The Critical 'I'

Read. React. Repeat.

Sunday, July 13, 2003

LAWS OF PROBABILITY AND MY IPOD
While I'm fairly comfortable in the realm of mathematics, I'm often dumbstruck by some of its real-life applications. This is especially so in the case of probability and randomness.

(I'm probably going to misuse some mathematically technical terms; I'm no expert, and I'm not getting paid for this, so you, gentle reader, will just have to live with my flubs. If you feel strongly enough about any particular error, feel free to comment and let me know. If you want some insight into a lot of stuff that, fascinating as it is, is somewhat over my head (at least for today), check out this, this and this.)

The particular real-life application that brings this to mind is my iPod. I have the bulk of my music collection loaded onto it: Around 60 hours of music, broken down into 722 mp3 files (I have a good amount of Christmas music and other odds and ends residing on my computer, but not loaded onto the iPod). Because I like variety, I've got the music player set to automatically shuffle through all the songs, presumably randomly, versus playing each song in alphabetical order according to song title, artist, album or genre. With so much loaded onto it (around 4.5MB), you'd think I'd be able to set the thing to play and experience a wide variety of sounds for hours on end.

Why is it, then, that every other song that cues up is a fucking Police song?

Now, I like The Police. Or at least, I used to until now. Police tunes come up so often on my allegedly random music shuffle that it's become a major distraction. I have to skip ahead to the next song every few minutes. What really drives me nuts is when I "fast-forward" (what a relic term now that cassette players are passe!) to the next song to avoid the Police song that's just cued up, I get served up with another damned Police song!

What's the cause of this? You'd have to naturally assume that I must have a ton of songs by The Police on my iPod. And I do. I own the complete recordings box set, and while I didn't rip everything off of it onto my hard drive, I did encode quite a bit. I transferred all those songs onto my iPod, along with the other artists and songs. The thing is, I have way more Police songs in this collection than any other single artist, and so that's what accounts for the preponderance of their songs over others in the shuffle.

But here's where the laws of probability come into play. Just how many Police songs must I have, among the 722 on that iPod, for them to cue up so disproportionately much?

That's the funny thing. I'd forgotten exactly how many Police songs I had loaded up, but thanks to their constantly cropping up on my random shuffle, and the total that was in that box set, I assumed it had to be around 100. That would represent about 15%, or one in every seven songs being Police tunes. That doesn't sound like a lot, does it?

Well, the joke was on me. Turns out there are only 69 Police songs, total, among my mp3s. That's all! Sixty-nine out of 722 files, barely one in ten. Yet they keep coming up on a random playlist! How is this possible?

Probability and randomness are tricky things. In common vernacular, we use both terms to mean non-exclusive variety. For instance, we figure leaving things to chance means that, if we flip a coin, it has an equal chance of coming up either heads or tails. For single-time uses, this works fine. The trouble comes when we flip the coin multiple times, and expect a different result basically every single time. People assume that random theory calls for a fairly steady alternation of heads and tails results--at least, "randomness" in this sense calls for no more than a three-in-a-row occurrence for any single result. In other words, we expect a certain degree of predictability in random actions. If the coin ends up coming up heads 12 times in a row, or even 11 out of 12 times, then we come to believe that there's something fishy going on.

In fact, randomness and probability don't operate that way. Unqualified randomness means that there's an equal chance for any available outcome each time the action occurs. More importantly, the preceding result has absolutely no impact on the next. So truly, the fact that you get heads on one coin flip has no bearing on what the next coin flip will bring. This assumes, of course, that nothing different is done each time you carry out that action: You use the same coin, flip it the same way, etc.

So, taking all this into consideration, it's easy to see why those Police songs come up so often on my iPod. Since the shuffle function works by picking through the entire cache of songs, without qualifying for artists or frequency of selection, it can theoretically choose Police songs 69 times in a row. Even though the Police lineup represents a minority of all songs on the iPod, they make up a plurality--no other single artist/act has nearly as many songs on my little mp3 player as them (I think maybe the Beastie Boys, or maybe Nirvana, even come close). Because of this, they stand a very good chance of getting cued up more than average.

Lest you think that all this is bunk, I experienced the same phenomenon on the Winamp player on my computer. Same setup, same results: Police songs would come up despite the random shuffling, much to my disgust. I solved that by removing all the Police songs from the main playlists.

And so, I'm going to take the same approach with my iPod: I'm removing all the Police tracks off of it. Maybe I'll leave a smaller number of them, but I'm so sick of hearing them by now, I think I'll just rid myself of them altogether.

This will, of course, free up quite a bit of space on the iPod's drive, meaning I should rip some new mp3s and transfer them over. Something for tonight.