Reading the Comics, February 11, 2016: Apples And Pointing Things Out Edition


I didn’t expect quite so many mathematically themed comic strips so soon after the last round. Most of them just highlight one or another familiar joke. So this edition is mostly just noting that yeah, the joke is there and has been successfully made. There’s an exception, though. Enjoy.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 7th of February is a cute chart. It’s got an unusual label to the x-axis. Now that I’ve seen it, I’m surprised not to see more jokes constructed this way.

Ruben Bolling’s Super-Fun-Pak Comix for the 7th of February was this essay’s Schrödinger’s Cat mention. I’m considering putting a moratorium on Schrödinger’s Cat strips, at least for a little while. I need to find something fresh to say about them.

Russell Myers’s Broom Hilda for the 8th of February inspires a Fermi problem. These are named for the great physicist Enrico Fermi, who often asked problems of estimation and order of magnitude. Given a few pieces of information, can you say about how big something might be? In this case, how many hours of work are spent peeling labels off grocery store apples? If we had the right information it would be easy to answer. How long does the average label take to peel off? How many apples get peeled each year? I admit not knowing either offhand. I would guess the average label-peeling time to be under five seconds, but if I wanted to be exact I’d get a bag, a stopwatch, and a sheet of paper for notes.

How many apples get peeled each year? That’s tougher. We might be able to get the total number of apples sold. But not every apple is sold with a label on it. A bag of apples doesn’t need individual labels, after all. But we might estimate what fraction of apples are sold loose and thus with labels by looking in local supermarkets. That requires assuming the turnover of apple stock is about the same whether the apple’s labelled or unlabelled. It also assumes our local supermarket is representative of the whole nation’s. But if we’re just looking for an idea of how big the number should be, or if we’re looking for what further information we have to determine, that’s good enough.

Wikipedia says the United States produced 4,100,046 metric tons of apples in 2012, the last year they have records for. If an apple is about a fifth of a kilogram, then, that implies something like 2,050,230,000 apples got sold in the United States that year. Let’s guess that three-quarters of them go right to industrial uses, into the hands of the Apple Pie Trusts and other corporate uses that don’t need labelling, while the remaining quarter go to consumers. That’s a wild guess on my part, but, industry is big. And of those, I’ll guess two-fifths get sold individually, with labels on. The rest can be sold in bags or whatnot. I’m basing that on what I kind of remember from my last trip to the farmer’s market with the free coffee bar and the bag-your-own candies.

So this implies something like 205,023,000 apples could be sold with labels. And if each label takes an average of five seconds, then this implies a total of 17,085,250 minutes spent unpeeling apple labels. That sounds like a big number, but it’s really only over 284,754 hours, or not quite 11,865 days. Of course, divided up among all the apple-eaters it’s not so much per year.

My number is wrong. I picked important bits of information out of thin air. But if I want to be more precise, I have an idea of what I need to learn. And I have an idea of how big I should expect the right answer to be. I can go from this to a better estimate, if I think now it’s worth being more exact.

Stephan Pastis’s Pearls Before Swine tries picking a fight with mathematicians on the 8th of February, with Rat boasting how he’s never used algebra. I’m not sure why bragging about not using algebra is supposed to be funny. The strip says it’s cathartic. I suppose. But it’s a joke that’s been told many times over and this doesn’t feel like a fresh use.

Rick Stromoski’s Soup To Nutz for the 8th of February is a fractions joke. Royboy perceives a difference between one-half of an orange and four-eighths of an orange. I can’t say there isn’t a difference in connotation between the two representations.

Percy Crosby’s Skippy for the 9th of February (a rerun from sometime 1928) shows Sookie with a ball. Well, a ball with a hole in it. A topologist would agree. If you’re interested in how the points on, or inside, an object connect to each other then a hoop like this is the same as a ball with a hole through it or a doughnut or bagel. This is my favorite for this group, because of the wonderful convergence of kid logic and serious mathematics.

Larry Wright’s Motley Classics for the 10th of February (a rerun from that date in 1988) is a joke about the terrors of word problems. I’m not convinced an authentic child would have trouble adding up all those cookies.

Hector D Cantu and Carlos Castellanos’s Baldo for the 11th of February reveals they have a week’s more lead time than most of the comics on the page.

Reading the Comics, December 2, 2015: The Art Of Maths Edition


Bill Amend’s FoxTrot Classics for the 28th of November (originally run in 2004) depicts a “Christmas Card For Smart People”. It uses the familiar motif of “ability to do arithmetic” as denoting smartness. The key to the first word is remembering that mathematicians use the symbol ‘e’ to represent a number that’s just a little over 2.71828. We call the number ‘e’, or something ‘the base of the natural logarithm’. It turns up all over the place. If you have almost any quantity that grows or that shrinks at a speed proportional to how much there is, and describe how much of stuff there is over time, you’ll find an ‘e’. Leonhard Euler, who’s renowned for major advances in every field of mathematics, is also renowned for major advances in notation in physics, and he gave us ‘e’ for that number.

The key to the second word there is remembering from physics that force equals mass times acceleration. Therefore the force divided by the acceleration is …

And so that inspires this essay’s edition title. There are several comics in this selection that are about the symbols or the representations of mathematics, and that touch on the subject as a visual art.

Matt Janz’s Out of the Gene Pool for the 28th of November first ran the 26th of October, 2002. It would make for a good word problem, too, with a couple of levels: given the constraints of (a slightly looser) budget, how do they get the greatest number of cookies? Or if some cookies are better than others, how do they get the most enjoyment from their cookie purchase? Working out the greatest amount of enjoyment within a given cookie budget, with different qualities of cookies, can be a good introduction to optimization problems and how subtle they can be.

Bill Holbrook’s On The Fastrack for the 29th of November speaks in support of accounting. It’s a worthwhile message. It doesn’t get much respect, not from the general public, and not from typical mathematics department. The general public maybe thinks of accounting as not much more than a way companies nickel-and-dime them. If the mathematics departments I’ve associated with are fair representatives, accounting isn’t even thought of except by the assistant professor doing a seminar on financial mathematics. (And I’m not sure accounting gets mentioned there, since there’s exciting stuff about the Black-Scholes Equation and options markets to think about instead.) This despite that accounting is probably, by volume, the most used part of mathematics. Anyway, Holbrook’s strip probably won’t get the field a better reputation. But it has got some great illustrations of doing things with numbers. The folks in mathematics departments certainly have had days feeling like they’ve done each of these things.

Fanciful representations of accounting: pulling numbers out of magic hats, wrangling numbers out of a herd, fixing up the interior of a number as if a car's engine, that sort of thing. Dethany respects Fi's abilities the more she sees them.
Bill Holbrook’s On The Fastrack for the 29th of November, 2015. While the strip’s focus is accountants, it is true that most mathematicians will spend hours overhauling their 6’s.

Dave Coverly’s Speed Bump for the 30th of November is a compound interest joke. I admit I’ve told this sort of joke myself, proposing that the hour cut out of the day in spring when Daylight Saving Time starts comes back as a healthy hour and three minutes in autumn when it’s taken out of saving. If I can get the delivery right I might have someone going for that three minutes.

Mikael Wulff and Anders Morgenthaler’s Truth Facts for the 30th of November is a Venn diagram joke for breakfast. I would bet they’re kicking themselves for not making the intersection be the holes in the center.

Mark Anderson’s Andertoons for this week interests me. It uses a figure to try explaining how to relate gallon and quart an pint and other units relate to each other. I like it, but I’m embarrassed to say how long it took in my life to work out the relations between pints, quarts, gallons, and particularly whether the quart or the pint was the larger unit. I blame part of that on my never really having to mix a pint of something with a quart of something else, which ought to have sorted that out. Anyway, let’s always cherish good representations of information. Good representations organize information and relationships in ways that are easy to remember, or easy to reconstruct or extend.

John Graziano’s Ripley’s Believe It or Not for the 2nd of December tries to visualize how many ways there are to arrange a Rubik’s Cube. Counting off permutations of things by how many seconds it’d take to get through them all is a common game. The key to producing a staggering length of time is that it one billion seconds are nearly 32 years, and the number of combinations of things adds up really really fast. There’s over eight billion ways to draw seven letters in a row, after all, if every letter is equally likely and if you don’t limit yourself to real or even imaginable words. Rubik’s Cubes have a lot of potential arrangements. Graziano misspells Rubik, but I have to double-check and make sure I’ve got it right every time myself. I didn’t know that about the pigeons.

Charles Schulz’s Peanuts for the 2nd of December (originally run in 1968) has Peppermint Patty reflecting on the beauty of numbers. I don’t think it’s unusual to find some numbers particularly pleasant and others not. Some numbers are easy to work with; if I’m trying to add up a set of numbers and I have a 3, I look instinctively for a 7 because of how nice 10 is. If I’m trying to multiply numbers, I’d so like to multiply by a 5 or a 25 than by a 7 or an 18. Typically, people find they do better on addition and multiplication with lower numbers like two and three, and get shaky with sevens and eights and such. It may be quirky. My love is a wizard with 7’s, but can’t do a thing with 8. But it’s no more irrational than the way a person might a pyramid attractive but a sphere boring and a stellated icosahedron ugly.

I’ve seen some comments suggesting that Peppermint Patty is talking about numerals, that is, the way we represent numbers. That she might find the shape of the 2 gentle, while 5 looks hostile. (I can imagine turning a 5 into a drawing of a shouting person with a few pencil strokes.) But she doesn’t seem to say one way or another. She might see a page of numbers as visual art; she might see them as wonderful things with which to play.