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.

The Geometry. A pair of parallel lines, one with a rectangular lump. 'Not true --- parallel lines *do* meet. In fact, Peter and I are expected.' ('We met at a crossroads in both our lives.')
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.

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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.

Joe: 'Grandpa, what's 5x7?' Grandpa: 'Why do you wanna know?' Joe: 'I'm testing your memory.' Grandpa: 'Oh! The answer's 35.' Joe: 'Thanks! Now what is 8x8?' Grandpa: 'Joe, is that last night's homework?' Joe: 'We're almost done! Only 19 more!'
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.

But they’re still going on the cartoonist’s web site, so there’s that.

Reading the Comics, July 15, 2017: Dawn Of Mathematics Jokes


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

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

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

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

TV Chef: 'Mix in one egg.' Cookie: 'See ... for us that would be 200 eggs.' TV Chef: 'Add a cup of flour.' Cookie: '200 cups of flour.' TV CHef: 'Now bake for two hours.' Cookie to Sarge: 'It'll be ready next week.'
Mort Walker’s Beetle Bailey Vintage for the 21st of December, 1960 and rerun the 14th of July, 2017. Wow, I remember when they’d put recipes like this on the not-actual-news segment of the 5:00 news or so, and how much it irritated me that there wasn’t any practical way to write down the whole thing and even writing down the address to mail in for the recipe seemed like too much, what with how long it took on average to find a sheet of paper and a writing tool. In hindsight, I don’t know why this was so hard for me.

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

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

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

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

Reading the Comics, June 10, 2017: Some Vintage Comics Edition


It’s too many comics to call this a famine edition, after last week’s feast. But there’s not a lot of theme to last week’s mathematically-themed comic strips. There’s a couple that include vintage comic strips from before 1940, though, so let’s run with that as a title.

Glenn McCoy and Gary McCoy’s The Flying McCoys for the 4th of June is your traditional blackboard full of symbols to indicate serious and deep thought on a subject. It’s a silly subject, but that’s fine. The symbols look to me gibberish, but clown research will go along non-traditional paths, I suppose.

Bill Hinds’s Tank McNamara for the 4th is built on mathematics’ successful invasion and colonization of sports management. Analytics, sabermetrics, Moneyball, whatever you want to call it, is built on ideas not far removed from the quality control techniques that changed corporate management so. Look for patterns; look for correlations; look for the things that seem to predict other things. It seems bizarre, almost inhuman, that we might be able to think of football players as being all of a kind, that what we know about (say) one running back will tell us something about another. But if we put roughly similarly capable people through roughly similar training and set them to work in roughly similar conditions, then we start to see why they might perform similarly. Models can help us make better, more rational, choices.

Morrie Turner’s Wee Pals rerun for the 4th is another word-problem resistance joke. I suppose it’s also a reminder about the unspoken assumptions in a problem. It also points out why mathematicians end up speaking in an annoyingly precise manner. It’s an attempt to avoid being shown up like Oliver is.

Which wouldn’t help with Percy Crosby’s Skippy for the 7th of April, 1930, and rerun the 5th. Skippy’s got a smooth line of patter to get out of his mother’s tutoring. You can see where Percy Crosby has the weird trait of drawing comics in 1930 that would make sense today still; few pre-World-War-II comics do.

Why some of us don't like math. One part of the brain: 'I'm trying to solve an equation, but it's HARD when someone in here keeps shouting FIGHT, FLIGHT, FIGHT, FLIGHT the whole time.' Another part: 'I know, but we should fight or run away.' Another part: 'I just want to cry.'
Niklas Eriksson’s Carpe Diem for the 7th of June, 2017. If I may intrude in someone else’s work, it seems to me that the problem-solver might find a hint to what ‘x’ is by looking to the upper right corner of the page and the x = \sqrt{13} already there.

Niklas Eriksson’s Carpe Diem for the 7th is a joke about mathematics anxiety. I don’t know that it actually explains anything, but, eh. I’m not sure there is a rational explanation for mathematics anxiety; if there were, I suppose it wouldn’t be anxiety.

George Herriman’s Krazy Kat for the 15th of July, 1939, and rerun the 8th, extends that odd little faintly word-problem-setup of the strips I mentioned the other day. I suppose identifying when two things moving at different speeds will intersect will always sound vaguely like a story problem.

Krazy: 'The ida is that I run this way at fotty miles a hour eh?' Ignatz: 'Right, and my good arm will speed this brick behind you, at a sixty-mile gait - come on - get going - ' And Krazy runs past a traffic signal. The brick reaches the signal, which has changed to 'stop', and drops dead. Ignatz: 'According to the ballistic law, my projectile must be well up to him by now.' Officer Pupp: 'Unless the traffic law interferes, mousie.'
George Herriman’s Krazy Kat for the 15th of July, 1939, as rerun the 8th of June, 2017. I know the comic isn’t to everyone’s taste, but I like it. I’m also surprised to see something as directly cartoonish as the brick stopping in midair like that in the third panel. The comic is usually surreal, yes, but not that way.

Tom Toles’s Randolph Itch, 2 am rerun for the 9th is about the sometimes-considered third possibility from a fair coin toss, and how to rig the results of that.