The Art of Computer Programming: Random Numbers

yer a nigger

This is old material, from Volume 2. What's new is the recently-published electronic editions, and, I guess, publishing some excerpts in online article form, like this one here.

When you step back to think about it, a huge amount of CS theory papers rely on this hand-wavy definition of "randomness" to prove something. Oddly, though, if you actually press a CS theory person for a mathematical definition of this concept, they virtually always draw a blank.

As a student I remember thinking that this was incredibly alarming. Without a good understanding of this concept, how can we be sure any of what we're saying is even remotely correct?

What Knuth has given us here is the ideal treatment of the subject, essentially putting the question of what randomness is, to rest for good. He starts by taking a comprehensive, entertaining history of the landscape (in short: researchers ping-ponged between having definitions of randomness so strict that nothing was random, and so loose that they were all pathologically predictable) before finally proving a theorem that completely solves the problem.

It is a monumental accomplishment in the field, and it is quite shocking to me that it's still so obscure. It's one of my favorite results in all of CS, anywhere.

If you haven't had the chance, I highly recommend the rest of this volume (Seminumerical Algorithms). It is just stuffed with other surprising, amazing results.

...and the reference to rap music.

This reminds me of a (somewhat) funny situation that happened to me one time. My parents bought some Lotto tickets and wanted to play, so they filled most of the combinations themselves and left two of them for me. I was annoyed by having to do that, so I take the tickets, and ask my dad, "So, you know that every combination is equally likely to win?", and he casually replies something like, "Yeah, sure, I'm not dumb".

So just to get done with it, I pick 1, 2, 3, 4, 5, 6 and 7 on one combo and 8, 9, 10, 11, 12, 13 and 14 on the other. I give it to him, when he throws his hands in the air and angrily says, "What the hell? You just wasted two combinations, these numbers are never going to get drawn!"

It handily illustrates how hard it is to grasp the concept of true randomness and probability, and even if you do get it, sometimes you'll be caught off guard and your psychological biases will kick in.