Several of the comic strips that’ve been sent my way the past couple days touch on cultural neutrality in mathematics problems. People like to think of mathematics as a universal language, which makes me think of, for example, the quipu — twisted woolen cords with smaller cords tied to the main one — that Incans used to represent numbers. Even knowing the number one is supposed to represent doesn’t help me work out how to read the thing, and that’s not even doing calculations, just representing a number.
Darby Conley’s Get Fuzzy (February 1) uses several mathematics questions as part of a “general knowledge” quiz. Mathematics questions, particularly reasoning questions, are held up a good bit as examples of general knowledge since we’ve always cherished reasoning as a particularly precious sort of thinking, and because it’s easy to convince oneself that arithmetic and logic problems are culturally neutral. They’re not, but I would agree that “one times four” or the candy-counting problem are more culture-neutral than naming places with “-ham” or (to invent something not in the strip) identifying prime ministers of Canada would be. Really intriguing to me, though, is that Conley has Bucky Katt mention the Times as a newspaper without comics and the Daily News as one with: I had believed the strip to be set in or around Boston in the past, while this is pretty soundly a New York reference. Perhaps Conley’s let his daily comics lapse into reruns because he’s been moving, very slowly, across Connecticut?
Mac and Bill King’s Magic in a Minute (February 1) isn’t really a mathematics puzzle, but it does employ mathematical symbols in a way that I remember fondly from a bunch of “stories with holes” — superficially nonsensical problems which have logical resolutions if you can avoid being hobbled by implicit assumptions — so it’s really well-fitted for kids of the right age.
Dan Dougherty’s Beardo (February 2) is a substitue teacher this week, and apparently in mathematics. There is a good probability problem to be worked out from Groundhog Day, and the attempt to determine whether groundhogs are any good at forecasting the back half of winter. The first step is that you have to define whether a spring has come early, or whether winter’s lasted long, and this is a good, meaty problem. You have to find some way to measure the end of winter, presumably based on the available weather statistics — temperature on a given day? Snowfall totals? Snow on the ground? Last day below freezing of the year? Mean temperature? — and then work out whether that measure accurately matches what people mean by an “early spring” or “last winter”. Once that’s done and we’ve worked out a way to test whether a groundhog’s prediction is correct, we can go on to check records and see how often a groundhog is right or wrong, and get to the relatively simple, Intro-to-Probability question, of whether the groundhog is right, or wrong, significantly more often than chance.
Anthony Blades’s Bewley (February 2) has the best answer for what to do if you haven’t got your mathematics homework. Give it a try.
Brian Boychuk and Ron Boychuk’s The Chuckle Brothers (February 2) is a pun strip, playing on mathematics thanks to a familiar old phrase. I can’t help noticing on the board that while world-famous equation E = mc2 doesn’t appear, it’s clearly in the cartoonists’ minds.
Rick Detorie’s One Big Happy (February 2, rerun) brings back my comments about culture-neutral problems again, although I would think that tacos have been thoroughly assimilated into American English at least, and if enchiladas aren’t quite there yet, they’re close. Of course the problem doesn’t depend on tacos or enchiladas or anything; they’re just named because … well, probably because making the problem about tangible goods makes it easier to visualize, but the problem would be the same if the platters held nickels and pennies, or checkers and pawns, or any pairs of things. But visualization only helps if it’s something meaningful. If I posed the problem as “set A contains three times as many microcanonical ensembles as set B”, I don’t imagine that’s helped most of my readers’ mental picture of the situation much, and I might as well have claimed were counting the “glokznarian thurbwart”.
Morrie Turner’s Wee Pals (February 2, rerun) depicts Mikki coming to grips with the discovery there are many pairs of numbers that add up to ten. I don’t remember encountering that difficulty when I was a kid, but, counting the number of ways to add up to a given number is called the problem of partitioning. For a problem that starts so simply it’s surprisingly fruitful; many problems are easy to understand but difficult to solve. For the record there are 42 distinct ways to add (positive) numbers up to 10, and go ahead and guess how many it takes to add up to 11 or 12. And if fiddling with the pure numbers bores you, you can make Tetris-block renditions of the partitions of a number, and create your own set of polyomino to play with.
Zach Weinersmith’s Saturday Morning Breakfast Cereal (February 3) mentions the Erdös Number, which is one of those bits of amusing mathematician fun. Paul Erdös, 1913 – 1996, was a remarkably prolific and nomadic mathematician, who worked a lot in set theory, number theory (the sort of thing that involves partitions), graph theory and probability. Erdös spent most of his life moving from conference to conference, staying with colleagues, and co-authoring papers with a striking number of them; Wikipedia credits him with 1,525 articles and 511 distinct collaborators. This led to the folklore of the Erdös Number: how many co-author links it takes to get to Paul Erdös. Erdös himself has number 0, of course; his co-authors have number 1. People who co-authored something with someone who wrote with Erdös have number 2. People who co-authored something with a person who co-authored something who co-authored something with Erdös have number 3, and so on.
If this strikes you as being pretty much Six Degrees Of Kevin Bacon but for Mathematicians, yes, you’re correct, although since the Erdös Number came first, it would be more historically proper to say Six Degrees Of Kevin Bacon is just the Erdös Number but for people anybody ever heard of. And since there are actors who are also mathematicians, yes, there are people who have both Erdös Numbers and Bacon Number, including Natalie Portman (Taffy Dale in the movie Mars Attacks), Mayim Bialik (Dr Fowler on The Big Bang Theory), and Danica McKellar (Winnie, from The Wonder Years). I imagine it is also possible for men to act and publish mathematics papers.
Of this bunch I think Bewley is the best strip: it nice and funny and should be a big help to anyone with mathematics, or other work, due.