## Reading the Comics, July 11, 2018: GoComics Hardly Needs Me Edition

The first half of last week’s comics are mostly ones from Comics Kingdom and Creators.com. That’s unusual. GoComics usually far outranks the other sites. Partly for sheer numbers; they have an incredible number of strips, many of them web-only, that Comics Kingdom and Creators.com don’t match. I think the strips on GoComics are more likely to drift into mathematical topics too. But to demonstrate that would take so much effort. Possibly any effort at all. Hm.

Bill Holbrook’s On the Fastrack for the 8th of July is premised on topographic maps. These are some of the tools we’ve made to understand three-dimensional objects with a two-dimensional representation. When topographic maps come to the mathematics department we tend to call them “contour maps” or “contour plots”. These are collections of shapes. They might be straight lines. They might be curved. They often form a closed loop. Each of these curves is called a “contour curve” or a “contour line” (even if it’s not straight). Or it’s called an “equipotential curve”, if someone’s being all fancy, or pointing out the link between potential functions and these curves.

Their purpose is in thinking of three-dimensional surfaces. We can represent a three-dimensional surface by putting up some reasonable coordinate system. For the sake of simplicity let’s suppose the “reasonable coordinate system” is the Cartesian one. So every point in space has coordinates named ‘x’, ‘y’, and ‘z’. Pick a value for ‘x’ and ‘y’. There’s at most one ‘z’ that’ll be on the surface. But there might be many sets of values of ‘x’ and ‘y’ together which have that height ‘z’. So what are all the values of ‘x’ and ‘y’ which match the same height ‘z’? Draw the curve, or curves, which match that particular value of ‘z’.

Topographical maps are a beloved example of this, to mathematicians, because we imagine everyone understands them. A particular spot on the ground at some given latitude and longitude is some particular height above sea level. OK. Imagine the slice of a hill representing all the spots that are exactly 10 feet above sea level, or whatever. That’s a curve. Possibly several curves, but we just say “a curve” for simplicity.

A topographical map will often include more than one curve. Often at regular intervals, say with one set of curves representing 10 feet elevation, another 20 feet, another 30 feet, and so on. Sometimes these curves will be very near one another, where a hill is particularly steep. Sometimes these curves will be far apart, where the ground is nearly level. With experience one can learn to read the lines and their spacing. One can see where extreme values are, and how far away they might be.

Topographical maps date back to 1789. These sorts of maps go back farther. In 1701 Edmond Halley, of comet fame, published maps showing magnetic compass variation. He had hopes that the difference between magnetic north and true north would offer a hint at how to find longitude. (The principle is good. But the lines of constant variation are too close to lines of latitude for the method to be practical. And variation changes over time, too.) And that shows how the topographical map idea can be useful to visualize things that aren’t heights. Weather maps include “isobars”, contour lines showing where the atmospheric pressure is a set vale. More advanced ones will include “isotherms”, each line showing a particular temperature. The isobar and isotherm lines can describe the weather and how it can be expected to change soon.

This idea, rendering three-dimensional information on a two-dimensional surface, is a powerful one. We can use it to try to visualize four-dimensional objects, by looking at the contour surfaces they would make in three dimensions. We can also do this for five and even more dimensions, by using the same stuff but putting a note that “D = 16” or the like in the corner of our image. And, yes, if Cartesian coordinates aren’t sensible for the problem you can use coordinates that are.

If you need a generic name for these contour lines that doesn’t suggest lines or topography or weather or such, try ‘isogonal curves’. Nobody will know what you mean, but you’ll be right.

Ted Key’s Hazel for the 9th is a joke about the difficulties in splitting the bill. It is archetypical of the sort of arithmetic people know they need to do in the real world. Despite that at least people in presented humor don’t get any better at it. I suppose real-world people don’t either, given some restaurants now list 15 and 20 percent tips on the bill. Well, at least everybody has a calculator on their phone so they can divide evenly. And I concede that, yeah, there isn’t really specifically a joke here. It’s just Hazel being competent, like the last time she showed up here.

Mark Anderson’s Andertoons for the 11th is the Mark Anderson’s Andertoons for the week. And it’s a bit of geometry wordplay, too. Also about how you can carry a joke over well enough even without understanding it, or the audience understanding it, if it’s delivered right.

Rick DeTorie’s One Big Happy for the 11th is another strip about arithmetic done in the real world. I’m also amused by Joe’s attempts to distract from how no kid that age has ever not known precisely how much money they have, and how much of it is fairly won.

Bill Griffith’s Zippy the Pinhead for the 11th is another example of using understanding algebra as a show of intelligence. And it follows that up with undrestanding quantum physics as a show of even greater intelligence. One can ask what’s meant by “understanding” quantum physics. Someday someone might even answer. But it seems likely that the ability to do calculations based on a model has to be part of fully understanding it.

I have even more Reading the Comics posts, gathered in reverse chronological order at this link. Other essays with On The Fastrack tagged are at this link. Other Reading the Comics posts that mention Hazel are at this link. Some of the many, many essays mentioning Andertoons are at this link. Posts with mention of One Big Happy, both then-current and then-rerun, are at this link. And other mentions of Zippy the Pinhead are at this link.

## Reading the Comics, May 29, 2018: Finding Reruns Edition

There were a bunch of mathematically-themed comic strips this past week. A lot of them are ones I’d seen before. One of them is a bit risque and I’ve put that behind a cut. This saves me the effort of thinking up a good nonsense name to give this edition, so there’s that going for me too.

Bill Amend’s FoxTrot Classics for the 24th of May ought to have run last Sunday, but I wasn’t able to make time to write about it. It’s part of a sequence of Jason tutoring Paige in geometry. She’s struggling with the areas of common shapes which is relatable. Many of these area formulas could be kept straight by thinking back to rectangles. The size of the area is equal to the length of the base times the length of the height. From that you could probably reason right away the area of a trapezoid. It would have the same area as a rectangle with a base of length the mean length of the trapezoid’s different-length sides. The parallelogram works like the rectangle, length of the base times the length of the height. That you can convince yourself of by imagining the parallelogram. Then imagine slicing a right triangle off one of its sides. Move that around to the other side. Put it together right and you have a rectangle. Already know the area of a rectangle. The triangle, then, you can get by imagining two triangles of the same size and shape. Rotate one of the triangles 180 degrees. Slide it over, so the two triangles touch. Do this right and you have a parallelogram and so you know the area. The triangle’s half the area of that parallelogram.

The circle, I don’t know. I think just remember that if someone says “pi” they’re almost certainly going to follow it with either “r squared” or “day”. One of those suggests an area; the other doesn’t. Best I can do.

Allison Barrows’s PreTeena rerun for the 27th discusses self-esteem as though it were a good thing that children ought to have. This is part of the strip’s work to help build up the Old Person Complaining membership that every comics section community group relies on. But. There is mathematics in Jeri’s homework. Not mathematics in the sense of something particular to calculate. There’s just nothing to do there. But it is mathematics, and useful mathematics, to work out the logic of how to satisfy multiple requirements. Or, if it’s impossible to satisfy them all at once, then to come as near satisfying them as possible. These kinds of problems are considered optimization or logistics problems. Most interesting real-world examples are impossibly hard, or at least become impossibly hard before you realize it. You can make a career out of doing as best as possible in the circumstances.

Charles Schulz’s Peanuts rerun for the 27th features an extended discussion by Lucy about the nature of … well, she explicitly talks about “nothing”. Is she talking about zero? Probably; you have to get fairly into mathematics or philosophy to start worrying about the difference between the number zero and the idea of nothing. In Algebra, mathematicians learn to work with systems of things that work like numbers enough that you can add and subtract and multiply them together, without committing to the idea that they’re working with numbers. They will have something that works like zero, though, a “nothing” that can be added to or subtracted from anything without changing it. And for which multiplication turns something into that “nothing”.

I’m with Charlie Brown in not understanding where Lucy was going with all this, though. Maybe she lost the thread herself.

Mark Anderson’sAndertoons for the 28th is Mark Anderson’sAndertoons for the week. Wavehead’s worried about the verbs of both squaring and rounding numbers. Will say it’s a pair of words with contrary alternate meanings that I hadn’t noticed before. I have always taken the use of “square” to reflect, well, if you had a square with sides of size 4, then you’d have a square with area of size 16. The link seems obvious and logical. So on reflection that’s probably not at all where English gets it from. I mean, not to brag or anything but I’ve been speaking English all my life. If I’ve learned anything about it, it’s that the origin is probably something daft like “while Tisquantum [Squanto] was in England he impressed locals with his ability to do arithmetic and his trick of multiplying one number by itself got nicknamed squantuming, which got shortened to squaning to better fit the meter in a music-hall song about him, and a textbook writer in 1704 thought that was a mistake and `corrected’ it to squaring and everyone copied that”. I’m not even going to venture a guess about the etymology of “rounding”.

Marguerite Dabaie and Tom Hart’s Ali’s House for the 28th sets up a homework-help session over algebra. Can’t say where exactly Maisa is going wrong. Her saying “x equals 30 but the train equals” looks like trouble to me. It’s often good practice to start by writing out what are the things in the problem that seem important. And what symbol one wants each to mean. And what one knows about the relationship between these things. It helps clarify why someone would want to do that instead of something else. This is a new comic strip tag and I don’t think I’ve ever had cause to discuss it before.

Hilary Price’s Rhymes With Orange for the 29th is a Rubik’s Cube joke. I’ve counted that as mathematical enough, usually. The different ways that you can rotate parts of the cube form a group. This is something like what I mentioned in the Peanuts discussion. The different rotations you can do can be added to or subtracted from each other, the way numbers can. (Multiplication I’m wary about.)

And now here’s the strip that is unsuitable for reading at work, owing to the appearance of an undressed woman.

## Reading the Comics, May 23, 2018: Nice Warm Gymnasium Edition

I haven’t got any good ideas for the title for this collection of mathematically-themed comic strips. But I was reading the Complete Peanuts for 1999-2000 and just ran across one where Rerun talked about consoling his basketball by bringing it to a nice warm gymnasium somewhere. So that’s where that pile of words came from.

Mark Anderson’s Andertoons for the 21st is the Mark Anderson’s Andertoons for this installment. It has Wavehead suggest a name for the subtraction of fractions. It’s not by itself an absurd idea. Many mathematical operations get specialized names, even though we see them as specific cases of some more general operation. This may reflect the accidents of history. We have different names for addition and subtraction, though we eventually come to see them as the same operation.

In calculus we get introduced to Maclaurin Series. These are polynomials that approximate more complicated functions. They’re the best possible approximations for a region around 0 in the domain. They’re special cases of the Taylor Series. Those are polynomials that approximate more complicated functions. But you get to pick where in the domain they should be the best approximation. Maclaurin series are nothing but a Taylor series; we keep the names separate anyway, for the reasons. And slightly baffling ones; James Gregory and Brook Taylor studied Taylor series before Colin Maclaurin did Maclaurin series. But at least Taylor worked on Taylor series, and Maclaurin on Macularin series. So for a wonder mathematicians named these things for appropriate people. (Ignoring that Indian mathematicians were poking around this territory centuries before the Europeans were. I don’t know whether English mathematicians of the 18th century could be expected to know of Indian work in the field, in fairness.)

In numerical calculus, we have a scheme for approximating integrals known as the trapezoid rule. It approximates the areas under curves by approximating a curve as a trapezoid. (Any questions?) But this is one of the Runge-Kutta methods. Nobody calls it that except to show they know neat stuff about Runge-Kutta methods. The special names serve to pick out particularly interesting or useful cases of a more generally used thing. Wavehead’s coinage probably won’t go anywhere, but it doesn’t hurt to ask.

Percy Crosby’s Skippy for the 22nd I admit I don’t quite understand. It mentions arithmetic anyway. I think it’s a joke about a textbook like this being good only if it’s got the questions and the answers. But it’s the rare Skippy that’s as baffling to me as most circa-1930 humor comics are.

Ham’s Life on Earth for the 23rd presents the blackboard full of symbols as an attempt to prove something challenging. In this case, to say something about the existence of God. It’s tempting to suppose that we could say something about the existence or nonexistence of God using nothing but logic. And there are mathematics fields that are very close to pure logic. But our scary friends in the philosophy department have been working on the ontological argument for a long while. They’ve found a lot of arguments that seem good, and that fall short for reasons that seem good. I’ll defer to their experience, and suppose that any mathematics-based proof to have the same problems.

Bill Amend’s FoxTrot Classics for the 23rd deploys a Maclaurin series. If you want to calculate the cosine of an angle, and you know the angle in radians, you can find the value by adding up the terms in an infinitely long series. So if θ is the angle, measured in radians, then its cosine will be:

$\cos\left(\theta\right) = \sum_{k = 0}^{\infty} \left(-1\right)^k \frac{\theta^k}{k!}$

60 degrees is $\frac{\pi}{3}$ in radians and you see from the comic how to turn this series into a thing to calculate. The series does, yes, go on forever. But since the terms alternate in sign — positive then negative then positive then negative — you have a break. Suppose all you want is the answer to within an error margin. Then you can stop adding up terms once you’ve gotten to a term that’s smaller than your error margin. So if you want the answer to within, say, 0.001, you can stop as soon as you find a term with absolute value less than 0.001.

For high school trig, though, this is all overkill. There’s five really interesting angles you’d be expected to know anything about. They’re 0, 30, 45, 60, and 90 degrees. And you need to know about reflections of those across the horizontal and vertical axes. Those give you, like, -30 degrees or 135 degrees. Those reflections don’t change the magnitude of the cosines or sines. They might change the plus-or-minus sign is all. And there’s only three pairs of numbers that turn up for these five interesting angles. There’s 0 and 1. There’s $\frac{1}{2}$ and $\frac{\sqrt{3}}{2}$. There’s $\frac{1}{\sqrt{2}}$ and $\frac{1}{\sqrt{2}}$. Three things to memorize, plus a bit of orienteering, to know whether the cosine or the sine should be the larger size and whether they should positive or negative. And then you’ve got them all.

You might get asked for, like, the sine of 15 degrees. But that’s someone testing whether you know the angle-addition or angle-subtraction formulas. Or the half-angle and double-angle formulas. Nobody would expect you to know the cosine of 15 degrees. The cosine of 30 degrees, though? Sure. It’s $\frac{\sqrt{3}}{2}$.

Mike Thompson’s Grand Avenue for the 23rd is your basic confused-student joke. People often have trouble going from percentages to decimals to fractions and back again. Me, I have trouble in going from percentage chances to odds, as in, “two to one odds” or something like that. (Well, “one to one odds” I feel confident in, and “two to one” also. But, say, “seven to five odds” I can’t feel sure I understand, other than that the second choice is a perceived to be a bit more likely than the first.)

… You know, this would have parsed as the Maclaurin Series Edition, wouldn’t it? Well, if only I were able to throw away words I’ve already written and replace them with better words before publishing, huh?

## 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, 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 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, 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, 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 11, 2018: February 11, 2018 Edition

And it’s not always fair to say that the gods mock any plans made by humans, but Comic Strip Master Command has been doing its best to break me of reading and commenting on any comic strip with a mathematical theme. I grant that I could make things a little easier if I demanded more from a comic strip before including it here. But even if I think a theme is slight that doesn’t mean the reader does, and it’s easy to let the eye drop to the next paragraph if the reader does think it’s too slight. The anthology nature of these posts is part of what works for them. And then sometimes Comic Strip Master Command sends me a day like last Sunday when everybody was putting in some bit of mathematics. There’ll be another essay on the past week’s strips, never fear. But today’s is just for the single day.

Susan Camilleri Konar’s Six Chix for the 11th illustrates the Lemniscate Family. The lemniscate is a shape well known as the curve made by a bit of water inside a narrow tube by people who’ve confused it with a meniscus. An actual lemniscate is, as the chain of pointing fingers suggests, a figure-eight shape. You get — well, I got — introduced to them in prealgebra. They’re shapes really easy to describe in polar coordinates but a pain to describe in Cartesian coordinates. There are several different kinds of lemniscates, each satisfying slightly different conditions while looking roughly like a figure eight. If you’re open to the two lobes of the shape not being the same size there’s even a kind of famous-ish lemniscate called the analemma. This is the figure traced out by the sun if you look at its position from a set point on the surface of the Earth at the same clock time each day over the course of the year. That the sun moves north and south from the horizon is easy to spot. That it is sometimes east or west of some reference spot is a surprise. It shows the difference between the movement of the mean sun, the sun as we’d see it if the Earth had a perfectly circular orbit, and the messy actual thing. Dr Helmer Aslasken has a fine piece about this, and how it affects when the sun rises earliest and latest in the year.

There’s also a thing called the “polynomial lemniscate”. This is a level curve of a polynomial. That is, what are all the possible values of the independent variable which cause the polynomial to evaluate to some particular number? This is going to be a polynomial in a complex-valued variable, in order to get one or more closed and (often) wriggly loops. A polynomial of a real-valued variable would typically give you a boring shape. There’s a bunch of these polynomial lemniscates that approximate the boundary of the Mandelbrot Set, that fractal that you know from your mathematics friend’s wall in 1992.

Mark Anderson’s Andertoons took care of being Mark Anderson’s Andertoons early in the week. It’s a bit of optimistic blackboard work.

Lincoln Pierce’s Big Nate features the formula for calculating the wind chill factor. Francis reads out what is legitimately the formula for estimating the wind chill temperature. I’m not going to get into whether the wind chill formula makes sense as a concept because I’m not crazy. The thinking behind it is that a windless temperature feels about the same as a different temperature with a particular wind. How one evaluates those equivalences offers a lot of room for debate. The formula as the National Weather Service, and Francis, offer looks frightening, but isn’t really hard. It’s not a polynomial, in terms of temperature and wind speed, but it’s close to that in form. The strip is rerun from the 15th of February, 2009, as Lincoln Pierce has had some not-publicly-revealed problem taking him away from the comic for about a month and a half now.

Jim Scancarelli’s Gasoline Alley included a couple of mathematics formulas, including the famous E = mc2 and the slightly less famous πr2, as part of Walt Wallet’s fantasy of advising scientists and inventors. (Scientists have already heard both.) There’s a curious stray bit in the corner, writing out 6.626 x 102 x 3 that I wonder about. 6.626 is the first couple digits of Planck’s Constant, as measured in Joule-seconds. (This is h, not h-bar, I say for the person about to complain.) It’d be reasonable for Scancarelli to have drawn that out of a physics book or reference page. But the exponent is all wrong, even if you suppose he mis-wrote 1023. It should be 6.626 x 10-34. So I don’t know whether Scancarelli got things very garbled, or if he just picked a nice sciencey-looking number and happened to hit on a significant one. (There’s enough significant science numbers that he’d have a fair chance of finding something.) The strip is a reprint from the 4th of February, 2007, as Jim Scancarelli has been absent for no publicly announced reason for four months now.

Greg Evans and Karen Evans’s Luann is not perfectly clear. But I think it’s presenting Gunther doing mathematics work to support his mother’s contention that he’s smart. There’s no working out what work he’s doing. But then we might ask how smart his mother is to have made that much food for just the two of them. Also that I think he’s eating a potato by hand? … Well, there are a lot of kinds of food that are hard to draw.

Greg Evans’s Luann Againn reprints the strip from the 11th of February (again), 1990. It mentions as one of those fascinating things of arithmetic an easy test to see if a number’s a multiple of nine. There are several tricks like this, although the only ones anybody can remember are finding multiples of 3 and finding multiples of 9. Well, they know the rules for something being a multiple of 2, 5, or 10, but those hardly look like rules, and there’s no addition needed. Similarly with multiples of 4.

Modular arithmetic underlies all these rules. Once you know the trick you can use it to work out your own add-up-the-numbers rules to find what numbers are multiples of small numbers. Here’s an example. Think of a three-digit number. Suppose its first digit is ‘a’, its second digit ‘b’, and its third digit ‘c’. So we’d write the number as ‘abc’, or, 100a + 10b + 1c. What’s this number equal to, modulo 9? Well, 100a modulo 9 has to be equal to whatever a modulo 9 is: (100 a) modulo 9 is (100) modulo 9 — that is, 1 — times (a) modulo 9. 10b modulo 9 is (10) modulo 9 — again, 1 — times (b) modulo 9. 1c modulo 9 is … well, (c) modulo 9. Add that all together and you have a + b + c modulo 9. If a + b + c is some multiple of 9, so must be 100a + 10b + 1c.

The rules about whether something’s divisible by 2 or 5 or 10 are easy to work with since 10 is a multiple of 2, and of 5, and for that matter of 10, so that 100a + 10b + 1c modulo 10 is just c modulo 10. You might want to let this settle. Then, if you like, practice by working out what an add-the-digits rule for multiples of 11 would be. (This is made a lot easier if you remember that 10 is equal to 11 – 1.) And if you want to show off some serious arithmetic skills, try working out an add-the-digits rule for finding whether something’s a multiple of 7. Then you’ll know why nobody has ever used that for any real work.

J C Duffy’s Lug Nuts plays on the equivalence people draw between intelligence and arithmetic ability. Also on the idea that brain size should have something particularly strong link to intelligence. Really anyone having trouble figuring out 15% of $10 is psyching themselves out. They’re too much overwhelmed by the idea of percents being complicated to realize that it’s, well, ten times 15 cents. ## Reading the Comics, January 22, 2018: Breaking Workflow Edition So I was travelling last week, and this threw nearly all my plans out of whack. We stayed at one of those hotels that’s good enough that its free Internet is garbage and they charge you by day for decent Internet. So naturally Comic Strip Master Command sent a flood of posts. I’m trying to keep up and we’ll see if I wrap up this past week in under three essays. And I am not helped, by the way, by GoComics.com rejiggering something on their server so that My Comics Page won’t load, and breaking their “Contact Us” page so that that won’t submit error reports. If someone around there can break in and turn one of their servers off and on again, I’d appreciate the help. Hy Eisman’s Katzenjammer Kids for the 21st of January is a curiously-timed Tax Day joke. (Well, the Katzenjammer Kids lapsed into reruns a dozen years ago and there’s probably not much effort being put into selecting seasonally appropriate ones.) But it is about one of the oldest and still most important uses of mathematics, and one that never gets respect. Morrie Turner’s Wee Pals rerun for the 21st gets Oliver the reputation for being a little computer because he’s good at arithmetic. There is something that amazes in a person who’s able to calculate like this without writing anything down or using a device to help. Steve Kelley and Jeff Parker’s Dustin for the 22nd seems to be starting off with a story problem. It might be a logic problem rather than arithmetic. It’s hard to say from what’s given. Mark Anderson’s Andertoons for the 22nd is the Mark Anderson’s Andertoons for the week. Well, for Monday, as I write this. It’s got your classic blackboard full of equations for the people in over their head. The equations look to me like gibberish. There’s a couple diagrams of aromatic organic compounds, which suggests some quantum-mechanics chemistry problem, if you want to suppose this could be narrowed down. Greg Evans’s Luann Againn for the 22nd has Luann despair about ever understanding algebra without starting over from scratch and putting in excessively many hours of work. Sometimes it feels like that. My experience when lost in a subject has been that going back to the start often helps. It can be easier to see why a term or a concept or a process is introduced when you’ve seen it used some, and often getting one idea straight will cause others to fall into place. When that doesn’t work, trying a different book on the same topic — even one as well-worn as high school algebra — sometimes helps. Just a different writer, or a different perspective on what’s key, can be what’s needed. And sometimes it just does take time working at it all. Richard Thompson’s Richard’s Poor Almanac rerun for the 22nd includes as part of a kit of William Shakespeare paper dolls the Typing Monkey. It’s that lovely, whimsical figure that might, in time, produce any written work you could imagine. I think I’d retired monkeys-at-typewriters as a thing to talk about, but I’m easily swayed by Thompson’s art and comic stylings so here it is. Darrin Bell and Theron Heir’s Rudy Park for the 18th throws around a lot of percentages. It’s circling around the sabermetric-style idea that everything can be quantified, and measured, and that its changes can be tracked. In this case it’s comments on Star Trek: Discovery, but it could be anything. I’m inclined to believe that yeah, there’s an astounding variety of things that can be quantified and measured and tracked. But it’s also easy, especially when you haven’t got a good track record of knowing what is important to measure, to start tracking what amounts to random noise. (See any of my monthly statistics reviews, when I go looking into things like views-per-visitor-per-post-made or some other dubiously meaningful quantity.) So I’m inclined to side with Randy and his doubts that the Math Gods sanction this much data-mining. ## Reading the Comics, January 20, 2018: Increased Workload Edition It wasn’t much of an increased workload, really. I mean, none of the comics required that much explanation. But Comic Strip Master Command donated enough topics to me last week that I have a second essay for the week. And here it is; sorry there’s no pictures. Mark Anderson’s Andertoons for the 17th is the Mark Anderson’s Andertoons we’ve been waiting for. It returns to fractions and their frustrations for its comic point. Jef Mallet’s Frazz for the 17th talks about story problems, although not to the extent of actually giving one as an example. It’s more about motivating word-problem work. Mike Thompson’s Grand Avenue for the 17th is an algebra joke. I’d call it a cousin to the joke about mathematics’s ‘x’ not coming back and we can’t say ‘y’. On the 18th was one mentioning mathematics, although in a joke structure that could have been any subject. Lorrie Ransom’s The Daily Drawing for the 18th is another name-drop of mathematics. I guess it’s easier to use mathematics as the frame for saying something’s just a “problem”. I don’t think of, say, identifying the themes of a story as a problem in the way that finding the roots of a quadratic is. Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 18th is an anthropomorphic-geometric-figures joke that I’m all but sure is a rerun I’ve shared here before. I’ll try to remember to check before posting this. Mikael Wulff and Anders Morgenthaler’s WuMo for the 20th gives us a return of the pie chart joke that seems like it’s been absent a while. Worth including? Eh, why not. ## Reading the Comics, January 6, 2018: Terms Edition The last couple days of last week saw a rush of comics, although most of them were simpler things to describe. Bits of play on words, if you like. Samson’s Dark Side of the Horse for the 4th of January, 2018, is one that plays on various meanings of “average”. The mean, alluded to in the first panel, is the average most people think of first. Where you have a bunch of values representing instances of something, add up the values, and divide by the number of instances. (Properly that’s the arithmetic mean. There’s some others, such as the geometric mean, but if someone’s going to use one of those they give you clear warning.) The median, in the second, is the midpoint, the number that half of all instances are less than. So you see the joke. If the distribution of intelligence is normal — which is a technical term, although it does mean “not freakish” — then the median and the mean should be equal. If you had infinitely many instances, and they were normally distributed, the two would be equal. With finitely many instances, the mean and the median won’t be exactly in line, for the same reason if you fairly toss a coin two million times it won’t turn up heads exactly one million times. Dark Side of the Horse for the 5th delivers the Roman numerals joke of the year. And I did have to think about whether ‘D’ is a legitimate Roman numeral. This would be easier to remember before 1900. Mike Lester’s Mike du Jour for the 4th is geometry wordplay. I’m not sure the joke stands up to scrutiny, but it lands well enough initially. Johnny Hart’s Back to BC for the 5th goes to the desire to quantify and count things. And to double-check what other people tell you about this counting. It’s easy, today, to think of the desire to quantify things as natural to humans. I’m not confident that it is. The history of statistics shows this gradual increase in the number and variety of things getting tracked. This strip originally ran the 11th of July, 1960. Bill Watterson’s Calvin and Hobbes for the 5th talks about averages again. And what a population average means for individuals. It doesn’t mean much. The glory of statistics is that groups are predictable in a way that individuals are not. John Graziano’s Ripley’s Believe It Or Not for the 5th features a little arithmetic coincidence, that multiplying 21,978 by four reverses its digits. It made me think of Ray Kassinger’s question the other day about parasitic numbers. But this isn’t a parasitic number. A parasitic number is one with a value, multiplied by a particular number, that’s the same as you get by moving its last digit to the front. Flipping the order of digits seems like it should be something and I don’t know what. Mark Anderson’s Andertoons for the 6th is a confident reassurance that 2018 is a normal, healthy year after all. Or can be. Prime numbers. Mark O’Hare’s Citizen Dog rerun for the 6th is part of a sequence in which Fergus takes a (human) child’s place in school. Mathematics gets used as a subject that’s just a big pile of unfamiliar terms if you just jump right in. Most subjects are like this if you take them seriously, of course. But mathematics has got an economy of technical terms to stuff into people’s heads, and that have to be understood to make any progress. In grad school my functional analysis professor took great mercy on us, and started each class with re-writing the definitions of all the technical terms introduced the previous class. Also of terms that might be a bit older, but that are important to get right, which is why I got through it confident I knew what a Sobolev Space was. (It’s a collection of functions that have enough derivatives to do your differential equations problem.) Numerator and denominator, we’re experts on by now. ## Reading the Comics, December 16, 2017: Andertoons Drought Ended Edition And now, finally, we get what we’ve been waiting so long for: my having enough energy and time to finish up last week’s comics. And I make excuses to go all fanboy over Elzie Segar’s great Thimble Theatre. Also more attention to Zach Weinersmith. You’ve been warned. Mark Anderson’s Andertoons for the 13th is finally a breath of Mark Anderson’s Andertoons around here. Been far too long. Anyway it’s an algebra joke about x’s search for identity. And as often happens I’m sympathetic here. It’s not all that weird to think of ‘x’ as a label for some number. Knowing whether it means “a number whose value we haven’t found yet” or “a number whose value we don’t care about” is one trick, though. It’s not something you get used to from learning about, like, ‘6’. And knowing whether we can expect ‘x’ to have held whatever value it represented before, or whether we can expect it to be something different, is another trick. Doug Bratton’s Pop Culture Shock Therapy for the 13th I feel almost sure has come up here before. Have I got the energy to find where? Oh, yes. It ran the 5th of September, 2015. David Gilbert’s Buckles for the 14th is a joke on animals’ number sense. In fairness, after that start I wouldn’t know whether to go for four or five barks myself. Bud Blake’s Tiger for the 15th is a bit of kid logic about how to make a long column of numbers easier to add. I endorse the plan of making the column shorter, although I’d do that by trying to pair up numbers that, say, add to 10 or 20 or something else easy to work with. Partial sums can make the overall work so much easier. And probably avoid mistakes. Elzie Segar’s Thimble Theatre for the 8th of July, 1931, is my most marginal inclusion yet. It was either that strip or the previous day’s worth including. I’m throwing it in here because Segar’s Thimble Theatre keeps being surprisingly good. And, heck, slowing a count by going into fractions is viable way to do it. As the clobbered General Bunzo points out, you can drag this out longer by going into hundredths. Or smaller units. There is no largest real number less than ten; if it weren’t incredibly against the rules, boxers could make use of that. Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is about those mathematics problems with clear and easy-to-understand statements whose answers defy intuition. Weinersmith is completely correct about all of this. I’m surprised he doesn’t mention the one about how you could divide an orange into five pieces, reassemble the pieces, and get back two spheres each the size of a sun. ## Reading the Comics, November 25, 2017: Shapes and Probability Edition This week was another average-grade week of mathematically-themed comic strips. I wonder if I should track them and see what spurious correlations between events and strips turn up. That seems like too much work and there’s better things I could do with my time, so it’s probably just a few weeks before I start doing that. Ruben Bolling’s Super-Fun-Pax Comics for the 19th is an installment of A Voice From Another Dimension. It’s in that long line of mathematics jokes that are riffs on Flatland, and how we might try to imagine spaces other than ours. They’re taxing things. We can understand some of the rules of them perfectly well. Does that mean we can visualize them? Understand them? I’m not sure, and I don’t know a way to prove whether someone does or does not. This wasn’t one of the strips I was thinking of when I tossed “shapes” into the edition title, but you know what? It’s close enough to matching. Olivia Walch’s Imogen Quest for the 20th — and I haven’t looked, but it feels to me like I’m always featuring Imogen Quest lately — riffs on the Monty Hall Problem. The problem is based on a game never actually played on Monty Hall’s Let’s Make A Deal, but very like ones they do. There’s many kinds of games there, but most of them amount to the contestant making a choice, and then being asked to second-guess the choice. In this case, pick a door and then second-guess whether to switch to another door. The Monty Hall Problem is a great one for Internet commenters to argue about while the rest of us do something productive. The trouble — well, one trouble — is that whether switching improves your chance to win the car is that whether it does depends on the rules of the game. It’s not stated, for example, whether the host must open a door showing a goat behind it. It’s not stated that the host certainly knows which doors have goats and so chooses one of those. It’s not certain the contestant even wants a car when, hey, goats. What assumptions you make about these issues affects the outcome. If you take the assumptions that I would, given the problem — the host knows which door the car’s behind, and always offers the choice to switch, and the contestant would rather have a car, and such — then Walch’s analysis is spot on. Jonathan Mahood’s Bleeker: The Rechargeable Dog for the 20th features a pretend virtual reality arithmetic game. The strip is of incredibly low mathematical value, but it’s one of those comics I like that I never hear anyone talking about, so, here. Richard Thompson’s Cul de Sac rerun for the 20th talks about shapes. And the names for shapes. It does seem like mathematicians have a lot of names for slightly different quadrilaterals. In our defense, if you’re talking about these a lot, it helps to have more specific names than just “quadrilateral”. Rhomboids are those parallelograms which have all four sides the same length. A parallelogram has to have two pairs of equal-sized legs, but the two pairs’ sizes can be different. Not so a rhombus. Mathworld says a rhombus with a narrow angle that’s 45 degrees is sometimes called a lozenge, but I say they’re fibbing. They make even more preposterous claims on the “lozenge” page. Todd Clark’s Lola for the 20th does the old “when do I need to know algebra” question and I admit getting grumpy like this when people ask. Do French teachers have to put up with this stuff? Brian Fies’s Mom’s Cancer rerun for the 23rd is from one of the delicate moments in her story. Fies’s mother just learned the average survival rate for her cancer treatment is about five percent and, after months of things getting haltingly better, is shaken. But as with most real-world probability questions context matters. The five-percent chance is, as described, the chance someone who’d just been diagnosed in the state she’d been diagnosed in would survive. The information that she’s already survived months of radiation and chemical treatment and physical therapy means they’re now looking at a different question. What is the chance she will survive, given that she has survived this far with this care? Mark Anderson’s Andertoons for the 24th is the Mark Anderson’s Andertoons for the week. It’s a protesting-student kind of joke. For the student’s question, I’m not sure how many sides a polygon has before we can stop memorizing them. I’d say probably eight. Maybe ten. Of the shapes whose names people actually care about, mm. Circle, triangle, a bunch of quadrilaterals, pentagons, hexagons, octagons, maybe decagon and dodecagon. No, I’ve never met anyone who cared about nonagons. I think we could drop heptagons without anyone noticing either. Among quadrilaterals, ugh, let’s see. Square, rectangle, rhombus, parallelogram, trapezoid (or trapezium), and I guess diamond although I’m not sure what that gets you that rhombus doesn’t already. Toss in circles, ellipses, and ovals, and I think that’s all the shapes whose names you use. Stephan Pastis’s Pearls Before Swine for the 25th does the rounding-up joke that’s been going around this year. It’s got a new context, though. ## Reading the Comics, October 14, 2017: Physics Equations Edition So that busy Saturday I promised for the mathematically-themed comic strips? Here it is, along with a Friday that reached the lowest non-zero levels of activity. Stephan Pastis’s Pearls Before Swine for the 13th is one of those equations-of-everything jokes. Naturally it features a panel full of symbols that, to my eye, don’t parse. There are what look like syntax errors, for example, with the one that anyone could see the { mark that isn’t balanced by a }. But when someone works rough they will, often, write stuff that doesn’t quite parse. Think of it as an artist’s rough sketch of a complicated scene: the lines and anatomy may be gibberish, but if the major lines of the composition are right then all is well. Most attempts to write an equation for everything are really about writing a description of the fundamental forces of nature. We trust that it’s possible to go from a description of how gravity and electromagnetism and the nuclear forces go to, ultimately, a description of why chemistry should work and why ecologies should form and there should be societies. There are, as you might imagine, a number of assumed steps along the way. I would accept the idea that we’ll have a unification of the fundamental forces of physics this century. I’m not sure I would believe having all the steps between the fundamental forces and, say, how nerve cells develop worked out in that time. Mark Anderson’s Andertoons makes it overdue appearance for the week on the 14th, with a chalkboard word-problem joke. Amusing enough. And estimating an answer, getting it wrong, and refining it is good mathematics. It’s not just numerical mathematics that will look for an approximate solution and then refine it. As a first approximation, 15 minus 7 isn’t far off 10. And for mental arithmetic approximating 15 minus 7 as 10 is quite justifiable. It could be made more precise if a more exact answer were needed. Maria Scrivan’s Half Full for the 14th I’m going to call the anthropomorphic geometry joke for the week. If it’s not then it’s just wordplay and I’d have no business including it here. Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 14th tosses in the formula describing how strong the force of gravity between two objects is. In Newtonian gravity, which is why it’s the Newton Police. It’s close enough for most purposes. I’m not sure how this supports the cause of world peace. Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 14th names Riemann’s Quaternary Conjecture. I was taken in by the panel, trying to work out what the proposed conjecture could even mean. The reason it works is that Bernhard Riemann wrote like 150,000 major works in every field of mathematics, and about 149,000 of them are big, important foundational works. The most important Riemann conjecture would be the one about zeroes of the Riemann Zeta function. This is typically called the Riemann Hypothesis. But someone could probably write a book just listing the stuff named for Riemann, and that’s got to include a bunch of very specific conjectures. ## Reading the Comics, October 4, 2017: Time-Honored Traditions Edition It was another busy week in mathematically-themed comic strips last week. Busy enough I’m comfortable rating some as too minor to include. So it’s another week where I post two of these Reading the Comics roundups, which is fine, as I’m still recuperating from the Summer 2017 A To Z project. This first half of the week includes a lot of rerun comics, and you’ll see why my choice of title makes sense. Lincoln Pierce’s Big Nate: First Class for the 1st of October reprints the strip from the 2nd of October, 1993. It’s got a well-formed story problem that, in the time-honored tradition of this setup, is subverted. I admit I kind of miss the days when exams would have problems typed out in monospace like this. Ashleigh Brilliant’s Pot-Shots for the 1st is a rerun from sometime in 1975. And it’s an example of the time-honored tradition of specifying how many statistics are made up. Here it comes in at 43 percent of statistics being “totally worthless” and I’m curious how the number attached to this form of joke changes over time. The Joey Alison Sayers Comic for the 2nd uses a blackboard with mathematics — a bit of algebra and a drawing of a sphere — as the designation for genius. That’s all I have to say about this. I remember being set straight about the difference between ponies and horses and it wasn’t by my sister, who’s got a professional interest in the subject. Mark Pett’s Lucky Cow rerun for the 2nd is a joke about cashiers trying to work out change. As one of the GoComics.com commenters mentions, the probably best way to do this is to count up from the purchase to the amount you have to give change for. That is, work out$12.43 to $12.50 is seven cents, then from$12.50 to $13.00 is fifty more cents (57 cents total), then from$13.00 to $20.00 is seven dollars ($7.57 total) and then from $20 to$50 is thirty dollars ($37.57 total). It does make me wonder, though: what did Neil enter as the amount tendered, if it wasn’t$50? Maybe he hit “exact change” or whatever the equivalent was. It’s been a long, long time since I worked a cash register job and while I would occasionally type in the wrong amount of money, the kinds of errors I would make would be easy to correct for. (Entering $30 instead of$20 for the tendered amount, that sort of thing.) But the cash register works however Mark Pett decides it works, so who am I to argue?

Keith Robinson’s Making It rerun for the 2nd includes a fair bit of talk about ratios and percentages, and how to inflate percentages. Also about the underpaying of employees by employers.

Mark Anderson’s Andertoons for the 3rd continues the streak of being Mark Anderson Andertoons for this sort of thing. It has the traditional form of the student explaining why the teacher’s wrong to say the answer was wrong.

Brian Fies’s The Last Mechanical Monster for the 4th includes a bit of legitimate physics in the mad scientist’s captioning. Ballistic arcs are about a thing given an initial speed in a particular direction, moving under constant gravity, without any of the complicating problems of the world involved. No air resistance, no curvature of the Earth, level surfaces to land on, and so on. So, if you start from a given height (‘y0‘) and a given speed (‘v’) at a given angle (‘θ’) when the gravity is a given strength (‘g’), how far will you travel? That’s ‘d’. How long will you travel? That’s ‘t’, as worked out here.

(I should maybe explain the story. The mad scientist here is the one from the first, Fleischer Studios, Superman cartoon. In it the mad scientist sends mechanical monsters out to loot the city’s treasures and whatnot. As the cartoon has passed into the public domain, Brian Fies is telling a story of that mad scientist, finally out of jail, salvaging the one remaining usable robot. Here, training the robot to push aside bank tellers has gone awry. Also, the ground in his lair is not level.)

Tom Toles’s Randolph Itch, 2 am rerun for the 4th uses the time-honored tradition of Albert Einstein needing a bit of help for his work.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th uses the time-honored tradition of little bits of physics equations as designation of many deep thoughts. And then it gets into a bit more pure mathematics along the way. It also reflects the time-honored tradition of people who like mathematics and physics supposing that those are the deepest and most important kinds of thoughts to have. But I suppose we all figure the things we do best are the things it’s important to do best. It’s traditional.

And by the way, if you’d like more of these Reading the Comics posts, I put them all in the category ‘Comic Strips’ and I just now learned the theme I use doesn’t show categories for some reason? This is unsettling and unpleasant. Hm.

## Reading the Comics, September 29, 2017: Anthropomorphic Mathematics Edition

The rest of last week had more mathematically-themed comic strips than Sunday alone did. As sometimes happens, I noticed an objectively unimportant detail in one of the comics and got to thinking about it. Whether I could solve the equation as posted, or whether at least part of it made sense as a mathematics problem. Well, you’ll see.

Patrick McDonnell’s Mutts for the 25th of September I include because it’s cute and I like when I can feature some comic in these roundups. Maybe there’s some discussion that could be had about what “equals” means in ordinary English versus what it means in mathematics. But I admit that’s a stretch.

Olivia Walch’s Imogen Quest for the 25th uses, and describes, the mathematics of a famous probability problem. This is the surprising result of how few people you need to have a 50 percent chance that some pair of people have a birthday in common. It then goes over to some other probability problems. The examples are silly. But the reasoning is sound. And the approach is useful. To find the chance of something happens it’s often easiest to work out the chance it doesn’t. Which is as good as knowing the chance it does, since a thing can either happen or not happen. At least in probability problems, which define “thing” and “happen” so there’s not ambiguity about whether it happened or not.

Piers Baker’s Ollie and Quentin rerun for the 26th I’m pretty sure I’ve written about before, although back before I included pictures of the Comics Kingdom strips. (The strip moved from Comics Kingdom over to GoComics, which I haven’t caught removing old comics from their pages.) Anyway, it plays on a core piece of probability. It sets out the world as things, “events”, that can have one of multiple outcomes, and which must have one of those outcomes. Coin tossing is taken to mean, by default, an event that has exactly two possible outcomes, each equally likely. And that is near enough true for real-world coin tossing. But there is a little gap between “near enough” and “true”.

Rick Stromoski’s Soup To Nutz for the 27th is your standard sort of Dumb Royboy joke, in this case about him not knowing what percentages are. You could do the same joke about fractions, including with the same breakdown of what part of the mathematics geek population ruins it for the remainder.

Nate Fakes’s Break of Day for the 28th is not quite the anthropomorphic-numerals joke for the week. Anthropomorphic mathematics problems, anyway. The intriguing thing to me is that the difficult, calculus, problem looks almost legitimate to me. On the right-hand-side of the first two lines, for example, the calculation goes from

$\int -8 e^{-\frac{ln 3}{14} t}$

to
$-8 -\frac{14}{ln 3} e^{-\frac{ln 3}{14} t}$

This is a little sloppy. The first line ought to end in a ‘dt’, and the second ought to have a constant of integration. If you don’t know what these calculus things are let me explain: they’re calculus things. You need to include them to express the work correctly. But if you’re just doing a quick check of something, the mathematical equivalent of a very rough preliminary sketch, it’s common enough to leave that out.

It doesn’t quite parse or mean anything precisely as it is. But it looks like the sort of thing that some context would make meaningful. That there’s repeated appearances of $- \frac{ln 3}{14}$, or $- \frac{14}{ln 3}$, particularly makes me wonder if Frakes used a problem he (or a friend) was doing for some reason.

Mark Anderson’s Andertoons for the 29th is a welcome reassurance that something like normality still exists. Something something student blackboard story problem something.

Anthony Blades’s Bewley rerun for the 29th depicts a parent once again too eager to help with arithmetic homework.

Maria Scrivan’s Half Full for the 29th gives me a proper anthropomorphic numerals panel for the week, and none too soon.

## Reading the Comics, September 22, 2017: Doughnut-Cutting Edition

The back half of last week’s mathematically themed comic strips aren’t all that deep. They make up for it by being numerous. This is how calculus works, so, good job, Comic Strip Master Command. Here’s what I have for you.

Mark Anderson’s Andertoons for the 20th marks its long-awaited return to these Reading The Comics posts. It’s of the traditional form of the student misunderstanding the teacher’s explanations. Arithmetic edition.

Marty Links’s Emmy Lou for the 20th was a rerun from the 22nd of September, 1976. It’s just a name-drop. It’s not like it matters for the joke which textbook was lost. I just include it because, what the heck, might as well.

Jef Mallett’s Frazz for the 21st uses the form of a story problem. It’s a trick question anyway; there’s really no way the Doppler effect is going to make an ice cream truck’s song unrecognizable, not even at highway speeds. Too distant to hear, that’s a possibility. Also I don’t know how strictly regional this is but the ice cream trucks around here have gone in for interrupting the music every couple seconds with some comical sound effect, like a “boing” or something. I don’t know what this hopes to achieve besides altering the timeline of when the ice cream seller goes mad.

Mark Litzler’s Joe Vanilla for the 21st I already snuck in here last week, in talking about ‘x’. The variable does seem like a good starting point. And, yeah, hypothesis block is kind of a thing. There’s nothing quite like staring at a problem that should be interesting and having no idea where to start. This happens even beyond grade school and the story problems you do then. What to do about it? There’s never one thing. Study it a good while, read about related problems a while. Maybe work on something that seems less obscure a while. It’s very much like writer’s block.

Ryan North’s Dinosaur Comics rerun for the 22nd straddles the borders between mathematics, economics, and psychology. It’s a problem about making forecasts about other people’s behavior. It’s a mystery of game theory. I don’t know a proper analysis for this game. I expect it depends on how many rounds you get to play: if you have a sense of what people typically do, you can make a good guess of what they will do. If everyone gets a single shot to play, all kinds of crazy things might happen.

Jef Mallet’s Frazz gets in again on the 22nd with some mathematics gibberish-talk, including some tossing around of the commutative property. Among other mistakes Caulfield was making here, going from “less is more to therefore more is less” isn’t commutation. Commutation is about binary operations, where you match a pair of things to a single thing. The operation commutes if it never matters what the order of the pair of things is. It doesn’t commute if it ever matters, even a single time, what the order is. Commutativity gets introduced in arithmetic where there are some good examples of the thing. Addition and multiplication commute. Subtraction and division don’t. From there it gets forgotten until maybe eventually it turns up in matrix multiplication, which doesn’t commute. And then it gets forgotten once more until maybe group theory. There, whether operations commute or not is as important a divide as the one between vertebrates and invertebrates. But I understand kids not getting why they should care about commuting. Early on it seems like a longwinded way to say what’s obvious about addition.

Michael Cavna’s Warped for the 22nd is the Venn Diagram joke for this round of comics.

Bud Blake’s Tiger rerun for the 23rd starts with a real-world example of your classic story problem. I like the joke in it, and I also like Hugo’s look of betrayal and anger in the second panel. A spot of expressive art will do so good for a joke.

## Reading the Comics, September 8, 2017: First Split Week Edition, Part 1

It was looking like another slow week for something so early in the (United States) school year. Then Comic Strip Master Commend sent a flood of strips in for Friday and Saturday, so I’m splitting the load. It’s not a heavy one, as back-to-school jokes are on people’s minds. But here goes.

Marcus Hamilton and Scott Ketcham’s Dennis the Menace for the 3rd of September, 2017 is a fair strip for this early in the school year. It’s an old joke about making subtraction understandable.

Mark Anderson’s Andertoons for the 3rd is the Mark Anderson installment for this week, so I’m glad to have that. It’s a good old classic cranky-students setup and it reminds me that “unlike fractions” is a thing. I’m not quibbling with the term, especially not after the whole long-division mess a couple weeks back. I just hadn’t thought in a long while about how different denominators do make adding fractions harder.

Jeff Harris’s Shortcuts informational feature for the 3rd I couldn’t remember why I put on the list of mathematically-themed comic strips. The reason’s in there. There’s a Pi Joke. But my interest was more in learning that strawberries are a hybrid created in France from a North American and a Chilean breed. Isn’t that intriguing stuff?

Bill Abbott’s Specktickles for the 8th uses arithmetic — multiplication flash cards — as emblem of stuff to study. About all I can say for that.

## Reading the Comics, August 17, 2017: Professor Edition

To close out last week’s mathematically-themed comic strips … eh. There’s only a couple of them. One has a professor-y type and another has Albert Einstein. That’s enough for my subject line.

Joe Martin’s Mr Boffo for the 15th I’m not sure should be here. I think it’s a mathematics joke. That the professor’s shown with a pie chart suggests some kind of statistics, at least, and maybe the symbols are mathematical in focus. I don’t know. What the heck. I also don’t know how to link to these comics that gives attention to the comic strip artist. I like to link to the site from which I got the comic, but the Mr Boffo site is … let’s call it home-brewed. I can’t figure how to make it link to a particular archive page. But I feel bad enough losing Jumble. I don’t want to lose Joe Martin’s comics on top of that.

Charlie Podrebarac’s meat-and-Elvis-enthusiast comic Cow Town for the 15th is captioned “Elvis Disproves Relativity”. Of course it hasn’t anything to do with experimental results or even a good philosophical counterexample. It’s all about the famous equation. Have to expect that. Elvis Presley having an insight that challenges our understanding of why relativity should work is the stuff for sketch comedy, not single-panel daily comics.

Paul Trap’s Thatababy for the 15th has Thatadad win his fight with Alexa by using the old Star Trek Pi Gambit. To give a computer an unending task any number would work. Even the decimal digits of, say, five would do. They’d just be boring if written out in full, which is why we don’t. But irrational numbers at least give us a nice variety of digits. We don’t know that Pi is normal, but it probably is. So there should be a never-ending variety of what Alexa reels out here.

By the end of the strip Alexa has only got to the 55th digit of Pi after the decimal point. For this I use The Pi-Search Page, rather than working it out by myself. That’s what follows the digits in the second panel. So the comic isn’t skipping any time.

Gene Mora’s Graffiti for the 16th, if you count this as a comic strip, includes a pun, if you count this as a pun. Make of it what you like.

Mark Anderson’s Andertoons for the 17th is a student-misunderstanding-things problem. That’s a clumsy way to describe the joke. I should look for a punchier description, since there are a lot of mathematics comics that amount to the student getting a silly wrong idea of things. Well, I learned greater-than and less-than with alligators that eat the smaller number first. Though they turned into fish eating the smaller number first because who wants to ask a second-grade teacher to draw alligators all the time? Cartoon goldfish are so much easier.

## Reading the Comics, August 12, 2017: August 10 and 12 Edition

The other half of last week’s comic strips didn’t have any prominent pets in them. The six of them appeared on two days, though, so that’s as good as a particular theme. There’s also some π talk, but there’s enough of that I don’t want to overuse Pi Day as an edition name.

Mark Anderson’s Andertoons for the 10th is a classroom joke. It’s built on a common problem in teaching by examples. The student can make the wrong generalization. I like the joke. There’s probably no particular reason seven was used as the example number to have zero interact with. Maybe it just sounded funnier than the other numbers under ten that might be used.

Mike Baldwin’s Cornered for the 10th uses a chalkboard of symbols to imply deep thinking. The symbols on the board look to me like they’re drawn from some real mathematics or physics source. There’s force equations appropriate for gravity or electric interactions. I can’t explain the whole board, but that’s not essential to work out anyway.

Marty Links’s Emmy Lou for the 17th of March, 1976 was rerun the 10th of August. It name-drops the mathematics teacher as the scariest of the set. Fortunately, Emmy Lou went to her classes in a day before Rate My Professor was a thing, so her teacher doesn’t have to hear about this.

Scott Hilburn’s The Argyle Sweater for the 12th is a timely remidner that Scott Hilburn has way more Pi Day jokes than we have Pi Days to have. Also he has octopus jokes. It’s up to you to figure out whether the etymology of the caption makes sense.

John Zakour and Scott Roberts’s Working Daze for the 12th presents the “accountant can’t do arithmetic” joke. People who ought to be good at arithmetic being lousy at figuring tips is an ancient joke. I’m a touch surprised that Christopher Miller’s American Cornball: A Laffopedic Guide to the Formerly Funny doesn’t have an entry for tips (or mathematics). But that might reflect Miller’s mission to catalogue jokes that have fallen out of the popular lexicon, not merely that are old.

Michael Cavna’s Warped for the 12th is also a Pi Day joke that couldn’t wait. It’s cute and should fit on any mathematics teacher’s office door.

## Reading the Comics, August 5, 2017: Lazy Summer Week Edition

It wasn’t like the week wasn’t busy. Comic Strip Master Command sent out as many mathematically-themed comics as I might be able to use. But they were again ones that don’t leave me much to talk about. I’ll try anyway. It was looking like an anthropomorphic-symboles sort of week, too.

Tom Thaves’s Frank and Ernest for the 30th of July is an anthropomorphic-symbols joke. The tick marks used for counting make an appearance and isn’t that enough? Maybe.

Dan Thompson’s Brevity for the 31st is another entry in the anthropomorphic-symbols joke contest. This one sticks to mathematical symbols, so if the Frank and Ernest makes the cut this week so must this one.

Eric the Circle for the 31st, this installment by “T daug”, gives the slightly anthropomorphic geometric figure a joke that at least mentions a radius, and isn’t that enough? What catches my imagination about this panel particularly is that the “fractured radius” is not just a legitimate pun but also resembles a legitimate geometry drawing. Drawing a diameter line is sensible enough. Drawing some other point on the circle and connecting that to the ends of the diameter is also something we might do.

Scott Hilburn’s The Argyle Sweater for the 1st of August is one of the logical mathematics jokes you could make about snakes. The more canonical one runs like this: God in the Garden of Eden makes all the animals and bids them to be fruitful. And God inspects them all and finds rabbits and doves and oxen and fish and fowl all growing in number. All but a pair of snakes. God asks why they haven’t bred and they say they can’t, not without help. What help? They need some thick tree branches chopped down. The bemused God grants them this. God checks back in some time later and finds an abundance of baby snakes in the Garden. But why the delay? “We’re adders,” explain the snakes, “so we need logs to multiply”. This joke absolutely killed them in the mathematics library up to about 1978. I’m told.

John Deering’s Strange Brew for the 1st is a monkeys-at-typewriters joke. It faintly reminds me that I might have pledged to retire mentions of the monkeys-at-typewriters joke. But I don’t remember so I’ll just have to depend on saying I don’t think I retired the monkeys-at-typewriters jokes and trust that someone will tell me if I’m wrong.

Dana Simpson’s Ozy and Millie rerun for the 2nd name-drops multiplication tables as the sort of thing a nerd child wants to know. They may have fit the available word balloon space better than “know how to diagram sentences” would.

Mark Anderson’s Andertoons for the 3rd is the reassuringly normal appearance of Andertoons for this week. It is a geometry class joke about rays, line segments with one point where there’s an end and … a direction where it just doesn’t. And it riffs on the notion of the existence of mathematical things. At least I can see it that way.

Rick Kirkman and Jerry Scott’s Baby Blues for the 5th is a rounding-up joke that isn’t about herds of 198 cattle.

Stephen Bentley’s Herb and Jamaal for the 5th tosses off a mention of the New Math as something well out of fashion. There are fashions in mathematics, as in all human endeavors. It startles many to learn this.

## Reading the Comics, July 1, 2017: Deluge Edition, Part 2

Last week started off going like Gangbusters, a phrase I think that’s too old-fashioned for my father to say but that I’ve picked up because I like listening to old-time radio and, you know, Gangbusters really does get going like that. Give it a try sometime, if you’re open to that old-fashioned sort of narrative style and blatant FBI agitprop. You might want to turn the volume down a little before you do. It slowed down the second half of the week, which is mostly fine as I’d had other things taking up my time. Let me finish off last week and hope there’s a good set of comics to review for next Sunday and maybe Tuesday.

Ted Shearer’s Quincy for the 4th of May, 1978 was rerun the 28th of June. It’s got the form of your student-resisting-the-word-problem joke. And mixes in a bit of percentages which is all the excuse I need to include it here. That and how Shearer uses halftone screening. It’s also a useful reminder of how many of our economic problems could be solved quickly if poor people got more money.

Olivia Walch’s Imogen Quest for the 28th features Gottfried Leibniz — missing his birthday by three days, incidentally — and speaks of the priority dispute about the invention of calculus. I’m not sure there is much serious questioning anymore about Leibniz’s contributions to mathematics. I think they might be even more strongly appreciated these days than they ever used to be, as people learn more about his work in computing machines and the attempt to automate calculation.

Mark Anderson’s Andertoons for the 28th is our soothing, familiar Andertoons for this essay. I remember in learning about equivalent forms of fractions wondering why anyone cared about reducing them. If two things have the same meaning, why do we need to go further? There are a couple answers. One is that it’s easier on us to understand a quantity if it’s a shorter, more familiar form. $\frac{3}{4}$ has a meaning that $\frac{1131}{1508}$ just does not. And another is that we often want to know whether two things are equivalent, or close. Is \frac{1147}{1517} more or less than $\frac{1131}{1508}$? Good luck eyeballing that.

And we learn, later on, that a lot of mathematics is about finding different ways to write the same thing. Each way has its uses. Sometimes a slightly more complicated way to write a thing makes proving something easier. There’s about two solids months of Real Analysis, for example, where you keep on writing that $x_{n} - x_{m} \equiv x_{n} - x + x - x_{m}$ and this “adding zero” turns out to make proofs possible. Even easy.

Mark Tatulli’s Heart of the City remains on my watch-with-caution list as the Math Camp story continues. But the strip from the 28th tickles me with the idea of crossing mathematics camp with Pinocchio‘s Pleasure Island. I’m imagining something where Heart starts laughing at something and ends up turning into something from Donald Duck’s Mathmagic land.

Dave Blazek’s Loose Parts for the 28th is your traditional blackboard-full-of-symbols joke. I’m amused.

Tony Rubino and Gary Markstein’s Daddy’s Home for the 1st of July is your traditional “mathematics is something hard” joke. I have the feeling it’s a rerun, but I lack the emotional investment in whether it is a rerun to check. The joke’s comfortable and familiar as it is, anyway.

## Reading the Comics, June 17, 2017: Icons Of Mathematics Edition

Comic Strip Master Command just barely missed being busy enough for me to split the week’s edition. Fine for them, I suppose, although it means I’m going to have to scramble together something for the Tuesday or the Thursday posting slot. Ah well. As befits the comics, there’s a fair bit of mathematics as an icon in the past week’s selections. So let’s discuss.

Mark Anderson’s Andertoons for the 11th is our Mark Anderson’s Andertoons for this essay. Kind of a relief to have that in right away. And while the cartoon shows a real disaster of a student at the chalkboard, there is some truth to the caption. Ruling out plausible-looking wrong answers is progress, usually. So is coming up with plausible-looking answers to work out whether they’re right or wrong. The troubling part here, I’d say, is that the kid came up with pretty poor guesses about what the answer might be. He ought to be able to guess that it’s got to be an odd number, and has to be less than 10, and really ought to be less than 7. If you spot that then you can’t make more than two wrong guesses.

Patrick J Marrin’s Francis for the 12th starts with what sounds like a logical paradox, about whether the Pope could make an infallibly true statement that he was not infallible. Really it sounds like a bit of nonsense. But the limits of what we can know about a logical system will often involve questions of this form. We ask whether something can prove whether it is provable, for example, and come up with a rigorous answer. So that’s the mathematical content which justifies my including this strip here.

Niklas Eriksson’s Carpe Diem for the 13th is a traditional use of the blackboard full of mathematics as symbolic of intelligence. Of course ‘E = mc2‘ gets in there. I’m surprised that both π and 3.14 do, too, for as little as we see on the board.

Mark Anderson’s Andertoons for the 14th is a nice bit of reassurance. Maybe the cartoonist was worried this would be a split-week edition. The kid seems to be the same one as the 11th, but the teacher looks different. Anyway there’s a lot you can tell about shapes from their perimeter alone. The one which most startles me comes up in calculus: by doing the right calculation about the lengths and directions of the edge of a shape you can tell how much area is inside the shape. There’s a lot of stuff in this field — multivariable calculus — that’s about swapping between “stuff you know about the boundary of a shape” and “stuff you know about the interior of the shape”. And finding area from tracing the boundary is one of them. It’s still glorious.

Samson’s Dark Side Of The Horse for the 14th is a counting-sheep joke and a Pi Day joke. I suspect the digits of π would be horrible for lulling one to sleep, though. They lack the just-enough-order that something needs for a semiconscious mind to drift off. Horace would probably be better off working out Collatz sequences.

Dana Simpson’s Phoebe and her Unicorn for the 14th mentions mathematics as iconic of what you do at school. Book reports also make the cut.

Dan Barry’s Flash Gordon for the 31st of July, 1962 and rerun the 16th I’m including just because I love the old-fashioned image of a mathematician in Professor Quita here. At this point in the comic strip’s run it was set in the far-distant future year of 1972, and the action here is on one of the busy multinational giant space stations. Flash himself is just back from Venus where he’d set up some dolphins as assistants to a fish-farming operation helping to feed that world and ours. And for all that early-60s futurism look at that gorgeous old adding machine he’s still got. (Professor Quinta’s discovery is a way to peer into alternate universes, according to the next day’s strip. I’m kind of hoping this means they’re going to spend a week reading Buck Rogers.)

## Reading the Comics, April 18, 2017: Give Me Some Word Problems Edition

I have my reasons for this installment’s title. They involve my deductions from a comic strip. Give me a few paragraphs.

Mark Anderson’s Andertoons for the 16th asks for attention from whatever optician-written blog reads the comics for the eye jokes. And meets both the Venn Diagram and the Mark Anderson’s Andertoons content requirements for this week. Good job! Starts the week off strong.

Lincoln Pierce’s Big Nate: First Class for the 16th, rerunning the strip from 1993, is about impossibly low-probability events. We can read the comic as a joke about extrapolating a sequence from a couple examples. Properly speaking we can’t; any couple of terms can be extended in absolutely any way. But we often suppose a sequence follows some simple pattern, as many real-world things do. I’m going to pretend we can read Jenny’s estimates of the chance she’ll go out with him as at all meaningful. If Jenny’s estimate of the chance she’d go out with Nate rose from one in a trillion to one in a billion over the course of a week, this could be a good thing. If she’s a thousand times more likely each week to date him — if her interest is rising geometrically — this suggests good things for Nate’s ego in three weeks. If she’s only getting 999 trillionths more likely each week — if her interest is rising arithmetically — then Nate has a touch longer to wait before a date becomes likely.

(I forget whether she has agreed to a date in the 24 years since this strip first appeared. He has had some dates with kids in his class, anyway, and some from the next grade too.)

J C Duffy’s Lug Nuts for the 16th is a Pi Day joke that ran late.

Jef Mallett’s Frazz for the 17th starts a little thread about obsolete references in story problems. It’s continued on the 18th. I’m sympathetic in principle to both sides of the story problem debate.

Is the point of the first problem, Farmer Joe’s apples, to see whether a student can do a not-quite-long division? Or is it to see whether the student can extract a price-per-quantity for something, and apply that to find the quantity to fit a given price? If it’s the latter then the numbers don’t make a difference. One would want to avoid marking down a student who knows what to do, and could divide 15 cents by three, but would freeze up if a more plausible price of, say, $2.25 per pound had to be divided by three. But then the second problem, Mr Schad driving from Belmont to Cadillac, got me wondering. It is about 84 miles between the two Michigan cities (and there is a Reed City along the way). The time it takes to get from one city to another is a fair enough problem. But these numbers don’t make sense. At 55 miles per hour the trip takes an awful 1.5273 hours. Who asks elementary school kids to divide 84 by 55? On purpose? But at the state highway speed limit (for cars) of 70 miles per hour, the travel time is 1.2 hours. 84 divided by 70 is a quite reasonable thing to ask elementary school kids to do. And then I thought of this: you could say Belmont and Cadillac are about 88 miles apart. Google Maps puts the distance as 86.8 miles, along US 131; but there’s surely some point in the one town that’s exactly 88 miles from some point in the other, just as there’s surely some point exactly 84 miles from some point in the other town. 88 divided by 55 would be another reasonable problem for an elementary school student; 1.6 hours is a reasonable answer. The (let’s call it) 1980s version of the question ought to see the car travel 88 miles at 55 miles per hour. The contemporary version ought to see the car travel 84 miles at 70 miles per hour. No reasonable version would make it 84 miles at 55 miles per hour. So did Mallett take a story problem that could actually have been on an era-appropriate test and ancient it up? Before anyone reports me to Comic Strip Master Command let me clarify what I’m wondering about. I don’t care if the details of the joke don’t make perfect sense. They’re jokes, not instruction. All the story problem needs to set up the joke is the obsolete speed limit; everything else is fluff. And I enjoyed working out variation of the problem that did make sense, so I’m happy Mallett gave me that to ponder. Here’s what I do wonder about. I’m curious if story problems are getting an unfair reputation. I’m not an elementary school teacher, or parent of a kid in school. I would like to know what the story problems look like. Do you, the reader, have recent experience with the stuff farmers, drivers, and people weighing things are doing in these little stories? Are they measuring things that people would plausibly care about today, and using values that make sense for the present day? I’d like to know what the state of story problems is. John Hambrock’s The Brilliant Mind of Edison Lee for the 18th uses mental arithmetic as the gauge of intelligence. Pretty harsly, too. I wouldn’t have known the square root of 8649 off the top of my head either, although it’s easy to tell that 92 can’t be right: the last digit of 92 squared has to be 4. It’s also easy to tell that 92 has to be about right, though, as 90 times 90 will be about 8100. Given this information, if you knew that 8,649 was a perfect square, you’d be hard-pressed to think of a better guess for its value than 93. But since most whole numbers are not perfect squares, “a little over 90” is the best I’d expect to do. ## Reading the Comics, April 15, 2017: Extended Week Edition It turns out last Saturday only had the one comic strip that was even remotely on point for me. And it wasn’t very on point either, but since it’s one of the Creators.com strips I’ve got the strip to show. That’s enough for me. Henry Scarpelli and Craig Boldman’s Archie for the 8th is just about how algebra hurts. Some days I agree. Ruben Bolling’s Super-Fun-Pak Comix for the 8th is an installation of They Came From The Third Dimension. “Dimension” is one of those oft-used words that’s come loose of any technical definition. We use it in mathematics all the time, at least once we get into Introduction to Linear Algebra. That’s the course that talks about how blocks of space can be stretched and squashed and twisted into each other. You’d expect this to be a warmup act to geometry, and I guess it’s relevant. But where it really pays off is in studying differential equations and how systems of stuff changes over time. When you get introduced to dimensions in linear algebra they describe degrees of freedom, or how much information you need about a problem to pin down exactly one solution. It does give mathematicians cause to talk about “dimensions of space”, though, and these are intuitively at least like the two- and three-dimensional spaces that, you know, stuff moves in. That there could be more dimensions of space, ordinarily inaccessible, is an old enough idea we don’t really notice it. Perhaps it’s hidden somewhere too. Amanda El-Dweek’s Amanda the Great of the 9th started a story with the adult Becky needing to take a mathematics qualification exam. It seems to be prerequisite to enrolling in some new classes. It’s a typical set of mathematics anxiety jokes in the service of a story comic. One might tsk Becky for going through university without ever having a proper mathematics class, but then, I got through university without ever taking a philosophy class that really challenged me. Not that I didn’t take the classes seriously, but that I took stuff like Intro to Logic that I was already conversant in. We all cut corners. It’s a shame not to use chances like that, but there’s always so much to do. Mark Anderson’s Andertoons for the 10th relieves the worry that Mark Anderson’s Andertoons might not have got in an appearance this week. It’s your common kid at the chalkboard sort of problem, this one a kid with no idea where to put the decimal. As always happens I’m sympathetic. The rules about where to move decimals in this kind of multiplication come out really weird if the last digit, or worse, digits in the product are zeroes. Mel Henze’s Gentle Creatures is in reruns. The strip from the 10th is part of a story I’m so sure I’ve featured here before that I’m not even going to look up when it aired. But it uses your standard story problem to stand in for science-fiction gadget mathematics calculation. Dave Blazek’s Loose Parts for the 12th is the natural extension of sleep numbers. Yes, I’m relieved to see Dave Blazek’s Loose Parts around here again too. Feels weird when it’s not. Bill Watterson’s Calvin and Hobbes rerun for the 13th is a resisting-the-story-problem joke. But Calvin resists so very well. John Deering’s Strange Brew for the 13th is a “math club” joke featuring horses. Oh, it’s a big silly one, but who doesn’t like those too? Dan Thompson’s Brevity for the 14th is one of the small set of punning jokes you can make using mathematician names. Good for the wall of a mathematics teacher’s classroom. Shaenon K Garrity and Jefferey C Wells’s Skin Horse for the 14th is set inside a virtual reality game. (This is why there’s talk about duplicating objects.) Within the game, the characters are playing that game where you start with a set number (in this case 20) tokens and take turn removing a couple of them. The “rigged” part of it is that the house can, by perfect play, force a win every time. It’s a bit of game theory that creeps into recreational mathematics books and that I imagine is imprinted in the minds of people who grow up to design games. ## Reading the Comics, March 27, 2017: Not The March 26 Edition My guide for how many comics to include in one of these essays is “at least five, if possible”. Occasionally there’s a day when Comic Strip Master Command sends that many strips at once. Last Sunday was almost but not quite such a day. But the business of that day did mean I had enough strips to again divide the past week’s entries. Look for more comics in a few days, if all goes well here. Thank you. Mark Anderson’s Andertoons for the 26th reminds me of something I had wholly forgot about: decimals inside fractions. And now that this little horror’s brought back I remember my experience with it. Decimals in fractions aren’t, in meaning, any different from division of decimal numbers. And the decimals are easily enough removed. But I get the kid’s horror. Fractions and decimals are both interesting in the way they represent portions of wholes. They spend so much time standing independently of one another it feels disturbing to have them interact. Well, Andertoons kid, maybe this will comfort you: somewhere along the lines decimals in fractions just stop happening. I’m not sure when. I don’t remember when the last one passed my experience. Hector Cantu and Carlos Castellanos’s Baldo for the 26th is built on a riddle. It’s one that depends on working in shifting addition from “what everybody means by addition” to “what addition means on a clock”. You can argue — I’m sure Gracie would — that “11 plus 3” does not mean “eleven o’clock plus three hours”. But on what grounds? If it’s eleven o’clock and you know something will happen in three hours, “two o’clock” is exactly what you want. Underlying all of mathematics are definitions about what we mean by stuff like “eleven” and “plus” and “equals”. And underlying the definitions is the idea that “here is a thing we should like to know”. Addition of hours on a clock face — I never see it done with minutes or seconds — is often used as an introduction to modulo arithmetic. This is arithmetic on a subset of the whole numbers. For example, we might use 0, 1, 2, and 3. Addition starts out working the way it does in normal numbers. But then 1 + 3 we define to be 0. 2 + 3 is 1. 3 + 3 is 2. 2 + 2 is 0. 2 + 3 is 1 again. And so on. We get subtraction the same way. This sort of modulo arithmetic has practical uses. Many cryptography schemes rely on it, for example. And it has pedagogical uses; modulo arithmetic turns up all over a mathematics major’s Introduction to Not That Kind Of Algebra Course. You can use it to learn a lot of group theory with something a little less exotic than rotations and symmetries of polygonal shapes or permutations of lists of items. A clock face doesn’t quite do it, though. We have to pretend the ’12’ at the top is a ‘0’. I’ve grown more skeptical about whether appealing to clocks is useful in introducing modulo arithmetic. But it’s been a while since I’ve needed to discuss the matter at all. Rob Harrell’s Big Top rerun for the 26th mentions sudoku. Remember when sudoku was threatening to take over the world, or at least the comics page? Also, remember comics pages? Good times. It’s not one of my hobbies, but I get the appeal. Bob Shannon’s Tough Town I’m not sure if I’ve featured here before. It’s one of those high concept comics. The patrons at a bar are just what you see on the label, and there’s a lot of punning involved. Now that I’ve over-explained the joke please enjoy the joke. There are a couple of strips prior to this one featuring the same characters; they just somehow didn’t mention enough mathematics words for me to bring up here. Norm Feuti’s Retail for the 27th is about the great concern-troll of mathematics education: can our cashiers make change? I’m being snottily dismissive. Shops, banks, accountants, and tax registries are surely the most common users of mathematics — at least arithmetic — out there. And if people are going to do a thing, ordinarily, they ought to be able to do it well. But, of course, the computer does arithmetic extremely well. Far better, or at least more indefatigably, than any cashier is going to be able to do. The computer will also keep track of the prices of everything, and any applicable sales or discounts, more reliably than the mere human will. The whole point of the Industrial Revolution was to divide tasks up and assign them to parties that could do the separate parts better. Why get worked up about whether you imagine the cashier knows what$22.14 minus \$16.89 is?

I will say the time the bookstore where I worked lost power all afternoon and we had to do all the transactions manually we ended up with only a one-cent discrepancy in the till, thank you.

## Reading the Comics, March 11, 2017: Accountants Edition

And now I can wrap up last week’s delivery from Comic Strip Master Command. It’s only five strips. One certainly stars an accountant. one stars a kid that I believe is being coded to read as an accountant. The rest, I don’t know. I pick Edition titles for flimsy reasons anyway. This’ll do.

Ryan North’s Dinosaur Comics for the 6th is about things that could go wrong. And every molecule of air zipping away from you at once is something which might possibly happen but which is indeed astronomically unlikely. This has been the stuff of nightmares since the late 19th century made probability an important part of physics. The chance all the air near you would zip away at once is impossibly unlikely. But such unlikely events challenge our intuitions about probability. An event that has zero chance of happening might still happen, given enough time and enough opportunities. But we’re not using our time well to worry about that. If nothing else, even if all the air around you did rush away at once, it would almost certainly rush back right away.

Steve Kelley and Jeff Parker’s Dustin for the 7th of March talks about the SATs and the chance of picking right answers on a multiple-choice test. I haven’t heard about changes to the SAT but I’ll accept what the comic strip says about them for the purpose of discussion here. At least back when I took it the SAT awarded one point to the raw score for a correct answer, and subtracted one-quarter point for a wrong answer. (The raw scores were then converted into a 200-to-800 range.) I liked this. If you had no idea and guessed on answers you should expect to get one in five right and four in five wrong. On average then you would expect no net change to your raw score. If one or two wrong answers can be definitely ruled out then guessing from the remainder brings you a net positive. I suppose the change, if it is being done, is meant to be confident only right answers are rewarded. I’m not sure this is right; it seems to me there’s value in being able to identify certainly wrong answers even if the right one isn’t obvious. But it’s not my test and I don’t expect to need to take it again either. I can expression opinions without penalty.

Mark Anderson’s Andertoons for the 7th is the Mark Anderson’s Andertoons for last week. It’s another kid-at-the-chalkboard panel. What gets me is that if the kid did keep one for himself then shouldn’t he have written 38?

Brian Basset’s Red and Rover for the 8th mentions fractions. It’s just there as the sort of thing a kid doesn’t find all that naturally compelling. That’s all right I like the bug-eyed squirrel in the first panel.

Bill Holbrook’s On The Fastrack for the 9th concludes the wedding of accountant Fi. It uses the square root symbol so as to make the cake topper clearly mathematical as opposed to just an age.

## Reading the Comics, February 23, 2017: The Week At Once Edition

For the first time in ages there aren’t enough mathematically-themed comic strips to justify my cutting the week’s roundup in two. No, I have no idea what I’m going to write about for Thursday. Let’s find out together.

Jenny Campbell’s Flo and Friends for the 19th faintly irritates me. Flo wants to make sure her granddaughter understands that just because it takes people on average 14 minutes to fall asleep doesn’t mean that anyone actually does, by listing all sorts of reasons that a person might need more than fourteen minutes to sleep. It makes me think of a behavior John Allen Paulos notes in Innumeracy, wherein the statistically wise points out that someone has, say, a one-in-a-hundred-million chance of being killed by a terrorist (or whatever) and is answered, “ah, but what if you’re that one?” That is, it’s a response that has the form of wisdom without the substance. I notice Flo doesn’t mention the many reasons someone might fall asleep in less than fourteen minutes.

But there is something wise in there nevertheless. For most stuff, the average is the most common value. By “the average” I mean the arithmetic mean, because that is what anyone means by “the average” unless they’re being difficult. (Mathematicians acknowledge the existence of an average called the mode, which is the most common value (or values), and that’s most common by definition.) But just because something is the most common result does not mean that it must be common. Toss a coin fairly a hundred times and it’s most likely to come up tails 50 times. But you shouldn’t be surprised if it actually turns up tails 51 or 49 or 45 times. This doesn’t make 50 a poor estimate for the average number of times something will happen. It just means that it’s not a guarantee.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 19th shows off an unusually dynamic camera angle. It’s in service for a class of problem you get in freshman calculus: find the longest pole that can fit around a corner. Oh, a box-spring mattress up a stairwell is a little different, what with box-spring mattresses being three-dimensional objects. It’s the same kind of problem. I want to say the most astounding furniture-moving event I’ve ever seen was when I moved a fold-out couch down one and a half flights of stairs single-handed. But that overlooks the caged mouse we had one winter, who moved a Chinese finger-trap full of crinkle paper up the tight curved plastic to his nest by sheer determination. The trap was far longer than could possibly be curved around the tube. We have no idea how he managed it.

J R Faulkner’s Promises, Promises for the 20th jokes that one could use Roman numerals to obscure calculations. So you could. Roman numerals are terrible things for doing arithmetic, at least past addition and subtraction. This is why accountants and mathematicians abandoned them pretty soon after learning there were alternatives.

Mark Anderson’s Andertoons for the 21st is the Mark Anderson’s Andertoons for the week. Probably anything would do for the blackboard problem, but something geometry reads very well.

Jef Mallett’s Frazz for the 21st makes some comedy out of the sort of arithmetic error we all make. It’s so easy to pair up, like, 7 and 3 make 10 and 8 and 2 make 10. It takes a moment, or experience, to realize 78 and 32 will not make 100. Forgive casual mistakes.

Bud Fisher’s Mutt and Jeff rerun for the 22nd is a similar-in-tone joke built on arithmetic errors. It’s got the form of vaudeville-style sketch compressed way down, which is probably why the third panel could be made into a satisfying final panel too.

Bud Blake’s Tiger rerun for the 23rd just name-drops mathematics; it could be any subject. But I need some kind of picture around here, don’t I?

Mike Baldwin’s Cornered for the 23rd is the anthropomorphic numerals joke for the week.

## Reading the Comics, February 2, 2017: I Haven’t Got A Jumble Replacement Source Yet

If there was one major theme for this week it was my confidence that there must be another source of Jumble strips out there. I haven’t found it, but I admit not making it a priority either. The official Jumble site says I can play if I activate Flash, but I don’t have enough days in the year to keep up with Flash updates. And that doesn’t help me posting mathematics-relevant puzzles here anyway.

Mark Anderson’s Andertoons for January 29th satisfies my Andertoons need for this week. And it name-drops the one bit of geometry everyone remembers. To be dour and humorless about it, though, I don’t think one could likely apply the Pythagorean Theorem. Typically the horizontal axis and the vertical axis in a graph like this measure different things. Squaring the different kinds of quantities and adding them together wouldn’t mean anything intelligible. What would even be the square root of (say) a squared-dollars-plus-squared-weeks? This is something one learns from dimensional analysis, a corner of mathematics I’ve thought about writing about some. I admit this particular insight isn’t deep, but everything starts somewhere.

Norm Feuti’s Gil rerun for the 30th is a geometry name-drop, listing it as the sort of category Jeopardy! features. Gil shouldn’t quit so soon. The responses for the category are “What is the Pythagorean Theorem?”, “What is acute?”, “What is parallel?”, “What is 180 degrees?” (or, possibly, 360 or 90 degrees), and “What is a pentagon?”.

Terri Libenson’s Pajama Diaries for the 1st of February shows off the other major theme of this past week, which was busy enough that I have to again split the comics post into two pieces. That theme is people getting basic mathematics wrong. Mostly counting. (You’ll see.) I know there’s no controlling what people feel embarrassed about. But I think it’s unfair to conclude you “can no longer” do mathematics in your head because you’re not able to make change right away. It’s normal to be slow or unreliable about something you don’t do often. Inexperience and inability are not the same thing, and it’s unfair to people to conflate them.

Gordon Bess’s Redeye for the 21st of September, 1970, got rerun the 1st of February. And it’s another in the theme of people getting basic mathematics wrong. And even more basic mathematics this time. There’s more problems-with-counting comics coming when I finish the comics from the past week.

Dave Whamond’s Reality Check for the 1st hopes that you won’t notice the label on the door is painted backwards. Just saying. It’s an easy joke to make about algebra, also, that it should put letters in to perfectly good mathematics. Letters are used for good reasons, though. We’ve always wanted to work out the value of numbers we only know descriptions of. But it’s way too wordy to use the whole description of the number every time we might speak of it. Before we started using letters we could use placeholder names like “re”, meaning “thing” (as in “thing we want to calculate”). That works fine, although it crashes horribly when we want to track two or three things at once. It’s hard to find words that are decently noncommittal about their values but that we aren’t going to confuse with each other.

So the alphabet works great for this. An individual letter doesn’t suggest any particular number, as long as we pretend ‘O’ and ‘I’ and ‘l’ don’t look like they do. But we also haven’t got any problem telling ‘x’ from ‘y’ unless our handwriting is bad. They’re quick to write and to say aloud, and they don’t require learning to write any new symbols.

Later, yes, letters do start picking up connotations. And sometimes we need more letters than the Roman alphabet allows. So we import from the Greek alphabet the letters that look different from their Roman analogues. That’s a bit exotic. But at least in a Western-European-based culture they aren’t completely novel. Mathematicians aren’t really trying to make this hard because, after all, they’re the ones who have to deal with the hard parts.

Bu Fisher’s Mutt and Jeff rerun for the 2nd is another of the basic-mathematics-wrong jokes. But it does get there by throwing out a baffling set of story-problem-starter points. Particularly interesting to me is Jeff’s protest in the first panel that they couldn’t have been doing 60 miles an hour as they hadn’t been out an hour. It’s the sort of protest easy to use as introduction to the ideas of average speed and instantaneous speed and, from that, derivatives.

## Reading the Comics, January 7, 2016: Just Before GoComics Breaks Everything Edition

Most of the comics I review here are printed on GoComics.com. Well, most of the comics I read online are from there. But even so I think they have more comic strips that mention mathematical themes. Anyway, they’re unleashing a complete web site redesign on Monday. I don’t know just what the final version will look like. I know that the beta versions included the incredibly useful, that is to say dumb, feature where if a particular comic you do read doesn’t have an update for the day — and many of them don’t, as they’re weekly or three-times-a-week or so — then it’ll show some other comic in its place. I mean, the idea of encouraging people to find new comics is a good one. To some extent that’s what I do here. But the beta made no distinction between “comic you don’t read because you never heard of Microcosm” and “comic you don’t read because glancing at it makes your eyes bleed”. And on an idiosyncratic note, I read a lot of comics. I don’t need to see Dude and Dude reruns in fourteen spots on my daily comics page, even if I didn’t mind it to start.

Anyway. I am hoping, desperately hoping, that with the new site all my old links to comics are going to keep working. If they don’t then I suppose I’m just ruined. We’ll see. My suggestion is if you’re at all curious about the comics you read them today (Sunday) just to be safe.

Ashleigh Brilliant’s Pot-Shots is a curious little strip I never knew of until GoComics picked it up a few years ago. Its format is compellingly simple: a little illustration alongside a wry, often despairing, caption. I love it, but I also understand why was the subject of endless queries to the Detroit Free Press (Or Whatever) about why was this thing taking up newspaper space. The strip rerun the 31st of December is a typical example of the strip and amuses me at least. And it uses arithmetic as the way to communicate reasoning, both good and bad. Brilliant’s joke does address something that logicians have to face, too. Whether an argument is logically valid depends entirely on its structure. If the form is correct the reasoning may be excellent. But to be sound an argument has to be correct and must also have its assumptions be true. We can separate whether an argument is right from whether it could ever possibly be right. If you don’t see the value in that, you have never participated in an online debate about where James T Kirk was born and whether Spock was the first Vulcan in Star Fleet.

Thom Bluemel’s Birdbrains for the 2nd of January, 2017, is a loaded-dice joke. Is this truly mathematics? Statistics, at least? Close enough for the start of the year, I suppose. Working out whether a die is loaded is one of the things any gambler would like to know, and that mathematicians might be called upon to identify or exploit. (I had a grandmother unshakably convinced that I would have some natural ability to beat the Atlantic City casinos if she could only sneak the underaged me in. I doubt I could do anything of value there besides see the stage magic show.)

Jack Pullan’s Boomerangs rerun for the 2nd is built on the one bit of statistical mechanics that everybody knows, that something or other about entropy always increasing. It’s not a quantum mechanics rule, but it’s a natural confusion. Quantum mechanics has the reputation as the source of all the most solid, irrefutable laws of the universe’s working. Statistical mechanics and thermodynamics have this musty odor of 19th-century steam engines, no matter how much there is to learn from there. Anyway, the collapse of systems into disorder is not an irrevocable thing. It takes only energy or luck to overcome disorderliness. And in many cases we can substitute time for luck.

Scott Hilburn’s The Argyle Sweater for the 3rd is the anthropomorphic-geometry-figure joke that’s I’ve been waiting for. I had thought Hilburn did this all the time, although a quick review of Reading the Comics posts suggests he’s been more about anthropomorphic numerals the past year. This is why I log even the boring strips: you never know when I’ll need to check the last time Scott Hilburn used “acute” to mean “cute” in reference to triangles.

Mike Thompson’s Grand Avenue uses some arithmetic as the visual cue for “any old kind of schoolwork, really”. Steve Breen’s name seems to have gone entirely from the comic strip. On Usenet group rec.arts.comics.strips Brian Henke found that Breen’s name hasn’t actually been on the comic strip since May, and D D Degg found a July 2014 interview indicating Thompson had mostly taken the strip over from originator Breen.

Mark Anderson’s Andertoons for the 5th is another name-drop that doesn’t have any real mathematics content. But come on, we’re talking Andertoons here. If I skipped it the world might end or something untoward like that.

Ted Shearer’s Quincy for the 14th of November, 1977, doesn’t have any mathematical content really. Just a mention. But I need some kind of visual appeal for this essay and Shearer is usually good for that.

Corey Pandolph, Phil Frank, and Joe Troise’s The Elderberries rerun for the 7th is also a very marginal mention. But, what the heck, it’s got some of your standard wordplay about angles and it’ll get this week’s essay that much closer to 800 words.

## Reading the Comics, December 30, 2016: New Year’s Eve Week Edition

So last week, for schedule reasons, I skipped the Christmas Eve strips and promised to get to them this week. There weren’t any Christmas Eve mathematically-themed comic strips. Figures. This week, I need to skip New Year’s Eve comic strips for similar schedule reasons. If there are any, I’ll talk about them next week.

Lorie Ransom’s The Daily Drawing for the 28th is a geometry wordplay joke for this installment. Two of them, when you read the caption.

John Graziano’s Ripley’s Believe It or Not for the 28th presents the quite believable claim that Professor Dwight Barkley created a formula to estimate how long it takes a child to ask “are we there yet?” I am skeptical the equation given means all that much. But it’s normal mathematician-type behavior to try modelling stuff. That will usually start with thinking of what one wants to represent, and what things about it could be measured, and how one expects these things might affect one another. There’s usually several plausible-sounding models and one has to select the one or ones that seem likely to be interesting. They have to be simple enough to calculate, but still interesting. They need to have consequences that aren’t obvious. And then there’s the challenge of validating the model. Does its description match the thing we’re interested in well enough to be useful? Or at least instructive?

Len Borozinski’s Speechless for the 28th name-drops Albert Einstein and the theory of relativity. Marginal mathematical content, but it’s a slow week.

John Allison’s Bad Machinery for the 29th mentions higher dimensions. More dimensions. In particular it names ‘ana’ and ‘kata’ as “the weird extra dimensions”. Ana and kata are a pair of directions coined by the mathematician Charles Howard Hinton to give us a way of talking about directions in hyperspace. They echo the up/down, left/right, in/out pairs. I don’t know that any mathematicians besides Rudy Rucker actually use these words, though, and that in his science fiction. I may not read enough four-dimensional geometry to know the working lingo. Hinton also coined the “tesseract”, which has escaped from being a mathematician’s specialist term into something normal people might recognize. Mostly because of Madeline L’Engle, I suppose, but that counts.

Samson’s Dark Side of the Horse for the 29th is Dark Side of the Horse‘s entry this essay. It’s a fun bit of play on counting, especially as a way to get to sleep.

John Graziano’s Ripley’s Believe It or Not for the 29th mentions a little numbers and numerals project. Or at least representations of numbers. Finding other orders for numbers can be fun, and it’s a nice little pastime. I don’t know there’s an important point to this sort of project. But it can be fun to accomplish. Beautiful, even.

Mark Anderson’s Andertoons for the 30th relieves us by having a Mark Anderson strip for this essay. And makes for a good Roman numerals gag.

Ryan Pagelow’s Buni for the 30th can be counted as an anthropomorphic-numerals joke. I know it’s more of a “ugh 2016 was the worst year” joke, but it parses either way.

John Atkinson’s Wrong Hands for the 30th is an Albert Einstein joke. It’s cute as it is, though.