Reading the Comics, November 16, 2018: The Rest Of The Week Edition


After that busy start last Sunday, Comic Strip Master Command left only a few things for the rest of the week. Here’s everything that seemed worthy of some comment to me:

Alex Hallatt’s Arctic Circle for the 12th is an arithmetic cameo. It’s used as the sort of thing that can be tested, with the straightforward joke about animal testing to follow. It’s not a surprise that machines should be able to do arithmetic. We’ve built machines for centuries to do arithmetic. Literally; Wilhelm Gottfried Leibniz designed and built a calculating machine able to add, subtract, multiply, and divide. This accomplishment from one of the founders of integral calculus is a potent reminder of how much we can accomplish if we’re supposed to be writing instead. (That link is to Robert Benchley’s classic essay “How To Get Things Done”. It is well worth reading, both because it is funny and because it’s actually good, useful advice.)

Rabbit, reading the paper: 'Artificial intelligence could make animal testing obsolete.' Polar Bear: 'Thank goodness.' Penguin imagines the Polar Bear in school, being asked by the teacher the square root of 121, with a robot beside him whispering '11'.
Alex Hallatt’s Arctic Circle for the 12th of November, 2018. Other essays based on Arctic Circle should be at this link.

But it’s also true that animals do know arithmetic. At least a bit. Not — so far as we know — to the point they ponder square roots and such. But certainly to count, to understand addition and subtraction roughly, to have some instinct for calculations. Stanislas Dehaene’s The Number Sense: How the Mind Creates Mathematics is a fascinating book about this. I’m only wary about going deeper into the topic since I don’t know a second (and, better, third) pop book touching on how animals understand mathematics. I feel more comfortable with anything if I’ve encountered it from several different authors. Anyway it does imply the possibility of testing a polar bear’s abilities at arithmetic, only in the real world.

In school. Binkley: 'Don't say anything, Ms Harlow, but a giant spotted snorkewacker from my closet full of anxieties has followed me to school and since experience has proven that he plans to grab me, I'd like permission to go home and hide.' Ms Harlow: 'Mr Binkley, that's the stinkiest excuse I've ever heard for getting out of a geometry exam. Go sit down.' Binkley's face-down at his desk; the Giant Spotted Snorklewacker asks, 'Pssst! What's the Pythagorean theorem?'
Berkeley Breathed’s Bloom County rerun for the 13th of November, 2018. It originally ran the 17th of February, 1983. Never mind the copyright notice; those would often show the previous year the first couple weeks of the year. Essays based on topics raised by Bloom County — original or modern continuation — should be at this link.

Berkeley Breathed’s Bloom County rerun for the 13th has another mathematics cameo. Geometry’s a subject worthy of stoking Binkley’s anxieties, though. It has a lot of definitions that have to be carefully observed. And while geometry reflects the understanding we have of things from moving around in space, it demands a precision that we don’t really have an instinct for. It’s a lot to worry about.

Written into two ring stains on a napkin: 'People who drink coffee'. 'People who drink tea'. Pointing to the intersection: 'People who share napkins.'
Terry Border’s Bent Objects for the 15th of November, 2018. Other essays based on Bent Objects will be at this link. It’s a new tag, so for now, there’s just that.

Terry Border’s Bent Objects for the 15th is our Venn Diagram joke for the week. I like this better than I think the joke deserves, probably because it is done in real materials. (Which is the Bent Objects schtick; it’s always photographs of objects arranged to make the joke.)

Teacher: 'I need to buy some graph paper for my students. Is there a convenience store near here?' Guy: 'Yeah, just two miles way from campus.' Later: Teacher, driving, realizes: 'Wait, he didn't specify a coordinate system. NOOOOOOO!' as her car leaps into the air.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th of November, 2018. In case there’s ever another essay which mentions Saturday Morning Breakfast Cereal it’ll be at this link.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is a joke on knowing how far to travel but not what direction. Normal human conversations carry contextually reasonable suppositions. Told something is two miles away, it’s probably along the major road you’re on, or immediately nearby. I’d still ask for clarification told something was “two miles away”. Two blocks, I’d let slide, on the grounds that it’s no big deal to correct a mistake.

Still, mathematicians carry defaults with them too. They might be open to a weird, general case, certainly. But we have expectations. There’s usually some obvious preferred coordinate system, or directions. If it’s important that we be ready for alternatives we highlight that. We specify the coordinate system we want. Perhaps we specify we’re taking that choice “without loss of generality”, that is, without supposing some other choice would be wrong.

I noticed the mathematician’s customized plate too. “EIPI1” is surely a reference to the expression e^{\imath \pi} + 1 . That sum, it turns out, equals zero. It reflects this curious connection between exponentiation, complex-valued numbers, and the trigonometric functions. It’s a weird thing to know is true, and it’s highly regarded in certain nerd circles for that weirdness.

The Odds. Guy checking his phone after his friend's been knocked down: 'There's tons of stuff about being struck by a bolt of lightning --- nothing about bolts of fabric.' [Title panel extra gag: 'Lucky for you it's soft and silky.']
Hilary Price’s Rhymes With Orange for the 16th of November, 2018. And times I’ve discussed something from Rhymes With Orange should be at this link.

Hilary Price’s Rhymes With Orange for the 16th features a what-are-the-odds sort of joke, this one about being struck by a bolt from the sky. Lightning’s the iconic bolt to strike someone, and be surprising about it. Fabric would be no less surprising, though. And there’s no end of stories of weird things falling from the skies. It’s easier to get stuff into the sky than you might think, and there are only a few options once that’s happened.


And as ever, all my Reading the Comics posts should all be at this link.

Through the end of December my Fall 2018 Mathematics A To Z continues. I’m still open for topics to discuss from the last half-dozen letters of the alphabet. Even if someone’s already given a word for some letter, suggest something anyway. You might inspire me in good ways.

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Reading the Comics, May 29, 2018: Finding Reruns Edition


There were a bunch of mathematically-themed comic strips this past week. A lot of them are ones I’d seen before. One of them is a bit risque and I’ve put that behind a cut. This saves me the effort of thinking up a good nonsense name to give this edition, so there’s that going for me too.

Bill Amend’s FoxTrot Classics for the 24th of May ought to have run last Sunday, but I wasn’t able to make time to write about it. It’s part of a sequence of Jason tutoring Paige in geometry. She’s struggling with the areas of common shapes which is relatable. Many of these area formulas could be kept straight by thinking back to rectangles. The size of the area is equal to the length of the base times the length of the height. From that you could probably reason right away the area of a trapezoid. It would have the same area as a rectangle with a base of length the mean length of the trapezoid’s different-length sides. The parallelogram works like the rectangle, length of the base times the length of the height. That you can convince yourself of by imagining the parallelogram. Then imagine slicing a right triangle off one of its sides. Move that around to the other side. Put it together right and you have a rectangle. Already know the area of a rectangle. The triangle, then, you can get by imagining two triangles of the same size and shape. Rotate one of the triangles 180 degrees. Slide it over, so the two triangles touch. Do this right and you have a parallelogram and so you know the area. The triangle’s half the area of that parallelogram.

Paige: 'OK, let me see if I've got these area formulas memorized. For a triangle, it's 1/2 bh. For a trapezoid, it's 1/2 (a + b)h. And for a circle, it's pi r^2.' Jason: 'Yes! Yes! Yes! You got them all right! You're going to ace this test! I'm going to make $10!' Paige: 'I always get confused --- does h stand for my height or the triangle's? ... Just kidding.' Jason: 'WILL YOU QUIT TOYING WITH ME?!'
Bill Amend’s FoxTrot Classics for the 24th of May, 2018. It originally ran the 30th of May, 1996.

The circle, I don’t know. I think just remember that if someone says “pi” they’re almost certainly going to follow it with either “r squared” or “day”. One of those suggests an area; the other doesn’t. Best I can do.

Jeri: 'Arrrrhh'. Teena: 'Sup?' Jeri: 'I'm having issues with this math issue. It's the way they phrase these word things. They're like trick questions. I can never figure them out.' Teena: 'Here, let me see what you're having trouble with. ... 'Sarah sits next to Stephen, who is very good at algebra. This causes Sarah, who has issues with BOTH Steven AND algebra, to feel bad But if Sarah moves next to someone else, Steven will feel bad. How do you protect Sarah's and Steven's self-esteem?' Jeri: 'I'm not that comfortable with my answer.' Teena: 'Which is?' Jeri: 'Eleven.' Teena: 'It must be very interesting in your school.'
Allison Barrows’s PreTeena rerun for the 27th of May, 2018. It originally ran the 15th of February, 2004.

Allison Barrows’s PreTeena rerun for the 27th discusses self-esteem as though it were a good thing that children ought to have. This is part of the strip’s work to help build up the Old Person Complaining membership that every comics section community group relies on. But. There is mathematics in Jeri’s homework. Not mathematics in the sense of something particular to calculate. There’s just nothing to do there. But it is mathematics, and useful mathematics, to work out the logic of how to satisfy multiple requirements. Or, if it’s impossible to satisfy them all at once, then to come as near satisfying them as possible. These kinds of problems are considered optimization or logistics problems. Most interesting real-world examples are impossibly hard, or at least become impossibly hard before you realize it. You can make a career out of doing as best as possible in the circumstances.

Charles Schulz’s Peanuts rerun for the 27th features an extended discussion by Lucy about the nature of … well, she explicitly talks about “nothing”. Is she talking about zero? Probably; you have to get fairly into mathematics or philosophy to start worrying about the difference between the number zero and the idea of nothing. In Algebra, mathematicians learn to work with systems of things that work like numbers enough that you can add and subtract and multiply them together, without committing to the idea that they’re working with numbers. They will have something that works like zero, though, a “nothing” that can be added to or subtracted from anything without changing it. And for which multiplication turns something into that “nothing”.

Charlie Brown, at Lucy's Psychiatric Help 5 cents booth: 'I always wanted to go up to that little red-haired girl and talk to her, but I just couldn't. I couldn't start a conversation because I was such a nothing and she was something. If she had wanted to talk to me, it would have been easy because someone who is really something can just go right up to someone who is nothing, and just talk.' Lucy: 'I think your problem is mathematical, Charlie Brown.' Charlie Brown: 'Mathematical?' Lucy: 'If you add nothing and something, what do you get?' Charlie Brown: 'Something, I guess.' Lucy: 'Right ... now, if you subtract nothing from something, what do you get?' Charlie Brown: 'Something.' Lucy: 'Very good ... now, if you multiply something by nothing, what do you get?' Charlie Brown: 'Nothing.' Lucy: 'Five cents, please.' Charlie Brown: 'When you're a nothing, you have a hard time understanding anything!'
Charles Schulz’s Peanuts rerun for the 27th of May, 2018. It originally ran the 30th of May, 1971. This strip originally ran during a time when, in-continuity, the Little Red-Haired Girl had moved away and Charlie Brown was coping with having never spoken to her. At some point she moved back, possibly because Schulz felt he had done everything he could with that or possibly because he forgot she had moved away.

I’m with Charlie Brown in not understanding where Lucy was going with all this, though. Maybe she lost the thread herself.

Mark Anderson’sAndertoons for the 28th is Mark Anderson’sAndertoons for the week. Wavehead’s worried about the verbs of both squaring and rounding numbers. Will say it’s a pair of words with contrary alternate meanings that I hadn’t noticed before. I have always taken the use of “square” to reflect, well, if you had a square with sides of size 4, then you’d have a square with area of size 16. The link seems obvious and logical. So on reflection that’s probably not at all where English gets it from. I mean, not to brag or anything but I’ve been speaking English all my life. If I’ve learned anything about it, it’s that the origin is probably something daft like “while Tisquantum [Squanto] was in England he impressed locals with his ability to do arithmetic and his trick of multiplying one number by itself got nicknamed squantuming, which got shortened to squaning to better fit the meter in a music-hall song about him, and a textbook writer in 1704 thought that was a mistake and `corrected’ it to squaring and everyone copied that”. I’m not even going to venture a guess about the etymology of “rounding”.

On the board: 2^2 = 4, 3^2 = 9, 4^2 = 16. Wavehead: 'Wait, we're squaring numbers now? We just figured out how to round them!'
Mark Anderson’sAndertoons for the 28th of May, 2018. But why would the examples be written out before the students were told what the were doing?

Marguerite Dabaie and Tom Hart’s Ali’s House for the 28th sets up a homework-help session over algebra. Can’t say where exactly Maisa is going wrong. Her saying “x equals 30 but the train equals” looks like trouble to me. It’s often good practice to start by writing out what are the things in the problem that seem important. And what symbol one wants each to mean. And what one knows about the relationship between these things. It helps clarify why someone would want to do that instead of something else. This is a new comic strip tag and I don’t think I’ve ever had cause to discuss it before.

Maisa: 'Can you help me with my homework?' Sahib: 'Dad promised me a hamburger.' Maisa: 'You see - x equals 30 but the train equals ... ' Sahib: 'Dad never makes hamburgers ... mutter mutter mutter.' Maisa: 'Look, I really need help with this.' Sahib: 'My brain isn't set on pay attention my brain is set on burger!'
Marguerite Dabaie and Tom Hart’s Ali’s House for the 28th of May, 2018. Relatable.

Hilary Price’s Rhymes With Orange for the 29th is a Rubik’s Cube joke. I’ve counted that as mathematical enough, usually. The different ways that you can rotate parts of the cube form a group. This is something like what I mentioned in the Peanuts discussion. The different rotations you can do can be added to or subtracted from each other, the way numbers can. (Multiplication I’m wary about.)

Rubik's Headquarters. It's a three-by-three wireframe with tiny offices inside. Person looking in: 'My corner office ... gone! I hate when they do a management shuffle.' [ Title panel, Other person: 'Rumor has it they're going to an open-concept model.' ]
Hilary Price’s Rhymes With Orange for the 29th of May, 2018. Pity whoever gets the center office, bottom layer.

And now here’s the strip that is unsuitable for reading at work, owing to the appearance of an undressed woman.

Continue reading “Reading the Comics, May 29, 2018: Finding Reruns Edition”

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.

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.

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, October 2017: Mathematics Anxiety Edition


Comic Strip Master Command hasn’t had many comics exactly on mathematical points the past week. I’ll make do. There are some that are close enough for me, since I like the comics already. And enough of them circle around people being nervous about doing mathematics that I have a title for this edition.

Tony Cochrane’s Agnes for the 24th talks about math anxiety. It’s not a comic strip that will do anything to resolve anyone’s mathematics anxiety. But it’s funny about its business. Agnes usually is; it’s one of the less-appreciated deeply-bizarre comics out there.

John Atkinson’s Wrong Hands for the 24th might be the anthropomorphic numerals joke for this week. Or it might be the anthropomorphic letters joke. Or something else entirely.

Charles Schulz’s Peanuts for the 24th reruns the comic from the 2nd of November, 1970. It has Sally discovering that multiplication is much easier than she imagined. As it is, she’s not in good shape. But if you accept ‘tooty-two’ as another name for ‘four’ and ‘threety-three’ as another name for ‘nine’, why not? And she might do all right in group theory. In that you can select a bunch of things, called ‘elements’, and describe their multiplication to fit anything you like, provided there’s consistency. There could be a four-forty-four if that seems to answer some question.

Patron of the Halloween Costume Advice booth: 'I want to be a zombie!' Regular character whose name I can't remember and can't find: 'That's a tough one ... we have to find a way to get you into character. Here [ handing a textbook over ] --- sit through one of Miss Barnes's math classes.'
Steve Kelley and Jeff Parker’s Dustin for the 25th of October, 2017. The kid’s premise this week is about advice for maximizing trick-or-treating hauls. So it circles around sabermetrics and the measurement of every possible metric relevant to a situation. It’s a bit baffling to me, since I just do not remember the quality of a costume relating to how much candy I’d gotten. Nor to what I give out, at least once you get past “high school kid not even bothering to dress up”. And even they’ll get a couple pieces although, yeah, if they did anything they’d get the full-size peanut butter cups. (We’re trying to build a reputation here.) What I’m saying is, I don’t see how the amount of candy depends on more than “have a costume” and “spend more time out there”. I mean, are people really withholding the fruit-flavored Tootsie Rolls because some eight-year-old doesn’t have an exciting enough costume? Really?

Steve Kelley and Jeff Parker’s Dustin for the 25th might be tied in to mathematics anxiety. At least it expresses how the thought of mathematics will cause some people to shut down entirely. Shame for them, but I can’t deny it’s so.

Young magician touching the wand to the whiteboard to show 15 divided by 3 is 5. His instructor: 'No relying on the wand --- I want to see how you arrived at the right answer.' (The title panel calls the strip The Tutor, with the tutor saying 'Someday when you're wizened you'll thank me.')
Hilary Price’s Rhymes with Orange for the 26th of October, 2017. The signature also credits Rina Piccolo, late of Six Chix and Tina’s Groove. The latter strip ended in July 2017, and she left the former last year. Maybe she’s picking up some hours part-timing on Rhymes With Orange; her signature’s been on many strips recently. Wikipedia doesn’t have anything relevant to say, and the credit on the web site doesn’t reflect Piccolo’s work, if she is a regular coauthor now.

Hilary Price’s Rhymes with Orange for the 26th is a calculator joke, made explicitly magical. I’m amused but also wonder if those are small wizards or large mushrooms. And it brings up again the question: why do mathematics teachers care about seeing how you got the answer? Who cares, as long as the answer is right? And my answer there is that yeah, sometimes all we care about is the answer. But more often we care about why someone knows the answer is this instead of that. The argument about what makes this answer right — or other answers wrong — should make it possible to tell why. And it often will help inform other problems. Being able to use the work done for one problem to solve others, or better, a whole family of problems, is fantastic. It’s the sort of thing mathematicians naturally try to do.

Jason Poland’s Robbie and Bobby for the 26th is an anthropomorphic geometry joke. And it’s a shape joke I don’t remember seeing, at least not under my Reading the Comics line of jokes. (Maybe I’ve just forgotten). Also, trapezoids: my most popular post of all time ever, even though it’s only got a couple months’ lead on the other perennial favorite, about how many grooves are on a record’s side.

Jeremy pours symbols from his mathematics notebook into a funnel in his head. They pour out his ears. He says 'My study habits are ineffective' to Pierce, who asks, 'Have you tried earplugs?'
Jerry Scott and Jim Borgman’s Zits for the 27th of October, 2017. I understand people who don’t find Zits a particularly strong comic. (My experience is it’s more loved by my parent’s cohort than by mine.) But I will say when Scott and Borgman go for visual metaphor the strip is easily ten times better. I think the cartoonists have some editorial-cartoon experience and they’ll sometimes put it to good use.

Jerry Scott and Jim Borgman’s Zits for the 27th uses mathematics as the emblem of complicated stuff in need of study. It’s a good visual. I have to say Jeremy’s material seems unorganized to start with, though.