My students can testify that I have often told them that anyone with a Ph.D. in physics can think up a b.s. explanation for anything. Sometimes this is just harmless fun, but sometimes it can cause real problems, even when it is done with no ill intentions. I'm afraid a recent study that has received publicity is likely to be entirely counterproductive. I am referring to the study by Oxford Professor David Robert Grimes that was summarized at sciencedaily.com under the title "Large-scale conspiracies would quickly reveal themselves, equations show" and by the BBC under the title "Maths study shows conspiracies 'prone to unravelling'"; because there are serious flaws in his approach, he is likely to increase the very skepticism he is trying to answer.
Let me start by saying that I understand exactly and sympathize with what he was trying to do, even without knowing the precise details of how he was trying to to do it.
For one thing, although I enjoy the thrill (and sometimes creepiness) of the "What if?" that was so embodied by the 1970's show "In Search Of...", starring Leonard Nimoy, the truth is that pseudoscience rapidly becomes unsatisfying because it is so limited. That nudges my relationship with potential X-Files material in a slightly antagonistic direction, but what really gives it a shove is the unhealthy pattern of thought that typifies the enthusiasts of Bigfoot, UFOs, and ghost hunting. For far too many of these enthusiasts, their chosen topic is only an excuse for their real interest, which is to play the role of a kind of high priest in a mystery religion that the general public is too stupid or fearful to understand and that is actively persecuted by a conspiracy of the government, the military, and the scientific community.
The other thing is, I understand first-hand how tempting it is for a physicist to build a simple model to see if it can provide at least a semi-quantitative explanation of a complicated phenomenon. What he was trying to do in modeling conspiracies is not very different from what I was trying to do when I modeled the NCAA basketball tournament.
All models are simplifications, but his model simplifies too much. All conspiracies have something to do with secrecy, but he appears to interpret this in an absolute sense, so that if any hint of the conspiracy were to become known, the conspiracy would immediately collapse. Of course, some conspiracies are in fact like that. For instance, if you are in North Korea, you had better hope that no one ever dreams that you are part of part of a conspiracy to assassinate Kim Jong Un, because even the merest suspicion of that is a Very Bad Thing for you.
Many, probably most, conspiracies are not like that, though. In some cases, the "signal" can be lost in the "noise". For instance, the Soviet Union got several key pieces of accurate intelligence that told exactly when Nazi Germany would attack them, but these were ignored because (a) Stalin didn't really want to believe them and (b) there were also a large number of contradictory, inaccurate reports.
Then there are "conspiracies" that merely have, to use a term from the Reagan years, "plausible deniability" -- and that "deniability" can be strongly influenced by biases and vested interests. I think most people today would say there was a conspiracy for decades to deny the health risks of smoking tobacco. There was evidence from fairly early on that smoking was unhealthy, but it is not what people wanted to hear, and the tobacco companies had a strong financial motivation to shout down that evidence and the resources with which to finance studies that would seem to cast doubt on the dangers of tobacco. The tobacco conspiracy did not unravel because of some single revelation, but because a critical mass of the public and the powers that be decided to stop pretending that smoking is no problem. [We have probably gone too far in the other direction now, but the point is that no one is now pretending tobacco is totally harmless.]
Another example that I think could be called a poorly hidden "conspiracy" is racial slavery. In order to "justify" slavery, it was necessary to provide arguments and evidence that blacks (and American Indians) are somehow inherently inferior to whites, either or in terms of their intellect, or their character, or both. Of course, the circumstances of slavery could easily be manipulated to provide "support" for the inferiority of slaves -- a lack of education could be called stupidity, for example. None of this was honest, and to quote Chesterton,
Against all this dance of doubt and degree stood something that can best be symbolised by a simple example. An ape cannot be a priest, but a negro can be a priest. The dogmatic type of Christianity, especially the Catholic type of Christianity, had riveted itself irrevocably to the manhood of all men. Where its faith was fixed by creeds and councils it could not save itself even by surrender. It could not gradually dilute democracy, as could a merely sceptical or secular democrat. There stood, in fact or in possibility, the solid and smiling figure of a black bishop.What put an end to the conspiracy of slavery was not the amazing discovery of "the manhood of all men," but the decision to stop pretending to be in doubt of what was known all along.
For one last example, consider the Tuskegee Experiment. It involved secrecy towards one group of people -- in particular, the black men who were the human guinea pigs -- but there was no secrecy about it at all among the medical research community.
They guys discuss the claim that Stanley Kubrick confessed on his deathbed to faking the moon landings.
What about the specific conspiracies addressed by Prof. Grimes? The mere fact that we have heard of them means that no one is claiming them to be perfect secrets, and in fact there are supposed insiders who have spilled the alleged beans. Prof. Grimes' model does not correctly describe its subject.
"Bob Lazar" claims to be a physicist who worked on alien technology at Area 51.
So the people who find these alleged conspiracies plausible would say we have a situation parallel to the tobacco conspiracy. They would tell us that the information is largely available, but that vested interests work hard to suppress and discredit that information, and most of the public simply does not want to know the truth.
In conclusion, there is no shortcut for evaluating whether or not an alleged conspiracy is true or even plausible. The only way to find that out is by examining the substance of the claims.