Forget computer architecture, I want to talk about statistics.
LET’S SAY that you invent a test that determines whether someone is in the Illuminati, and it’s 99.9% accurate. Now, let’s say 0.1% of the world’s population is actually in the Illuminati. Someone takes the test, and it claims they’re Illuminati. What are the odds they’re really a member of a shadow government?
Well, gee, it’s like a 99.9% chance, right? Or, 99.8% or something to account for inaccuracy? No. It’s 50%, as good as a coin flip. So, congratulations. Your 99.9%-accurate test is worthless. And if you want to know why, look to conditional probability.
See, until the 1700s, statistics wasn’t much further along than “lol coin flips”. Then, in 1763, Bayes published an essay that asked (and answered) a new question: how do statistics change if the probability of an event depends on the probability of another event? Like, the probability of a test saying you’re in the Illuminati depends on the probability of you actually being in the Illuminati.
This whole sub-branch of statistics is called conditional probability — as in, the probability something happens given the condition that something else happens. It’s great, because the math involved is simple, but some of the results throw our human intuitions for a loop.
Statistics textbooks usually start abstracting out from here and it gets easy for your eyes to glaze over, but as I said, the math is simple:
|ARE YOU ILLUMINATI?||WHAT DOES THE TEST SAY?||CHANCE OF HAPPENING|
|TOTALLY, SHADOWS AND STUFF (0.1%)||DAMN DUDE (99.9%)||0.0999%|
|NAH BRAH (0.1%)||0.00001%|
|WHAT? NO (99.9%)||DAMN DUDE (0.1%)||0.0999%|
|NAH BRAH (99.9%)||99.8001%|
What are the chances you’ll be told you’re Illuminati correctly? (0.1% chance you’re Illuminati * 99.9% chance test calls it) = 0.0999% chance.
What are the chances you’ll be told you’re Illuminati incorrectly? (99.9% chance you’re boring as shit * 0.1% chance the test is wrong) = 0.0999%, or, the same damn likelihood.
IN CONCLUSION: if any of you think I’m part of the Illuminati, no matter how much evidence you have, you’re probably wrong. Hint hint.