## Reading the Comics, May 18, 2018: Quincy Doesn’t Make The Cut Edition

I hate to disillusion anyone but I lack hard rules about what qualifies as a mathematically-themed comic strip. During a slow week, more marginal stuff makes it. This past week was going slow enough that I tagged Wednesday’s Quincy rerun, from March of 1979 for possible inclusion. And all it does is mention that Quincy’s got a mathematics test due. Fortunately for me the week picked up a little. It cheats me of an excuse to point out Ted Shearer’s art style to people, but that’s not really my blog’s business.

Also it may not surprise you but since I’ve decided I need to include GoComics images I’ve gotten more restrictive. Somehow the bit of work it takes to think of a caption and to describe the text and images of a comic strip feel like that much extra work.

Roy Schneider’s The Humble Stumble for the 13th of May is a logic/geometry puzzle. Is it relevant enough for here? Well, I spent some time working it out. And some time wondering about implicit instructions. Like, if the challenge is to have exactly four equally-sized boxes after two toothpicks are moved, can we have extra stuff? Can we put a toothpick where it’s just a stray edge, part of no particular shape? I can’t speak to how long you stay interested in this sort of puzzle. But you can have some good fun rules-lawyering it.

Jeff Harris’s Shortcuts for the 13th is a children’s informational feature about Aristotle. Aristotle is renowned for his mathematical accomplishments by many people who’ve got him mixed up with Archimedes. Aristotle it’s harder to say much about. He did write great texts that pop-science writers credit as giving us the great ideas about nature and physics and chemistry that the Enlightenment was able to correct in only about 175 years of trying. His mathematics is harder to summarize though. We can say certainly that he knew some mathematics. And that he encouraged thinking of subjects as built on logical deductions from axioms and definitions. So there is that influence.

Dan Thompson’s Brevity for the 15th is a pun, built on the bell curve. This is also known as the Gaussian distribution or the normal distribution. It turns up everywhere. If you plot how likely a particular value is to turn up, you get a shape that looks like a slightly melted bell. In principle the bell curve stretches out infinitely far. In practice, the curve turns into a horizontal line so close to zero you can’t see the difference once you’re not-too-far away from the peak.

Jason Chatfield’s Ginger Meggs for the 16th I assume takes place in a mathematics class. I’m assuming the question is adding together four two-digit numbers. But “what are 26, 24, 33, and 32” seems like it should be open to other interpretations. Perhaps Mr Canehard was asking for some class of numbers those all fit into. Integers, obviously. Counting numbers. Compound numbers rather than primes. I keep wanting to say there’s something deeper, like they’re all multiples of three (or something) but they aren’t. They haven’t got any factors other than 1 in common. I mention this because I’d love to figure out what interesting commonality those numbers have and which I’m overlooking.

Ed Stein’s Freshly Squeezed for the 17th is a story problem strip. Bit of a passive-aggressive one, in-universe. But I understand why it would be formed like that. The problem’s incomplete, as stated. There could be some fun in figuring out what extra bits of information one would need to give an answer. This is another new-tagged comic.

Henry Scarpelli and Craig Boldman’s Archie for the 19th name-drops calculus, credibly, as something high schoolers would be amazed to see one of their own do in their heads. There’s not anything on the blackboard that’s iconically calculus, it happens. Dilton’s writing out a polynomial, more or less, and that’s a fit subject for high school calculus. They’re good examples on which to learn differentiation and integration. They’re a little more complicated than straight lines, but not too weird or abstract. And they follow nice, easy-to-summarize rules. But they turn up in high school algebra too, and can fit into geometry easily. Or any subject, really, as remember, everything is polynomials.

Mark Anderson’s Andertoons for the 19th is Mark Anderson’s Andertoons for the week. Glad that it’s there. Let me explain why it is proper construction of a joke that a Fibonacci Division might be represented with a spiral. Fibonacci’s the name we give to Leonardo of Pisa, who lived in the first half of the 13th century. He’s most important for explaining to the western world why these Hindu-Arabic numerals were worth learning. But his pop-cultural presence owes to the Fibonacci Sequence, the sequence of numbers 1, 1, 2, 3, 5, 8, and so on. Each number’s the sum of the two before it. And this connects to the Golden Ratio, one of pop mathematics’ most popular humbugs. As the terms get bigger and bigger, the ratio between a term and the one before it gets really close to the Golden Ratio, a bit over 1.618.

So. Draw a quarter-circle that connects the opposite corners of a 1×1 square. Connect that to a quarter-circle that connects opposite corners of a 2×2 square. Connect that to a quarter-circle connecting opposite corners of a 3×3 square. And a 5×5 square, and an 8×8 square, and a 13×13 square, and a 21×21 square, and so on. Yes, there are ambiguities in the way I’ve described this. I’ve tried explaining how to do things just right. It makes a heap of boring words and I’m trying to reduce how many of those I write. But if you do it the way I want, guess what shape you have?

And that is why this is a correctly-formed joke about the Fibonacci Division.

## Reading the Comics, May 12, 2018: New Nancy Artist Edition

And now, closer to deadline than I like, let me wrap up last week’s mathematically-themed comic strips. I had a lot happening, that’s all I can say.

Glenn McCoy and Gary McCoy’s The Flying McCoys for the 10th is another tragic moment in the mathematics department. I’m amused that white lab coats are taken to read as “mathematician”. There are mathematicians who work in laboratories, naturally. Many interesting problems are about real-world things that can be modelled and tested and played with. It’s hardly the mathematics-department uniform, but then, I’m not sure mathematicians have a uniform. We just look like academics is all.

It also shows off that motif of mathematicians as doing anything with numbers in a more complicated way than necessary. I can’t imagine anyone in an emergency trying to evoke 9-1-1 by solving any kind of puzzle. But comic strip characters are expected to do things at least a bit ridiculously. I suppose.

Mark Litzler’s Joe Vanilla for the 11th is about random numbers. We need random numbers; they do so much good. Getting them is hard. People are pretty lousy at picking random numbers in their head. We can say what “lousy” random numbers look like. They look wrong. There’s digits that don’t get used as much as the others do. There’s strings of digits that don’t get used as much as other strings of the same length do. There are patterns, and they can be subtle ones, that just don’t look right.

And yet we have a terrible time trying to say what good random numbers look like. Suppose we want to have a string of random zeroes and ones: is 101010 better or worse than 110101? Or 000111? Well, for a string of digits that short there’s no telling. It’s in big batches that we should expect to see no big patterns. … Except that occasionally randomness should produce patterns. How often should we expect patterns, and of what size? This seems to depend on what patterns we’ve found interesting enough to look for. But how can the cultural quirks that make something seem interesting be a substantial mathematical property?

Olivia Jaimes’s Nancy for the 11th uses mathematics-assessment tests for its joke. It’s of marginal relevance, yes, but it does give me a decent pretext to include the new artist’s work here. I don’t know how long the Internet is going to be interested in Nancy. I have to get what attention I can while it lasts.

Scott Hilburn’s The Argyle Sweater for the 12th is the anthropomorphic-geometry joke for the week. Unless there was one I already did Sunday that I already forgot. Oh, no, that was anthropomorphic-numerals. It’s easy to see why a circle might be labelled irrational: either its radius or its area has to be. Both can be. The triangle, though …

Well, that’s got me thinking. Obviously all the sides of a triangle can be rational, and so its perimeter can be too. But … the area of an equilateral triangle is $\frac{1}{2}\sqrt{3}$ times the square of the length of any side. It can have a rational side and an irrational area, or vice-versa. Just as the circle has. If it’s not an equilateral triangle?

Can you have a triangle that has three rational sides and a rational area? And yes, you can. Take the right triangle that has sides of length 5, 12, and 13. Or any scaling of that, larger or smaller. There is indeed a whole family of triangles, the Heronian Triangles. All their sides are integers, and their areas are integers too. (Sides and areas rational are just as good as sides and areas integers. If you don’t see why, now you see why.) So there’s that at least. The name derives from Heron/Hero, the ancient Greek mathematician whom we credit with that snappy formula that tells us, based on the lengths of the three sides, what the area of the triangle is. Not the Pythagorean formula, although you can get the Pythagorean formula from it.

Still, I’m going to bet that there’s some key measure of even a Heronian Triangle that ends up being irrational. Interior angles, most likely. And there are many ways to measure triangles; they can’t all end up being rational at once. There are over two thousand ways to define a “center” of a triangle, for example. The odds of hitting a rational number on all of them at once? (Granted, most of these triangle centers are unknown except to the center’s discoverer/definer and that discoverer’s proud but baffled parents.)

Carla Ventresca and Henry Beckett’s On A Claire Day for the 12th mentions taking classes in probability and statistics. They’re the classes nobody doubts are useful in the real world. It’s easy to figure probability is more likely to be needed than functional analysis on some ordinary day outside the university. I can’t even compose that last sentence without the language of probability.

I’d kind of agree with calling the courses intense, though. Well, “intense” might not be the right word. But challenging. Not that you’re asked to prove anything deep. The opposite, really. An introductory course in either provides a lot of tools. Many of them require no harder arithmetic work than multiplication, division, and the occasional square root. But you do need to learn which tool to use in which scenario. And there’s often not the sorts of proofs that make it easy to understand which tool does what. Doing the proofs would require too much fussing around. Many of them demand settling finicky little technical points that take you far from the original questions. But that leaves the course as this archipelago of small subjects, each easy in themselves. But the connections between them are obscured. Is that better or worse? It must depend on the person hoping to learn.

## Reading the Comics, May 5, 2018: Does Anyone Know Where The Infinite Hotel Comes From Edition

With a light load of mathematically-themed comic strips I’m going to have to think of things to write about twice this coming week. Fortunately, I have plans. We’ll see how that works out for me. So far this year I’m running about one-for-eight on my plans.

Mort Walker and Dik Browne’s Hi and Lois for the 1st of November, 1960 looks pretty familiar somehow. Having noticed what might be the first appearance of “the answer is twelve?” in Peanuts I’m curious why Chip started out by guessing twelve. Probably just coincidence. Possibly that twelve is just big enough to sound mathematical without being conspicuously funny, like 23 or 37 or 42 might be. I’m a bit curious that after the first guess Sally looked for smaller numbers than twelve, while Chip (mostly) looked for larger ones. And I see a logic in going from a first guess of 12 to a second guess of either 4 or 144. The 32 is a weird one.

Tom Toles’s Randolph Itch, 2 am for the 30th of April, 2018 is on at least its third appearance around here. I suppose I have to retire the strip from consideration for these comics roundups. It didn’t run that long, sad to say, and I think I’ve featured all its mathematical strips. I’ll go on reading, though, as I like the style and Toles’s sense of humor.

John McNamee’s Pie Comic for the 4th of May riffs on some ancient story-problems built on infinite sets. I don’t know the original source. I assume a Martin Gardiner pop-mathematics essay. I don’t know, though, and I’m curious if anyone does know.

Often I see these kinds of problem as set at the Hilbert Hotel. This references David Hilbert, the late-19th/early-20th century mastermind behind the 20th century’s mathematics field. They try to challenge people’s intuitions about infinitely large sets. Ponder a hotel with one room for each of the counting numbers. Suppose it’s full. How many guests can you add to it? Can you add infinitely many more guests, and still have room for them all? If you do it right, and if “infinitely many more guests” means something particular, yes. If certain practical points don’t get in the way. I mean practical for a hotel with infinitely many rooms.

This is a new-tag comic.

Dave Whamond’s Reality Check for the 4th is a riff on Albert Einstein’s best-known equation. He had some other work, granted. But who didn’t?

## Reading the Comics, April 28, 2018: Friday Is Pretty Late Edition

I should have got to this yesterday; I don’t know. Something happened. Should be back to normal Sunday.

Bill Rechin’s Crock rerun for the 26th of April does a joke about picking-the-number-in-my-head. There’s more clearly psychological than mathematical content in the strip. It shows off something about what people understand numbers to be, though. It’s easy to imagine someone asked to pick a number choosing “9”. It’s hard to imagine them picking “4,796,034,621,322”, even though that’s just as legitimate a number. It’s possible someone might pick π, or e, but only if that person’s a particular streak of nerd. They’re not going to pick the square root of eleven, or negative eight, or so. There’s thing that are numbers that a person just, offhand, doesn’t think of as numbers.

Mark Anderson’s Andertoons for the 26th sees Wavehead ask about “borrowing” in subtraction. It’s a riff on some of the terminology. Wavehead’s reading too much into the term, naturally. But there are things someone can reasonably be confused about. To say that we are “borrowing” ten does suggest we plan to return it, for example, and we never do that. I’m not sure there is a better term for this turning a digit in one column to adding ten to the column next to it, though. But I admit I’m far out of touch with current thinking in teaching subtraction.

Greg Cravens’s The Buckets for the 26th is kind of a practical probability question. And psychology also, since most of the time we don’t put shirts on wrong. Granted there might be four ways to put a shirt on. You can put it on forwards or backwards, you can put it on right-side-out or inside-out. But there are shirts that are harder to mistake. Collars or a cut around the neck that aren’t symmetric front-to-back make it harder to mistake. Care tags make the inside-out mistake harder to make. We still manage it, but the chance of putting a shirt on wrong is a lot lower than the 75% chance we might naively expect. (New comic tag, by the way.)

Charles Schulz’s Peanuts rerun for the 27th is surely set in mathematics class. The publication date interests me. I’m curious if this is the first time a Peanuts kid has flailed around and guessed “the answer is twelve!” Guessing the answer is twelve would be a Peppermint Patty specialty. But it has to start somewhere.

Knowing nothing about the problem, if I did get the information that my first guess of 12 was wrong, yeah, I’d go looking for 6 or 4 as next guesses, and 12 or 48 after that. When I make an arithmetic mistake, it’s often multiplying or dividing by the wrong number. And 12 has so many factors that they’re good places to look. Subtracting a number instead of adding, or vice-versa, is also common. But there’s nothing in 12 by itself to suggest another place to look, if the addition or subtraction went wrong. It would be in the question which, of course, doesn’t exist.

Maria Scrivan’s Half-Full for the 28th is the Venn Diagram joke for this week. It could include an extra circle for bloggers looking for content they don’t need to feel inspired to write. This one isn’t a new comics tag, which surprises me.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th uses the M&oum;bius Strip. It’s an example of a surface that you could just go along forever. There’s nothing topologically special about the M&oum;bius Strip in this regard, though. The mathematician would have as infinitely “long” a résumé if she tied it into a simple cylindrical loop. But the M&oum;bius Strip sounds more exotic, not to mention funnier. Can’t blame anyone going for that instead.

## Reading the Comics, April 25, 2018: Coronet Blue Edition

You know what? Sometimes there just isn’t any kind of theme for the week’s strips. I can use an arbitrary name.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st of April, 2018 would have gone in last week if I weren’t preoccupied on Saturday. The joke is aimed at freshman calculus students and then intro Real Analysis students. The talk about things being “arbitrarily small” turns up a lot in these courses. Why? Well, in them we usually want to show that one thing equals another. But it’s hard to do that. What we can show is some estimate of how different the first thing can be from the second. And if you can show that that difference can be made small enough by calculating it correctly, great. You’ve shown the two things are equal.

Delta and epsilon turn up in these a lot. In the generic proof of this you say you want to show the difference between the thing you can calculate and the thing you want is smaller than epsilon. So you have the thing you can calculate parameterized by delta. Then your problem becomes showing that if delta is small enough, the difference between what you can do and what you want is smaller than epsilon. This is why it’s an appropriately-formed joke to show someone squeezed by a delta and an epsilon. These are the lower-case delta and epsilon, which is why it’s not a triangle on the left there.

For example, suppose you want to know how long the perimeter of an ellipse is. But all you can calculate is the perimeter of a polygon. I would expect to make a proof of it look like this. Give me an epsilon that’s how much error you’ll tolerate between the polygon’s perimeter and the ellipse’s perimeter. I would then try to find, for epsilon, a corresponding delta. And that if the edges of a polygon are never farther than delta from a point on the ellipse, then the perimeter of the polygon and that of the ellipse are less than epsilon away from each other. And that’s Calculus and Real Analysis.

John Zakour and Scott Roberts’s Maria’s Day for the 22nd is the anthropomorphic numerals joke for this week. I’m curious whether the 1 had a serif that could be wrestled or whether the whole number had to be flopped over, as though it were a ruler or a fat noodle.

Anthony Blades’s Bewley for the 23rd offers advice for what to do if you’ve not got your homework. This strip’s already been run, and mentioned here. I might drop this from my reading if it turns out the strip is done and I’ve exhausted all the topics it inspires.

Dave Whamond’s Reality Check for the 23rd is designed for the doors of mathematics teachers everywhere. It does incidentally express one of those truths you barely notice: that statisticians and mathematicians don’t seem to be quite in the same field. They’ve got a lot of common interest, certainly. But they’re often separate departments in a college or university. When they do share a department it’s named the Department of Mathematics and Statistics, itself an acknowledgement that they’re not quite the same thing. (Also it seems to me it’s always Mathematics-and-Statistics. If there’s a Department of Statistics-and-Mathematics somewhere I don’t know of it and would be curious.) This has to reflect historical influence. Statistics, for all that it uses the language of mathematics and that logical rigor and ideas about proofs and all, comes from a very practical, applied, even bureaucratic source. It grew out of asking questions about the populations of nations and the reliable manufacture of products. Mathematics, even the mathematics that is about real-world problems, is different. A mathematician might specialize in the equations that describe fluid flows, for example. But it could plausibly be because they have interesting and strange analytical properties. It’d be only incidental that they might also say something enlightening about why the plumbing is stopped up.

Neal Rubin and Rod Whigham’s Gil Thorp for the 24th seems to be setting out the premise for the summer storyline. It’s sabermetrics. Or at least the idea that sports performance can be quantized, measured, and improved. The principle behind that is sound enough. The trick is figuring out what are the right things to measure, and what can be done to improve them. Also another trick is don’t be a high school student trying to lecture classmates about geometry. Seriously. They are not going to thank you. Even if you turn out to be right. I’m not sure how you would have much control of the angle your ball comes off the bat, but that’s probably my inexperience. I’ve learned a lot about how to control a pinball hitting the flipper. I’m not sure I could quantize any of it, but I admit I haven’t made a serious attempt to try either. Also, when you start doing baseball statistics you run a roughly 45% chance of falling into a deep well of calculation and acronyms of up to twelve letters from which you never emerge. Be careful. (This is a new comic strip tag.)

Randy Glasbergen’s Glasbergen Cartoons rerun for the 25th feels a little like a slight against me. Well, no matter. Use the things that get you in the mood you need to do well. (Not a new comic strip tag because I’m filing it under ‘Randy Glasbergen’ which I guess I used before?)

## Reading the Comics, April 19, 2018: Late Because Of Pinball Edition

Hi, all. I apologize for being late in posting this, but my Friday and Saturday were eaten up by pinball competition. Pinball At The Zoo, particularly, in Kalamazoo, Michigan. There, Friday, I stepped up first thing and put in four games on the Classics, pre-1985, tournament bank and based on my entry scores was ranked the second-best player there. And then over the day my scores dwindled lower and lower on the list of what people had entered until, in the last five minutes of qualifying, they dropped off the roster altogether and I was knocked out. Meanwhile in the main tournament, I was never even close to making playoffs. But I did have a fantastic game of Bally/Midway’s World Cup Soccer, a game based on how much the United States went crazy for soccer that time we hosted the World Cup for some reason. The game was interrupted by one of the rubber straps around one of the kickers (the little triangular table just past the flippers that you would think would be called the bumpers) breaking, and then by the drain breaking in a way that later knocked the game entirely out of the competition. So anyway besides that glory I’ve been very busy trying to figure out what’s gone wrong and stepping outside to berate the fox squirrels out back, and that’s why I’m late with all this. I’m sure you relate.

Bill Holbrook’s Kevin and Kell rerun for the 15th is the anthropomorphic numerals strip for the week. Also the first of the anthropomorphic strips for the week. Calculating taxes has always been one of the compelling social needs for mathematics, arithmetic especially. If we consider the topic to be “accounting” then that might be the biggest use of mathematics in society. At least by humans; I’m not sure how to rate the arithmetic that computers do even for not explicitly mathematical tasks like sending messages back and forth. New comic strip tag for around here, too.

Bill Schorr’s The Grizzwells for the 17th sees Fauna not liking trigonometry class. I’m sympathetic. I remember it as seeming to be a lot of strange new definitions put to vague purposes. On the bright side, when you get into calculus trigonometry starts solving more problems than it creates. On the dim side, at least when I took it they tried to pass off “trigonometric substitution” as a thing we might need. (OK, it’s come in useful sometimes, but not as often as the presentation made it look.) Also a new comic strip tag.

Eric the Circle for the 18th, this one by sdhardie, is a joke in the Venn Diagram mode. The strip’s a little unusual for not having one of the circles be named Eric. Not a new comic strip tag.

Ham’s Life on Earth for the 19th leaves me feeling faintly threatened. Maybe it’s just me. Also not a new comic strip tag, somehow.

Lord Birthday’s Dumbwitch Castle for the 19th is a small sketch and mostly a list of jokes. This is the normal format for this strip, which tests the idea of what makes something a comic strip. I grant it’s a marginal inclusion, but I am tickled by the idea of a math slap so here you go. This one’s another new comic strip tag.

## Reading the Comics, April 14, 2018: Friday the 13th Edition?

And now I can close out last week’s mathematically-themed comic strips. There was a bunch toward the end of the week. And I’m surprised that none of the several comics to appear on Friday the 13th had anything to do with the calendar. Or at least not enough for me to talk about them.

Julie Larson’s Dinette Set rerun for the 12th is a joke built on the defining feature of (high school) algebra. The use of a number whose value we hope to figure out isn’t it. Those appear from the start of arithmetic, often as an empty square or circle or a spot of ____ that’s to be filled out. We used to give these numbers names like “thing” or “heap” or “it” or the like. Something pronoun-like. The shift to using ‘x’ as the shorthand is a legacy of the 16th century, the time when what we see as modern algebra took shape. People are frightened by it, to suddenly see letters in the midst of a bunch of numbers. But it’s no more than another number. And it communicates “algebra” in a way maybe nothing else does.

Ruben Bolling’s Tom the Dancing Bug rerun for the 12th is one of the God-Man stories. I’m delighted by the Freshman Philosophy-Major Man villain. The strip builds on questions of logic, and about what people mean by “omnipotence”. I don’t know how much philosophy of mathematics the average major takes. I suspect it’s about as much philosophy of mathematics as the average mathematics major is expected to take. (It’s an option, but I don’t remember anyone suggesting I do it, and I do feel the lost opportunity.) But perhaps later on Freshman Philosophy-Major Man would ask questions like what do we mean by “one” and “plus” and “equals” and “three”. And whether anything could, by a potent enough entity, be done about them. For the easiest way to let an omnipotent creature change something like that. WordPress is telling me this is a new tag for me. That can’t be right.

Mike Thompson’s Grand Avenue for the 13th is another resisting-the-story-problem joke, attacking the idea that a person would have ten apples. People like to joke about story problems hypothesizing people with ridiculous numbers of pieces of fruit. But ten doesn’t seem like an excessive number of apples to me; my love and I could eat that many in two weeks without trying hard. The attempted diversion would work better if it were something like forty watermelons or the like.

Mark Tatulli’s Heart of the City for the 13th has Heart and Dean complaining about their arithmetic class. I rate it as enough to include here because they go into some detail about things. I find it interesting they’re doing story problems with decimal points; that seems advanced for what I’d always taken their age to be. But I don’t know. I have dim memories of what elementary school was like, and that was in a late New Math-based curriculum.

Nick Galifianakis’s Nick and Zuzu for the 13th is a Venn diagram joke, the clearest example of one we’ve gotten in a while. I believe WordPress when it tells me this is a new tag for the comic strip.

Mark Anderson’s Andertoons for the 14th is the Mark Anderson’s Andertoons for the week. It starts at least with teaching ordinal numbers. In normal English that’s the adjective form of a number. Ordinal numbers reappear in the junior or senior year of a mathematics major’s work, as they learn enough set theory to be confused by infinities. In this guise they describe the sizes of sets of things. And they’re introduced as companions to cardinal numbers, which also describe the sizes of sets of things. They’re different, in ways that I feel like I always forget in-between reading books about infinitely large sets. The kids don’t need to worry about this yet.

## Reading the Comics, April 11, 2018: Obscure Mathematical Terms Edition

I’d like to open today’s installment with a trifle from Thomas K Dye. He’s a friend, and the cartoonist behind the long-running web comic Newshounds, its new spinoff Infinity Refugees, and some other projects.

Dye also has a Patreon, most recently featuring a subscribers-only web comic. And he’s good enough to do the occasional bit of spot art to spruce up my work here.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 9th of April, 2018 is, for me, relatable. I think I’ve read off this anecdote before. The first time I took Real Analysis I was completely lost. Getting me slightly less lost was borrowing a library book on Real Analysis from the mathematics library. The book was in French, a language I can only dimly read. But the different presentation and, probably, the time I had to spend parsing each sentence helped me get a basic understanding of the topic. So maybe trying algebra upside-down isn’t a ridiculous idea.

Lincoln Pierce’s Big Nate rerun for the 9th presents an arithmetic sequence, which is always exciting to work with, if you’re into sequences. I had thought Nate was talking about mathematics quizzes but I see that’s not specified. Could be anything. … And yes, there is something cool in finding a pattern. Much of mathematics is driven by noticing, or looking for, patterns in things and then describing the rules by which new patterns can be made. There’s many easy side questions to be built from this. When would quizzes reach a particular value? When would the total number of points gathered reach some threshold? When would the average quiz score reach some number? What kinds of patterns would match the 70-68-66-64 progression but then do something besides reach 62 next? Or 60 after that? There’s some fun to be had. I promise.

Mike Thompson’s Grand Avenue for the 10th is one of the resisting-the-teacher’s-problem style. The problem’s arithmetic, surely for reasons of space. The joke doesn’t depend on the problem at all.

Dave Whamond’s Reality Check for the 10th similarly doesn’t depend on what the question is. It happens to be arithmetic, but it could as easily be identifying George Washington or picking out the noun in a sentence.

Leigh Rubin’s Rubes for the 10th riffs on randomness. In this case it’s riffing on the unpredictability and arbitrariness of random things. Random variables are very interesting in certain fields of mathematics. What makes them interesting is that any specific value — the next number you generate — is unpredictable. But aggregate information about the values is predictable, often with great precision. For example, consider normal distributions. (A lot of stuff turns out to be normal.) In that case we can be confident that the values that come up most often are going to be close to the arithmetic mean of a bunch of values. And that there’ll be about as many values greater than the mean as there are less than the mean. And this will be only loosely true if you’ve looked at a handful of values, at ten or twenty or even two hundred of them. But if you looked at, oh, a hundred thousand values, these truths would be dead-on. It’s wonderful and it seems to defy intuition. It just works.

John Atkinson’s Wrong Hands for the 10th is the anthropomorphic numerals joke for the week. It’s easy to think of division as just making numbers smaller: 4 divided by 6 is less than either 4 or 6. 1 divided by 4 is less than either 1 or 4. But this is a bad intuition, drawn from looking at the counting numbers that don’t look boring. But 4 divided by 1 isn’t less than either 1 or 4. Same with 6 divided by 1. And then when we look past counting numbers we realize that’s not always so. 6 divided by ½ gives 12, greater than either of those numbers, and I don’t envy the teachers trying to explain this to an understandably confused student. And whether 6 divided by -1 gives you something smaller than 6 or smaller than -1 is probably good for an argument in an arithmetic class.

Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 11th has an argument about predicting humans mathematically. It’s so very tempting to think people can be. Some aspects of people can. In the founding lore of statistics is the astonishment at how one could predict how many people would die, and from what causes, over a time. No person’s death could be forecast, but their aggregations could be. This unsettles people. It should: it seems to defy reason. It seems to me even people who embrace a deterministic universe suppose that while, yes, a sufficiently knowledgeable creature might forecast their actions accurately, mere humans shouldn’t be sufficiently knowledgeable.

No strips are tagged for the first time this essay. Just noticing.

## Reading the Comics, April 2018: Another Normal Week Edition

And for another week running the pace of mathematically-themed comic strips has been near normal. There’s nowhere near enough to split the essay into two pieces, which is fine. There is some more work involved in including images for all the strips I discuss and this pace better fits the time I could make for writing this week. Will admit I’m scared of what’s going to happen when I have a busy week and Comic Strip Master Command orders more comics for me. I admit this isn’t an inspired name for the Edition. But the edition names are mostly there so people have a chance of telling whether they’ve read an installment before. The date alone doesn’t do it. A couple of words will. Maybe I should give up on meaningful names if there isn’t an obvious theme for the week. It’s got to be at least as good to name something “Coronet Blue Edition” as to name it “Lots Of Andertoons Edition”.

Frank Cho’s Liberty Meadows rerun for the 1st riffs on quantum computers. You’ve maybe seen much talk about them in pop science columns and blogs. They require a bunch of stuff that gets talked about as if it were magical. Quantum mechanics, obviously, the biggest bit of magic in popular science today. Complex-valued numbers, which make for much more convenient mathematical descriptions. Probability, which everyone thinks they understand and which it turns out nobody does. Vector spaces and linear algebra, which mathematics (and physics) majors get to know well. The mathematics of how a quantum computer computes is well-described as this sort of matrix and vector work. Quantum computing promises to be a really good way to do problems where the best available approach is grinding it out: testing every possibility and finding the best ones. No part of making a quantum computer is easy, though, so it’s hard to say when we’ll have the computing power to make a version of SimCity with naturally curving roads. (This is a new tag for my Reading the Comics essays, but I’ve surely featured the strip some before.)

Niklas Eriksson’s Carpe Diem for the 2nd is a mathematics-education-these-days joke. The extremely small child talking about counting-without-a-calculator as a subject worth studying. People are always complaining that people don’t do arithmetic well enough in their heads. I understand the frustration, considering last week I stymied a cashier at a Penn Station by giving $22.11 for my$11.61 order. I don’t know why he put in my payment as $20; why not let the machine designed to do this work, do the work? He did fine working out that I should get$10 in bills back but muddled up the change. As annoyances go it ranks up there with the fast food cashier asking my name for the order and entering it as “Joeseph”.

Lard’s World Peace Tips for the 4th mentions the Möbius Strip. It’s got to be the most famous exotic piece of geometry to have penetrated the popular culture. It’s also a good shape to introduce geometry students to a “non-orientable” surface. Non-orientable means about what you’d imagine. There’s not a way to put coordinates on it that don’t get weird. For example, try drawing an equator on the surface of the strip. Any curve along the surface that doesn’t run off the edges will do. The curve just has to meet itself. It looks like this divides the strip into two pieces. Fine, then; which of these two pieces is “north” and which is “south” of this equator? There’s not a way to do that. You get surprising results if you try.

Karen Montague-Reyes’s Clear Blue Water rerun for the 5th has Eve deploying a mathematical formula. She’s trying to describe the way that perception of time changes over the course of events. It’s not a bad goal. Many things turn out to be mathematically describable. I don’t see what the equation is supposed to even mean, but then, I haven’t seen the model she developed that implies this equation. (This is not a new tag and I’m surprised by that.)

Dan Thompson’s Brevity for the 6th is some mathematics wordplay, built on the abacus. I’m not sure there’s more to say about this, past that you can do much more on an abacus. You can, at least. I keep reading directions about how to multiply with it and then I look at mine and I feel helpless.

Bil Keane and Jeff Keane’s Family Circus for the 7th is a kids-mispronouncing-a-mathematics-word strip. I have even less to say about this. It’s a normal week.

## Reading the Comics, March 31, 2018: A Normal Week Edition

I have a couple loose rules about these Reading the Comics posts. At least one a week, whether there’s much to talk about or not. Not too many comics in one post, because that’s tiring to read and tiring to write. Trying to write up each day’s comics on the day mitigates that some, but not completely. So I tend to break up a week’s material if I can do, say, two posts of about seven strips each. This year, that’s been necessary; I’ve had a flood of comics on-topic or close enough for me to write about. This past week was a bizarre case. There really weren’t enough strips to break up the workload. It was, in short, a normal week, as strange as that is to see. I don’t know what I’m going to do Thursday. I might have to work.

Aaron McGruder’s Boondocks for the 25th of March is formally just a cameo mention of mathematics. There is some serious content to it. Whether someone likes to do a thing depends, to an extent, on whether they expect to like doing a thing. It seems likely to me that if a community encourages people to do mathematics, then it’ll have more people who do mathematics well. Mathematics does at least have the advantage that a lot of its fields can be turned into games. Or into things like games. Is one knot the same as another knot? You can test the laborious but inevitably correct way, trying to turn one into the other. Or you can find a polynomial that describes both knots and see if those two are the same polynomials. There’s fun to be had in this. I swear. And, of course, making arguments and finding flaws in other people’s arguments is a lot of mathematics. And good fun for anybody who likes that sort of thing. (This is a new tag for me.)

Ted Shearer’s Quincy for the 30th of January, 1979 and rerun the 26th names arithmetic as the homework Quincy’s most worried about. Or would like to put off the most. Harmless enough.

Mike Thompson’s Grand Avenue for the 26th is a student-resisting-the-problem joke. A variable like ‘x’ serves a couple of roles. One of them is the name for a number whose value we don’t explicitly know, but which we hope to work out. And that’s the ‘x’ seen here. The other role of ‘x’ is the name for a number whose value we don’t know and don’t particularly care about. Since those are different reasons to use ‘x’ maybe we ought to have different names for the concepts. But we don’t and there’s probably no separating them now.

Tony Cochran’s Agnes for the 27th grumbles that mathematics and clairvoyance are poorly taught. Well, everyone who loves mathematics grumbles that the subject is poorly taught. I don’t know what the clairvoyants think but I’ll bet the same.

Mark Pett’s Lucky Cow rerun for the 28th is about sudoku. As with any puzzle the challenge is having rules that are restrictive enough to be interesting. This is also true of any mathematical field, though. You want ideas that imply a lot of things are true, but that also imply enough interesting plausible things are not true.

Rick DeTorie’s One Big Happy rerun for the 30th has Ruthie working on a story problem. One with loose change, which seems to turn up a lot in story problems. I never think of antes for some reason.

Stephen Beals’s Adult Children for the 31st depicts mathematics as the stuff of nightmares. (Although it’s not clear to me this is meant to recount a nightmare. Reads like it, anyway.) Calculus, too, which is an interesting choice. Calculus seems to be a breaking point for many people. A lot of people even who were good at algebra or trigonometry find all this talk about differentials and integrals and limits won’t cohere into understanding. Isaac Asimov wrote about this several times, and the sad realization that for as much as he loved mathematics there were big important parts of it that he could not comprehend.

I’m curious why calculus should be such a discontinuity, but the reasons are probably straightforward. It’s a field where you’re less interested in doing things to numbers and more interested in doing things to functions. Or to curves that a function might represent. It’s a field where information about a whole region is important, rather than information about a single point. It’s a field where you can test your intuitive feeling for, say, a limit by calculating a couple of values, but for which those calculations don’t give the right answer. Or at least can’t be guaranteed to be right. I don’t know if the choice of what to represent mathematics was arbitrary. But it was a good choice certainly. (This is another newly-tagged strip.)

## Reading the Comics, March 24, 2018: Arithmetic and Information Edition

And now I can bring last week’s mathematically-themed comics into consideration here. Including the whole images hasn’t been quite as much work as I figured. But that’s going to change, surely. One of about four things I know about life is that if you think you’ve got your workflow set up to where you can handle things you’re about to be surprised. Can’t wait to see how this turns out.

John Deering’s Strange Brew for the 22nd is edging its way toward an anthropomorphic numerals joke.

Brant Parker and Johnny Hart’s Wizard of Id for the 22nd is a statistics joke. Really a demographics joke. Which still counts; much of the historical development of statistics was in demographics. That it was possible to predict accurately the number of people in a big city who’d die, and what from, without knowing anything about whether any particular person would die was strange and astounding. It’s still an astounding thing to look directly at.

Hilary Price and Rina Piccolo’s Rhymes with Orange for the 23rd has the form of a story problem. I could imagine turning this into a proper story problem. You’d need some measure of how satisfying the 50-dollar wines are versus the 5-dollar wines. Also how much the wines affect people’s ability to notice the difference. You might be able to turn this into a differential equations problem, but that’s probably overkill.

Mark Anderson’s Andertoons for the 23rd is Mark Anderson’s Andertoons for this half of the week. It’s a student-avoiding-the-problem joke. Could be any question. But arithmetic has the advantages of being plausible, taking up very little space to render, and not confusing the reader by looking like it might be part of the joke.

John Zakour and Scott Roberts’s Working Daze for the 23rd has another cameo appearance by arithmetic. It’s also a cute reminder that there’s no problem you can compose that’s so simple someone can’t over-think it. And it puts me in mind of the occasional bit where a company’s promotional giveaway will technically avoid being a lottery by, instead of awarding prizes, awarding the chance to demonstrate a skill. Demonstration of that skill, such as a short arithmetic quiz, gets the prize. It’s a neat bit of loophole work and does depend, as the app designers here do, on the assumption there’s some arithmetic that people can be sure of being able to do.

Teresa Burritt’s Frog Applause for the 24th is its usual bit of Dadist nonsense. But in the talk about black holes it throws in an equation: $S = \frac{A k c^3}{4 G \hbar}$. This is some mathematics about black holes, legitimate and interesting. It is the entropy of a black hole. The dazzling thing about this is all but one of those symbols on the right is the same for every black hole. ‘c’ is the speed of light, as in ‘E = mc2‘. G is the gravitational constant of the universe, a measure of how strong gravity is. $\hbar$ is Planck’s constant, a kind of measure of how big quantum mechanics effects are. ‘k’ is the Boltzmann constant, which normal people never heard of but that everyone in physics and chemistry knows well. It’s what you multiply by to switch from the temperature of a thing to the thermal energy of the thing, or divide by to go the other way. It’s the same number for everything in the universe.

The only thing custom to a particular black hole is ‘A’, which is the surface area of the black hole. I mean the surface area of the event horizon. Double the surface area of the event horizon and you double its entropy. (This isn’t doubling the radius of the event horizon, but you know how much growth in the radius it is.) Also entropy. Hm. Everyone who would read this far into a pop mathematics blog like this knows that entropy is “how chaotic a thing is”. Thanks to people like Boltzmann we can be quantitative, and give specific and even exact numbers to the entropy of a system. It’s still a bit baffling since, superficially, a black hole seems like it’s not at all chaotic. It’s a point in space that’s got some mass to it, and maybe some electric charge and maybe some angular momentum. That’s about it. How messy can that be? It doesn’t even have any parts. This is how we can be pretty sure there’s stuff we don’t understand about black holes yet. Also about entropy.

This strip might be an oblique and confusing tribute to Dr Stephen Hawking. The entropy formula described was demonstrated by Drs Jacob Bekenstein and Stephen Hawking in the mid-1970s. Or it might be coincidence.

## Reading the Comics, March 21, 2018: Old Mathematics Jokes Edition

For this, the second of my Reading the Comics postings with all the comics images included, I’ve found reason to share some old and traditional mathematicians’ jokes. I’m not sure how this happened, but sometimes it just does.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th brings to mind a traditional mathematics joke. A dairy hires a mathematician to improve operations. She tours the place, inspecting the cows and their feeding and the milking machines. She speaks with the workers. She interviews veterinarians. She talks with the truckers who haul out milk. She interviews the clients. Finally she starts to work on a model of better milk production. The first line: “Assume a spherical cow.”

One big field of mathematics is model-building. When doing that you have to think about the thing you model. It’s hard. You have to throw away all the complicating stuff that makes your questions too hard to answer. But you can’t throw away all the complicating stuff or you have a boring question to answer. Depending on what kinds of things you want to know, you’ll need different models. For example, for some atmosphere problems you’ll do fine if you assume the air has no viscosity. For others that’s a stupid assumption. For some you can ignore that the planet rotates and is heated on one side by the sun. For some you don’t dare do that. And so on. The simplifications you can make aren’t always obvious. Sometimes you can ignore big stuff; a satellite’s orbit, for example, can be treated well by pretending that the whole universe except for the Earth doesn’t exist. Depends what you’re looking for. If the universe were homogenous enough, it would all be at the same temperature. Is that useful to your question? That’s the trick.

Mark Anderson’s Andertoons for the 20th is the Mark Anderson’s Andertoons for this essay. It’s just a student trying to distract the issue from fractions. I suppose mathematics was chosen for the blackboard problem because if it were, say, a history or an English or a science question someone would think that was part of the joke and be misled. Fractions, though, those have the signifier of “the thing we’d rather not talk about”.

Daniel Beyer’s Long Story Short for the 21st is a mathematicians-mindset sort of joke. Let me offer another. I went to my love’s college reunion. On the mathematics floor of the new sciences building the dry riser was labelled as “N Bourbaki”. Let me explain why is a correctly-formed and therefore very funny mathematics joke. “Nicolas Bourbaki” was the pseudonym used by the mathematical equivalent of an artist’s commune, in France, through several decades of the mid-20th century. Their goal was setting mathematics on a rigorous and intuition-free basis, the way mathematicians sometimes like to pretend it is. Bourbaki’s influential nonexistence lead to various amusing-for-academia problems and you can see why a fake office is appropriately named so, then. (This is the first time I’ve tagged this strip, looks like.)

Harley Schwadron’s 9 to 5 for the 21st is a name-drop of Einstein’s famous equation as a power tie. I must agree this meets the literal specification of a power tie since, you know, c2 is in it. Probably something more explicitly about powers wouldn’t communicate as well. Possibly Fermat’s Last Theorem, although I’m not sure that would fit and be legible on the tie as drawn.

Mark Pett’s Lucky Cow rerun for the 21st has the generally inept Neil work out a geometry problem in his head. The challenge is having a good intuitive model for what the relationship between the shapes should be. I’m relieved to say that Neil is correct, to the number of decimal places given. I’m relieved because I’ve spent embarrassingly long at this. My trouble was missing, twice over, that the question gave diameters instead of radiuses. Pfaugh. Saving me was just getting answers that were clearly crazy, including at one point 21 1/3.

Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 21st mentions Euler’s Theorem in the first panel. Trouble with saying “Euler’s Theorem” is that Euler had something like 82 trillion theorems. If you ever have to bluff your way through a conversation with a mathematician mention “Euler’s Theorem”. You’ll probably have said something on point, if closer to the basics of the problem than people figured. But the given equation — $e^{\imath \pi} + 1 = 0$ — is a good bet for “the” Euler’s Theorem. It’s a true equation, and it ties together a lot of interesting stuff about complex-valued numbers. It’s the way mathematicians tie together exponentials and simple harmonic motion. It makes so much stuff easier to work with. It would not be one of the things presented in a Distinctly Useless Mathematics text. But it would be mentioned along the way to something fascinating and useless. It turns up everywhere. (This is another strip I’m tagging for the first time.)

Wulff and Morgenthaler’s WuMo for the 21st uses excessively complicated mathematics stuff as a way to signify intelligence. Also to name-drop Massachusetts Institute of Technology as a signifier of intelligence. (My grad school was Rensselaer Polytechnic Institute, which would totally be MIT’s rival school if we had enough self-esteem to stand up to MIT. Well, on a good day we can say snarky stuff about the Rochester Institute of Technology if we don’t think they’re listening.) Putting the “Sigma” in makes the problem literally nonsense, since “Sigma” doesn’t signify any particular number. The rest are particular numbers, though. π/2 times 4 is just 2π, a bit more than 6.28. That’s a weird number of apples to have but it’s perfectly legitimate a number. The square root of the cosine of 68 … ugh. Well, assuming this is 68 as in radians I don’t have any real idea what that would be either. If this is 68 degrees, then I do know, actually; the cosine of 68 degrees is a little smaller than ½. But mathematicians are trained to suspect degrees in trig functions, going instead for radians.

Well, hm. 68 would be between 11 times 2π and 12 times 2π. I think that’s just a little more than 11 times 2π. Oh, maybe it is something like ½. Let me check with an actual calculator. Huh. It is a little more than 0.440. Well, that’s a once-in-a-lifetime shot. Anyway the square root of that is a little more than 0.663. So you’d be left with about five and a half apples. Never mind this Sigma stuff. (A little over 5.619, to be exact.)

## Reading the Comics, March 17, 2018: Pi Day 2018 Edition

So today I am trying out including images for all the mathematically-themed comic strips here. This is because of my discovery that some links even on GoComics.com vanish without warning. I’m curious how long I can keep doing this. Not for legal reasons. Including comics for the purpose of an educational essay about topics raised by the strips is almost the most fair use imaginable. Just because it’s a hassle copying the images and putting them up on WordPress.com and that’s even before I think about how much image space I have there. We’ll see. I might try to figure out a better scheme.

Also in this batch of comics are the various Pi Day strips. There was a healthy number of mathematically-themed comics on the 14th of March. Many of those were just coincidence, though, with no Pi content. I’ll group the Pi Day strips together.

Tom Batiuk’s Funky Winkerbean for the 2nd of April, 1972 is, I think, the first appearance of Funky Winkerbean around here. Comics Kingdom just started running the strip, as well as Bud Blake’s Tiger and Bill Hoest’s Lockhorns, from the beginning as part of its Vintage Comics roster. And this strip really belonged in Sunday’s essay, but I noticed the vintage comics only after that installment went to press. Anyway, this strip — possibly the first Sunday Funky Winkerbean — plays off a then-contemporary fear of people being reduced to numbers in the face of a computerized society. If you can imagine people ever worrying about something like that. The early 1970s were a time in American society when people first paid attention to the existence of, like, credit reporting agencies. Just what they did and how they did it drew a lot of critical examination. Josh Lauer’s recently published Creditworthy: a History of Consumer Surveillance and Financial Identity in America gets into this.

Bob Scott’s Bear With Me for the 14th sees Molly struggling with failure on a mathematics test. Could be any subject and the story would go as well, but I suppose mathematics gets a connotation of the subject everybody has to study for, even the geniuses. (The strip used to be called Molly and the Bear. In either name this seems to be the first time I’ve tagged it, although I only started tagging strips by name recently.)

Bud Fisher’s Mutt and Jeff rerun for the 14th is a rerun from sometime in 1952. I’m tickled by the problem of figuring out how many times Fisher and his uncredited assistants drew Mutt and Jeff. Mutt saying that the boss “drew us 14,436 times” is the number of days in 45 years, so that makes sense if he’s counting the number of strips drawn. The number of times that Mutt and Jeff were drawn is … probably impossible to calculate. There’s so many panels each strip, especially going back to earlier and earlier times. And how many panels don’t have Mutt or don’t have Jeff or don’t have either in them? Jeff didn’t appear in the strip until March of 1908, for example, four months after the comic began. (With a different title, so the comic wasn’t just dangling loose all that while.)

Doug Savage’s Savage Chickens for the 14th is a collection of charts. Not all pie charts. And yes, it ran the 14th but avoids the pun it could make. I really like the tart charts, myself.

And now for the Pi Day strips proper.

Scott Hilburn’s The Argyle Sweater for the 14th starts the Pi Day off, of course, with a pun and some extension of what makes 3/14 get its attention. And until Hilburn brought it up I’d never thought about the zodiac sign for someone born the 14th of March, so that’s something.

Mark Parisi’s Off The Mark for the 14th riffs on one of the interesting features of π, that it’s an irrational number. Well, that its decimal representation goes on forever. Rational numbers do that too, yes, but they all end in the infinite repetition of finitely many digits. And for a lot of them, that digit is ‘0’. Irrational numbers keep going on with more complicated patterns. π sure seems like it’s a normal number. So we could expect that any finite string of digits appears somewhere in its decimal expansion. This would include a string of digits that encodes any story you like, The Neverending Story included. This does not mean we might ever find where that string is.

Michael Cavna’s Warped for the 14th combines the two major joke threads for Pi Day. Specifically naming Archimedes is a good choice. One of the many things Archimedes is famous for is finding an approximation for π. He’d worked out that π has to be larger than 310/71 but smaller than 3 1/7. Archimedes used an ingenious approach: we might not know the precise area of a circle given only its radius. But we can know the area of a triangle if we know the lengths of its legs. And we can draw a series of triangles that are enclosed by a circle. The area of the circle has to be larger than the sum of the areas of those triangles. We can draw a series of triangles that enclose a circle. The area of the circle has to be less than the sum of the areas of those triangles. If we use a few triangles these bounds are going to be very loose. If we use a lot of triangles these bounds can be tight. In principle, we could make the bounds as close together as we could possibly need. We can see this, now, as a forerunner to calculus. They didn’t see it as such at the time, though. And it’s a demonstration of what amazing results can be found, even without calculus, but with clever specific reasoning. Here’s a run-through of the process.

John Zakour and Scott Roberts’s Working Daze for the 15th is a response to Dr Stephen Hawking’s death. The coincidence that he did die on the 14th of March made for an irresistibly interesting bit of trivia. Zakour and Roberts could get there first, thanks to working on a web comic and being quick on the draw. (I’m curious whether they replaced a strip that was ready to go for the 15th, or whether they normally work one day ahead of publication. It’s an exciting but dangerous way to go.)

## Reading the Comics, March 13, 2018: One Of My Assumptions Is Shaken Edition

I learn, from reading not-yet-dead Usenet group rec.arts.comics.strips, that Rick Stromoski is apparently ending the comic Soup To Nutz. This is sad enough. But worse, GoComics.com has removed all but the current day’s strip from its archives. I had trusted that GoComics.com links were reliable in a way that Comics Kingdom and Creators.com weren’t. Now I learn that maybe I need to include images of the comics I review and discuss here lest my essays become unintelligible in the future? That’s not a good sign. I can do it, mind you. I just haven’t got started. You’ll know when I swing into action.

Norm Feuti, of Retail, still draws Sunday strips for Gil. They’re to start appearing on GoComics.com soon, and I can talk about them from my regular sources after that. But for now I follow the strip on Twitter. And last Sunday he posted this one.

It’s sort of a protesting-the-problem question. It’s also a reaction a lot of people have to “explain how you found the answer” questions. In a sense, yeah, the division shows how the answer was found. But what’s wanted — and what’s actually worth learning — is to explain why you did this calculation. Why, in this case, 216 divided by 8? Why not 216 times 8? Why not 8 divided by 216? Why not 216 minus 8? “How you found your answer” is probably a hard question to make interesting on arithmetic, unfortunately. If you’re doing a long sheet of problems practicing division, it’s not hard to guess that dividing is the answer. And that it’s the big number divided by the small. It can be good training to do blocks of problems that use the same approach, for the same reason it can be good training to focus on any exercise a while. But this does cheat someone of the chance to think about why one does this rather than that.

Patrick Roberts’s Todd the Dinosaur for the 11th has mathematics as the thing Todd’s trying to get out of doing. (I suppose someone could try to argue the Y2K bug was an offshoot of mathematics, on the grounds that computer science has so much to do with mathematics. I wouldn’t want to try defending that, though.) I grant that most fraction-to-decimal conversion problems hit that sweet spot of being dull, tedious, and seemingly pointless. There’s some fun decimal expansions of fractions. The sevenths and the elevenths and 1/243 have charm to them. There’s some kid who’ll become a mathematician because at the right age she was told about $\frac{1}{8991}$. 3/16th? Eh.

Mark Anderson’s Andertoons for the 11th is the Mark Anderson’s Andertoons for the week. I don’t remember seeing a spinny wheel like this used to introduce probability. It’s a good prop, though. I would believe in a class having it.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 11th is built on the Travelling Salesman Problem. It’s one of the famous unsolved and hard problems of mathematics. Weinersmith’s joke is a nice gag about one way to “solve” the problem, that of making it irrelevant. But even if we didn’t need to get to a collection of places efficiently mathematicians would still like to know good ways to do it. It turns out that finding the shortest (quickest, cheapest, easiest, whatever) route connecting a bunch of places is great problem. You can phrase enormously many problems about doing something as well as possible as a Travelling Salesman Problem. It’s easy conceptually to find the answer: try out all the possibilities and pick the best one. But if there’s more than a handful of cities, there are so many possible routes there’s no checking them all, not before you die of old age. We can do very well finding approximate answers, including by my specialization of Monte Carlo methods. In those you take a guess at an answer. Then make, randomly, a change. You’ll either have made things better or worse. If you’ve made it better, keep the change. If you’ve made it worse, usually you reject the change but sometimes you keep it. And repeat. In surprisingly little time you’ll get a really good answer. Maybe not the best possible, but a great answer for how straightforward setting it up was.

Dan Thompson’s Brevity for the 12th is a Rubik’s Cube joke. There’s not a lot of mathematics to that. But I do admire how Thompson was careful enough to draw a Rubik’s Cube that actually looks like the real article; it’s not just an isometric cube with thick lines partitioning it. Look at the corners of each colored sub-cube. I may be the only reader to notice this but I’m glad Thompson did the work.

Mason Mastroianni’s The Wizard of Id for the 12th gets Sir Rodney in trouble with the King for doing arithmetic. I haven’t read the comments on GoComics.com. I’d like to enter “three” as my guess for how many comments one would have to read before finding the “weapons of math instruction” joke in there.

Jef Mallett’s Frazz for the 13th has mathematics homework given as the thing lost by the time change. It’s just a cameo mention.

Steve Moore’s In The Bleachers for the 13th features a story problem as a test of mental acuity. When the boxer can’t work out what the heck the trains-leaving-Penn-Station problem even means he’s ruled unfit to keep boxing. The question is baffling, though. As put, the second train won’t ever overtake the first. The question: did Moore just slip up? If the first train were going 30 miles per hour and the second 40 there would be a perfectly good, solvable question in this. Or was Moore slipping in an extra joke, making the referee’s question one that sounds like it was given wrong? Don’t know, so I’ll suppose the second.

## Reading the Comics, March 10, 2018: I Will Get To Pi Day Edition

There were fewer Pi Day comic strips than I had expected for this year. It’s gotten much more public mention than I had expected a pop-mathematics bit of whimsy might. But I’m still working off last week’s strips; I’ll get to this week’s next week. This makes sense to me, which is as good as making sense at all.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 7th is a percentages joke, as applied to hair. Lard doesn’t seem clear whether this would be 10% off the hair by individual strand length or by total volume. Either way, Lard’s right to wonder about the accuracy.

Mark Pett’s Mr Lowe rerun for the 7th is a standardized test joke. Part of the premise of Pett’s strip is that Mister Lowe is a brand-new teacher, which is why he makes mistakes like this problem. (This is touchy to me, as in grad school I hoped to make some spare money selling questions to a standardized testing company. I wasn’t good enough at it, and ultimately didn’t have the time to train up to their needs.) A multiple-choice question needs to clear and concise and to have one clearly best answer. As the given question’s worded, though, I could accept ‘2’ or ’12’ as a correct answer. With a bit of experience Lowe would probably clarify that Tommy and Suzie are getting the same number of apples and that together they should have 20 total.

Then on the 9th Mr Lowe has a joke about cultural bias in standardized tests. It uses an arithmetic problem as the type case. Mathematicians like to think of themselves as working in a universal, culturally independent subject. I suppose it is, but only in ways that aren’t interesting: if you suppose these rules of logic and these axioms and these definitions then these results follow, and it doesn’t matter who does the supposing. But start filtering that by stuff people care about, such as the time it takes for two travelling parties to meet, and you’ve got cultural influence. (Back when this strip was new the idea that a mathematics exam could be culturally biased was a fresh new topic of mockery among people who don’t pay much attention to the problems of teaching but who know what those who do are doing wrong.)

Ralph Hagen’s The Barn for the 8th — a new tag for my comics, by the way — lists a bunch of calculation tools and techniques as “obsolete” items. I’m assuming Rory means that longhand multiplication is obsolete. I’m not sure that it is, but I have an unusual perspective on this.

Thaves’s Frank and Ernest for the 8th is an anthropomorphic-numerals joke. I was annoyed when I first read this because I thought, wait, 97 isn’t a prime number. It is, of course. I have no explanation for my blunder.

Jon Rosenberg’s Scenes from a Multiverse has restarted its run on GoComics. The strip for the 8th is a riff on Venn Diagrams. And, it seems to me, about those logic-bomb problems about sets consisting of sets that don’t contain themselves and the like. You get weird and apparently self-destructive results pondering that stuff. The last time GoComics ran the Scenes from a Multiverse series I did not appreciate right away that there were many continuing stories. There might be follow-ups to this Former Venn Prime Universe story.

Brian Fies’s The Last Mechanical Monster for the 9th has the Mad Scientist, struggling his way into the climax of the story, testing his mind by calculating a Fibonacci Sequence. Whatever keeps you engaged and going. You can build a Fibonacci Sequence from any two starting terms. Each term after the first two is the sum of the previous two. If someone just says “the Fibonacci Sequence” they mean the sequence that starts with 0, 1, or perhaps with 1, 1. (There’s no interesting difference.) Fibonacci Sequences were introduced to the west by Leonardo of Pisa, who did so much to introduce Hindu-Arabic Numerals to a Europe that didn’t know it wanted this stuff. They touch on some fascinating stuff: the probability of not getting two tails in a row of a set number of coin tosses. Chebyshev polynomials. Diophantine equations. They also touch on the Golden Ratio, which isn’t at all important but that people like.

Nicholas Gurewitch’s Perry Bible Fellowship for the 9th just has a blackboard of arithmetic to stand in for schoolwork.

## Reading the Comics, March 5, 2018: If It’s Even Mathematics Edition

Many of the strips from the first half of last week are ones that just barely touch on mathematical content. I’m not sure how relevant they all are. I hope you like encountering them anyway.

Bill Griffith’s Zippy the Pinhead for the 4th of March offers “an infinite number of mathematicians walk into a bar” as a joke’s setup. Mathematics popularizers have a small set of jokes about infinite numbers of mathematicians, often arriving at hotels. They’re used to talk about how we now understand infinitely large sets. There’s often counter-intuitive or just plain weird results that follow. And presenting it as a joke works surprisingly well in introducing the ideas. There’s a kind of joke that is essentially a tall tale, spinning out an initial premise to as far and as absurd a consequence as you can get. In structure, that’s not much different to a proof, a discussion of the consequences of an idea. It’s a shame that it’s hard to make jokes or anecdotes about more fields of mathematics. Somehow infinitely large groups of people are funnier than, say, upper-bounded nondecreasing sequences.

Mike Baldwin’s Cornered for the 4th has a bit of fraction-based wordplay. I’m not sure how mathematical this is, but I grinned.

Bill Amend’s FoxTrot for the 4th has Jason try to make a “universal” loot box that consists of zeroes and ones. As he says, accumulate enough and put them in the right order and you have any digital prize imaginable. Implementation is, as joked, the problem. Assembling ones and zeroes at random isn’t likely to turn up anything you might care about in a reasonable time. (It’s the monkeys-at-typewriters problem.) If you know how to assemble ones and zeroes to get what you want, well, what do you need Jason’s boxes for? As with most clever ideas by computer-oriented boys it shouldn’t really be listened to.

Mark Pett’s Lucky Cow rerun for the 4th has Neil make an order-of-magnitude error estimating what animal power can do. We’ve all made them. They’re particularly easy to make when switching the unit measure. Trying to go from meters to kilometers and multiplying the distance by a thousand, say. Which is annoying since often it’s easiest to estimate the order of magnitude of something first. I can’t find easily an estimate of how many calories a hamster eats over the course of the day. That seems like it would give an idea of how much energy a hamster could possibly be expected to provide, and so work out whether the estimate of four million hamsters to power a car is itself plausible. If someone has information, I’d take it.

Jonathan Lemon’s Rabbits Against Magic for the 4th is a Rubik’s Cube joke. Also a random processes joke. If a blender could turn the faces of a cube, and could turn them randomly, and could run the right period of time … well, yeah, it could unscramble a cube. But see the previous talk about Jason Fox and the delivery of ones and zeroes.

Mark Tatulli’s Lio for the 5th is a solid geometry joke. I’ve put more thought into whether and where to put hyphens in the last three words of that sentence than is worth it.

Steve Sicula’s Home and Away rerun for the 6th has the father and son happily doing some mathematics. It’s in the service of better gambling on sports. But at least they know why they would like to do these calculations.

## Reading the Comics, March 2, 2018: Socks Edition

There were enough comics last week to justify splitting them across two posts. But several of them were on a single theme. So they’re bundled together and you see what the theme is already if you pay attention to the edition titles.

Jeff Mallet’s Frazz on the 26th of February had a joke about a story problem going awry. Properly this should’ve been included in the Sunday update, but the theme was riffed on the next several days, and so I thought moving this made for a better split. In this case the kids resist the problem on the grounds that the cost ($1.50 for a pair of socks) is implausibly low. And now I’m reminded that a couple months ago I wondered if a comic strip (possibly Frazz again) gave a plausible price for apples. And I go to a great farmer’s market nearly every week and look at the apple prices and never think to write them down so I can check. But the topic, and the attempt to use the price of socks as a joke, continued on the 27th. Here the resistance was on the grounds there might be a sale on. Fair enough, although the students should feel free to ask about sales. And the teacher ought to be able to offer that. Also, it seems to me that “twice$5” is a different problem to “twice $1.50”, at least at this level. An easier one, I’d say, too. If the pair of socks were$4.50 it would preserve what I imagine is the point being tested. I think that’s how to multiply a compound fraction or a number with a decimal. But Frazz’s characters know the objectives better than I do.

The topic gets clarified on the 28th, which doesn’t end the students’ resistance on the grounds of plausibility. This seems to portray the kids as more conscious of clothing prices than I think I was as a kid, but it’s Mallet’s comic strip. He knows what his kids care about. The sequence closes out the 1st of March with a coda that’s the sort of joke every academic department tells about the others.

Julie Larson’s Dinette Set rerun for the 27th is an extended bit of people not understanding two-for-one sales. I’m tickled by it, but I won’t think ill of you if you decide you don’t want to read all those word balloons. There’s some further jokes in the signs and the t-shirts people are wearing, but they’re not part of the main joke. (Larson would often include stray extra jokes like that. It always confuses people who didn’t get the strip’s humor style.)

Dan Thompson’s Brevity for the 1st of March is close enough to the anthropomorphic numerals joke of the week.

Jeffery Lambros’s Domestic Abuse for the 1st is the spare numerical symbols joke for the week, too.

## Reading the Comics, February 26, 2018: Possible Reruns Edition

Comic Strip Master Command spent most of February making sure I could barely keep up. It didn’t slow down the final week of the month either. Some of the comics were those that I know are in eternal reruns. I don’t think I’m repeating things I’ve already discussed here, but it is so hard to be sure.

Bill Amend’s FoxTrot for the 24th of February has a mathematics problem with a joke answer. The approach to finding the area’s exactly right. It’s easy to find areas of simple shapes like rectangles and triangles and circles and half-circles. Cutting a complicated shape into known shapes, finding those areas, and adding them together works quite well, most of the time. And that’s intuitive enough. There are other approaches. If you can describe the outline of a shape well, you can use an integral along that outline to get the enclosed area. And that amazes me even now. One of the wonders of calculus is that you can swap information about a boundary for information about the interior, and vice-versa. It’s a bit much for even Jason Fox, though.

Jef Mallett’s Frazz for the 25th is a dispute between Mrs Olsen and Caulfield about whether it’s possible to give more than 100 percent. I come down, now as always, on the side that argues it depends what you figure 100 percent is of. If you mean “100% of the effort it’s humanly possible to expend” then yes, there’s no making more than 100% of an effort. But there is an amount of effort reasonable to expect for, say, an in-class quiz. It’s far below the effort one could possibly humanly give. And one could certainly give 105% of that effort, if desired. This happens in the real world, of course. Famously, in the right circles, the Space Shuttle Main Engines normally reached 104% of full throttle during liftoff. That’s because the original specifications for what full throttle would be turned out to be lower than was ultimately needed. And it was easier to plan around running the engines at greater-than-100%-throttle than it was to change all the earlier design documents.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 25th straddles the line between Pi Day jokes and architecture jokes. I think this is a rerun, but am not sure.

Matt Janz’s Out of the Gene Pool rerun for the 25th tosses off a mention of “New Math”. It’s referenced as a subject that’s both very powerful but also impossible for Pop, as an adult, to understand. It’s an interesting denotation. Usually “New Math”, if it’s mentioned at all, is held up as a pointlessly complicated way of doing simple problems. This is, yes, the niche that “Common Core” has taken. But Janz’s strip might be old enough to predate people blaming everything on Common Core. And it might be character, that the father is old enough to have heard of New Math but not anything in the nearly half-century since. It’s an unusual mention in that “New” Math is credited as being good for things. (I’m aware this strip’s a rerun. I had thought I’d mentioned it in an earlier Reading the Comics post, but can’t find it. I am surprised.)

Mark Anderson’s Andertoons for the 26th is a reassuring island of normal calm in these trying times. It’s a student-at-the-blackboard problem.

Morrie Turner’s Wee Pals rerun for the 26th just mentions arithmetic as the sort of homework someone would need help with. This is another one of those reruns I’d have thought has come up here before, but hasn’t.

## Reading the Comics, February 24, 2018: My One Boring Linear Algebra Anecdote Edition

Wait for it.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st mentions mathematics — geometry, primarily — as something a substitute teacher has tried teaching with the use of a cucumber and condom. These aren’t terrible examples to use to make concrete the difference between volumes and surface areas. There are limitations, though. It’s possible to construct a shape that has a finite volume but an infinitely large surface area, albeit not using cucumbers.

There’s also a mention of the spring constant, and physics. This isn’t explicitly mathematical. But the description of movement on a spring are about the first interesting differential equation of mathematical physics. The solution is that of simple harmonic motion. I don’t think anyone taking the subject for the first time would guess at the answer. But it’s easy enough to verify it’s right. And this motion — sine waves — just turns up everywhere in mathematical physics.

Bud Blake’s Tiger rerun for the 23rd just mentions mathematics as a topic Hugo finds challenging, and what’s challenging about it. So a personal story: when I took Intro to Linear Algebra my freshman year one day I spaced on the fact we had an exam. So, I put the textbook on the shelf under my desk, and then forgot to take it when I left. The book disappeared, of course, and the professor never heard of it being turned in to lost-and-found or anything. Fortunately the homework was handwritten questions passed out on photocopies (ask your parents), so I could still do the assignments, but for all those, you know, definitions and examples I had to rely on my own notes. I don’t know why I couldn’t ask a classmate. Shyness, probably. Came through all right, though.

Cathy Law’s Claw for the 23rd technically qualifies as an anthropomorphic-numerals joke, in this panel about the smothering of education by the infection of guns into American culture.

Jim Meddick’s Monty for the 23rd has wealthy child Wedgwick unsatisfied with a mere ball of snow. He instead has a snow Truncated Icosahedron (the hyphens in Jarvis’s word balloon may baffle the innocent reader). This is a real shape, one that’s been known for a very long time. It’s one of the Archimedean Solids, a set of 13 solids that have convex shapes (no holes or indents or anything) and have all vertices the same, the identical number of edges coming in to each point in the same relative directions. The truncated icosahedron you maybe also know as the soccer ball shape, at least for those old-style soccer balls made of patches that were hexagons and pentagons. An actual truncated icosahedron needs twelve pentagons, so the figure drawn in the third panel isn’t quite right. At least one pentagonal face would be visible. But that’s also tricky to draw. The aerodynamics of a truncated icosahedron are surely different from those of a sphere. But in snowball-fight conditions, probably not different enough to even notice.

Mark Litzler’s Joe Vanilla for the 24th uses a blackboard full of formulas to represent an overcomplicated answer. The formulas look, offhand, like gibberish to me. But I’ll admit uncertainty since the odd capitalization of “iG(p)” at the start makes me think of some deeper group theory or knot theory symbols. And to see an “m + p” and an “m – p” makes me think of quantum mechanics of atomic orbitals. (But then an “m – p2” is weird.) So if this were anything I’d say it was some quantum chemistry formula. But my gut says if Litzler did take the blackboard symbols from anything, it was without going back to references. (Which he has no need to do, I should point out; the joke wouldn’t be any stronger — or weaker — if the blackboard meant anything.)

## Reading the Comics, February 20, 2018: Bob the Squirrel Edition

So one comic strip was technically on point all this week, without ever quite giving me a specific thing to talk about. And I came to conclude there was another comic strip I could drop from my consideration. Which all were they? Read on.

Frank Page’s Bob the Squirrel for the 18th of February isn’t really about the Rubik’s Cube. It’s just something to occupy Bob’s mind until a deeper mystery emerges. Rubik’s Cubes, meanwhile, are everyone’s favorite group theory pastime, although I’m not sure how many people have learned group theory starting from that point. Where flies come from in the middle of winter I don’t know. We’ve been dealing with box elder bugs ourselves. (We’ve been scooping them up and tossing them outside where they can hopefully find the trees they should be using instead.)

Bob the Squirrel went on, during the week, to start a sequence about Lauren needing a geometry tutor. The story hasn’t done much that geometry-specific — Saturday’s was the most approximately on point — but it’s a comic strip I like. Squirrel fans might agree. (The strip for the 22nd has most tickled me.)

Allison Barrows’s PreTeena rerun for the 19th has a student teacher starting off her experience with a story problem. Your classic time-estimation problem.

Jack Pullan’s Boomerangs rerun for the 20th is one that mentions entropy and that I’ve already talked about at least twice before. These were times in January 2017 and also in November 2013. Given that the strip’s no longer in production and that I’m clearly on at least my third go-round I suppose I’ll retire it from my daily read. I’m curious why, if it was about 14 months between the last appearance and this appearance of this strip, why I didn’t have it at all in 2015 or 2016. Maybe I missed it, or it came a week there was enough to write about that I didn’t need to include a marginal strip.

Christopher Grady’s Lunarbaboon for the 20th is intended to be a heartwarming little story of encouragement and warm feelings. (Most Lunarbaboon strips are intended to be a heartwarming little story of encouragement and warm feelings.) That it’s mathematics the kid struggles with is incidental to the story setup. But it does make it easy to picture a kid struggling and a couple kind words offering some motivation, or at least better feelings.

Richard Thompson’s Richard’s Poor Almanac for the 20th is a casual mention of sudoku and a publication error that would supposedly have made it impossible. If the numbers were transposed consistently — everything that ought to have been a ‘2’ printed as a ‘5’, and everything that ought to have been ‘5’ printed as ‘2’ — the problem would be exactly as solvable. This is why you can sometimes see sudoku-type puzzles that use symbols or letters or other characters. But if, say, the third and the second rows were transposed then there’s a chance the incorrect puzzle would be solvable. Transposing a bunch of squares, like, the top three rows with the bottom three rows, wouldn’t make the puzzle unsolvable. This serves as a reminder that if you make enough mistakes you can still turn out all right, a comforting message for our times. Also I know I’ve featured Richard’s Poor Almanac several times over, but I’m a Richard Thompson fan so I’m not dropping that from my feed.

Will Henry’s Wallace the Brave — to be newspaper-syndicated from the 26th of March, by the way, and I’m glad for that as Wallace and I share the same favorite pinball game — just mentions mathematics as a subject Wallace isn’t thinking enough about. I’m also fond of the Loch Ness Monster, so, all the better.

I’m not surprised that this seems to be the first time I’ve had Lunarbabboon tagged. I am surprised that Bob the Squirrel seems not to have been tagged here before. Maybe I didn’t give the tag suggested-completion enough time to figure out what to do with ‘bob the’. We’ve been having odd little net glitches that mostly pass quickly, but that kill any sort of client-side Javascript-based page rendering. You know, like every web page does anymore because somehow “the web server puts together a bunch of stuff and transmits that to the reader” is too inefficient a system.