Reading the Comics, February 15, 2017: SMBC Cuts In Line Edition
It’s another busy enough week for mathematically-themed comic strips that I’m dividing the harvest in two. There’s a natural cutting point since there weren’t any comics I could call relevant for the 15th. But I’m moving a Saturday Morning Breakfast Cereal of course from the 16th into this pile. That’s because there’s another Saturday Morning Breakfast Cereal of course from after the 16th that I might include. I’m still deciding if it’s close enough to on topic. We’ll see.
John Graziano’s Ripley’s Believe It Or Not for the 12th mentions the “Futurama Theorem”. The trivia is true, in that writer Ken Keeler did create a theorem for a body-swap plot he had going. The premise was that any two bodies could swap minds at most one time. So, after a couple people had swapped bodies, was there any way to get everyone back to their correct original body? There is, if you bring two more people in to the body-swapping party. It’s clever.
From reading comment threads about the episode I conclude people are really awestruck by the idea of creating a theorem for a TV show episode. The thing is that “a theorem” isn’t necessarily a mind-boggling piece of work. It’s just the name mathematicians give when we have a clearly-defined logical problem and its solution. A theorem and its proof can be a mind-wrenching bit of work, like Fermat’s Last Theorem or the Four-Color Map Theorem are. Or it can be on the verge of obvious. Keeler’s proof isn’t on the obvious side of things. But it is the reasoning one would have to do to solve the body-swap problem the episode posited without cheating. Logic and good story-telling are, as often, good partners.
Teresa Burritt’s Frog Applause is a Dadaist nonsense strip. But for the 13th it hit across some legitimate words, about a 14 percent false-positive rate. This is something run across in hypothesis testing. The hypothesis is something like “is whatever we’re measuring so much above (or so far below) the average that it’s not plausibly just luck?” A false positive is what it sounds like: our analysis said yes, this can’t just be luck, and it turns out that it was. This turns up most notoriously in medical screenings, when we want to know if there’s reason to suspect a health risk, and in forensic analysis, when we want to know if a particular person can be shown to have been a particular place at a particular time. A 14 percent false positive rate doesn’t sound very good — except.
Suppose we are looking for a rare condition. Say, something one person out of 500 will have. A test that’s 99 percent accurate will turn up positives for the one person who has got it and for five of the people who haven’t. It’s not that the test is bad; it’s just there are so many negatives to work through. If you can screen out a good number of the negatives, though, the people who haven’t got the condition, then the good test will turn up fewer false positives. So suppose you have a cheap or easy or quick test that doesn’t miss any true positives but does have a 14 percent false positive rate. That would screen out 430 of the people who haven’t got whatever we’re testing for, leaving only 71 people who need the 99-percent-accurate test. This can make for a more effective use of resources.
Gary Wise and Lance Aldrich’s Real Life Adventures for the 13th is an algebra-in-real-life joke and I can’t make something deeper out of that.
Mike Shiell’s The Wandering Melon for the 13th is a spot of wordplay built around statisticians. Good for taping to the mathematics teacher’s walls.
Eric the Circle for the 14th, this one by “zapaway”, is another bit of wordplay. Tans and tangents.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 16th identifies, aptly, a difference between scientists and science fans. Weinersmith is right that loving trivia is a hallmark of a fan. Expertise — in any field, not just science — is more about recognizing patterns of problems and concepts, ways to bring approaches from one field into another, this sort of thing. And the digits of π are great examples of trivia. There’s no need for anyone to know the 1,681st digit of π. There’s few calculations you could ever do when you needed more than three dozen digits. But if memorizing digits seems like fun then π is a great set to learn. e is the only other number at all compelling.
The thing is, it’s very hard to become an expert in something without first being a fan of it. It’s possible, but if a field doesn’t delight you why would you put that much work into it? So even though the scientist might have long since gotten past caring how many digits of π, it’s awfully hard to get something memorized in the flush of fandom out of your head.
I know you’re curious. I can only remember π out to 3.14158926535787962. I might have gotten farther if I’d tried, but I actually got a digit wrong, inserting a ‘3’ before that last ’62’, and the effort to get that mistake out of my head obliterated any desire to waste more time memorizing digits. For e I can only give you 2.718281828. But there’s almost no hope I’d know that far if it weren’t for how e happens to repeat that 1828 stanza right away.