I’m sorry to have fallen behind on my mathematics-comics posts, but I’ve been very busy wielding a cudgel at Microsoft IIS all week in the service of my day job. And since I telecommute it’s quite hard to convincingly threaten the server, however much it deserves it. Sorry. Comic Strip Master Command decided to send me three hundred billion gazillion strips, too, so this is going to be a bit of a long post.
Jenny Campbell’s Flo and Friends (January 19) is almost a perfect example of the use of calculus as a signifier of “something really intelligent people think of”. Which is flattening to mathematicians, certainly, although I worry that attitude does make people freeze up in panic when they hear that they have to take calculus.
The Amazing Yet Tautological feature of Ruben Bolling’s Super-Fun-Pak Comix (January 19) lives up to its title, at least provided we are all in agreement about what “average” means. From context this seems to be the arithmetic mean — that’s usually what people, mathematicians included mean by “average” if they don’t specify otherwise — although you can produce logical mischief by slipping in an alternate average, such as the “median” — the amount that half the results are less than and half are greater than — or the “mode” — the most common result. There are other averages too, but they’re not so often useful. On the 21st Super-Fun-Pak Comix returned with another installation of Chaos Butterfly, by the way.
Griffinetsabine wrote a couple of Eric the Circle strips, first for the 20th of January, and then for the 24th, at the Shape Singles Bar. It’s room for a couple of mathematics-themed puns, which come pretty close to that of Dave Blazek’s Loose Parts for the 21st of January. There’s a certain kind of mind that can’t resist playing on “acute” for “a cute” and I choose not to judge them.
John Zakour and Scott Roberts’s Maria’s Day has been resisting mathematics problems lately, with right triangles appearing on the 20th and then travel time problems on the 22nd.
Harley Schwadron’s 9 to 5 (January 21) does the obvious gag about the position of the statistics department. You may wonder why it is surveys seem to always have a margin of error of plus or minus four percent. When you sample something, you’re taking a couple measurements of some bigger, more complicated thing, and trusting that, say, the average from your sample is going to be about the average of the population. Unless you’re very unlucky, your average from the sample shouldn’t be very far from the average of the population. Most things that you might measure are spread out around their average in a pattern called the Gaussian distribution, and how common that is gets shown by that distribution’s alternate name of the “normal distribution”.
If we suppose the sample fairly reflects the original population, then, we can tell how much the values of whatever we’re measuring are spread out. And we can conclude the chance that the thing we really want, the population’s average, is inside some particular range of values. The broader that range, the higher the chance we’re right, but the broader the range the less interesting the result is. (It tells us nothing useful to say one candidate is favored by 65 percent plus or minus 50 percent of the public, even if we can be 99.999 percent sure we’re right.) By taking a bigger sample we can narrow down the range that we’re, say, 95 percent sure the actual value has to be within, although taking a bigger sample takes more time and work and there is a deadline to meet and a budget that’s not big enough for all this. For public-opinion type surveys, a 95 percent chance of being within three or four percentage points of the right answer represents a good compromise: it’s a tight enough range to be interesting, likely enough to be right to be convincing, and not so hard to run that you can’t run the survey in a reasonable time. And it doesn’t matter much what’s being surveyed and not at all how big the population is; the same factors apply, so you see these error bars of three or four percent all over the place.
Bill Watterson’s Calvin and Hobbes (January 21) is built around the names for enormously large numbers. The word “million” dates in English and French back to the late 1300s; billion and trillion took another couple centuries to get sorted out but by the 15th century Nicholas Chuquet had a pretty neatly organized system of billion, trillion, quadrillion, and so on, and despite some disagreements about whether “billion” should be “a thousand million” or “a million million”, the system has come down to us pretty much as late 15th-century French mathematicians would understand. A handful of exceptional numbers, like the googol and the googolplex, have gotten special names, but as novelty acts and as shorthand ways to express “a really huge number”.
Patrick Roberts has Todd the Dinosaur get teased (on January 22) with the prospect of good mathematics grades letting him become an accountant. That’s not by itself a bad fate — Arthur C Clarke and Bob Newhart were both accountants, although I can’t say they made their marks on history as such, what with their attitudes of “that’s probably close enough” — but Todd points out how you can make any job more than it already is.
Greg Cravens’s The Buckets (January 22) shows Toby fantasizing about a job he figures involves no mathematics skills: overbooking airline flights. But this is a real application of statistics and optimization. The airline’s problem is that empty seats on an airplane are lost money, and airlines don’t really have the money to lose. A certain number of people who buy flights are going to not take them, for one reason or another, so it’s absurd to fly empty seats if you could just sell them to passengers who make it. But you can’t overbook too much or you have quite correctly angry customers to deal with, and dealing with them costs money too.
The principle applies broadly: it’s wasteful to have more of anything than is actually needed at the moment, but it can be disastrous to have too little of it when needed. Thus the need to balance how many roads to build, how many check-out aisles to have staffed at the moment, how much cash to keep in the ATM, how much insurance to have for your venture. There’s important mathematics skills involved in selling too many airplane seats.
Dave Whamond’s Reality Check (January 23) is about one of the real-world uses for mathematics later in life. I sympathize.
Scott Adams’s Dilbert (January 24) shows the “one out of ten” guy, the one person in ten who has some particular problem and who suffers from the impression that his being in a group keeps nine other people safe. And Dilbert’s correct; it doesn’t work like that. If something has a one-in-ten chance of happening and there are ten chances for it to happen, then yes, it’s most likely that it’ll turn up once. But if you include one instance of the thing happening and nine cases where something has a one-in-ten chance of happening, then, you’re most likely to see 1.9 cases of it, which I’d round off to two.
It also brings to mind the story of the guy who was obsessed with the idea of there being a bomb on his plane flight, and while the chance of a bomb on a flight was tiny it wasn’t tiny enough. So he brought his own bomb on the plane, confident that the chance of two bombs on a flight was far too small to worry about.
Of the strips, I think that the Amazing Yet Tautological and the Calvin and Hobbes were the funniest, and you can see which strip gave me the most to think about.