Reading the Comics, March 24, 2018: Arithmetic and Information Edition


And now I can bring last week’s mathematically-themed comics into consideration here. Including the whole images hasn’t been quite as much work as I figured. But that’s going to change, surely. One of about four things I know about life is that if you think you’ve got your workflow set up to where you can handle things you’re about to be surprised. Can’t wait to see how this turns out.

John Deering’s Strange Brew for the 22nd is edging its way toward an anthropomorphic numerals joke.

Man, to woman at candlelit dinner: 'I can still remember the cute little number you were wearing the day we first met.' He's wearing the number 72102; she, 67350.
John Deering’s Strange Brew for the 22nd of March, 2018. I like to think she was wearing something from the Gary Larson collection.

Brant Parker and Johnny Hart’s Wizard of Id for the 22nd is a statistics joke. Really a demographics joke. Which still counts; much of the historical development of statistics was in demographics. That it was possible to predict accurately the number of people in a big city who’d die, and what from, without knowing anything about whether any particular person would die was strange and astounding. It’s still an astounding thing to look directly at.

The Duke: 'Sire, I have worked out some amazing statistics, here.' The King: 'Let's hear them.' The Duke: 'My figures show that the odds against a short man outliving a tall man are 5 to 1.' The King: 'Have the royal basketball team report to the gallows.'
Brant Parker and Johnny Hart’s Wizard of Id for the 25th of March 1968, and rerun the 22nd of March, 2018. That’s an interesting demographic the Kingdom of Id has there. Just saying.

Hilary Price and Rina Piccolo’s Rhymes with Orange for the 23rd has the form of a story problem. I could imagine turning this into a proper story problem. You’d need some measure of how satisfying the 50-dollar wines are versus the 5-dollar wines. Also how much the wines affect people’s ability to notice the difference. You might be able to turn this into a differential equations problem, but that’s probably overkill.

The Pop^Cork Quiz. Hostess with bottles of wine. Caption: 'If Laura owns 5 bottles of 50-dollar wine and 5 bottles of 5-dollar wine, how many bottles of 50-dollar wine must she serve in order to switch to the 5-dollar wine without anyone noticing?'
Hilary Price and Rina Piccolo’s Rhymes with Orange for the 23rd of March, 2018. Fortunately, one of Laura’s guests brought Jesus of Nazareth along as his `plus one’.

Mark Anderson’s Andertoons for the 23rd is Mark Anderson’s Andertoons for this half of the week. It’s a student-avoiding-the-problem joke. Could be any question. But arithmetic has the advantages of being plausible, taking up very little space to render, and not confusing the reader by looking like it might be part of the joke.

Kid at the blackboard, pondering 72 / 8: 'I know the answer, I'm just letting the suspense build.'
Mark Anderson’s Andertoons for the 23rd of March, 2018. Yeah, don’t try this with your thesis committee. Word to the wise.

John Zakour and Scott Roberts’s Working Daze for the 23rd has another cameo appearance by arithmetic. It’s also a cute reminder that there’s no problem you can compose that’s so simple someone can’t over-think it. And it puts me in mind of the occasional bit where a company’s promotional giveaway will technically avoid being a lottery by, instead of awarding prizes, awarding the chance to demonstrate a skill. Demonstration of that skill, such as a short arithmetic quiz, gets the prize. It’s a neat bit of loophole work and does depend, as the app designers here do, on the assumption there’s some arithmetic that people can be sure of being able to do.

Ed: 'The trick to making an easy quiz app is to come up with questions anybody could get right.' Rita: 'One plus one. Well, that's easy. It's two. No, wait. It's a trick question. It's eleven. Right? Unless ... ' Roy, thinking: 'This is going to be harder than we thought.'
John Zakour and Scott Roberts’s Working Daze for the 23rd of March, 2018. Ask your friend who does web stuff about Javascript and addition. You won’t understand the results but that’s all right; neither do they.

Teresa Burritt’s Frog Applause for the 24th is its usual bit of Dadist nonsense. But in the talk about black holes it throws in an equation: S = \frac{A k c^3}{4 G \hbar} . This is some mathematics about black holes, legitimate and interesting. It is the entropy of a black hole. The dazzling thing about this is all but one of those symbols on the right is the same for every black hole. ‘c’ is the speed of light, as in ‘E = mc2‘. G is the gravitational constant of the universe, a measure of how strong gravity is. \hbar is Planck’s constant, a kind of measure of how big quantum mechanics effects are. ‘k’ is the Boltzmann constant, which normal people never heard of but that everyone in physics and chemistry knows well. It’s what you multiply by to switch from the temperature of a thing to the thermal energy of the thing, or divide by to go the other way. It’s the same number for everything in the universe.

Woman's legs emerging from a portable hole, in three panels. The caption: 'Help! I'm defying the laws of gravity while also being sucked into a black hole that's supposed to be invisible --- except when the hole is in a comic strip!' (And on the side, S = Akc^3/4G h-bar.) 'Holy Hawking! As the space-time continuum continuums, I'm being warped into a state of striped-pants disreality teetering on a crummy fulcrum of fugly shoes. And even if I shout, 'I've fallen in a black hole and I can't get out', I'll forever be sinking deeper into a lamer surreality that never reaches the tendency pit of analyticity.'
Teresa Burritt’s Frog Applause for the 24th of March, 2018. Honestly surprised I didn’t see talk about striped-pants direality in Zippy the Pinhead first.

The only thing custom to a particular black hole is ‘A’, which is the surface area of the black hole. I mean the surface area of the event horizon. Double the surface area of the event horizon and you double its entropy. (This isn’t doubling the radius of the event horizon, but you know how much growth in the radius it is.) Also entropy. Hm. Everyone who would read this far into a pop mathematics blog like this knows that entropy is “how chaotic a thing is”. Thanks to people like Boltzmann we can be quantitative, and give specific and even exact numbers to the entropy of a system. It’s still a bit baffling since, superficially, a black hole seems like it’s not at all chaotic. It’s a point in space that’s got some mass to it, and maybe some electric charge and maybe some angular momentum. That’s about it. How messy can that be? It doesn’t even have any parts. This is how we can be pretty sure there’s stuff we don’t understand about black holes yet. Also about entropy.

This strip might be an oblique and confusing tribute to Dr Stephen Hawking. The entropy formula described was demonstrated by Drs Jacob Bekenstein and Stephen Hawking in the mid-1970s. Or it might be coincidence.

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


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

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

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

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

Teacher: 'Who would like to come up here and work this converting-fractions-to-decimals problem on the board? Let's see ... how about you, Todd?' Todd: 'Look out! Y2K! AAAGH! This is terrible! Just terrible! It finally caught up with us! Goodbye, electricity! Goodbye, civilized society!' Todd: 'Nice try, Todd. Y2K never happened!' Todd: 'Uh, yeah, I knew that. I was just saying' that Y2K is the answer to that problem on the board!' Teacher: 'Also a nice try. Now get up here!'
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.

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, December 23, 2017: Slow Week Edition


Comic Strip Master Command apparently wants everybody to have a quiet time ahead of Christmas. How quiet? Quiet enough that I’m including a strip I skipped last week and probably shouldn’t have. Here goes.

Ruben Bolling’s Super-Fun-Pak Comix for the 15th was an installment of Uncle Cap’n’s Puzzle Pontoon, an activity puzzle that’s always about Uncle Cap’n running some low-competence scam. In this case the scam is bitcoins, which makes me wonder how old this particular panel rerun is. (I thought I saw a bitcoin joke in Barney Google, mind, although I can’t find the reference to prove it.)

I don’t feel confident that I understand the full mathematics behind the scheme, so I’ll pass on that. I can talk about the SHA-256 Hash Function and what it’s for, though. To be part of the bitcoin process your computer needs to do two things: it has to do some computing work, and it has to convince other computers that it’s done that. The trick is to prove it was done without giving the original work away. The answer is one that humans have known for centuries. Probably millennia. Possibly since the invention of secrets. To show you’re in on a secret, publicize something that makes no sense except to other people who know the secret. A hash is one way to do it.

It’s a function which matches a string of numbers that represent your original message to the real numbers. It should be easy to make the hash from the original string. But it should be hard to go from the hash back to the original string. So then you can publicize the hash of whatever your secret is. And someone else can know that they have the same secret by checking whether it hashes to the same number. (I’m reminded of how Galileo secured his priority of the discovery that Venus shows phases by writing a short sentence describing the phenomenon, and then publicizing an anagram of it. The anagram made no sense, but if you knew his original message you verify that yes, indeed, he did publicize that string of letters. I suppose that’s not properly a hash, but it serves much the same role.) It’s an easy enough way to add some authentication to a message, and to make it more tamper-proof. Hash functions for this kind of security are believed to be reasonably collision-proof. It might be possible to find two original messages with the same hash. But we believe it would take so long to do that it would be more effective to just break into your target’s house and steal their computer instead of counterfeiting the message.

'So, I finally used my Algebra 2 ... helping my kid with his Algebra 2.'
Hilary Price (w/KG)’s Rhymes with Orange for the 17th of December, 2017. I’m not sure who KG is. Daily strips lately have been co-signed by Rina Piccolo, formerly of Tina’s Groove.

Hilary Price’s Rhymes with Orange for the 17th is a joke about the uselessness of Algebra 2. It’s a joke of a kind with jokes about philosophy professors having jobs training students to be philosophy professors (a joke mathematicians get too, come to think of it). I’m a bit more sympathetic to joking about Algebra 2, rather than Algebra at all. There are some classes with a purpose that doesn’t seem quite clear. I’m more likely to name pre-algebra as a course whose purpose I can’t quite pin down. Algebra 2 I would, generically, expect to cover stuff like functions of several variables that you’re prepared for the first time you take Algebra, and you should be comfortable with before you start Calculus (or Pre-Calculus), but that aren’t essential to knowing algebra in the first place.

Sam Hurt’s Eyebeam for the 18th is the anthropomorphic numerals segment for this slow week and makes literal an ancient joke. Incidentally, has anyone else been seeing the follow-up joke on their social media feeds? I don’t remember seeing it before about two months ago. (The follow up is, why was it that seven ate nine? … Because one should eat three-square meals a day.)

Brant Parker and Johnny Hart’s Wizard of Id Classics for the 21st mentions mathematicians, engineers, and wizards as the epitome of intelligence and ability. Flattering thought. My love’s father just yesterday proclaimed his confidence that as a mathematics PhD I could surely figure out how to do something mechanical. Related note: in three decades of being in an adult-like state I have never once successfully changed my car’s tire without outside aid. The strip originally ran the 25th of December, 1967.

There’s no Andertoons this week. I told you it was slow.

Reading the Comics, July 8, 2017: Mostly Just Pointing Edition


Won’t lie: I was hoping for a busy week. While Comic Strip Master Command did send a healthy number of mathematically-themed comic strips, I can’t say they were a particularly deep set. Most of what I have to say is that here’s a comic strip that mentions mathematics. Well, you’re reading me for that, aren’t you? Maybe. Tell me if you’re not. I’m curious.

Richard Thompson’s Cul de Sac rerun for the 2nd of July is the anthropomorphic numerals joke for the week. And a great one, as I’d expect of Thompson, since it also turns into a little bit about how to create characters.

Ralph Dunagin and Dana Summers’s Middletons for the 2nd uses mathematics as the example of the course a kid might do lousy in. You never see this for Social Studies classes, do you?

Mark Tatulli’s Heart of the City for the 3rd made the most overtly mathematical joke for most of the week at Math Camp. The strip hasn’t got to anything really annoying yet; it’s mostly been average summer-camp jokes. I admit I’ve been distracted trying to figure out if the minor characters are Tatulli redrawing Peanuts characters in his style. I mean, doesn’t Dana (the freckled girl in the third panel, here) look at least a bit like Peppermint Patty? I’ve also seen a Possible Marcie and a Possible Shermy, who’s the Peanuts character people draw when they want an obscure Peanuts character who isn’t 5. (5 is the Boba Fett of the Peanuts character set: an extremely minor one-joke character used for a week in 1963 but who appeared very occasionally in the background until 1983. You can identify him by the ‘5’ on his shirt. He and his sisters 3 and 4 are the ones doing the weird head-sideways dance in A Charlie Brown Christmas.)

Mark Pett’s Lucky Cow rerun for the 4th is another use of mathematics, here algebra, as a default sort of homework assignment.

Brant Parker and Johnny Hart’s Wizard of Id Classics for the 4th reruns the Wizard of Id for the 7th of July, 1967. It’s your typical calculation-error problem, this about the forecasting of eclipses. I admit the forecasting of eclipses is one of those bits of mathematics I’ve never understood, but I’ve never tried to understand either. I’ve just taken for granted that the Moon’s movements are too much tedious work to really enlighten me and maybe I should reevaluate that. Understanding when the Moon or the Sun could be expected to disappear was a major concern for people doing mathematics for centuries.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 5th is a Special Relativity joke, which is plenty of mathematical content for me. I warned you it was a week of not particularly deep discussions.

Ashleigh Brilliant’s Pot-Shots rerun for the 5th is a cute little metric system joke. And I’m going to go ahead and pretend that’s enough mathematical content. I’ve come to quite like Brilliant’s cheerfully despairing tone.

Jason Chatfield’s Ginger Meggs for the 7th mentions fractions, so you can see how loose the standards get around here when the week is slow enough.

Snuffy Smith: 'I punched Barlow 'cuz I knew in all probability he wuz about to punch me, yore honor!!' Judge: 'Th' law don't deal in probabilities, Smif, we deal in CERTAINTIES!!' Snuffy, to his wife: '... An' th'minute he said THAT, I was purty CERTAIN whar I wuz headed !!'
John Rose’s Barney Google and Snuffy Smith for the 8th of July, 2017. So I know it’s a traditional bit of comic strip graphic design to avoid using a . at the end of sentences, as it could be too easily lost — or duplicated — in a printing error. Thus the long history of comic strip sentences that end with a ! mark, unambiguous even if the dot goes missing or gets misaligned. But double exclamation points for everything? What goes on here?

John Rose’s Barney Google and Snuffy Smith for the 8th finally gives me a graphic to include this week. It’s about the joke you would expect from the topic of probability being mentioned. And, as might be expected, the comic strip doesn’t precisely accurately describe the state of the law. Any human endeavour has to deal with probabilities. They give us the ability to have reasonable certainty about the confusing and ambiguous information the world presents.

Einstein At Eight: equations scribbled all over the wall. Einstein Mom: 'Just look at what a mess you made here!' Einstein Dad: 'You've got some explaining to do, young man.'
Vic Lee’s Pardon My Planet for the 8th of July, 2017. I gotta say, I look at that equation in the middle with m raised to the 7th power and feel a visceral horror. And yet I dealt with exactly this horrible thing once and it came out all right.

Vic Lee’s Pardon My Planet for the 8th is another Albert Einstein mention. The bundle of symbols don’t mean much of anything, at least not as they’re presented, but of course superstar equation E = mc2 turns up. It could hardly not.

Reading the Comics, April 1, 2017: Connotations Edition


Last week ended with another little string of mathematically-themed comic strips. Most of them invited, to me, talk about the cultural significance of mathematics and what connotations they have. So, this title for an artless essay.

Berkeley Breathed’s Bloom County 2017 for the 28th of March uses “two plus two equals” as the definitive, inarguable truth. It always seems to be “two plus two”, doesn’t it? Never “two plus three”, never “three plus three”. I suppose I’ve sometimes seen “one plus one” or “two times two”. It’s easy to see why it should be a simple arithmetic problem, nothing with complicated subtraction or division or numbers as big as six. Maybe the percussive alliteration of those repeated two’s drives the phrase’s success. But then why doesn’t “two times two” show up nearly as often? Maybe the phrase isn’t iambic enough. “Two plus two” allows (to my ear) the “plus” sink in emphasis, while “times” stays a little too prominent. We need a wordsmith in to explore it. (I’m open to other hypotheses, including that “two times two” gets used more than my impression says.)

Christiann MacAuley’s Sticky Comics for the 28th uses mathematics as the generic “more interesting than people” thing that nerds think about. The thing being thought of there is the Mandelbrot Set. It’s built on complex-valued numbers. Pick a complex number, any you like; that’s called ‘C’. Square the number and add ‘C’ back to itself. This will be some new complex-valued number. Square that new number and add the original ‘C’ back to it again. Square that new number and add the original ‘C’ back once more. And keep at this. There are two things that might happen. These squared numbers might keep growing infinitely large. They might be negative, or imaginary, or (most likely) complex-valued, but their size keeps growing. Or these squared numbers might not grow arbitrarily large. The Mandelbrot Set is the collection of ‘C’ values for which the numbers don’t just keep growing in size. That’s the sort of lumpy kidney bean shape with circles and lightning bolts growing off it that you saw on every pop mathematics book during the Great Fractal Boom of the 80s and 90s. There’s almost no point working it out in your head; the great stuff about fractals almost requires a computer. They take a lot of computation. But if you’re just avoiding conversation, well, anything will do.

Olivia Walch’s Imogen Quest for the 29th riffs on the universe-as-simulation hypothesis. It’s one of those ideas that catches the mind and is hard to refute as long as we don’t talk to the people in the philosophy department, which we’re secretly scared of. Anyway the comic shows one of the classic uses of statistical modeling: try out a number of variations of a model in the hopes of understanding real-world behavior. This is an often-useful way to balance how the real world has stuff going on that’s important and that we don’t know about, or don’t know how to handle exactly.

Mason Mastroianni’s The Wizard of Id for the 31st uses a sprawl of arithmetic as symbol of … well, of status, really. The sort of thing that marks someone a white-collar criminal. I suppose it also fits with the suggestion of magic that accompanies huge sprawls of mathematical reasoning. Bundle enough symbols together and it looks like something only the intellectual aristocracy, or at least secret cabal, could hope to read.

Bob Shannon’s Tough Town for the 1st name-drops arithmetic. And shows off the attitude that anyone we find repulsive must also be stupid, as proven by their being bad at arithmetic. I admit to having no discernable feelings about the Kardashians; but I wouldn’t be so foolish as to conflate intelligence and skill-at-arithmetic.