Here's an attempt at using Bayes' Theorem (conditional probability) to show mathematically that mass surveillance systems such as those in the original article can't work (at least, not as advertised). The reasoning seems a bit simplistic, but I think the basic premise is reasonable.
The US Census shows that there are about 300 million people living in the USA.
Suppose that there are 1,000 terrorists there as well, which is probably a high estimate. The base-rate would be 1 terrorist per 300,000 people. In percentages, that is .00033%, which is way less than 1%. Suppose that NSA surveillance has an accuracy rate of .40, which means that 40% of real terrorists in the USA will be identified by NSA's monitoring of everyone's email and phone calls. This is probably a high estimate, considering that terrorists are doing their best to avoid detection. There is no evidence thus far that NSA has been so successful at finding terrorists. And suppose NSA's misidentification rate is .0001, which means that .01% of innocent people will be misidentified as terrorists, at least until they are investigated, detained and interrogated. Note that .01% of the US population is 30,000 people. With these suppositions, then the probability that people are terrorists given that NSA's system of surveillance identifies them as terrorists is only p=0.0132, which is near zero, very far from one. Ergo, NSA's surveillance system is useless for finding terrorists.
(...)
Suppose that NSA's system is really, really, really good, really, really good, with an accuracy rate of .90, and a misidentification rate of .00001, which means that only 3,000 innocent people are misidentified as terrorists. With these suppositions, then the probability that people are terrorists given that NSA's system of surveillance identifies them as terrorists is only p=0.2308, which is far from one and well below flipping a coin. NSA's domestic monitoring of everyone's email and phone calls is useless for finding terrorists.
NSA knows this. Bayes' Theorem is elementary common knowledge. So, why does NSA spy on Americans knowing it's not possible to find terrorists that way? Mass surveillance of the entire population is logically sensible only if there is a higher base-rate. Higher base-rates arise from two lines of thought, neither of them very nice:
1. McCarthy-type national paranoia;
2. political espionage.
http://www.counterpunch.org/rudmin05242006.htmlThe original article shows that even the government customer doesn't believe that any system they've tried to implement to date is even close to being highly accurate. There's no way their misidentification rate is less than .001%, we've seen too many examples of that (Gitmo, no-fly lists, etc.)! Assuming they really just want to find terrorists, then they're just hoping that someone will come along and magically solve their problem. But they've also shown that they're not too concerned with getting it wrong.