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Conspiracies And Probability
guttentag writes "Sunday's New York Times Magazine is running a feature that looks at the rumored conspiracy that allegedly killed nearly a dozen bioterror and germ warfare researchers during a four month period following the U.S. anthrax scare. "What are the odds," people ask, despite the fact that a "one-in-a-million miracle" will statistically occur 280 times a day in the U.S. These strange things happen all the time, but we hype them because they provide the spice in literature and the comfort of comprehension."
You could find the odds exactly if you knew several figures:
What is the number of bio-whatnot researchers in the group?
What are the odds of one dying in a given time period?
And this is the hardest: How many comparable groups are there in society? For example, politicians dying would be noticed. Baseball players dying would be noticed. And how big are these groups?
If you answer these simple questions, you can answer the main topic.
Stanislaw Lem's "The Chain of Chance" deals with just about this very sort of thing, actually. Emergent properties of large populations, more, though.
Google for "operation northwoods" and you will discover that the military, in the 1960s, as a matter of public record, were laying plans to attack American citizens in order to stir up support for a war on Cuba.
That's not speculation, that is public record, learned through researching and the Freedom Of Information Act. They didn't actually carry out any of these plans, or blow up John Glenn's orbital space flight, because saner heads, including McNamara, refused to even consider allowing the military to make attacks on the country's own citizens for PR reasons.
The plans were still being seriously put forth.
How are you going to explain to people that this was reality, public record, proven, and that the anthrax/researcher killings you're talking about are not proven to that level of confidence? You will only make people less willing to believe the proven and important facts about the military making plans to target US civilians.
And I think that is too high a price to pay. This is the time where people need to learn to listen, not be confused by wild stories.
Choose your stories carefully, and talk about them carefully. It's like traditional investigative journalism- you don't charge madly ahead or you get discredited and lose everything you worked for.
I am always amazed by the gullibility of the general populice. How can people honestly believe that a modern government could harbour ANY kind of conspiracy given that they can't even keep the affair of a President with an intern secret?? If there really were aliens on earth, UFOs circling the solar system, etc., you'd be guaranteed that somebody, somewhere who wasn't hushed up by "the government" would have reported it on the 'net. Conspiracy theories are just another method for selling media to the masses.
I've had this argument with my wife once. It starts out like this:
...
WIFE: Did you buy a lottery ticket like I asked?
ME: Yes.
WIFE What numbers did you pick?
ME: 1, 2, 3, 4, 5, 6.
WIFE: WHAT? What are the chancs of that coming up?
taken! (by Davidleeroth) Thanks Bingo Foo!
Richard Dawkins has an excellent chapter in his book "Rainbow" where he describes a concept called a PETWHAC. This roughly translates into: Population of Events That Would Have Appeared Coincidental. He notes that for any seemingly impossible coincidence, oftentimes it can be dispelled simply by figuring out what events would be included in the PETWHAC: and usually you get a very high number. We have so many opportunities for amazing coincidences every day that it's almost mathematically inevitable that some will happen to us once and awhile. Coupled with the number of people out there, it's no wonder that seemingly amazing and inexplicable coincidences are reported all over the place: they are quite likely.
Efron is a venerable statistician, but this is plain wrong. There are many things that are so unlikely that, for practical purposes, they simply do not occur in this universe. For example, all the air molecules in a room don't all get on one half of the room, leaving the other half with a vacuum. Statistically, this arrangement is (approximately) as probable as any other. But there aren't enough rooms in the universe to make this an event that could occur with "fairly high" probability.
Much of physics relies on things that are "astronomically unlikely", and much of engineering consists of changing conditions so that something that is very unlikely becomes common. We have enshrined these "astronomically unlikely" principle as a the laws of thermodynamics, and we don't even bother to say "a perpetual motion machine is possible but very, very unlikely", we just say "you can't build one", because for practical purposes, you can't.
[Tibshirani] ''The chance of getting a royal flush is very low,'' he says, ''and if you were to get a royal flush, you would be surprised. But the chance of any hand in poker is low. You just don't notice when you get all the others; you notice when you get the royal flush.''
This is true but not relevant. If you randomly think of some particular hand and then have it dealt, you do have reason to be surprised, although, since the prior probability on the existence ESP or telekinesis is so minute, you should probably still attribute it to randomness. On the other hand, you have no reason to be surprised if you get a royal flush once over many games, just like you have no reason to be surprised to get any particular hand once in many games.
Similarly, statistically, having all the air molecules in a room be present only on one side of the room is (approximately) as probable as any other particular arrangement of air molecules, but I guarantee that if you were in that room, you would notice, and you would have reason to be surprised. In fact, you would almost certainly be correct in concluding that that arrangement of air molecules didn't come about by chance but involved something like a vacuum pump and a partition.
Which brings us to the death of Benito Que, who was not, despite reports to the contrary, actually a microbiologist. He was a researcher in a lab at the University of Miami Sylvester Cancer Center, where he was testing various agents as potential cancer drugs.
Now we are getting to the good stuff. The problem with the conspiracy surrounding these cases has nothing to do with statistics or people's ignorance of it.
The death of half a dozen germ warfare experts under the age of 60 within a span of four months would be an unlikely event, whether or not it follows 9/11. Not astronomically unlikely, but something that would certainly warrant closer investigation. If you assume that there are maybe 100 such world experts, you can look at standard mortality tables to bound the probability of this event occurring.
What's wrong with that analysis is that these people were not "germ warfare specialists"--they were biologists. Journalists constructed the label "germ warfare specialists" after the fact. But there are a lot of biologists in the world. The death of half a dozen biologists over a four month period is a much more probable event--simply because there are a lot more biologists around.