Reading the Comics, March 9, 2018: Some Old Lines Edition

To close out last week’s comics I got a bunch of strips that were repeats, or that touch on topics I’ve discussed quite a bit around these parts already. I’m pretty sure all the words I have here are new in their specific organization. The words themselves are pretty old.

Maria Scrivan’s Half Full for the 4th is the Rubik’s Cube joke for the week. I ought to write up a proper description of the algebra of Rubik’s Cubes. The real stuff is several books’ worth of material, yes. But a couple hundred words about what’s interesting should be doable. … Or I could just ask folks if they’ve read good descriptions of the group theory that cubes show off. I’m always open to learning other people have said stuff better than me. This is part of why I’ve never published an essay about Cantor’s Diagonal Proof; many people have written such essays and I couldn’t add anything useful to that heap of words.

Maria Scrivan’s Half Full for the 4th of June, 2018. Yeah, uh, it me.

Ryan North’s Dinosaur Comics for the 5th is about the heap paradox. Or the sorites paradox, depending on what book you’ve been reading from. The problem is straightforward enough. As God, in the strip says, a big pile of sand is clearly a heap. One or two grains of sand is clearly not. If you remove grains from the heap, eventually, you lose the heap-ness. T-Rex suggests solving the question of when that happens by statistical survey, finding what people on average find to be the range where things shift over.

Ryan North’s Dinosaur Comics for the 5th of June, 2018. I get that part of the setup of these comics is that T-Rex is nerdy-smart, but I can also imagine the philosophers rolling their eyes at how he’s missed the point. Maybe if he were asked about the density of a single molecule of water he’d understand better why the question can’t be obvious. (And T-Rex does sometimes revisit issues with deeper understanding of the issues. This might have happened between when this strip first appeared on qwantz.com and when it appeared on GoComics.com.

As with many attempts to apply statistical, or experimental, methods to philosophical questions it misses the point. There are properties that things seem to have only as aggregations. Where do they come from? How can there be something true about a collection of things that isn’t true about any part of the thing? This is not just about messy real-world properties either; we can say stuff about groups of mathematical objects that aren’t true about individual objects within the set. For example, suppose we want to draw a real number at random, uniformly, from the continuous interval 0 to 10. There’s a 50% chance we’ll draw a number greater than 5. The chance of drawing any specific number greater than 5, though, is zero. But we can always draw one. Something weird is happening here, as often happens with questions we’ve been trying to answer for thousands of years.

Norm Feuti’s Retail for the 6th of June, 2018. This joke, though not this strip, was also run the 26th of June, 2017. There I share my one great retail-mathematics anecdote.

Norm Feuti’s Retail for the 6th is a new strip, although the joke’s appeared before. There’s some arithmetic calculations that are easy to do, or that become easy because you do them a lot. Or because you see them done a lot and learn what the patterns are. A handful of basic tricks — like that 80 percent off is 20 percent of something, or that 20 percent of a thing is one-fifth the original thing — can be stunning. Stage magicians find the same effect.

John Zakour and Scott Roberts’s Working Daze for the 6th of June, 2018. It ran the 22nd of October, 2014, although that was as part of a “Best Of” week. No idea when it originally ran.

John Zakour and Scott Roberts’s Working Daze for the 6th is another chance for me to talk about the supposed folly of giving 110 percent. Or point you to where I did already. I’m forgiving of the use of the phrase.

Bob Shannon’s Tough Town for the 7th of June, 2018. The strip is one about all sorts of odd creatures hanging out in the bar, so, you’re not misunderstanding this.

Bob Shannon’s Tough Town for the 7th is the anthropomorphized abacus joke of the week. Been a while since we had one of those. I suppose an adding machine would be at least as good a representative of the abstract concept of doing arithmetic, but it’s likely harder to draw too. This is just tiring to draw.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th of June, 2018. Admit I do wonder how often cave people needed to track the number of rocks they had. I mean, how often do we need to count our rocks? Aren’t the rocks themselves an adequate representation of the number of rocks around?

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th presents the old complaint about mathematics’s utility, here in an ancient setting. I’m intereste that the caveman presents counting in terms of matching up other things to his fingers. We use this matching of one set of things to another even today. It gets us to ordinal and cardinal numbers, and the to what we feel pretty sure about with infinitely large sets. An idea can be ancient and basic and still be vital.

Steve Sicula’s Home and Away rerun for the 9th of June, 2018. The strip originally ran the 6th of March, 2011. … How does Karen there say “Uuuhhhggghh”?

Steve Sicula’s Home and Away for the 9th is about the hatred people profess for mathematics. Some of that is more hatred of how it’s taught, which is too often as a complicated and apparently pointless activity. Some of that is hatred of how it’s used, since it turns up in a lot of jobs. And for some reason we’ve designed society so that we do jobs we don’t like. I don’t know why we think that’s a good idea. We should work on that.

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Reading the Comics, June 4, 2018: Weezer’s Africa Edition

Once again the name of this Reading the Comics edition has nothing to do with any of the strips. I’m just aware that Weezer’s cover of Africa is quite popular right now and who am I to deny people things they want? (I like the cover, but it’s not different enough for me to feel satisfied by it. I tend to like covers that highlight something minor in the original, or that go in a strange direction. Shifting a peppy song into a minor key doesn’t count anymore. But bear in mind, I’m barely competent at listening to music. Please now enjoy my eight hours of early electronica in which various beeps and whistles are passed off as music.)

Samson’s Dark Side of the Horse for the 3rd is the Roman numerals joke for the week. And a welcome return for Dark Side of the Horse. It feels like it’s been gone a while. I wouldn’t try counting by Roman numerals to lull myself to sleep; it seems like too much fussy detail work. But I suppose if you’ve gotten good at it, it’s easy.

Samson’s Dark Side of the Horse for the 3rd of June, 2018. Have to say that’s an adorable medical sheep in the third panel.

Jef Mallett’s Frazz for the 3rd builds on removing statistics from their context. It’s a common problem. It’s possible to measure so very many things. Without a clear idea of what we should expect as normal the measurement doesn’t tell us much. And it can be hard to know what the right context for something even is. Let me deconstruct Caulfield’s example. We’re supposed to reflect on and consider that 40% of all weekdays are Monday and Friday too. But it’s not only weekdays that people work. Even someone working a Sunday might take a sick day. Monday and Friday are a bit over 28% of the whole week. But more people do work Monday-to-Friday than do Saturdays and Sundays, so the Sunday sick day is surely rarer than the Monday. So even if we grant Caulfield’s premise, what does it tell us?

Jef Mallett’s Frazz for the 3rd of June, 2018. So Jef Mallett lives in the same metro area I do, which means I could in principle use this to figure out how far ahead of deadline he wrote this strip. Except that’s a fraud since we never had a first nice day of spring this year. We just had a duplicate of March for all of April and the first three weeks of May, and then had a week of late July before settling into early summer. Just so you know.

Jason Chatfield’s Ginger Meggs for the 3rd is a bit of why-learn-mathematics propaganda. Megg’s father has a good answer. But it does shift the question back one step. Also I see in the top row that Meggs has one of those comic-strip special editions where the name of the book is printed on the back cover instead. (I’m also skeptical of the photo and text layout on the newspaper Megg’s father is reading. But I don’t know the graphic design style of Australian, as opposed to United States, newspapers.)

Jason Chatfield’s Ginger Meggs for the 3rd of June, 2018. So … I guess Ginger Megg’s father is an accountant? I’m assuming because it makes the joke land better?

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 3rd may belong on some philosopher’s Reading the Comics blog instead. No matter. There’s some mathematical-enough talk going on here. There’s often many ways to approach the same problem. For example, approaching a system as a handful of items. Or as a huge number of them. Or as infinitely many things. Or as a continuum of things. There are advantages each way. A handful of things, for example, we can often model as interactions between pairs of things. We can model a continuum as a fluid. A vast number of things can let one’s computer numerically approximate a fluid. Or infinitely many particles if that’s more convenient.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 3rd of June, 2018. Also I’m not sure where the professor figures he’s going with this but my understanding is it’s rather key to our understanding of quantum mechanics that, say, every atom of Carbon-12 in our bodies is the same as every other atom. At least apart from accidental properties like which compound it might happen to be in at the moment and where it is in that compound. That is, if you swapped two of the same isotope there’d be no way to tell you had.

To describe all these different models as sharing an “ontology-space” is good mathematical jargon too. In this context the “-space” would mean the collection of all these things that are built by the same plan but with different values of whichever parameter matters.

Bud Blake’s Tiger for the 6th of August, 1965. It was rerun the 4th of June, 2018. I confess I’m not sure exactly what the joke is. If it’s not that Suzy has no idea what’s being written but wants to say something nice about Julian’s work … all right, and I guess that’s an unremarkable attitude for a cartoonist to express in 1965, but it’s a weak joke.

Bud Blake’s Tiger for the 6th of August, 1965 features Einstein’s famous equation. I suppose it’s showing how well-informed Julian is, that he knows and can present such a big result. There is beauty in mathematics (and physics). Mathematicians (and physicists) find the subject beautiful to start with, and try to find attractive results. I’m curious what the lay reader makes of mathematical symbols, though, just as pieces of art. I remember as a child finding this beauty in a table of integrals in the front of one of my mother’s old college textbooks. All those parallel rows of integral symbols drew me in though nothing I’d seen in mathematics had prepared me to even read it. I still find that beautiful, but I can’t swear that I would even if I hadn’t formed that impression early in life. Are lay and professional readers’ views of mathematical-expression beauty similar? How are they different?

Reading the Comics, May 30, 2018: Spherical Photos Edition

Last week’s offerings from Comic Strip Master Command got away from me. Here’s some more of the strips that had some stuff worth talking about. I should have another installment this week. I’m back to nonsense edition names; sorry.

Lincoln Pierce’s Big Nate for the 29th of May is about the gambler’s fallacy. Everyone who learns probability learns about it. The fallacy builds on indisputable logic: your chance of losing at something eighteen times in a row is less than the chance of your losing at that thing seventeen times in a row. So it makes sense that if you’ve lost seventeen times in a row then you must be due.

And that’s one of those lies our intuition tells us about probability. What’s important to Nate here is not the chance he’s in an 18-at-bat losing streak. What’s important is the chance that he’s in an 18-at-bat losing streak, given that he’s already failed 17 times in a row. These are different questions. The chance of an 18th at-bat in a row being a failure (for him) is much larger than the chance of an 18-at-bat losing streak starting from scratch.

Lincoln Pierce’s Big Nate rerun for the 29th of May, 2018. The strip first ran the 18th of May, 2010. I’ve not heard anything about why Pierce has been away from the strip since the start of the year.

That said I can’t go along with Francis’s claim that the chance of Nate getting a hit isn’t enhanced by his long dry spell. We can, and often do, model stuff like at-bats as though they’re independent. That is, that the chance of getting a hit doesn’t depend on what came before. Doing it this way gives results that look like real sports matches do. But it’s very hard to quantify things like losing streaks or their opposite, hot hands. It’s hard to dismiss the evidence of people who compete, though. Everyone who does has known the phenomenon of being “in the zone”, where things seem easier. I was in it for two games out of five just last night at pinball league. (I was dramatically out of it for the other three. I nearly doubled my best-ever game of Spider-Man and still came in second place. And by so little a margin my opponent thought the bonus might make the difference. Such heartbreak.)

But there is a huge psychological component to how one plays at a game. Nate thinks differently about what he’s doing going up to bat after seventeen failures in a row than he would after, say, three home runs in a row. It’s hard to believe that this has no effect on how he plays, even if it’s hard to track down a consistent signal through the noise. Maybe it does wash out. Maybe sometimes striking out the first three at-bats in a game makes the batter give up on the fourth. Meanwhile other times it makes the batter focus better on the fourth, and there’s no pinning down which effect will happen. But I can’t go along with saying there’s no effect.

John Zakour and Scott Roberts’s Working Daze for the 29th of May, 2018. Earlier in the sequence they had the Zootopia sloth replacing Ed, but there’s no making that on topic for my blog here.

John Zakour and Scott Roberts’s Working Daze for the 29th is an infinite-monkeys joke. Well, given some reasonable assumptions we can suppose that sufficiently many monkeys on typewriters will compose whatever’s needed, given long enough. Figuring someone’s work will take fewer monkeys and less time is a decent probability-based insult.

Ted Key’s Hazel rerun for the 30th of May, 2018. I can’t say when this first ran. I’m not sure what the kid’s name is, sorry.

Ted Key’s Hazel for the 30th has the maid doing a bit of tutoring work. That’s about all I can make of this either. Doesn’t seem like a lot of fun, but there is only so much to do with arithmetic computation like this. It’s convenient to know a times table by memory.

Scott Hilburn’s The Argyle Sweater for the 30th of May, 2018. Are … Einstein, Galileo, and Confucius really famous teachers? Calling Socrates a teacher is a lesser stretch.

Scott Hilburn’s The Argyle Sweater for the 30th has a chalkboard full of mathematical symbols as iconic for deep thinking. And it’s even Einstein’s chalkboard. And it’s even stuff that could plausibly be on Einstein’s chalkboard at some point. Besides E = mc² the other formulas are familiar ones from relativity. They’re about the ways our ideas of how much momentum or mass a thing has has to change if we see the thing in motion. (I’m a little less sure about that expression, but I think I can work something out.) And as a bonus it includes the circle-drawing compass as Galileo might have used. Well, he surely used a compass; I’m just not sure that the model shown wouldn’t be anachronistic. As though that matters; fortune cookies, after all, are a 20th century American invention and we’re letting that pass.

Zach Weinersmiths’s Saturday Morning Breakfast Cereal for the 30th of May, 2018. Kind of curious what sorts of drinks you get from putting in infinitesimals. (You get milk or espresso with a homeopathic bit of the other.)

Zach Weinersmiths’s Saturday Morning Breakfast Cereal for the 30th builds on a fun premise. Underneath the main line it gets into some whimsical ratios built on important numbers you’d never use for this sort of thing, such as π, and the imaginary unit . The Golden Ratio makes an appearance too, sneaking a definition for φ in in terms of espresso and milk. Here’s a free question: is there a difference between the “infiniccino” and “just espresso” except for the way it’s presented? … Well, presentation can be an important part of a good coffee.

π is well-known. Not sure I have anything interesting to add to its legend. φ is an irrational number a bit larger than 1.6. I’m not sure if I’ve ever called it the Boba Fett of numbers, but I should have. It’s a cute enough number, far more popular than its importance would suggest. is far more important. Suppose that there is some number, which we give that name, with the property that equals -1. Then we get complex-valued numbers, which let us solve problems we’d like to know but couldn’t do before. It’s a great advance.

The name tells you how dubiously people approached this number, when it was first noticed. I wonder if people would be less uneasy with “imaginary numbers” if it weren’t for being told how there’s no such thing as the square root of minus one for years before algebra comes along and says, well, yes there is. It’s hard to think of a way that, say, “negative four” is more real than , after all, and people are mostly all right with -4. And I understand why people are more skeptical of -4 than they are of, say, 6. Still, I wonder how weird would look if people weren’t primed to think it was weird.

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

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

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

Bill Rechin’s Crock rerun for the 26th of April, 2018. Going ahead and guessing there’s another Crock with the same setup, except the prisoner guesses nine, and Crock says it was 4,796,034,621,322, and then in the final panel we see that Crock really had thought nine and lied.

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

Mark Anderson’s Andertoons for the 26th of April, 2018. This is Mark Anderson’s Andertoons for the week.

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

Greg Cravens’s The Buckets for the 26th of April, 2018. I’m not sure Larry (the father)’s disbelief at his kid figuring putting the shirt on all wrong was bound to happen. It’s a mistake we all make; accepting the inevitability of that doesn’t seem that wrong.

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

Charles Schulz’s Peanuts rerun for the 27th of April, 2018. This strip first ran the 30th of April, 1971. It also was rerun the 25th of April, 2003, with a different colorization scheme for some reason.

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

Maria Scrivan’s Half-Full for the 28th of April, 2018. Hey, cartoonists deserve easy days at work too. And there’s not always a convenient holiday they can have the cast just gather around and wish everyone a happy instance of.

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

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th of April, 2018. If I had seen this strip in 2007 maybe I would’ve got that tenure-track posting instead of going into the world of technically being an extant mathematics blog.

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

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

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

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

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

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st of April, 2018. I feel vaguely personally called out by the calculus teacher wearing cargo shorts, tall white socks, and sandals.

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

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

John Zakour and Scott Roberts’s Maria’s Day for the 22nd of April, 2018. I’m curious whether Zakour and Roberts deliberately put 2 and 3 to the left, with pain stars indicating they’ve been beaten already, while the bigger numbers are off to the side. Or was it just an arbitrary choice? The numbers are almost in order, left to right, except that the 7’s out of place. So maybe the ordering is just coincidence?

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

Anthony Blades’s Bewley for the 23rd of April, 2018. Whenever a comic strip with this setup begins I think of the time in geometry class when I realized I hadn’t done any homework and wondered if I could get something done in the time it took papers to be passed up. This in a class of twelve students. No, there was not, even though the teacher started from the other side of the classroom.

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

Dave Whamond’s Reality Check for the 23rd of April, 2018. I’m not sure I’ve laughed more at a dumb joke than I have at this in a long while.

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

Neal Rubin and Rod Whigham’s Gil Thorp for the 24th of April, 2018. Are … both word balloons coming from the same guy? In the last panel there. I understand one guy starting and another closing a thought but that’s usually something you do with an established in-joke that anyone can feed and anyone else can finish. A spontaneous insult like this seems like it only needs the one person, but the word balloon tails are weird if they’re both from the same guy.

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

Randy Glasbergen’s Glasbergen Cartoons rerun for the 25th of April, 2018. OK, but what’s his guitar plugged in to?

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

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

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

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th of March, 2018. Temperature’s a great subject though, and I’ve been thinking for ages about doing a series on it just because I want to explain negative temperatures Kelvin.

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

Mark Anderson’s Andertoons for the 20th of March, 2018. Okay, but why the poster with the octopus on it?

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

Daniel Beyer’s Long Story Short for the 21st of March, 2018. Not to nitpick but shouldn’t it be 1½ ± ½?

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

Harley Schwadron’s 9 to 5 for the 21st of March, 2018. I understand the tie has to face the audience to make the joke work, but isn’t it more fun to imagine that it’s actually a pyramidal tie, like, a solid triangular projection of tie material, and we see one side of it and maybe there’s another equation written on the other side? Please vote in the comments.

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

Mark Pett’s Lucky Cow for the 21st of March, 2018. I preferred Ding Dongs eater myself. But my heart was with the Suzy Q’s, if we’re not letting Tastykake into the discussion.

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

Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 21st of March, 2018. I would like to give you more context for this but I confess I haven’t been able to follow the storyline. I don’t know why but this is one of the strips I don’t get the flow of.

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

Wulff and Morgenthaler’s WuMo for the 21st of March, 2018. Fun fact: since 68 is a rational number, the cosine of 68 has to be transcendental. All right, but it’s fun to me and whose blog is this? Thank you. But the cosine of any rational number other than zero is transcendental. Ditto the sine and the tangent.

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

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

Reading the Comics, March 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.

GIL 3/11 "Do the Math." Read new GIL comics every Sunday in The @projo and at https://t.co/tMk3d9G9M0! pic.twitter.com/NyACje5au0

— Norm Feuti (@normfeuti) March 11, 2018

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 . 3/16th? Eh.

Patrick Roberts’s Todd the Dinosaur for the 11th of March, 2018. I’m not sure that the loss of electricity would actually keep someone from doing chalkboard work, especially if there’s as many windows as we see here to let light in. I mean, yes, there’d be problems after school, but just during school? The end of civilization is not the cure-all people present it as being.

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.

Computer science prof tells students one of the major problems in theoretical computer science is to prove P = NP; less than stellar student announces that P = 0 is a solution. https://t.co/xH9l8xkzzn

— math prof (@mathematicsprof) March 18, 2018

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.

Bud Blake’s Tiger rerun for the 23rd of February, 2018. Whose house are they at? I mean, did Tiger bring his dog to Hugo’s, or did Hugo bring his homework to Tiger’s house? I guess either’s not that odd, especially if they just got out of school, but then Hugo’s fussing with his homework when he’s right out of school and with Tiger?

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 and reprinted the 9th of February, 2018. I’m not sure just what mathematics homework Quincy could be doing to inspire him to write a book, but then, it’s not like my mind doesn’t drift while doing mathematics either. And book-writing’s a common enough daydream that most people are too sensible to act on.

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 and reprinted the 10th of February, 2018. I realized I didn’t know the father’s name and looked it up, and Wikipedia revealed to me that he’s named Redeye. You know, like the comic strip implies right there in the title. Look, I just read the comics, I can’t be expected to think about the comics too.

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.

Hilary Price and Rina Piccolo’s Rhymes with Orange for the 1st of February, 2018. All right, but they’re line segments, but I suppose you can’t reasonably draw infinitely vast things in a daily newspaper strip’s space. The lean of that triangle makes it look way more skeptical, even afraid, than I think Price and Piccolo intended, but I’m not sure there’s a better way to get these two in frame without making the composition weird.

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.

Reading the Comics, January 23, 2018: Adult Content Edition

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 and adding 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 — except that you omit any terms that have your favorite string there. So, if you picked 23, don’t add , or , or 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. That’s the sort of punch line that really brings out the comically-anachronistic Old West theme.

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. Not listed: the rate of exchange for paczki, which reappeared this week.

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.

John Rose’s Barney Google and Snuffy Smith for the 14th of January, 2018. The commenters at Comics Kingdom don’t know where this Lucius character came from so I guess now suddenly everybody in Hootin Holler is a twin and we never knew it before I started asking questions?

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 of December, 2017. I quite like Buckles’s little off-put look in the final panel. It’s very dog considering the situation.

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 of December, 2017. One of my love’s favorite recurring motifs in Peanuts is when Sally works out some ridiculous string of not-quite-reasoning and Charlie Brown just sits and watches and kind of stares at the reader through it. Tiger is definitely doing that same “… what?” look as Hugo figures out his strategy.

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, and rerun the 15th of December, 2017. If I’m not missing, this week has included Popeye’s first claims about spinach providing him with superior strength. And I know you’re looking at the referee there and thinking J Wellington Wimpy. I’m not sure, since I haven’t checked the complete collection to read ahead in the story, but I think this is merely a proto-Wimpy. (Mind, the Wikipedia entry on this is a complete mess. Bud Sagendorf’s Popeye: The First Fifty Years says Wimpy was derived from a minor character in Segar’s earlier The Five-Fifteen strip, which would itself turn into Sappo. But that proto-Wimpy didn’t have much personality or even a name.)

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 of December, 2017. And some attention, please, for Ruthie there. She’s completely irrelevant to the action, but it makes sense for her to be there if Grandpa is walking them to school, and she adds action — and acting — to the scenes.

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.

#fractionchat #mathcomic from @andertoons https://t.co/XSXgmAVszF Looks like @nebusj got the math drought fixed.

— John Golden 🔗 (@mathhombre) December 7, 2017

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 of November, 2017. So do always remember the old advice for attorneys and people doing investigative commissions: never ask a question you don’t already know the answer to.

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 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.