In Little Brother, the February alternative reading (#1alt140), the plot hinges on the fact that if you’re testing for anything, you test needs to have an accuracy that matches the frequency of occurrence of what you’re testing for. Doctorow provides a great explanation in the text but, of necessity he uses words, not math.
I say of necessity because our mathematical education (I’m talking USA but I think it’s safe to generalize) is inadequate. Even Docotorow’s good, clear words leave many of us scratching our heads. I had to come at the paradox of the false positive from several perspectives before it clarified itself in my mind.
So let me try to explain it with a simple picture and a concrete example.
Consider Atlanta Georgia’s Hartsfield Airport. By some estimates it is the world’s busiest, serving 250,000 passengers a day. The image below is made of 250,000 pixels, one for each daily passenger:
Can you find the terrorist?
They all look pretty much alike, don’t they. But one passenger is a terrorist. He’s trying to blend in, of course, but he’s detectable if you look hard enough. You can see him, can’t you? Here’s a hint, he’s the gray pixel. Did that help? Of course not. It will take a detailed, intrusive search to find that one gray pixel.
That leads to my main point, finding the terrorist is hard, really hard. For the sake of argument, let’s say you have a “find the terrorist” test that is 99% effective. This means two things:
The test will find 99 percent of the terrorists there are to detect. That means if 100 terrorists travel through Hartsfield, 99 are detected, and presumably detained, but 1 gets through to further his plan for terror. This is not good. One terrorist is one too many. I think we can all agree to that.
But it also means that one time in a hundred, it will declare an innocent person a terrorist. This is really not good, Remember our 250,000 people traveling through Hartsfield? Every day one out of one hundred will be identified as a terrorist, detained and, one hopes, later released. That’s 2,500 people a day who are detained, will likely missed their flight, and may be subjected to intense interrogation.
Now let’s use our 99% acurate terrorist test for 100 days — a little more than three months. In that time the test will have:
- Detained 250,000 innocent people
- Caught 99 terrorists
- Let 1 terrorist through
Now this 99% accurate test will likely involve invasive searches of person and property, aggressive interrogation, and people in body armor carrying automatic weapons. Does that remind you a police state? If it does, comfort yourself with this thought — No one’s trying to create a police state, it’s just the way the math works out.
When we all signed up for the Patriot Act, very few of us did the math. Unfortunately, thanks to our educational system, most of us couldn’t do the math even if we wanted to.
So one final question, if you do the math and it comes out the way I described it above, would you have encouraged your representatives to support the Patriot Act?