Inferring and Explaining

50 InferrIng and exPlaInIng Tere are thirty-six Pink Martini songs in Johnson’s iPod. What are the odds of his imag- ined encore occurring on the drive home? Let’s spend just a minute and fgure that out. “Lilly” came up as the next to the last song played. Te odds of this happening are straightforward. Any one of thirty-six songs could have come up here, so the odds are 1/36. But to have the encore, you had to also have “Que Sera Sera” come up last. So what are the odds of that happening? It’s actually easy to fgure out. We already know the odds of “Lilly,” so it’s a question of “Lilly” and “Que Sera Sera.” Since “Lilly” has already been played, the odds of “Que Sera Sera” are 1/35, and the odds of “Lilly” and “Que Sera Sera” are 1/36 × 1/35, or 1/1,260. But of course, I would have also had my encore if the last two songs had been “Que Sera Sera” and then “Lilly.”Te odds of this hap- pening fgure out exactly the same—1/1,260. So the odds of my encore popping up—“Lilly” and “Que Sera Sera” or “Que Sera Sera” and “Lilly” are 1/1,260 + 1/1,260, or 1/630. Certainly, one thing that would explain that 1/630 shot coming up on the ride home is that my imagined encore was composed of my two favorite (and most listened to) Pink Martini songs, and the program was illegitimately tak- ing this into account in generating the “random” play order. But I hope it’s obvious bynow, it’s easy enough to think of lots of rival explanations. t 1 . This was just a true, 1/630 coincidence. t 2 . This is not a software glitch; the iPod soft- ware is designed to do exactly this. t 3 . The iPod software is illegitimately weigh- ing things, not by number of times played, but something else—length of the songs, where they occur in the album, and so on. t 4 . The philosopher set his iPod incorrectly. t 5 . The philosopher dozed in and out on the drive home and only thought that these two songs came up last. t 6 . The problem is in Johnson’s iPod—the hardware, not the software. My students have been worrying about what happened for the last several years on quizzes, ever since this really happened on a drive back from the Oregon League of Cities. Tey pretty generally rank the coincidence hypothesis as a much better explanation, though they are ofen surprised once they see the math that the odds are really 1/630. Tey also don’t seem to have too much confdence in their profes- sor, since explanations such as t 4 and t 5 are consistently ranked ahead of t 0 . So accord- ing to the inference-to-the-best-explanation recipe, these students are committed to saying that Johnson’s evidence for the glitch theory is pretty weak. Why Don’t You Just Test It? I’ve told you this little anecdote for two very diferent reasons. One, of course, is I wanted a little exercise that would allow you to apply the inference-to-the-best-explanation test from chapter 5 to an argument. Te other, though, is to tell you about a very common feature that my students have felt compelled to add to their dis- cussions. Tere is almost a sense of frustration or least the need to lecture their professor. Tey suggest, indeed insist on, a very simple test of the glitch hypothesis. Look, isn’t there an obvious way to settle this matter? Turn of the iPod, reset everything, play