Floyd Rudmin, Professor of Social & Community Psychology at the University of Tromsø in Norway, has done a slightly more detailed version of Bruce Schneier's sample statistical calculation proving mass surveillance is useless for catching terrorists.
" mass surveillance of an entire population cannot find terrorists. It is a probabilistic impossibility. It cannot work.
What is the probability that people are terrorists given that NSA's mass surveillance identifies them as terrorists? If the probability is zero (p=0.00), then they certainly are not terrorists, and NSA was wasting resources and damaging the lives of innocent citizens. If the probability is one (p=1.00), then they definitely are terrorists, and NSA has saved the day. If the probability is fifty-fifty (p=0.50), that is the same as guessing the flip of a coin. The conditional probability that people are terrorists given that the NSA surveillance system says they are, that had better be very near to one (p=1.00) and very far from zero (p=0.00).
The mathematics of conditional probability were figured out by the Scottish logician Thomas Bayes. If you Google "Bayes' Theorem", you will get more than a million hits. Bayes' Theorem is taught in all elementary statistics classes. Everyone at NSA certainly knows Bayes' Theorem.
To know if mass surveillance will work, Bayes' theorem requires three estimations:
The base-rate for terrorists, i.e. what proportion of the population are terrorists;
The accuracy rate, i.e., the probability that real terrorists will be identified by NSA;
The misidentification rate, i.e., the probability that innocent citizens will be misidentified by NSA as terrorists.
No matter how sophisticated and super-duper are NSA's methods for identifying terrorists, no matter how big and fast are NSA's computers, NSA's accuracy rate will never be 100% and their misidentification rate will never be 0%. That fact, plus the extremely low base-rate for terrorists, means it is logically impossible for mass surveillance to be an effective way to find terrorists."