Saturday, December 15, 2007

OMG my iPod likes Barbara Streisand

A few days ago, I updated my iPod with some new songs (I was getting kinda bored listening the same ones for about two years now). I put most of these new songs in my 80's playlist (about a dozen new songs altogether). So, the last few days I had my iPod on every time I went home from work and noticed one strange thing - every time I listened to it, one of the songs was "The way we were" by Barbara Streisand (yes, I occasionly listen to Barbara, so what of it?). What was strange about it is that the shuffle option was always on and that there were 95 other songs in the playlist. To give the exact numbers, I heard Barbara four out of four days in a row, where I listened about 15 songs each day (the commute home takes about 45 minutes - that's 3 minutes per song), and, as I said, there were 96 songs in total to choose from.
This somehow seemed odd to me, not to say wierd. That's why I decided to see just what is the probability to observe this strange behaviour. So, back to basic statistics. The probability that any song will be selected from a playlist of 96 songs is 1/96. However, as one song finishes, the next one is selected from the remaining 95 songs (I assume that this is how the iPod's shuffle works - it shouldn't select a song that was already played until all others are played). So the probability that any song will be selected if two songs are played is 1/96 + 1/95. You get the picture how the story goes from here... So, the probability that you heard a song after playing 15 of them (in a playlist of 96 songs) equals to 1/96 + ... + 1/82 = 0.1689, that is, around 17%. This means that I have a 17% chance to hear "The way we were" on one of my trips home. However, I heard it four days in a row. Since hearing a particular song on one of my trips can be regarded as an experiment with two outcomes (I either heard it or not), and since I start the new shuffle every day (meaning that each experiment is independent of the previous one), we can say that we are talking about a binomial distribution. In such a setting, we can easily compute the probability that I hear Barbara four days in a row - it's simply 0.1689^4 = 8.145 * 10^-4. That is, there is an 8 in 10000 chance that I will hear Barbara four days in a row if I put my iPod on shuffle. Yet, there it was, I heard it. Four days in a row. As my knowledge of statistics ends here, I will not try to do a hypotesis test or anything like that. If there is someone out there that is willing and capable to do this, I would love to hear from him/her.
All this lead me to do some research online. Well, it turns out I'm not the only one having this shuffle issue. Many users have already complained how the "random" playing isn't random at all and how their iPods have souls. Here's just two references - The second one is a really interesting paper with some more references to people with the same problem. So, it turns out that the machines have already started developing their own "mind". Yes, our machine overlords are taking over the world, and they have started with picking their favourite music. I'm just glad to know my iPod loves Barbara Streisand - I think it'll make an ok master.

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