 | 4.3 years |
The takeaway: conspiracies involving hundreds of thousands of people simply cannot survive more than a few years. The math makes it impossible.
But Here's What Makes It Interesting for Us
The model doesn't say conspiracies don't exist. It says they're mathematically guaranteed to be exposed. And the timeline depends on two variables: how many people know, and how long it's been.
This is exactly what They Knew documents. Every claim in our database is a conspiracy that leaked. The Grimes model explains why it leaked and predicts when it should have.
Consider the real examples in our database:
- MKUltra involved ~80 institutions over 20 years. The model predicts a high leak probability — and it leaked through a FOIA accident.
- Jeffrey Epstein's operation involved a small circle (<50 core people) and survived for 15+ years. Small circles can last decades — exactly what the math predicts.
- NSA mass surveillance involved thousands of people at the NSA and telecom companies. It was exposed by a single whistleblower — Snowden — exactly as the model predicts for large operations.
How We Use It
Every claim on They Knew now includes a Conspiracy Viability Score in the sidebar. It calculates:
- Estimated conspirators — based on the category and scope of the claim
- Years the secret was kept — from the original claim date to when it was exposed
- Leak probability— the Grimes formula applied: what were the mathematical odds this would come out?
- Time to 95% exposure — how long until the math says it was almost certain to leak
The Small Circle Problem
Here's where it gets uncomfortable. The Grimes model shows that conspiracies involving small numbers of people — under 50 — can remain hidden for centuries. The math says a conspiracy with 10 people has a less than 1% chance of leaking in a human lifetime.
This means the conspiracies we know about are, by definition, the ones that failed. The ones that involved too many people, lasted too long, or had someone brave enough to talk. What we don't know — and what the math suggests is entirely plausible — is how many small-circle conspiracies have never been exposed at all.
“The absence of evidence is not the evidence of absence. The conspiracies we document are the ones that leaked. The math tells us they had to.”
The Paper
Grimes, D.R. (2016). “On the Viability of Conspiratorial Beliefs”. PLOS ONE 11(1): e0147905. University of Oxford.
Thanks to Reddit user Blitzer046 on r/conspiracytheories for pointing us to this paper.