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

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

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

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

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

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

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

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

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

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

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

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

Wait for it.

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

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

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

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

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

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

## Reading the Comics, February 10, 2018: I Meant To Post This Thursday Edition

Ah, yes, so, in the midst of feeling all proud that I’d gotten my Reading the Comics workflow improved, I went out to do my afternoon chores without posting the essay. I’m embarrassed. But it really only affects me looking at the WordPress Insights page. It publishes this neat little calendar-style grid that highlights the days when someone’s posted and this breaks up the columns. This can only unnerve me. I deserve it.

Tom Thaves’s Frank and Ernest for the 8th of February is about the struggle to understand zero. As often happens, the joke has a lot of truth to it. Zero bundles together several ideas, overlapping but not precisely equal. And part of that is the idea of “nothing”. Which is a subtly elusive concept: to talk about the properties of a thing that does not exist is hard. As adults it’s easy to not notice this anymore. Part’s likely because mastering a concept makes one forget what it took to understand. Part is likely because if you don’t have to ponder whether the “zero” that’s “one less than one” is the same as the “zero” that denotes “what separates the count of thousands from the count of tens in the numeral 2,038” you might not, and just assume you could explain the difference or similarity to someone who has no idea.

John Zakour and Scott Roberts’s Maria’s Day for the 8th has maria and another girl bonding over their hatred of mathematics. Well, at least they’re getting something out of it. The date in the strip leads me to realize this is probably a rerun. I’m not sure just when it’s from.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th proposes a prank based on mathematical use of the word “arbitrarily”. This is a word that appears a lot in analysis, and the strip makes me realize I’m not sure I can give a precise definition. An “arbitrarily large number”, for example, would be any number that’s large enough. But this also makes me realize I’m not sure precisely what joke Weinersmith is going for. I suppose that if someone were to select an arbitrarily large number they might pick 53, or a hundred, or million billion trillion. I suppose Weinersmith’s point is that in ordinary speech an arbitrarily made choice is one selection from all the possible alternatives. In mathematical speech an arbitrarily made choice reflects every possible choice. To speak of an arbitrarily large number is to say that whatever selection is made, we can go on to show this interesting stuff is true. We’d typically like to prove the most generically true thing possible. But picking a single example can be easier to prove. It can certainly be easier to visualize. 53 is probably easier to imagine than “every number 52 or larger”, for example.

Ted Shearer’s Quincy for the 16th of December, 1978 was rerun the 9th of February. It just shows Quincy at work on his mathematics homework, and considering dedicating it to his grandmother. Mathematics books have dedications, just as any other book does. I’m not aware of dedications of proofs or other shorter mathematics works, but there’s likely some. There’s often a note of thanks, usually given to people who’ve made the paper’s writers think harder about the subjects. But I don’t think there’s any reason a paper wouldn’t thank someone who provided “mere” emotional support. I just don’t have examples offhand.

Jef Mallet’s Frazz for the 9th looks like one of those creative-teaching exercises I sometimes see in Mathematics Education Twitter: the teacher gives answers and the students come up with story problems to match. That’s not a bad project. I’m not sure how to grade it, but I haven’t done anything that creative when I’ve taught. I’m sorry I haven’t got more to say about it since the idea seems fun.

Gordon Bess’s Redeye for the 30th of September, 1971 was rerun the 10th. It’s a bit of extremely long division and I don’t blame Pokey for giving up on that problem. Starting from 5,967,342 divided by 973 I’d say, well, that’s about six million divided by a thousand, so the answer should be near six thousand. I don’t think the last digits of 2 and 3 suggest anything about what the final digit should be, if this divides evenly. So the only guidance I have is that my answer ought to be around six thousand and then we have to go into actually working. It turns out that 973 doesn’t go into 5,967,342 a whole number of times, so I sympathize more with Pokey. The answer is a little more than 6,132.9311.

## Reading the Comics, February 3, 2018: Overworked Edition

And this should clear out last week’s mathematically-themed comic strips. I didn’t realize just how busy last week had been until I looked at what I thought was a backlog of just two days’ worth of strips and it turned out to be about two thousand comics. I exaggerate, but as ever, not by much. This current week seems to be a more relaxed pace. So I’ll have to think of something to write for the Tuesday and Thursday slots. Hm. (I’ll be all right. I’ve got one thing I need to stop bluffing about and write, and there’s usually a fair roundup of interesting tweets or articles I’ve seen that I can write. Those are often the most popular articles around here.)

Hilary Price and Rina Piccolo’s Rhymes with Orange for the 1st of February, 2018 gives us an anthropomorphic geometric figures joke for the week. Also a side of these figures that I don’t think I’ve seen in the newspaper comics before. It kind of raises further questions.

Jason Chatfield’s Ginger Meggs for the 1st just mentions that it’s a mathematics test. Ginger isn’t ready for it.

Mark Tatulli’s Heart of the City rerun for the 1st finally has some specific mathematics mentioned in Heart’s efforts to avoid a mathematics tutor. The bit about the sum of adjacent angles forming a right line being 180 degrees is an important one. A great number of proofs rely on it. I can’t deny the bare fact seems dull, though. I know offhand, for example, that this bit about adjacent angles comes in handy in proving that the interior angles of a triangle add up to 180 degrees. At least for Euclidean geometry. And there are non-Euclidean geometries that are interesting and important and for which that’s not true. Which inspires the question: on a non-Euclidean surface, like say the surface of the Earth, is it that adjacent angles don’t add up to 180 degrees? Or does something else in the proof of a triangle’s interior angles adding up to 180 degrees go wrong?

The Eric the Circle rerun for the 2nd, by JohnG, is one of the occasional Erics that talk about π and so get to be considered on-topic here.

Bill Whitehead’s Free Range for the 2nd features the classic page full of equations to demonstrate some hard mathematical work. And it is the sort of subject that is done mathematically. The equations don’t look to me anything like what you’d use for asteroid orbit projections. I’d expect forecasting just where an asteroid might hit the Earth to be done partly by analytic formulas that could be done on a blackboard. And then made precise by a numerical estimate. The advantage of the numerical estimate is that stuff like how air resistance affects the path of something in flight is hard to deal with analytically. Numerically, it’s tedious, but we can let the computer deal with the tedium. So there’d be just a boring old computer screen to show on-panel.

Bud Fisher’s Mutt and Jeff reprint for the 2nd is a little baffling. And not really mathematical. It’s just got a bizarre arithmetic error in it. Mutt’s fiancee Encee wants earrings that cost ten dollars (each?) and Mutt takes this to be fifty dollars in earring costs and I have no idea what happened there. Thomas K Dye, the web cartoonist who’s done artwork for various article series, has pointed out that the lettering on these strips have been redone with a computer font. (Look at the letters ‘S’; once you see it, you’ll also notice it in the slightly lumpy ‘O’ and the curly-arrow ‘G’ shapes.) So maybe in the transcription the earring cost got garbled? And then not a single person reading the finished product read it over and thought about what they were doing? I don’t know.

Zach Weinersmith’s Saturday Morning Breakfast Cereal reprint for the 2nd is based, as his efforts to get my attention often are, on a real mathematical physics postulate. As the woman postulates: given a deterministic universe, with known positions and momentums of every particle, and known forces for how all these interact, it seems like it should be possible to predict the future perfectly. It would also be possible to “retrodict” the past. All the laws of physics that we know are symmetric in time; there’s no reason you can’t predict the motion of something one second into the past just as well as you an one second into the future. This fascinating observation took a lot of battery in the 19th century. Many physical phenomena are better described by statistical laws, particularly in thermodynamics, the flow of heat. In these it’s often possible to predict the future well but retrodict the past not at all.

But that looks as though it’s a matter of computing power. We resort to a statistical understanding of, say, the rings of Saturn because it’s too hard to track the billions of positions and momentums we’d need to otherwise. A sufficiently powerful mathematician, for example God, would be able to do that. Fair enough. Then came the 1890s. Henri Poincaré discovered something terrifying about deterministic systems. It’s possible to have chaos. A mathematical representation of a system is a bit different from the original system. There’s some unavoidable error. That’s bound to make some, larger, error in any prediction of its future. For simple enough systems, this is okay. We can make a projection with an error as small as we need, at the cost of knowing the current state of affairs with enough detail. Poincaré found that some systems can be chaotic, though, ones in which any error between the current system and its representation will grow to make the projection useless. (At least for some starting conditions.) And so many interesting systems are chaotic. Incredibly simplified models of the weather are chaotic; surely the actual thing is. This implies that God’s projection of the universe would be an amusing but almost instantly meaningless toy. At least unless it were a duplicate of the universe. In which case we have to start asking our philosopher friends about the nature of identity and what a universe is, exactly.

Ruben Bolling’s Super-Fun-Pak Comix for the 2nd is an installment of Guy Walks Into A Bar featuring what looks like an arithmetic problem to start. It takes a turn into base-ten jokes. There are times I suspect Ruben Bolling to be a bit of a nerd.

Nate Fakes’s Break of Day for the 3rd looks like it’s trying to be an anthropomorphic-numerals joke. At least it’s an anthropomorphic something joke.

Percy Crosby’s Skippy for the 3rd originally ran the 8th of December, 1930. It alludes to one of those classic probability questions: what’s the chance that in your lungs is one of the molecules exhaled by Julius Caesar in his dying gasp? Or whatever other event you want: the first breath you ever took, or something exhaled by Jesus during the Sermon on the Mount, or exhaled by Sue the T-Rex as she died. Whatever. The chance is always surprisingly high, which reflects the fact there’s a lot of molecules out there. This also reflects a confidence that we can say one molecule of air is “the same” as some molecule if air in a much earlier time. We have to make that supposition to have a problem we can treat mathematically. My understanding is chemists laugh at us if we try to suggest this seriously. Fair enough. But whether the air pumped out of a bicycle tire is ever the same as what’s pumped back in? That’s the same kind of problem. At least some of the molecules of air will be the same ones. Pretend “the same ones” makes sense. Please.

## Reading the Comics, January 27, 2018: Working Through The Week Edition

And today I bring the last couple mathematically-themed comic strips sent my way last week. GoComics has had my comics page working intermittently this week. And I was able to get a response from them, by e-mailing their international sales office, the only non-form contact I could find. Anyway, this flood of comics does take up the publishing spot I’d figured for figuring how I messed up Wronski’s formula. But that’s all right, as I wanted to spend more time thinking about that. Here’s hoping spending more time thinking works out for me.

Nate Fakes’s Break of Day for the 24th was the big anthropomorphic numerals joke for the week. And it’s even dubbed the numbers game.

Mark Tatulli’s Heart of the City from the 24th got into a storyline about Heart needing a mathematics tutor. It’s a rerun sequence, although if you remember a particular comic storyline from 2009 you’re doing pretty well. Nothing significantly mathematical has turned up in the story so far, past the mention of fractions as things that exist and torment students. But the stories are usually pretty good for this sort of strip.

Mikael Wulff and Anders Morganthaler’s WuMo for the 24th includes a story problems freak out. I’m not sure what’s particularly implausible about buying nine apples. I’d agree a person is probably more likely to buy an even number of things, since we seem to like numbers like “ten” and “eight” so well, but it’s hardly ridiculous.

Tim Rickard’s Brewster Rockit for the 25th is an arithmetic class on the Snowman Planet. So there’s some finger-counting involved.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th is a reminder that most of my days are spent seeing how Zach Weinersmith wants my attention. It also includes what I suppose is a legitimate attempt to offer a definition for what all mathematics is. It’s hard to come up with something that does cover all the stuff mathematicians do. Bear in mind, this includes counting, calculating how far the Sun is based on the appearance of a lunar eclipse, removing static from a recording, and telling how many queens it’s possible to place eight queens on a chess board that’s wrapped around a torus without any being able to capture another, among other problems. My instinct is to dismiss the proposed “anything you can think deeply about that has no reference to the real world”. That seems over-broad, and to cover a lot of areas that are really philosophy’s beat. And I think there’s something unseemly in mathematicians gloating about their work having no “practical” use. I grant I come from an applied school, and I came to there through an interest in physics. But to build up “inapplicability to the real word” as if it were some ideal, as opposed to just how something has turned out to be right now, strikes me as silly. Applicability is so dependent on context, on culture, and accidents of fate that there’s no way it can be important to characterizing mathematics. And it would imply that once we found a use for something it would stop being mathematically interesting. I don’t see evidence of that in mathematical history.

Mikael Wulff and Anders Morganthaler’s WuMo pops back in on the 27th with an appearance of sudoku, presenting the logic puzzle as one of the many things beyond the future Disgraced Former President’s abilities.

I was all set to say how complaining about GoComics.com’s pages not loading had gotten them fixed. But they only worked for Monday alone; today they’re broken again. Right. I haven’t tried sending an error report again; we’ll see if that works. Meanwhile, I’m still not through last week’s comic strips and I had just enough for one day to nearly enough justify an installment for the one day. Should finish off the rest of the week next essay, probably in time for next week.

Mark Leiknes’s Cow and Boy rerun for the 23rd circles around some of Zeno’s Paradoxes. At the heart of some of them is the question of whether a thing can be divided infinitely many times, or whether there must be some smallest amount of a thing. Zeno wonders about space and time, but you can do as well with substance, with matter. Mathematics majors like to say the problem is easy; Zeno just didn’t realize that a sum of infinitely many things could be a finite and nonzero number. This misses the good question of how the sum of infinitely many things, none of which are zero, can be anything but infinitely large? Or, put another way, what’s different in adding $\frac11 + \frac12 + \frac13 + \frac14 + \cdots$ and adding $\frac11 + \frac14 + \frac19 + \frac{1}{16} + \cdots$ that the one is infinitely large and the other not?

Or how about this. Pick your favorite string of digits. 23. 314. 271828. Whatever. Add together the series $\frac11 + \frac12 + \frac13 + \frac14 + \cdots$except that you omit any terms that have your favorite string there. So, if you picked 23, don’t add $\frac{1}{23}$, or $\frac{1}{123}$, or $\frac{1}{802301}$ or such. That depleted series does converge. The heck is happening there? (Here’s why it’s true for a single digit being thrown out. Showing it’s true for longer strings of digits takes more work but not really different work.)

J C Duffy’s Lug Nuts for the 23rd is, I think, the first time I have to give a content warning for one of these. It’s a porn-movie advertisement spoof. But it mentions Einstein and Pi and has the tagline “she didn’t go for eggheads … until he showed her a new equation!”. So, you know, it’s using mathematics skill as a signifier of intelligence and riffing on the idea that nerds like sex too.

John Graziano’s Ripley’s Believe It or Not for the 23rd has a trivia that made me initially think “not”. It notes Vince Parker, Senior and Junior, of Alabama were both born on Leap Day, the 29th of February. I’ll accept this without further proof because of the very slight harm that would befall me were I to accept this wrongly. But it also asserted this was a 1-in-2.1-million chance. That sounded wrong. Whether it is depends on what you think the chance is of.

Because what’s the remarkable thing here? That a father and son have the same birthday? Surely the chance of that is 1 in 365. The father could be born any day of the year; the son, also any day. Trusting there’s no influence of the father’s birthday on the son’s, then, 1 in 365 it is. Or, well, 1 in about 365.25, since there are leap days. There’s approximately one leap day every four years, so, surely that, right?

And not quite. In four years there’ll be 1,461 days. Four of them will be the 29th of January and four the 29th of September and four the 29th of August and so on. So if the father was born any day but leap day (a “non-bissextile day”, if you want to use a word that starts a good fight in a Scrabble match), the chance the son’s birth is the same is 4 chances in 1,461. 1 in 365.25. If the father was born on Leap Day, then the chance the son was born the same day is only 1 chance in 1,461. Still way short of 1-in-2.1-million. So, Graziano’s Ripley’s is wrong if that’s the chance we’re looking at.

Ah, but what if we’re looking at a different chance? What if we’re looking for the chance that the father is born the 29th of February and the son is also born the 29th of February? There’s a 1-in-1,461 chance the father’s born on Leap Day. And a 1-in-1,461 chance the son’s born on Leap Day. And if those events are independent, the father’s birth date not influencing the son’s, then the chance of both those together is indeed 1 in 2,134,521. So Graziano’s Ripley’s is right if that’s the chance we’re looking at.

Which is a good reminder: if you want to work out the probability of some event, work out precisely what the event is. Ordinary language is ambiguous. This is usually a good thing. But it’s fatal to discussing probability questions sensibly.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 23rd presents his mathematician discovering a new set of numbers. This will happen. Mathematics has had great success, historically, finding new sets of things that look only a bit like numbers were understood. And showing that if they follow rules that are, as much as possible, like the old numbers, we get useful stuff out of them. The mathematician claims to be a formalist, in the punch line. This is a philosophy that considers mathematical results to be the things you get by starting with some symbols and some rules for manipulating them. What this stuff means, and whether it reflects anything of interest in the real world, isn’t of interest. We can know the results are good because they follow the rules.

This sort of approach can be fruitful. It can force you to accept results that are true but intuition-defying. And it can give results impressive confidence. You can even, at least in principle, automate the creating and the checking of logical proofs. The disadvantages are that it takes forever to get anything done. And it’s hard to shake the idea that we ought to have some idea what any of this stuff means.

## Reading the Comics, January 16, 2017: Better Workflow Edition

So one little secret of my Reading the Comics posts is I haven’t been writing them in a way that makes sense to me. To me, I should take each day’s sufficiently relevant comics, describe them in a paragraph or two, and then have a nice pile of text all ready for the posting Sunday and, if need be, later. I haven’t been doing that. I’ve let links pile up until Friday or Saturday, and then try to process them all, and if you’ve ever wondered why the first comic of the week gets 400 words about some subtlety while the last gets “this is a comic that exists”, there you go. This time around, let me try doing each day’s strips per day and see how that messes things up.

Jef Mallett’s Frazz for the 14th of January is another iteration of the “when will we ever use mathematics” complaint. The answer of “you’ll use it on the test” is unsatisfactory. But somehow, the answer of “you’ll use it to think deeply about something you had never considered before” also doesn’t satisfy. Anyway I’d like to see the idea that education is job-training abolished; I think it should be about making a person conversant with the history of human thought. That can’t be done perfectly, and we might ask whether factoring 32 is that important a piece, but it should certainly be striven for.

Ham’s Life on Earth for the 14th is a Gary Larsonesque riff on that great moment of calculus and physics history, Newton’s supposition that gravity has to follow a universally true law. I’m not sure this would have made my cut if I reviewed a week’s worth of strips at a time. Hm.

Mason Mastroianni’s B.C. for the 15th is a joke about story problem construction, and how the numbers in a story problem might be obvious nonsense. It’s also a cheap shot at animal hoarders, I suppose, but that falls outside my territory here.

Anthony Blades’s Bewley rerun for the 15th riffs on the natural number sense we all have. And we do have a number sense, remarkably. We might not be able to work out 9 times 6 instantly. But asked to pick from a list of possible values, we’re more likely to think that 58 is credible than that 78 or 38 are. It’s quite imprecise, but isn’t it amazing that it’s there at all?

Bill Amend’s FoxTrot Classics for the 15th is a story problem joke, in this case, creating one with a strong motivation for its solution to be found. The strip originally ran the 22nd of January, 1996.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 16th is maybe marginal to include, too. It’s about the kinds of logic puzzles that mathematicians grow up reading and like to pass around. And the way you can fake out someone by presenting a problem with too obvious a solution. It’s not just professors who’ll be stymied by having the answer look too obvious, by the way. Everyone’s similarly vulnerable. To see anything, including an abstract thing like the answer to a puzzle, you need some idea of what you are looking at. If you don’t think the answer could be something that simple, you won’t see it there.

Gordon Bess’s Redeye for the 6th of September, 1971, was reprinted the 17th. It’s about the fun of teaching a subject you aren’t all that good on yourself. The mathematics is a name-drop here, but the joke wouldn’t make sense if it were about social studies.

Elzie Segar’s Thimble Theatre for the 10th of August, 1931, was also reprinted the 17th. It’s an old gag, even back when it was first run. But I suppose there’s some numerical-conversion mathematics to wring out of it. Given the rate of exchange, a pezozee would seem to be 24 pazimees. I’m not sure we need so many units in-between the pazimee and the pezozee, but perhaps King Blozo’s land set its units in a time when fractions were less familiar to the public. The punch line depends on the pazimee being worth nothing and, taken literally, that has sad implications for the pezozee too. If you take the King as speaking roughly, though, sixteen times a small amount is … at least a less small amount. It wouldn’t take many doublings to go from an infinitesimally tiny sum to a respectable one.

And it turns out there were enough comic strips I need to split this into two segments. So I should schedule that to appear. It’s already written and everything.

## Reading the Comics, January 13, 2018: Barney Google Is Messing With My Head For Some Reason Edition

I do not know what’s possessed John Rose, cartoonist for Barney Google and Snuffy Smith — possibly the oldest syndicated comic strip not in perpetual reruns — to decide he needs to mess with my head. So far as I’m aware we haven’t ever even had any interactions. While I’ll own up to snarking about the comic strip here and there, I mean, the guy draws Barney Google and Snuffy Smith. He won’t attract the snark community of, say, Marmaduke, but he knew the job was dangerous when he took it. There’s lots of people who’ve said worse things about the comic than I ever have. He can’t be messing with them all.

There’s no mathematical content to it, but here, continuing the curious thread of Elviney and Miss Prunelly looking the same, and Elviney turning out to have a twin sister, is the revelation that Elviney’s husband also has a twin.

This means something and I don’t know what.

To mathematics:

Zach Weinersmith’s Saturday Morning Breakfast Cereal gets my attention again for the 10th. There is this famous quotation from Leopold Kronecker, one of the many 19th century German mathematicians who challenged, and set, our ideas of what mathematics is. In debates about what should count as a proof Kronecker said something translated in English to, “God created the integers, all else is the work of man”. He favored proofs that only used finite numbers, and only finitely many operations, and was skeptical of existence proofs. Those are ones that show something with desired properties must exist, without necessarily showing how to find it. Most mathematicians accept existence proofs. If you can show how to find that thing, that’s a constructive proof. Usually mathematicians like those better.

Mark Tatulli’s Heart of the City for the 11th uses a bunch of arithmetic and word problems to represent all of Dean’s homework. All looks like reasonable homework for my best guess about his age.

Jon Rosenberg’s Scenes From A Multiverse for the 11th is a fun, simple joke with some complex stuff behind it. It’s riffing on the kind of atheist who wants moral values to come from something in the STEM fields. So here’s a mathematical basis for some moral principles. There are, yes, ethical theories that have, or at least imply having, mathematics behind them. Utilitarianism at least supposes that ethical behavior can be described as measurable and computable quantities. Nobody actually does that except maybe to make video games more exciting. But it’s left with the idea that one could, and hope that this would lead to guidance that doesn’t go horribly wrong.

Don Asmussen’s Bad Reporter for the 12th uses knowledge of arithmetic as a signifier of intelligence. Common enough joke style.

Thom Bluemel’s Birdbrains for the 13th starts Pi Day observances early, or maybe supposed the joke would be too out of season were it to come in March.

Greg Evans and Karen Evans’s Luann for the 13th uses mathematics to try building up the villainy of one of the strip’s designated villains. Ann Eiffel, there, uses a heap of arithmetic to make her lingerie sale sound better. This isn’t simply a riff on people not wanting to do arithmetic, although I understand people not wanding to work out what five percent of a purchase of over $200 is. There’s a good deal of weird psychology in getting people to buy things. Merely naming a number, for example, gets people to “anchor” their expectations to it. To speak of a free gift worth$75 makes any purchase below $75 seem more economical. To speak of a chance to win$1,000 prepares people to think they’ve got a thousand dollars coming in, and that they can safely spend under that. It’s amazing stuff to learn about, and it isn’t all built on people being too lazy to figure out what five percent off of $220 would be. T Lewis and Michael Fry’s Over the Hedge for the 13th uses &infty; along the way to making nonsense out of ice-skating judging. It’s a good way to make a hash of a rating system. Most anything done with infinitely large numbers or infinitely large sets challenges one’s intuition at least. This is part of what Leopold Kronecker was talking about. ## 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, December 9, 2017: Zach Weinersmith Wants My Attention Edition If anything dominated the week in mathematically-themed comic strips it was Zach Weinersmith’s Saturday Morning Breakfast Cereal. I don’t know how GoComics selects the strips to (re?)print on their site. But there were at least four that seemed on-point enough for me to mention. So, okay. He’s got my attention. What’s he do with it? On the 3rd of December is a strip I can say is about conditional probability. The mathematician might be right that the chance someone will be murdered by a serial killer are less than one in ten million. But that is the chance of someone drawn from the whole universe of human experiences. There are people who will never be near a serial killer, for example, or who never come to his attention or who evade his interest. But if we know someone is near a serial killer, or does attract his interest? The information changes the probability. And this is where you get all those counter-intuitive and somewhat annoying logic puzzles about, like, the chance someone’s other child is a girl if the one who just walked in was, and how that changes if you’re told whether the girl who just entered was the elder. On the 5th is a strip about sequences. And built on the famous example of exponential growth from doubling a reward enough times. Well, you know these things never work out for the wise guy. The “Fibonacci Spiral” spoken of in the next-to-last panel is a spiral, like you figure. The dimensions of the spiral are based on those of golden-ratio rectangles. It looks a great deal like a logarithmic spiral to the untrained eye. Also to the trained eye, but you knew that. I think it’s supposed to be humiliating that someone would call such a spiral “random”. But I admit I don’t get that part. The strip for the 6th has a more implicit mathematical content. It hypothesizes that mathematicians, given the chance, will be more interested in doing recreational puzzles than even in eating and drinking. It’s amusing, but I’ll admit I’ve found very few puzzles all that compelling. This isn’t to say there aren’t problems I keep coming back to because I’m curious about them, just that they don’t overwhelm my common sense. Don’t ask me when I last received actual pay for doing something mathematical. And then on the 9th is one more strip, about logicians. And logic puzzles, such as you might get in a Martin Gardner collection. The problem is written out on the chalkboard with some shorthand logical symbols. And they’re symbols both philosophers and mathematicians use. The letter that looks like a V with a crossbar means “for all”. (The mnemonic I got was “it’s an A-for-all, upside-down”. This paired with the other common symbol, which looks like a backwards E and means there exists: “E-for-exists, backwards”. Later I noticed upside-down A and backwards E could both be just 180-degree-rotated A and E. But try saying “180-degree-rotated” in a quick way.) The curvy E between the letters ‘x’ and ‘S’ means “belongs to the set”. So that first line says “for all x that belong to the set S this follows”. Writing out “isLiar(x)” instead of, say, “L(x)”, is more a philosopher’s thing than a mathematician’s. But it wouldn’t throw anyway. And the T just means emphasizing that this is true. And that is as much about Saturday Morning Breakfast Cereal as I have to say this week. Sam Hurt’s Eyebeam for the 4th tells a cute story about twins trying to explain infinity to one another. I’m not sure I can agree with the older twin’s assertion that infinity means there’s no biggest number. But that’s just because I worry there’s something imprecise going on there. I’m looking forward to the kids learning about negative numbers, though, and getting to wonder what’s the biggest negative real number. Percy Crosby’s Skippy for the 4th starts with Skippy explaining a story problem. One about buying potatoes, in this case. I’m tickled by how cranky Skippy is about boring old story problems. Motivation is always a challenge. The strip originally ran the 7th of October, 1930. Dave Whamond’s Reality Check for the 6th uses a panel of (gibberish) mathematics as an example of an algorithm. Algorithms are mathematical, in origin at least. The word comes to us from the 9th century Persian mathematician Al-Khwarizmi’s text about how to calculate. The modern sense of the word comes from trying to describe the methods by which a problem can be solved. So, legitimate use of mathematics to show off the idea. The symbols still don’t mean anything. Rick Detorie’s One Big Happy for the 7th has Joe trying to get his mathematics homework done at the last minute. … And it’s caused me to reflect on how twenty multiplication problems seems like a reasonable number to do. But there’s only fifty multiplications to even do, at least if you’re doing the times tables up to the 10s. No wonder students get so bored seeing the same problems over and over. It’s a little less dire if you’re learning times tables up to the 12s, but not that much better. Yow. Olivia Walch’s Imogen Quest for the 8th looks pretty legitimate to me. It’s going to read as gibberish to people who haven’t done parametric functions, though. Start with the plane and the familiar old idea of ‘x’ and ‘y’ representing how far one is along a horizontal and a vertical direction. Here, we’re given a dummy variable ‘t’, and functions to describe a value for ‘x’ and ‘y’ matching each value of ‘t’. The plot then shows all the points that ever match a pair of ‘x’ and ‘y’ coordinates for some ‘t’. The top drawing is a shape known as the cardioid, because it kind of looks like a Valentine-heart. The lower figure is a much more complicated parametric equation. It looks more anatomically accurate, Still no sign of Mark Anderson’s Andertoons and the drought is worrying me, yes. But they’re still going on the cartoonist’s web site, so there’s that. ## Reading the Comics, December 2, 2017: Showing Intelligence Edition November closed out with another of those weeks not quite busy enough to justify splitting into two. I blame Friday and Saturday. Nothing mathematically-themed was happening them. Suppose some days are just like that. Johnny Hart’s Back To BC for the 26th is an example of using mathematical truths as profound statements. I’m not sure that I’d agree with just stating the Pythagorean Theorem as profound, though. It seems like a profound statement has to have some additional surprising, revelatory elements to it. Like, knowing the Pythagorean theorem is true means we can prove there’s exactly one line parallel to a given line and passing through some point. Who’d see that coming? I don’t blame Hart for not trying to fit all that into one panel, though. Too slow a joke. The strip originally ran the 4th of September, 1960. Tom Toles’s Randolph Itch, 2 am rerun for the 26th is a cute little arithmetic-in-real-life panel. I suppose arithmetic-in-real-life. Well, I’m amused and stick around for the footer joke. The strip originally ran the 24th of February, 2002. Zach Weinersmith’s Saturday Morning Breakfast Cereal makes its first appearance for the week on the 26th. It’s an anthropomorphic-numerals joke and some wordplay. Interesting trivia about the whole numbers that never actually impresses people: a whole number is either a perfect square, like 1 or 4 or 9 or 16 are, or else its square root is irrational. There’s no whole number with a square root that’s, like, 7.745 or something. Maybe I just discuss it with people who’re too old. It seems like the sort of thing to reveal to a budding mathematician when she’s eight. Saturday Morning Breakfast Cereal makes another appearance the 29th. The joke’s about using the Greek ε, which has a long heritage of use for “a small, positive number”. We use this all the time in analysis. A lot of proofs in analysis are done by using ε in a sort of trick. We want to show something is this value, but it’s too hard to do. Fine. Pick any ε, a positive number of unknown size. So then we’ll find something we can calculate, and show that the difference between the thing we want and the thing we can do is smaller than ε. And that the value of the thing we can calculate is that. Therefore, the difference between what we want and what we can do is smaller than any positive number. And so the difference between them must be zero, and voila! We’ve proved what we wanted to prove. I have always assumed that we use ε for this for the association with “error”, ideally “a tiny error”. If we need another tiny quantity we usually go to δ, probably because it’s close to ε and ‘d’ is still a letter close to ‘e’. (The next letter after ε is ζ, which carries other connotations with it and is harder to write than δ is.) Anyway, Weinersmith is just doing a ha-ha, your penis is small joke. Samson’s Dark Side of the Horse for the 28th is a counting-sheep joke. It maybe doesn’t belong here but I really, really like the art of the final panel and I want people to see it. Bud Grace’s Piranha Club for the 29th is, as with Back to BC, an attempt at showing intelligence through mathematics. There are some flaws in the system. Fun fact: since one million is a perfect square, Arnold could have answered within a single panel. (Also fun fact: I am completely unqualified to judge whether something is a “fun” fact.) Jason Chatfield’s Ginger Meggs for the 29th is Ginger subverting the teacher’s questions, like so many teacher-and-student jokes will do. Dan Thompson’s Brevity for the 30th is the anthropomorphic geometric figures joke for the week. There seems to be no Mark Anderson’s Andertoons for this week. There’ve been some great ones (like on the 26th or the 28th and the 29th) but they’re not at all mathematical. I apologize for the inconvenience and am launching an investigation into this problem. ## Reading the Comics, November 18, 2017: Story Problems and Equation Blackboards Edition It was a normal-paced week at Comic Strip Master Command. It was also one of those weeks that didn’t have anything from Comics Kingdom or Creators.Com. So I’m afraid you’ll all just have to click the links for strips you want to actually see. Sorry. Bill Amend’s FoxTrot for the 12th has Jason and Marcus creating “mathic novels”. They, being a couple of mathematically-gifted smart people, credit mathematics knowledge with smartness. A “chiliagon” is a thousand-sided regular polygon that’s mostly of philosophical interest. A regular polygon with a thousand equal sides and a thousand equal angles looks like a circle. There’s really no way to draw one so that the human eye could see the whole figure and tell it apart from a circle. But if you can understand the idea of a regular polygon it seems like you can imagine a chilagon and see how that’s not a circle. So there’s some really easy geometry things that can’t be visualized, or at least not truly visualized, and just have to be reasoned with. Rick Detorie’s One Big Happy for the 12th is a story-problem-subversion joke. The joke’s good enough as it is, but the supposition of the problem is that the driving does cover fifty miles in an hour. This may not be the speed the car travels at the whole time of the problem. Mister Green is maybe speeding to make up for all the time spent travelling slower. Brandon Sheffield and Dami Lee’s Hot Comics for Cool People for the 13th uses a blackboard full of equations to represent the deep thinking being done on a silly subject. Shannon Wheeler’s Too Much Coffee Man for the 15th also uses a blackboard full of equations to represent the deep thinking being done on a less silly subject. It’s a really good-looking blackboard full of equations, by the way. Beyond the appearance of our old friend E = mc2 there’s a lot of stuff that looks like legitimate quantum mechanics symbols there. They’re at least not obvious nonsense, as best I can tell without the ability to zoom the image in. I wonder if Wheeler didn’t find a textbook and use some problems from it for the feeling of authenticity. Samson’s Dark Side of the Horse for the 16th is a story-problem subversion joke. Jef Mallett’s Frazz for the 18th talks about making a bet on the World Series, which wrapped up a couple weeks ago. It raises the question: can you bet on an already known outcome? Well, sure, you can bet on anything you like, given a willing partner. But there does seem to be something fundamentally different between betting on something whose outcome isn’t in principle knowable, such as the winner of the next World Series, and betting on something that could be known but happens not to be, such as the winner of the last. We see this expressed in questions like “is it true the 13th of a month is more likely to be Friday than any other day of the week?” If you know which month and year is under discussion the chance the 13th is Friday is either 1 or 0. But we mean something more like, if we don’t know what month and year it is, what’s the chance this is a month with a Friday the 13th? Something like this is at work in this World Series bet. (The Astros won the recently completed World Series.) Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th is also featured on some underemployed philosopher’s “Reading the Comics” WordPress blog and fair enough. Utilitarianism exists in an odd triple point, somewhere on the borders of ethics, economics, and mathematics. The idea that one could quantize the good or the utility or the happiness of society, and study how actions affect it, is a strong one. It fits very well the modern mindset that holds everything can be quantified even if we don’t know how to do it well just yet. And it appeals strongly to a mathematically-minded person since it sounds like pure reason. It’s not, of course, any more than any ethical scheme can be. But it sounds like the ethics a Vulcan would come up with and that appeals to a certain kind of person. (The comic is built on one of the implications of utilitarianism that makes it seem like the idea’s gone off the rails.) There’s some mathematics symbols on The Utilitarian’s costume. The capital U on his face is probably too obvious to need explanation. The $\sum u$ on his chest relies on some mathematical convention. For maybe a half-millennium now mathematicians have been using the capital sigma to mean “take a sum of things”. The things are whatever the expression after that symbol is. Usually, the Sigma will have something below and above which carries meaning. It says what the index is for the thing after the symbol, and what the bounds of the index are. Here, it’s not set. This is common enough, though, if this is understood from context. Or if it’s obvious. The small ‘u’ to the right suggests the utility of whatever’s thought about. (“Utility” being the name for the thing measured and maximized; it might be happiness, it might be general well-being, it might be the number of people alive.) So the symbols would suggest “take the sum of all the relevant utilities”. Which is the calculation that would be done in this case. ## Reading the Comics, November 8, 2017: Uses Of Mathematics Edition Was there an uptick in mathematics-themed comic strips in the syndicated comics this past week? It depends how tight a definition of “theme” you use. I have enough to write about that I’m splitting the week’s load. And I’ve got a follow-up to that Wronski post the other day, so I’m feeling nice and full of content right now. So here goes. Zach Weinersmith’s Saturday Morning Breakfast Cereal posted the 5th gets my week off to an annoying start. Science and mathematics and engineering people have a tendency to be smug about their subjects. And to see aptitude or interest in their subjects as virtue, or at least intelligence. (If they see a distinction between virtue and intelligence.) To presume that an interest in the field I like is a demonstration of intelligence is a pretty nasty and arrogant move. And yes, I also dislike the attitude that school should be about training people. Teaching should be about letting people be literate with the great thoughts people have had. Mathematics has a privileged spot here. The field, as we’ve developed it, seems to build on human aptitudes for number and space. It’s easy to find useful sides to it. Doesn’t mean it’s vocational training. Lincoln Peirce’s Big Nate on the 6th discovered mathematics puzzles. And this gave him the desire to create a new mathematical puzzle that he would use to get rich. Good luck with that. Coming up with interesting enough recreational mathematics puzzles is hard. Presenting it in a way that people will buy is another, possibly greater, challenge. It takes luck and timing and presentation, just as getting a hit song does. Sudoku, for example, spent five years in the Dell Magazine puzzle books before getting a foothold in Japanese newspapers. And then twenty years there before being noticed in the English-speaking puzzle world. Big Nate’s teacher tries to encourage him, although that doesn’t go as Mr Staples might have hoped. (The storyline continues to the 11th. Spoiler: Nate does not invent the next great recreational mathematics puzzle.) Jef Mallett’s Frazz for the 7th start out in a mathematics class, at least. I suppose the mathematical content doesn’t matter, though. Mallett’s making a point about questions that, I confess, I’m not sure I get. I’ll leave it for wiser heads to understand. Mike Thompson’s Grand Avenue for the 8th is a subverted word-problem joke. And I suppose a reminder about the need for word problems to parse as things people would do, or might be interested in. I can’t go along with characterizing buying twelve candy bars “gluttonous” though. Not if they’re in a pack of twelve or something like that. I may be unfair to Grand Avenue. Mind, until a few years ago I was large enough my main method of getting around was “being rolled by Oompa-Loompas”, so I could be a poor judge. Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 8th does a rounding joke. It’s not much, but I’ve included appearances of this joke before and it seems unfair to skip it this time. ## 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, July 15, 2017: Dawn Of Mathematics Jokes

So I try to keep up with nearly all the comic strips run on Comics Kingdom and on GoComics. This includes some vintage strips: take some ancient comic like Peanuts or Luann and rerun it, day at a time, from the beginning. This is always enlightening. It’s always interesting to see a comic in that first flush of creative energy, before the characters have quite settled in and before the cartoonist has found stock jokes that work so well they don’t even have to be jokes anymore. One of the most startling cases for me has been Johnny Hart’s B.C. which, in its Back To B.C. incarnation, has been pretty well knocking it out of the park.

Not this week, I’m sad to admit. This week it’s been doing a bunch of mathematics jokes, which is what gives me my permission to talk about it here. The jokes have been, eh, the usual, given the setup. A bit fresher, I suppose, for the characters in the strip having had fewer of their edges worn down by time. Probably there’ll be at least one that gets a bit of a grin.

Back To B.C. for the 11th sets the theme going. On the 12th it gets into word problems. And then for the 13th of July it turns violent and for my money funny.

Mark Tatulli’s Heart of the City has a number appear on the 12th. That’s been about as much mathematical content as Heart’s experience at Math Camp has taken. The story’s been more about Dana, her camp friend, who’s presented as good enough at mathematics to be bored with it, and the attempt to sneak out to the nearby amusement park. What has me distracted is wondering what amusement park this could be, given that Heart’s from Philadelphia and the camp’s within bus-trip range and in the forest. I can’t rule out that it might be Knoebels Amusement Park, in Elysburg, Pennsylvania, in which case Heart and Dana are absolutely right to sneak out of camp because it is this amazing place.

Mort Walker’s Beetle Bailey Vintage for the 21st of December, 1960 was rerun the 14th. I can rope this into mathematics. It’s about Cookie trying to scale up a recipe to fit Camp Swampy’s needs. Increasing the ingredient count is easy, or at least it is if your units scale nicely. I wouldn’t want to multiple a third of a teaspoon by 200 without a good stretching beforehand and maybe a rubdown afterwards. But the time needed to cook a multiplied recipe, that gets mysterious. As I understand it — the chemistry of cooking is largely a mystery to me — the center of the trouble is that to cook a thing, heat has to reach throughout the interior. But heat can only really be applied from the surfaces of the cooked thing. (Yes, theoretically, a microwave oven could bake through the entire volume of something. But this would require someone inventing a way to bake using a microwave.) So we must balance the heat that can be applied over what surface to the interior volume and any reasonable time to cook the thing. Won’t deny that at some point it seems easier to just make a smaller meal.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 14th goes to the old “inference testing” well again. This comes up from testing whether something strange is going on. Measure something in a sample. Is the result appreciably different from what would be a plausible result if nothing interesting is going on? The null hypothesis is the supposition that there isn’t anything interesting going on: the measurement’s in the range of what you’d expect given that the world is big and complicated. I’m not sure what the physicist’s exact experiment would have been. I suppose it would be something like “you lose about as much heat through your head as you do any region of skin of about the same surface area”. So, yeah, freezing would be expected, considering.

Percy Crosby’s Skippy for the 17th of May, 1930, and rerun the 15th, maybe doesn’t belong here. It’s just about counting. Never mind. I smiled at it, and I’m a fan of the strip. Give it a try; it’s that rare pre-Peanuts comic that still feels modern.

And, before I forget: Have any mathematics words or terms you’d like to have explained? I’m doing a Summer 2017 A To Z and taking requests! Please offer them over there, for convenience. I mean mine.

## Reading the Comics, June 26, 2017: Deluge Edition, Part 1

So this past week saw a lot of comic strips with some mathematical connection put forth. There were enough just for the 26th that I probably could have done an essay with exclusively those comics. So it’s another split-week edition, which suits me fine as I need to balance some of my writing loads the next couple weeks for convenience (mine).

Tony Cochrane’s Agnes for the 25th of June is fun as the comic strip almost always is. And it’s even about estimation, one of the things mathematicians do way more than non-mathematicians expect. Mathematics has a reputation for precision, when in my experience it’s much more about understanding and controlling error methods. Even in analysis, the study of why calculus works, the typical proof amounts to showing that the difference between what you want to prove and what you can prove is smaller than your tolerance for an error. So: how do we go about estimating something difficult, like, the number of stars? If it’s true that nobody really knows, how do we know there are some wrong answers? And the underlying answer is that we always know some things, and those let us rule out answers that are obviously low or obviously high. We can make progress.

Russell Myers’s Broom Hilda for the 25th is about one explanation given for why time keeps seeming to pass faster as one age. This is a mathematical explanation, built on the idea that the same linear unit of time is a greater proportion of a young person’s lifestyle so of course it seems to take longer. This is probably partly true. Most of our senses work by a sense of proportion: it’s easy to tell a one-kilogram from a two-kilogram weight by holding them, and easy to tell a five-kilogram from a ten-kilogram weight, but harder to tell a five from a six-kilogram weight.

As ever, though, I’m skeptical that anything really is that simple. My biggest doubt is that it seems to me time flies when we haven’t got stories to tell about our days, when they’re all more or less the same. When we’re doing new or exciting or unusual things we remember more of the days and more about the days. A kid has an easy time finding new things, and exciting or unusual things. Broom Hilda, at something like 1500-plus years old and really a dour, unsociable person, doesn’t do so much that isn’t just like she’s done before. Wouldn’t that be an influence? And I doubt that’s a complete explanation either. Real things are more complicated than that yet.

Mac and Bill King’s Magic In A Minute for the 25th features a form-a-square puzzle using some triangles. Mathematics? Well, logic anyway. Also a good reminder about open-mindedness when you’re attempting to construct something.

Norm Feuti’s Retail for the 26th is about how you get good at arithmetic. I suspect there’s two natural paths; you either find it really interesting in your own right, or you do it often enough you want to find ways to do it quicker. Marla shows the signs of learning to do arithmetic quickly because she does it a lot: turning “30 percent off” into “subtract ten percent three times over” is definitely the easy way to go. The alternative is multiplying by seven and dividing by ten and you don’t want to multiply by seven unless the problem gives a good reason why you should. And I certainly don’t fault the customer not knowing offhand what 30 percent off \$25 would be. Why would she be in practice doing this sort of problem?

Johnny Hart’s Back To B.C. for the 26th reruns the comic from the 30th of December, 1959. In it … uh … one of the cavemen guys has found his calendar for the next year has too many days. (Think about what 1960 was.) It’s a common problem. Every calendar people have developed has too few or too many days, as the Earth’s daily rotations on its axis and annual revolution around the sun aren’t perfectly synchronized. We handle this in many different ways. Some calendars worry little about tracking solar time and just follow the moon. Some calendars would run deliberately short and leave a little stretch of un-named time before the new year started; the ancient Roman calendar, before the addition of February and January, is famous in calendar-enthusiast circles for this. We’ve now settled on a calendar which will let the nominal seasons and the actual seasons drift out of synch slowly enough that periodic changes in the Earth’s orbit will dominate the problem before the error between actual-year and calendar-year length will matter. That’s a pretty good sort of error control.

8,978,432 is not anywhere near the number of days that would be taken between 4,000 BC and the present day. It’s not a joke about Bishop Ussher’s famous research into the time it would take to fit all the Biblically recorded events into history. The time is something like 24,600 years ago, a choice which intrigues me. It would make fair sense to declare, what the heck, they lived 25,000 years ago and use that as the nominal date for the comic strip. 24,600 is a weird number of years. Since it doesn’t seem to be meaningful I suppose Hart went, simply enough, with a number that was funny just for being riotously large.

Mark Tatulli’s Heart of the City for the 26th places itself on my Grand Avenue warning board. There’s plenty of time for things to go a different way but right now it’s set up for a toxic little presentation of mathematics. Heart, after being grounded, was caught sneaking out to a slumber party and now her mother is sending her to two weeks of Math Camp. I’m supposing, from Tatulli’s general attitude about how stuff happens in Heart and in Lio that Math Camp will not be a horrible, penal experience. But it’s still ominous talk and I’m watching.

Brian Fies’s Mom’s Cancer story for the 26th is part of the strip’s rerun on GoComics. (Many comic strips that have ended their run go into eternal loops on GoComics.) This is one of the strips with mathematical content. The spatial dimension of a thing implies relationships between the volume (area, hypervolume, whatever) of a thing and its characteristic linear measure, its diameter or radius or side length. It can be disappointing.

Nicholas Gurewitch’s Perry Bible Fellowship for the 26th is a repeat of one I get on my mathematics Twitter friends now and then. Should warn, it’s kind of racy content, at least as far as my usual recommendations here go. It’s also a little baffling because while the reveal of the unclad woman is funny … what, exactly, does it mean? The symbols don’t mean anything; they’re just what fits graphically. I think the strip is getting at Dr Loring not being able to see even a woman presenting herself for sex as anything but mathematics. I guess that’s funny, but it seems like the idea isn’t quite fully developed.

Zach Weinersmith’s Saturday Morning Breakfast Cereal Again for the 26th has a mathematician snort about plotting a giraffe logarithmically. This is all about representations of figures. When we plot something we usually start with a linear graph: a couple of axes perpendicular to one another. A unit of movement in the direction of any of those axes represents a constant difference in whatever that axis measures. Something growing ten units larger, say. That’s fine for many purposes. But we may want to measure something that changes by a power law, or that grows (or shrinks) exponentially. Or something that has some region where it’s small and some region where it’s huge. Then we might switch to a logarithmic plot. Here the same difference in space along the axis represents a change that’s constant in proportion: something growing ten times as large, say. The effective result is to squash a shape down, making the higher points more nearly flat.

And to completely smother Weinersmith’s fine enough joke: I would call that plot semilogarithmically. I’d use a linear scale for the horizontal axis, the gazelle or giraffe head-to-tail. But I’d use a logarithmic scale for the vertical axis, ears-to-hooves. So, linear in one direction, logarithmic in the other. I’d be more inclined to use “logarithmic” plots to mean logarithms in both the horizontal and the vertical axes. Those are useful plots for turning up power laws, like the relationship between a planet’s orbital radius and the length of its year. Relationships like that turn into straight lines when both axes are logarithmically spaced. But I might also describe that as a “log-log plot” in the hopes of avoiding confusion.

## Reading the Comics, June 24, 2017: Saturday Morning Breakfast Cereal Edition

Somehow this is not the title of every Reading The Comics review! But it is for this post and we’ll explore why below.

Dave Coverly’s Speed Bump for the 18th is not exactly an anthropomorphic-numerals joke. It is about making symbols manifest in the real world, at least. The greater-than and less-than signs as we know them were created by the English mathematician Thomas Harriot, and introduced to the world in his posthumous Artis Analyticae Praxis (1631). He also had an idea of putting a . between the numerals of an expression and the letters multiplied by them, for example, “4.x” to mean four times x. We mostly do without that now, taking multiplication as assumed if two meaningful quantities are put next to one another. But we will use, now, a vertically-centered dot to separate terms multiplied together when that helps our organization. The equals sign we trace to the 16th century mathematician Robert Recorde, whose 1557 Whetsone of Witte uses long but recognizable equals signs. The = sign went into hibernation after that, though, until the 17th century and it took some time to quite get well-used. So it often is with symbols.

Ted Shearer’s Quincy for the 25th of April, 1978 and rerun the 19th of June, starts from the history of zero. It’s worth noting there are a couple of threads woven together in the concept of zero. One is the idea of “nothing”, which we’ve had just forever. I mean, the idea that there isn’t something to work with. Another is the idea of the … well, the additive identity, there being some number that’s one less than one and two less than two. That you can add to anything without changing the thing. And then there’s symbols. There’s the placeholder for “there are no examples of this quantity here”. There’s the denotation of … well, the additive identity. All these things are zeroes, and if you listen closely, they are not quite the same thing. Which is not weird. Most words mean a collection of several concepts. We’re lucky the concepts we mean by “zero” are so compatible in meaning. Think of the poor person trying to understand the word “bear”, or “cleave”.

John Deering’s Strange Brew for the 19th is a “New Math” joke, fittingly done with cavemen. Well, numerals were new things once. Amusing to me is that — while I’m not an expert — in quite a few cultures the symbol for “one” was pretty much the same thing, a single slash mark. It’s hard not to suppose that numbers started out with simple tallies, and the first thing to tally might get dressed up a bit with serifs or such but is, at heart, the same thing you’d get jabbing a sharp thing into a soft rock.

Guy Gilchrist’s Today’s Dogg for the 19th I’m sure is a rerun and I think I’ve featured it here before. So be it. It’s silly symbol-play and dog arithmetic. It’s a comic strip about how dogs are cute; embrace it or skip it.

Zach Weinersmith’s Saturday Morning Breakfast Cereal is properly speaking reruns when it appears on GoComics.com. For whatever reason Weinersmith ran a patch of mathematics strips there this past week. So let me bundle all that up. On the 19th he did a joke mathematicians get a lot, about how the only small talk anyone has about mathematics is how they hated mathematics. I’m not sure mathematicians have it any better than any other teachers, though. Have you ever known someone to say, “My high school gym class gave me a greater appreciation of the world”? Or talk about how grade school history opened their eyes to the wonders of the subject? It’s a sad thing. But there are a lot of things keeping teachers from making students feel joy in their subjects.

For the 21st Weinersmith makes a statisticians joke. I can wrangle some actual mathematics out of an otherwise correctly-formed joke. How do we ever know that something is true? Well, we gather evidence. But how do we know the evidence is relevant? Even if the evidence is relevant, how do we know we’ve interpreted it correctly? Even if we have interpreted it correctly, how do we know that it shows what we want to know? Statisticians become very familiar with hypothesis testing, which amounts to the question, “does this evidence indicate that some condition is implausibly unlikely”? And they can do great work with that. But “implausibly unlikely” is not the same thing as “false”. A person knowledgeable enough and honest turns out to have few things that can be said for certain.

The June 23rd strip I’ve seen go around Mathematics Twitter several times, as see above tweet, about the ways in which mathematical literacy would destroy modern society. It’s a cute and flattering portrait of mathematics’ power, probably why mathematicians like passing it back and forth. But … well, how would “logic” keep people from being fooled by scams? What makes a scam work is that the premise seems logical. And real-world problems — as opposed to logic-class problems — are rarely completely resolvable by deductive logic. There have to be the assumptions, the logical gaps, and the room for humbuggery that allow hoaxes and scams to slip through. And does anyone need a logic class to not “buy products that do nothing”? And what is “nothing”? I have more keychains than I have keys to chain, even if we allow for emergencies and reasonable unexpected extra needs. This doesn’t stop my buying keychains as souvenirs. Does a Penn Central-logo keychain “do nothing” merely because it sits on the windowsill rather than hold any sort of key? If so, was my love foolish to buy it as a present? Granted that buying a lottery ticket is a foolish use of money; is my life any worse for buying that than, say, a peanut butter cup that I won’t remember having eaten a week afterwards? As for credit cards — It’s not clear to me that people max out their credit cards because they don’t understand they will have to pay it back with interest. My experience has been people max out their credit cards because they have things they must pay for and no alternative but going further into debt. That people need more money is a problem of society, yes, but it’s not clear to me that a failure to understand differential equations is at the heart of it. (Also, really, differential equations are overkill to understand credit card debt. A calculator with a repeat-the-last-operation feature and ten minutes to play is enough.)

## Reading the Comics, June 3, 2017: Feast Week Conclusion Edition

And now finally I can close out last week’s many mathematically-themed comic strips. I had hoped to post this Thursday, but the Why Stuff Can Orbit supplemental took up my writing energies and eventually timeslot. This also ends up being the first time I’ve had one of Joe Martin’s comic strips since the Houston Chronicle ended its comics pages and I admit I’m not sure how I’m going to work this. I’m also not perfectly sure what the comic strip means.

So Joe Martin’s Mister Boffo for the 1st of June seems to be about a disastrous mathematics exam with a kid bad enough he hasn’t even got numbers exactly to express the score. Also I’m not sure there is a way to link to the strip I mean exactly; the archives for Martin’s strips are not … organized the way I would have done. Well, they’re his business.

Greg Evans’s Luann Againn for the 1st reruns the strip from the 1st of June, 1989. It’s your standard resisting-the-word-problem joke. On first reading the strip I didn’t get what the problem was asking for, and supposed that the text had garbled the problem, if there were an original problem. That was my sloppiness is all; it’s a perfectly solvable question once you actually read it.

J C Duffy’s Lug Nuts for the 1st — another day that threatened to be a Reading the Comics post all on its own — is a straggler Pi Day joke. It’s just some Dadaist clowning about.

Doug Bratton’s Pop Culture Shock Therapy for the 1st is a wordplay joke that uses word problems as emblematic of mathematics. I’m okay with that; much of the mathematics that people actually want to do amounts to extracting from a situation the things that are relevant and forming an equation based on that. This is what a word problem is supposed to teach us to do.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 1st — maybe I should have done a Reading the Comics for that day alone — riffs on the idle speculation that God would be a mathematician. It does this by showing a God uninterested in two logical problems. The first is the question of whether there’s an odd perfect number. Perfect numbers are these things that haunt number theory. (Everything haunts number theory.) It starts with idly noticing what happens if you pick a number, find the numbers that divide into it, and add those up. For example, 4 can be divided by 1 and 2; those add to 3. 5 can only be divided by 1; that adds to 1. 6 can be divided by 1, 2, and 3; those add to 6. For a perfect number the divisors add up to the original number. Perfect numbers look rare; for a thousand years or so only four of them (6, 28, 496, and 8128) were known to exist.

All the perfect numbers we know of are even. More, they’re all numbers that can be written as the product $2^{p - 1} \cdot \left(2^p - 1\right)$ for certain prime numbers ‘p’. (They’re the ones for which $2^p - 1$ is itself a prime number.) What we don’t know, and haven’t got a hint about proving, is whether there are any odd prime numbers. We know some things about odd perfect numbers, if they exist, the most notable of them being that they’ve got to be incredibly huge numbers, much larger than a googol, the standard idea of an incredibly huge number. Presumably an omniscient God would be able to tell whether there were an odd perfect number, or at least would be able to care whether there were. (It’s also not known if there are infinitely many perfect numbers, by the way. This reminds us that number theory is pretty much nothing but a bunch of easy-to-state problems that we can’t solve.)

Some miscellaneous other things we know about an odd perfect number, other than whether any exist: if there are odd perfect numbers, they’re not divisible by 105. They’re equal to one more than a whole multiple of 12. They’re also 117 more than a whole multiple of 468, and they’re 81 more than a whole multiple of 324. They’ve got to have at least 101 prime factors, and there have to be at least ten distinct prime factors. There have to be at least twelve distinct prime factors if 3 isn’t a factor of the odd perfect number. If this seems like a screwy list of things to know about a thing we don’t even know exists, then welcome to number theory.

The beard question I believe is a reference to the logician’s paradox. This is the one postulating a village in which the village barber shaves all, but only, the people who do not shave themselves. Given that, who shaves the barber? It’s an old joke, but if you take it seriously you learn something about the limits of what a system of logic can tell you about itself.

Bud Blake’s Tiger rerun for the 2nd has Tiger’s arithmetic homework spill out into real life. This happens sometimes.

George Herriman’s Krazy Kat for the 10th of July, 1939 was rerun the 2nd of June. I’m not sure that it properly fits here, but the talk about Officer Pupp running at 60 miles per hour and Ignatz Mouse running forty and whether Pupp will catch Mouse sure reads like a word problem. Later strips in the sequence, including the ways that a tossed brick could hit someone who’d be running faster than it, did not change my mind about this. Plus I like Krazy Kat so I’ll take a flimsy excuse to feature it.

## Reading the Comics, April 24, 2017: Reruns Edition

I went a little wild explaining the first of last week’s mathematically-themed comic strips. So let me split the week between the strips that I know to have been reruns and the ones I’m not so sure were.

Bill Amend’s FoxTrot for the 23rd — not a rerun; the strip is still new on Sundays — is a probability question. And a joke about story problems with relevance. Anyway, the question uses the binomial distribution. I know that because the question is about doing a bunch of things, homework questions, each of which can turn out one of two ways, right or wrong. It’s supposed to be equally likely to get the question right or wrong. It’s a little tedious but not hard to work out the chance of getting exactly six problems right, or exactly seven, or exactly eight, or so on. To work out the chance of getting six or more questions right — the problem given — there’s two ways to go about it.

One is the conceptually easy but tedious way. Work out the chance of getting exactly six questions right. Work out the chance of getting exactly seven questions right. Exactly eight questions. Exactly nine. All ten. Add these chances up. You’ll get to a number slightly below 0.377. That is, Mary Lou would have just under a 37.7 percent chance of passing. The answer’s right and it’s easy to understand how it’s right. The only drawback is it’s a lot of calculating to get there.

So here’s the conceptually harder but faster way. It works because the problem says Mary Lou is as likely to get a problem wrong as right. So she’s as likely to get exactly ten questions right as exactly ten wrong. And as likely to get at least nine questions right as at least nine wrong. To get at least eight questions right as at least eight wrong. You see where this is going: she’s as likely to get at least six right as to get at least six wrong.

There’s exactly three possibilities for a ten-question assignment like this. She can get four or fewer questions right (six or more wrong). She can get exactly five questions right. She can get six or more questions right. The chance of the first case and the chance of the last have to be the same.

So, take 1 — the chance that one of the three possibilities will happen — and subtract the chance she gets exactly five problems right, which is a touch over 24.6 percent. So there’s just under a 75.4 percent chance she does not get exactly five questions right. It’s equally likely to be four or fewer, or six or more. Just-under-75.4 divided by two is just under 37.7 percent, which is the chance she’ll pass as the problem’s given. It’s trickier to see why that’s right, but it’s a lot less calculating to do. That’s a common trade-off.

Ruben Bolling’s Super-Fun-Pax Comix rerun for the 23rd is an aptly titled installment of A Million Monkeys At A Million Typewriters. It reminds me that I don’t remember if I’d retired the monkeys-at-typewriters motif from Reading the Comics collections. If I haven’t I probably should, at least after making a proper essay explaining what the monkeys-at-typewriters thing is all about.

Ted Shearer’s Quincy from the 28th of February, 1978 reveals to me that pocket calculators were a thing much earlier than I realized. Well, I was too young to be allowed near stuff like that in 1978. I don’t think my parents got their first credit-card-sized, solar-powered calculator that kind of worked for another couple years after that. Kids, ask about them. They looked like good ideas, but you could use them for maybe five minutes before the things came apart. Your cell phone is so much better.

Bil Watterson’s Calvin and Hobbes rerun for the 24th can be classed as a resisting-the-word-problem joke. It’s so not about that, but who am I to slow you down from reading a Calvin and Hobbes story?

Garry Trudeau’s Doonesbury rerun for the 24th started a story about high school kids and their bad geography skills. I rate it as qualifying for inclusion here because it’s a mathematics teacher deciding to include more geography in his course. I was amused by the week’s jokes anyway. There’s no hint given what mathematics Gil teaches, but given the links between geometry, navigation, and geography there is surely something that could be relevant. It might not help with geographic points like which states are in New England and where they are, though.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 24th is built on a plot point from Carl Sagan’s science fiction novel Contact. In it, a particular “message” is found in the digits of π. (By “message” I mean a string of digits that are interesting to us. I’m not sure that you can properly call something a message if it hasn’t got any sender and if there’s not obviously some intended receiver.) In the book this is an astounding thing because the message can’t be; any reasonable explanation for how it should be there is impossible. But short “messages” are going to turn up in π also, as per the comic strips.

I assume the peer review would correct the cartoon mathematicians’ unfortunate spelling of understanding.