Reading the Comics, September 28, 2019: Laconic Edition


There were more mathematically-themed comic strips last week than I had time to deal with. This is in part because of something Saturday which took several more hours than I had expected. So let me start this week with some of the comics that, last week, mentioned mathematics in a marginal enough way there’s nothing to say about them besides yeah, that’s a comic strip which mentioned mathematics.

Joey Alison Sayers and Jonathan Lemon’s Little Oop — a variation of Alley Oop — for the 22nd has the caveman struggling with mathematics homework. It’s fun that he has an abacus. Also that the strip keeps with the joke from earlier this year about their only dreaming of a number larger than three.

Jef Mallett’s Frazz for the 22nd sees Caulfield stressing out over a mathematics test.

Ralph Dunagin and Dana Summers’s The Middletons for the 24th has more kids stressing out over a mathematics test. Also about how time is represented in numbers.

Mark Parisi’s Off The Mark for the 24th is a bit of animal-themed wordplay on the New Math.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 24th has a parent offering excuses for not helping with mathematics homework.

Eric the Circle for the 27th, by GeoMaker this time, tries putting out a formula for the area of Eric the circle.

Jef Mallett’s Frazz for the 27th has a kid wondering why they need in-person instruction for arithmetic. (I’d agree that rehearsing arithmetic skills is very easy to automate. You can make practice problems pretty near without limit. How much this has to do with mathematics is a point of debate.)

Glenn McCoy and Gary McCoy’s The Flying McCoys for the 27th is a bit of wordplay and numerals humor.

Daniel Beyer’s Long Story Short for the 28th uses arithmetic, the ever-famous 2 + 2 =, as symbol for knowing anything.


With that, I’ve cleared the easy part of comics for the past week. When I get to the comics needing discussion the essay should post here, likely on Monday. And the Fall 2019 A to Z series should post on Tuesday, with ‘I’. Thanks for reading and for your forbearance.

Reading the Comics, July 12, 2019: Ricci Tensor Edition


So a couple days ago I was chatting with a mathematician friend. He mentioned how he was struggling with the Ricci Tensor. Not the definition, not exactly, but its point. What the Ricci Tensor was for, and why it was a useful thing. He wished he knew of a pop mathematics essay about the thing. And this brought, slowly at first, to my mind that I knew of one. I wrote such a pop-mathematics essay about the Ricci Tensor, as part of my 2017 A To Z sequence. In it, I spend several paragraphs admitting that I’m not sure I understand what the Ricci tensor is for, and why it’s a useful thing.

Caption: 'Physics Hypotheses That Are Still on The Table'. The No-Boundary Proposal (illustrated with a wireframe of what looks like an open wine glass). The Weyl Conjecture (illustrated with a wireframe of what looks like a football). The Victoria Principal (illustrated with a tableful of cosmetics).
Daniel Beyer’s Long Story Short for the 11th of July, 2019. Essays inspired by something mentioned in Long Story Short should be at this link.

Daniel Beyer’s Long Story Short for the 11th mentions some physics hypotheses. These are ideas about how the universe might be constructed. Like many such cosmological thoughts they blend into geometry. The no-boundary proposal, also known as the Hartle-Hawking state (for James Hartle and Stephen Hawking), is a hypothesis about the … I want to write “the start of time”. But I am not confident that this doesn’t beg the question. Well, we think we know what we mean by “the start of the universe”. A natural question in mathematical physics is, what was the starting condition? At the first moment that there was anything, what did it look like? And this becomes difficult to answer, difficult to even discuss, because part of the creation of the universe was the creation of spacetime. In this no-boundary proposal, the shape of spacetime at the creation of the universe is such that there just isn’t a “time” dimension at the “moment” of the Big Bang. The metaphor I see reprinted often about this is how there’s not a direction south of the south pole, even though south is otherwise a quite understandable concept on the rest of the Earth. (I agree with this proposal, but I feel like analogy isn’t quite tight enough.)

Still, there are mathematical concepts which seem akin to this. What is the start of the positive numbers, for example? Any positive number you might name has some smaller number we could have picked instead, until we fall out of the positive numbers altogether and into zero. For a mathematical physics concept there’s absolute zero, the coldest temperature there is. But there is no achieving absolute zero. The thermodynamical reasons behind this are hard to argue. (I’m not sure I could put them in a two-thousand-word essay, not the way I write.) It might be that the “moment of the Big Bang” is similarly inaccessible but, at least for the correct observer, incredibly close by.

The Weyl Curvature is a creation of differential geometry. So it is important in relativity, in describing the curve of spacetime. It describes several things that we can think we understand. One is the tidal forces on something moving along a geodesic. Moving along a geodesic is the general-relativity equivalent of moving in a straight line at a constant speed. Tidal forces are those things we remember reading about. They come from the Moon, sometimes the Sun, sometimes from a black hole a theoretical starship is falling into. Another way we are supposed to understand it is that it describes how gravitational waves move through empty space, space which has no other mass in it. I am not sure that this is that understandable, but it feels accessible.

The Weyl tensor describes how the shapes of things change under tidal forces, but it tracks no information about how the volume changes. The Ricci tensor, in contrast, tracks how the volume of a shape changes, but not the shape. Between the Ricci and the Weyl tensors we have all the information about how the shape of spacetime affects the things within it.

Ted Baum, writing to John Baez, offers a great piece of advice in understanding what the Weyl Tensor offers. Baum compares the subject to electricity and magnetism. If one knew all the electric charges and current distributions in space, one would … not quite know what the electromagnetic fields were. This is because there are electromagnetic waves, which exist independently of electric charges and currents. We need to account for those to have a full understanding of electromagnetic fields. So, similarly, the Weyl curvature gives us this for gravity. How is a gravitational field affected by waves, which exist and move independently of some source?

I am not sure that the Weyl Curvature is truly, as the comic strip proposes, a physics hypothesis “still on the table”. It’s certainly something still researched, but that’s because it offers answers to interesting questions. But that’s also surely close enough for the comic strip’s needs.

Elderly man: 'Remember coefficients?' Elderly woman: 'No.' Elderly man: 'Me neither.' Caption: 'Nostalgebra.'
Dave Coverly’s Speed Bump for the 11th of July, 2019. Essays which discuss something that appeared in Speed Bump should be at this link.

Dave Coverly’s Speed Bump for the 11th is a wordplay joke, and I have to admit its marginality. I can’t say it’s false for people who (presumably) don’t work much with coefficients to remember them after a long while. I don’t do much with French verb tenses, so I don’t remember anything about the pluperfect except that it existed. (I have a hazy impression that I liked it, but not an idea why. I think it was something in the auxiliary verb.) Still, this mention of coefficients nearly forms a comic strip synchronicity with Mike Thompson’s Grand Avenue for the 11th, in which a Math Joke allegedly has a mistaken coefficient as its punch line.

Gabby: 'It's craft time here at summer camp.' Michael: 'Finally! An activity that won't hurt my brain. Are we weaving? Painting? Making placemats?' Gabby: 'No. We're making probability flash cards.' Michael: 'The probability of us enjoying that activity? Zero.' Gabby: 'Finally! An answer at math camp that we can get right.'
Mike Thompson’s Grand Avenue for the 12th of July, 2019. The fair number of essays in which I complain about Grand Avenue I gather at this link.

Mike Thompson’s Grand Avenue for the 12th is the one I’m taking as representative for the week, though. The premise has been that Gabby and Michael were sent to Math Camp. They do not want to go to Math Camp. They find mathematics to be a bewildering set of arbitrary and petty rules to accomplish things of no interest to them. From their experience, it’s hard to argue. The comic has, since I started paying attention to it, consistently had mathematics be a chore dropped on them. And not merely from teachers who want them to solve boring story problems. Their grandmother dumps workbooks on them, even in the middle of summer vacation, presenting it as a chore they must do. Most comic strips present mathematics as a thing students would rather not do, and that’s both true enough and a good starting point for jokes. But I don’t remember any that make mathematics look so tedious. Anyway, I highlight this one because of the Math Camp jokes it, and the coefficients mention above, are the most direct mention of some mathematical thing. The rest are along the lines of the strip from the 9th, asserting that the “Math Camp Activity Board” spelled the last word wrong. The joke’s correct but it’s not mathematical.


So I had to put this essay to bed before I could read Saturday’s comics. Were any of them mathematically themed? I may know soon! And were there comic strips with some mention of mathematics, but too slight for me to make a paragraph about? What could be even slighter than the mathematical content of the Speed Bump and the Grand Avenue I did choose to highlight? Please check the Reading the Comics essay I intend to publish Tuesday. I’m curious myself.

Reading the Comics, March 30, 2019: Comics Kingdom is Screwed Up Edition


It doesn’t affect much this batch of comics, as they’re a bunch that all came from GoComics.com. But Comics Kingdom suffered a major redesign of the web site this week, and so it’s lost a lot of functionality. The ability to load your whole comics page at once, for example. Or the ability of archives to work. I’d had the URL for one strip copied down because it mentioned mathematics, albeit in so casual a manner I didn’t mean to write a paragraph about it. Good luck that I didn’t, as that URL now directs to a Spanish translation of a Katzenjammer Kids strip. Why? That’s a good question, and one that deserves an answer.

Anyway, I’m hoping that Comics Kingdom is able to get over their redesign soon. But I know they won’t. There’s never been a web site redesign that lowered functionality and made the page more infuriating to work with that was ever abandoned for the older, working version instead.

Enough about Comics Kingdom. Let me share a couple comic strips from a web site that works, although not as well as it did before its 2018 redesign.

Jim Meddick’s Monty for the 27th is part of a fun storyline. In it Monty and Moondog’s cell phones start texting on their own. It’s presented as the start of an Artificial Intelligence-based singularity, computers transcending human thought and going into business for themselves. This is shown by their working out mathematical truths, starting with arithmetic and going into Boolean algebra. Humans learn arithmetic first and Boolean algebra — logical statements and their combinations — later on, if ever.

Monty: 'Doc! Glad you're here! Our phones started texting without us!' Moondog: 'Now they're doing math!' (The phones text '2 x 2 = 4' and '4^4 = 256'.) Monty: 'They started with 2x2 = 4'. Professor Xemit: 'And now they're swapping advanced Boolean algebraic operations!' Monty: 'Doc ... what's going on?' Xemit: 'A dangerous nexus of AI has formed in your devices! And it must be stopped before it surpasses the combined intellect of all humanity!' Moondog: 'Not sure what that means, but it sounds like some serious data charges.'
Jim Meddick’s Monty for the 27th of March, 2019. Essays discussing anything from Monty should appear at this link.

Computers are certainly able to discover mathematics on their own. Or at least without close guidance; someone still has to write a program to do it. Automated proof finders are a well-established thing, though. They have not, so far as I’ve heard, discovered anything likely to threaten humanity.

Prisoner number 81861^3, talking to prisoner 3757^5: 'Man, this is one *big* prison!'
Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 28th of March, 2019. Appearances of The Chuckle Brothers in this line of essays should be gathered here.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 28th is built on representing huge numbers. 818613 is a big number: 548,568,842,280,381. Even bigger is 37575: it’s 748,524,423,279,410,560. It’s silly to imagine needing an identification number that large. But it’s also a remarkable coincidence that both prisoners here have numbers that can be represented with no more than six digits. There aren’t so many 15-digit numbers that could be represented with as few as six digits. But then it would be an absurdly large prison if it “only” had 818,613 prisoners in it. That seems like the joke would have been harder to recognize, though.

Anthropomorphic numeral 9, looking at temperatures on the Weather Channel. Caption: 'Nate wanted to work at the Weather Channel but didn't have a degree.'
Mark Parisi’s Off The Mark for the 28th of March, 2019. Essays inspired by something mentioned in Off The Mark should be gathered here.

Mark Parisi’s Off The Mark for the 28th is sort of the anthropomorphic numerals joke for the week. It’s also a joke for my friend with the meteorology degree, who I think doesn’t actually read these posts. Well, he probably got the comic forwarded to him anyway.

Daniel Beyer’s Long Story Short for the 29th is another prison joke. I’m not sure if someone at Comic Strip Master Command was worried about something. But a scrawl of mathematics is used as icon of skills learned in prison.

Prisoner, to the other in his cell: 'You learn new skills after being here awhile.' On his wall are several lines of mathematical scrawls.
Daniel Beyer’s Long Story Short for the 29th of March, 2019. Essays discussing topics raised by Long Story Short should be here. There aren’t many, yet.

Mathematics has the reputation of being a subject someone can still do useful work in while in prison. Maybe even do more work, as it seems to offer the prospect of undistracted time to think. And there are examples of mathematicians doing noteworthy work while imprisoned. Bertrand Russell wrote the Introduction To Mathematical Philosophy while jailed for protesting the First World War. André Weil advanced his work in arithmetic geometry while in prison for resisting service in the Second World War. Évariste Galois spent six months in prison shortly before the end of his life, and used some of the time to work on the theory of equations for which we still remember him. I would not recommend prison as a way to advance one’s mathematical research. But it’s something which could happen.

Colin, showing a card: 'Check it out, Dad! This is one of the most powerful Spen-Yo-Do Cards, the Crystal Conquerer! It's worth 2500 power units, has a multiplier ratio of 10, and a destruction ratio of 2 over 15! It can only be defeated by a mage card of equal value or greater!' Dad: 'That's fine, Colin, but I came to check your homework. C'mon, what's 9 divided by 3?' Colin: 'How am I supposed to know?!'
Terry LaBan and Patty LaBan’s Edge City rerun for the 30th of March, 2019. It originally ran in 2004; I can’t say whether it ran the 30th of March then. And topics raised by Edge City should be discussed at this link.

Terry LaBan and Patty LaBan’s Edge City for the 30th showcases the motivation problem. Colin, like many people, is easily able to do complicated algorithms to do something he likes doing. Arithmetic drills, though, not so much. This is why we end up writing story problems with dubious amounts of story in them.


And I don’t want to devote too much space to this. But Brian Fies’s The Last Mechanical Monster for the 29th included the lead character, the Mad Scientist, working out the numbers of the Fibonacci sequence as a way to keep his mind going. The strip is a rerun and I discussed it when it first ran on GoComics.


There were quite a lot of mathematically-themed comic strips the week of the 24th of March. I’ll get to the actual strips of the past week soon, at this link. Also if anyone knows a way to get the old Comics Kingdom back please let me know.

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.”

[Pro Tip: this is the answer to any thermodynamics question that requires you to determine an object's temperature: ] T = 2.73 K (assume well-mixed Cosmos)
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.

On the board: 1/2 - 1/8 = ?. Student: 'Apropos of nothing, I have two cats.'
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”.

Woman: 'And if you haven't figured it out yet, this is the math department lavatory'. The door reads 1 +/- 2
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.)

Employee: 'Cool 'power tie' boss'. The tie reads E = mc^2.
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.

Clare: 'How many cylinders with length 3 and diameter 1.5 equal the volume of a sphere with diameter 3?' Neil: 'Um ... 2.6. no, 2.7!' Clare: 'Neil, how on earth did you know that?' Neil: 'It's simple, Clare! I converted the cylinder to 'Ho Hos' and the sphere to Hostess 'Sno Balls', then I imagined eating them!' Clare: 'Um ... wow.' Neil: 'My brain's only average, but my tummy's a genius!'
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.

Professor in girl's daydream: 'But don't take my word for it. It's Euler's theorem.' (Points to e^{i pi} + 1 = 0 on the board.) Girl: 'Greg! Greg! I've changed my mind! Let's be colleagues again! ... Greg?' (Sees a closet jammed shut by a door.) Person inside: 'Help! I'm stuck!' (She unjams the door.) Person inside: 'Did she leave? Where's ray? Someone has to stop her!' Girl: 'That's like trying to stop a yeti!' Person inside: 'By my calculations it's far worse.' (Looks over sheet labelled 'Monster Unit Conversions', with Wray worked out to be 8 orcs or 3 trolls or 6 werewolves or werebears or 2.788 Yetis.)
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 — e^{\imath \pi} + 1 = 0 — is a good bet for “the” Euler’s Theorem. It’s a true equation, and it ties together a lot of interesting stuff about complex-valued numbers. It’s the way mathematicians tie together exponentials and simple harmonic motion. It makes so much stuff easier to work with. It would not be one of the things presented in a Distinctly Useless Mathematics text. But it would be mentioned along the way to something fascinating and useless. It turns up everywhere. (This is another strip I’m tagging for the first time.)

[ Cybil used to teach at MIT ] Cybil, teaching: 'If you've got pi/2 x 4 apples, and you eat Sigma x square root of cos(68) apples, how many apples do you have?' The class looks baffled.
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.)