Jan 28 2016

Math vs Conspiracies

A recent paper in PLOS One explores the mathematical probability of a grand conspiracy being revealed from within. The paper, of course, does not disprove any particular conspiracy theory, but it does make a compelling argument by putting into rigorous form a frequent argument against grand conspiracies, that they are too big not to fail.

As an aside, I love reading dry technical papers that are well-written. There is a certain efficiency and clarifying poetry to a precise technical discussion. It feels like it must be true because it sounds so objective and factual. A well crafted technical paper can slice through confusion and ambiguity like a scalpel.

For example, the author of this paper, David Robert Grimes, writes about conspiracies.

Conspiratorial ideation is the tendency of individuals to believe that events and power relations are secretly manipulated by certain clandestine groups and organisations. Many of these ostensibly explanatory conjectures are non-falsifiable, lacking in evidence or demonstrably false, yet public acceptance remains high. Efforts to convince the general public of the validity of medical and scientific findings can be hampered by such narratives, which can create the impression of doubt or disagreement in areas where the science is well established.

See what I mean – this is a conceptually dense statement, which has a poetry all to itself.

Grand Conspiracies

Whenever I write about conspiracies I frequently get questions challenging my apparent dismissal of the notion of conspiracies, complete with historical examples of actual conspiracies. So to clarify up front what we are discussion here, it is the so-called “grand conspiracy.”

Actual conspiracies of course exist. Whenever two or more people get together and agree to commit an illegal or nefarious act, there is a conspiracy. When we interviewed Gerald Posner on this topic, he called such conspiracies, “kitchen conspiracies,” because they could be perpetrated by a few people sitting in someone’s kitchen.

There is a continuum, of course, and no sharp line between a regular conspiracy and a grand conspiracy. Rather, the larger a claimed conspiracy gets, the more unlikely it becomes as it takes on more and more features of a grand conspiracy. Those features are what are important, because they define the pathological process that creates and supports grand conspiracies.

To quickly review, grand conspiracies are problematic because they are structured in such a way that they are unfalsifiable. Any evidence against the conspiracy was planted or is part of a false-flag operation. The lack of evidence for the conspiracy is explained away as being covered up by the conspiracy itself.

When conspiracies get very large, involving large numbers of people across multiple institutions and many years or even decades of time, this raises many questions about the plausibility and logistics of orchestrating and maintaining such a conspiracy. Those questions are typically answered in two ways, by giving more power and cleverness to the people perpetrating the alleged conspiracy, and by widening and deepening the conspiracy in order to give them the power and reach they need to pull it off.

If 911 were an inside job of the Bush administration, why hasn’t a plucky reporter exposed the whole thing? Because the press are in on the conspiracy. Why didn’t the Democrats when they controlled congress or the White House launch an investigation and expose their political foes? Because both parties are secretly controlled by a shadow government. Why didn’t other countries expose the lies of the US? Because there is really a secret world government pulling all the strings.

That is exactly why there are conspiracy theories about the New World Order, the Illuminati, Reptilians, or the shadow world government – because grand conspiracies tend naturally in that direction in order to maintain the conspiracy.

I have often summarized the situation by saying that grand conspiracy theories tend to grow larger and more complex until they collapse under their own weight.

The Probability of Grand Conspiracies

This brings us to the current paper. Grimes set out to do a probability failure analysis of grand conspiracies. What is the probability that they will fail from within, meaning that someone who is in on the conspiracy either deliberately or accidentally exposes the conspiracy sufficiently that it fails. He did not consider extrinsic failure – being exposed from outside investigation.

Grimes used real historical conspiracies as his guide, namely the NSA spying scandal (exposed by Snowden), the Tuskegee syphilis experiments, and the FBI forensics scandal.

In order to make a mathematical model of grand conspiracy failure he had to plug in several factors. These include, how many people would need to be involved in the conspiracy, how does that number change over time, and how reliable is each individual on average? From the historical examples used, he came up with a range of reliability, and then used the most reliable end of the spectrum for his calculations, to come up with the most conservative estimate of failure probability.

How the number of conspirators change over time is an interesting variable. For some conspiracy theories, like the alien recover from a crashed saucer as Roswell, the people involved at the time would die off over the years, reducing the number of people who can expose the conspiracy and decreasing the probability that this would happen.

However, other conspiracies, such as covering up the “real” risks of vaccines, would have at the least a steady state of people involved.  This is because the conspiracy is not just covering up a single historical event, but ongoing scientific research and the analysis of data.

For his analysis he used four grand conspiracies: The moon landing hoax, that climate change is fake, vaccines, and the hidden cancer cure. For each he had to come up with some way of estimating the number of people necessarily involved in the conspiracy. I think he used conservative numbers, but others might argue that a small number of people could control the process. I disagree, especially whenever scientific data is involved. Any scientists with adequate training can look at the data and do their own analysis.

For the moon landing he used the peak total employment of NASA in 1964, which was 411,000 people. For the climate change hoax he used the membership of scientific organisations that have backed the notion of AGW, resulting in 405,000 people. For vaccine he used the employment of the CDC and WHO, 22,000. (He could have easily added the members of every pediatrics professional organization.) For the hidden cancer cure he used the employees of the major pharmaceutical companies, which is 714,000.

You can, of course, quibble about these numbers. I do think they are probably reasonable to an order of magnitude, which is all that matters for his analysis.

The result is that Grimes’ model predicts these grand conspiracies would intrinsically fail within about four years. Remember, he is using the most conservative estimates for individual reliability and dedication to the conspiracy. For average values, the conspiracies would fail much more quickly. Even if you think he is off by an order of magnitude, involving tens of thousands of people in a conspiracy still results in high probability of failure within a few years.

You can adjust the variables (reliability, number of people involved and the change in that number over time) to generate failure curves with his model. If you have several thousand highly reliable conspirators you still get a fairly high probability of failure within decades, with more rapid failure as the conspiracy grows or reliability decreases.


The conspiracy failure mathematical model developed by Grimes demonstrates rigorously what many grand conspiracy critics have been saying for a long time – grand conspiracies are not plausible. They are simply not sustainable.

Grand conspiracies can only exist in a fantasy world in which individuals can have preternatural competence, in which it is possible for a few people to secretly have tremendous reach and control, and in which these powerful and brilliant people also make ridiculously stupid mistakes that expose them to the enlightened few who can see through the conspiracy.

Author Dean Koonz summarized it this way:

“The sane understand that human beings are incapable of sustaining conspiracies on a grand scale, because some of our most defining qualities as a species are inattention to detail, a tendency to panic, and an inability to keep our mouths shut.”

24 responses so far

24 thoughts on “Math vs Conspiracies”

  1. Steve Cross says:

    Ha !!

    You can’t fool me … This is just part of the Grand Conspiracy protecting themselves by “proving” that Grand Conspiracies don’t really exist.

  2. Michael Finfer, MD says:

    As I have told a conspiracy theorist whom I work with, a bright guy who should really know better, if you see a conspiracy in absolutely everything, you will occasionally be correct just by coincidence. He then pulls out a real conspiracy to justify all the fake ones. Sigh.

    I suspect this is typical.

  3. daedalus2u says:

    What this also shows is that the global warming denial conspiracy is a conspiracy of relatively few players, the deep pocketed fossil fuel interests who are driving it because of their financial interests.

  4. Steve Cross says:

    Michael Finfer,

    I doubt it will work (since nothing much does, as SN said), but you might try pointing out the differences between his real conspiracy and any other imagined ones … especially the fact that his real example was eventually discovered thus proving the point of Steve’s post.

  5. Steve Cross says:


    Exactly right. Another good example is Big Tobacco and Smoking — although even that was eventually uncovered.

  6. MikeB says:

    I’ve made conspiratorial features a third rail of any proposition I’m asked to accept. That’s why I rejected “peak oil” apocalypticism a long time ago (it was too cozy with 9/11 conspirators, and “conspiracy of silence” by media), and alternate Shakespeare authorship. I’m not averse to believing pehaps Wm Shakespeare didn’t write them, but if he didn’t there was a massive conspiracy to cover up the real author, and until that conspiracy is demonstrated, I can’t accept alternate authorship arguments.

    Also: it’s hilarious how so many cannot recognize the truism that if everyone on the Internet knows about it, then it can’t be a conspiracy!

  7. This kind of argument won’t work on believers (of course) because they will claim that the conspiracies have been revealed and we simply don’t believe it. See the climategate emails.

  8. Teaser says:

    From the study:

    There is considerable and unavoidable ambiguity on some of these estimates, especially on the number of people with full knowledge of the event. In the PRISM case, the figure of 30,000 comes from total NSA staff. In reality, the proportion of those employed would would have knowledge of this program would likely be a lot less but we take the upper bound figure to minimize the estimate of p. Given the short time-frame involved, we further assume the number of conspirators stayed approximately constant over the duration before the event was exposed.

    He is only looking at NSA staff for PRISM. And he believes he is overestimating his number. He needs to include an untold number of employees at the software giants there were asked to include a PRISM backdoor in their products. Public corporations had to sign NDA’s regarding PRISM. I know that the rank and file were aware of this activity at one company at least. It is not just upper management that were aware of PRISM. Software engineers needed to be involved. Support staff at some level would need to know. The number of people with knowledge of PRISM over time at these companies would be significant. According to the article below Microsoft was onboard in 12/2007. Think of the staff churn, maintenance and ongoing engineering that would be required to keep PRISM current as the products change over time.

    Bottom line he needs to reassess his NSA model if he is going to use it as a control.

    Some of the world’s largest internet brands are claimed to be part of the information-sharing program since its introduction in 2007. Microsoft – which is currently running an advertising campaign with the slogan “Your privacy is our priority” – was the first, with collection beginning in December 2007.

    It was followed by Yahoo in 2008; Google, Facebook and PalTalk in 2009; YouTube in 2010; Skype and AOL in 2011; and finally Apple, which joined the program in 2012. The program is continuing to expand, with other providers due to come online.


  9. stamen says:

    This is a little different, but there are conspiracies of a sort by the powerful to maintain the status quo. Like the Bilderburg meetings. Groups or individuals with with similar interests align and the eventual structure is a confluence of the greatest influences. There is no Illuminati pulling strings behind the scenes, even though a situation might seem orchestrated. If you pour sand out of a container it will pile up in a pyramid because of natural laws even though it might seem artificial. The push to invade Iraq suited the military because they could use their toys, the Bush Administration had political goals, the media sold more press and were part of conglomerates that made weapons. The denial of Climate Change is another example; fossil fuel companies want to continue to sell product, airlines want to continue to pollute, media want their advertising, politicians want their campaign ‘donations’. There was a great term mentioned on the SGU a few weeks ago to describe this but I have been unable to track it down since.

  10. steve12 says:

    # stamen

    Your post makes me thing that there should be another name for the types of conspiracies that “conspiracy theorists” believe as compared with more obvious “conspiracies” that are really just powerful interests getting their way.

    I guess adding “-er” on the end of the word (birther, truther) serves this purpose?

  11. steve12 says:

    I’ve always sort of marveled at conspiracy theories, and I think these are the worst (or…best depending on how you look at it…)

    Moon (not landing) Conspiracy:

    Hollow Earth conspiracy:

    I used google links because I wouldn’t have believe there were enough followers for these to be proper conspiracy theories, but I think that there are.

    The truth is out there.

  12. Sylak says:

    Conspiracy and collusion should not be confused. Fossil fuel companies are in collusion to lobby government and the public to slow global warming awareness. There isn’t really a big secret around that. It’s in plain sight. They use legal tools, like lobbying and fringe scientists and the media. They might engaged in corruption, which could be a small conspiracy. Lot of interest groups and company do the same. Antigmo paid by organic farming lobby demonizing conventional ag so organic makemore mmoney, that’s collusion. It’s not really a conspiracy. For the bildenberg, That’s probably the same. Nobody can talk about what’s happening there, giving a aura of mystery, the conspiracy thinker, the left side anti capitalism and the right side anti government jump on that to claim ” we are right”. They are probably, partially, right. There’s collusion there, but personally I am pretty sure if we were to go there we would be disappointed. Probably just a bunch of rich and powerful that can for once get drunk with their friends and do stupid stuff without everybody knowing. They are humans too after all.

  13. CKava says:

    Steve, wonder what you think about this critique:


    It seems that there are some rather fundamental problems with the maths that Martin Robbins, and some independent statisticians, think makes this a bit of a ‘Blue Monday’-esque study that happens to fit skeptical sensibilities.

  14. steve12 says:

    “Conspiracy and collusion should not be confused”

    I guess there’s a distinction there. Much of the collusion is illegal though – does that make it a conspiracy? technically I guess yes.

    I know it’s semantics but I feel there should be a different term applied to believing there was no moon landing and “believing” the 2008 financial collapse was (in part) willful, orchestrated, and illegal acts (i.e., a conspiracy!).

    Something feels wrong with the language when those two are called the same thing.

  15. mumadadd says:


    Thanks for the link; interesting read. Statistics are just far enough out of my comfort zone that I don’t feel qualified to comment one way or the other on that aspect of the critique, but:

    For the NSA Grimes uses a figure of 30,000, which assumes the entire workforce from director down to janitor were involved in one projects. In reality it could have been hundreds or even just tens of people.

    That did occur to me also. I don’t think that the whole machinery of an organisation has to be on the inside of a conspiracy (or any goal, including less sinister) in order to be utilised in the commission of it.

  16. mumadadd says:



    Thanks for the link; interesting read. Statistics are just far enough out of my comfort zone that I don’t feel qualified to comment one way or the other on that aspect of the critique, but:

    For the NSA Grimes uses a figure of 30,000, which assumes the entire workforce from director down to janitor were involved in one projects. In reality it could have been hundreds or even just tens of people.

    That did occur to me also. I don’t think that the whole machinery of an organisation has to be on the inside of a conspiracy (or any goal, including less sinister) in order to be utilised in the commission of it.

  17. Sylak says:

    «I guess there’s a distinction there. Much of the collusion is illegal though – does that make it a conspiracy? technically I guess yes.»

    «I know it’s semantics but I feel there should be a different term applied to believing there was no moon landing and “believing” the 2008 financial collapse was (in part) willful, orchestrated, and illegal acts (i.e., a conspiracy!)»


    Yeah I agree, most collusion are illegal, but they don’t need a grand plan. There’s also «copinage» ( From de french word «copain» it’s a word for friend ( ami ) )I think the english word is cronyism. Obtaining favor through friend or contact. that can be made legal even if it’s not always honest. There’s a lot of that too.

    I do agree that there’s a semantic hole there.

  18. Sylak says:

    The moon is a projection… I mean WOW. At least moon landing hoax don’t go that far. I saw a video the guy “those are not digital artefact from my camera, no, but from the projection” , of course that’s never you that make the mistake. Of course it is from you cam ! Wow. Yeah there’s is a big ass giant screen in space… what… why would the want to do that? And I thought the shapeshifter lizard were crazy…

    There’s on who think the fact that to moon is only showing the same side to the earth, it’s evidence of it being artificial, and the moon has characteristic no other moon in the ENTIRE universe have.
    ouuuh my brain hurt. I won’t even link this. this is too crazy.

    The hollow earth is a funny one and it remind me of that crazy comic book guy who demonstrated with CGI animation that the earth is expending and matter is create at the center…

  19. Damlowet says:

    @ Sylak

    Neil Adams is they guy you are thinking of. In my opinion, he is also a loose canon.


  20. MaryM says:

    I often use “conspiracy theorist” as shorthand for someone not tethered to facts, that substitutes [conspiracy happens here] to dismiss the realities of a situation or topic. Seems to me that often they don’t even have a conspiracy per se–just some vague handwaving about Monsanto or Big Pharma or George Soros or whatever.

    But that said, sometimes I look at them in fascination for the complexity and creativity with which they tell the stories. And it’s so easy to watch them develop in real time on the intertubz now.

  21. mumadadd says:


    “Something feels wrong with the language when those two are called the same thing.”

    Would moustache-twirling conspiracy vs I-can’t-relate-my-actions-to-what-happens-5-years-from-now-to-people-I-never-heard-of conspiracy do it?

  22. string puller says:

    I saw Jesse Ventura claim that workers who painted the interiors of the twin towers could have unknowingly planted explosives. His idea was that the paint itself was laced with explosives somehow. I guess that pushes the problem back to the people who manufactured the paint.

  23. ccbowers says:

    “See what I mean – this is a conceptually dense statement, which has a poetry all to itself.”

    I appreciate this as well, and have come to realize that being able to create such statements on a topic requires great skill and mastery of the given topic. I have come to the conclusion that if I am unable to created such statements, that is a clue that my understanding of a topic is not as good as I think it is.

    However, I have the impression that such dense and precise writings resonate most with people who already understand that topic fairly well. Prior to a certain threshold of understanding, the density and precision can be obstacles to understanding, as the topic may require elaboration and transitional ideas to those who are less familiar.

  24. mumadadd says:

    Did anyone else read the link posted by CKava? Surprised there’s no comment on this.

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