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, November 27, 2015: 30,000 Edition


By rights, if this installment has any title it should be “confident ignorance”. That state appears in many of the strips I want to talk about. But according to WordPress, my little mathematics blog here reached its 30,000th page view at long last. This is thanks largely to spillover from The Onion AV Club discovering my humor blog and its talk about the late comic strip Apartment 3-G. But a reader is a reader. And I want to celebrate reaching that big, round number. As I write this I’m at 30,162 page views, because there were a lot of AV Club-related readers.

Bob Weber Jr’s Slylock Fox for the 23rd of November maybe shouldn’t really be here. It’s just a puzzle game that depends on the reader remembering that two rectangles put against the other can be a rectangle again. It also requires deciding whether the frame of the artwork counts as one of the rectangles. The commenters at Comics Kingdom seem unsure whether to count squares as rectangles too. I don’t see any shapes that look more clearly like squares to me. But it’s late in the month and I haven’t had anything with visual appeal in these Reading the Comics installments in a while. Later we can wonder if “counting rectangles in a painting” is the most reasonable way a secret agent has to pass on a number. It reminds me of many, many puzzle mysteries Isaac Asimov wrote that were all about complicated ways secret agents could pass one bit of information on.

'The painting (of interlocking rectangles) is really a secret message left by an informant. It reveals the address of a house where stolen artwork is being stashed. The title, Riverside, is the street name, and the total amount of rectangles is the house number. Where will Slylock Fox find the stolen artwork?
Bob Weber Jr’s Slylock Fox for the 23rd of November, 2015. I suppose the artist is lucky they weren’t hiding out at number 38, or she wouldn’t have been able to make such a compellingly symmetric diagram.

Ryan North’s Dinosaur Comics for the 23rd of November is a rerun from goodness knows when it first ran on Quantz.com. It features T Rex thinking about the Turing Test. The test, named for Alan Turing, says that while we may not know what exactly makes up an artificial intelligence, we will know it when we see it. That is the sort of confident ignorance that earned Socrates a living. (I joke. Actually, Socrates was a stonecutter. Who knew, besides the entire philosophy department?) But the idea seems hard to dispute. If we can converse with an entity in such a way that we can’t tell it isn’t human, then, what grounds do we have for saying it isn’t human?

T Rex has an idea that the philosophy department had long ago, of course. That’s to simply “be ready for any possible opening with a reasonable conclusion”. He calls this a matter of brute force. That is, sometimes, a reasonable way to solve problems. It’s got a long and honorable history of use in mathematics. The name suggests some disapproval; it sounds like the way you get a new washing machine through a too-small set of doors. But sometimes the easiest way to find an answer is to just try all the possible outcomes until you find the ones that work, or show that nothing can. If I want to know whether 319 is a prime number, I can try reasoning my way through it. Or I can divide it by all the prime numbers from 2 up to 17. (The square root of 319 is a bit under 18.) Or I could look it up in a table someone already made of the prime numbers less than 400. I know what’s easier, if I have a table already.

The problem with brute force — well, one problem — is that it can be longwinded. We have to break the problem down into each possible different case. Even if each case is easily disposed of, the number of different cases can grow far too fast to be manageable. The amount of working time required, and the amount of storage required, can easily become too much to deal with. Mathematicians, and computer scientists, have a couple approaches for this. One is getting bigger computers with more memory. We might consider this the brute force method to solving the limits of brute force methods.

Or we might try to reduce the number of possible cases, so that less work is needed. Perhaps we can find a line of reasoning that covers many cases. Working out specific cases, as brute force requires, can often give us a hint to what a general proof would look like. Or we can at least get a bunch of cases dealt with, even if we can’t get them all done.

Jim Unger’s Herman rerun for the 23rd of November turns confident ignorance into a running theme for this essay’s comic strips.

Eric Teitelbaum and Bill Teitelbaum’s Bottomliners for the 24th of November has a similar confient ignorance. This time it’s of the orders of magnitude that separate billions from trillions. I wanted to try passing off some line about how there can be contexts where it doesn’t much matter whether a billion or a trillion is at stake. But I can’t think of one that makes sense for the Man At The Business Company Office setting.

Reza Farazmand’s Poorly Drawn Lines for the 25th of November is built on the same confusion about the orders of magnitude that Bottomliners is. In this case it’s ants that aren’t sure about how big millions are, so their confusion seems more natural.

The ants are also engaged in a fun sort of recreational mathematics: can you estimate something from little information? You’ve done that right, typically, if you get the size of the number about right. That it should be millions rather than thousands or hundreds of millions; that there should be something like ten rather than ten thousand. These kinds of problems are often called Fermi Problems, after Enrico Fermi. This is the same person the Fermi Paradox is named after, but that’s a different problem. The Fermi Paradox asks if there are extraterrestrial aliens, why we don’t see evidence of them. A Fermi Problem is simpler. Its the iconic example is, “how many professional piano tuners are there in New York?” It’s easy to look up how big is the population of New York. It’s possible to estimate how many pianos there should be for a population that size. Then you can guess how often a piano needs tuning, and therefore, how many full-time piano tuners would be supported by that much piano-tuning demand. And there’s probably not many more professional piano tuners than there’s demand for. (Wikipedia uses Chicago as the example city for this, and asserts the population of Chicago to be nine million people. I will suppose this to be the Chicago metropolitan region, but that still seems high. Wikipedia says that is the rough population of the Chicago metropolitan area, but it’s got a vested interest in saying so.)

Mark Anderson’s Andertoons finally appears on the 27th. Here we combine the rational division of labor with resisting mathematics problems.