While I had previously worked with false positives in various statistic problems, I never considered the implications behind it. Cory Doctorow addresses this “false positive paradox” in his book Little Brother.
In the story, the narrator, Marcus, talks about a “99 percent accurate” test for “Super-AIDS” (Doctorow 47). However, this means the test is one percent inaccurate. One percent of one million is 10,000. Only one of those people will actually have the disease, and thus, the “99 percent accurate test will perform with 99.99 percent inaccuracy” (Doctorow 47).
This was extremely interesting, as I had never considered how inaccurate these tests really were. The statistics and numbers had always seemed solid. It made sense, and 99% seemed like an extremely high percentages. But Doctorow makes an intriguing analogy. Pointing at a single pixel on your screen with a sharp pencil works. However, pointing at a single atom with a sharp pencil would be extremely inaccurate. This essentially highlights the flaws in any test that could potentially produce false positives. Whether detecting diseases or terrorism, these tests could result in large wastes of resources, such as time and money.
This could also be connected to the process of cracking ciphers. For example, when searching for cribs in an Enigma deciphered message, a crib may make sense in a particular context but could turn out to be an incorrect decipherment for the whole message . Even in general cryptanalysis, you could potentially make progress on deciphering a message. After hours of working on a message, you could realize that you made a mistake originally and your previous progress had simply been a “false positive”. Clearly, false positives can be quite dangerous and misleading. The false positive paradox further magnifies the huge effect these false positive readings can have on carrying out important tests or examinations, and the consequences could be devastating. Imagine administering a drug thought to combat a certain disease to a patient who really didn’t have the disease. Because the patient was perfectly fine, this drug actually resulted in the patients’ children having birth defects. A simple false positive could cause tragic repercussions.
