Reading the Comics, November 18, 2017: Story Problems and Equation Blackboards Edition


It was a normal-paced week at Comic Strip Master Command. It was also one of those weeks that didn’t have anything from Comics Kingdom or Creators.Com. So I’m afraid you’ll all just have to click the links for strips you want to actually see. Sorry.

Bill Amend’s FoxTrot for the 12th has Jason and Marcus creating “mathic novels”. They, being a couple of mathematically-gifted smart people, credit mathematics knowledge with smartness. A “chiliagon” is a thousand-sided regular polygon that’s mostly of philosophical interest. A regular polygon with a thousand equal sides and a thousand equal angles looks like a circle. There’s really no way to draw one so that the human eye could see the whole figure and tell it apart from a circle. But if you can understand the idea of a regular polygon it seems like you can imagine a chilagon and see how that’s not a circle. So there’s some really easy geometry things that can’t be visualized, or at least not truly visualized, and just have to be reasoned with.

Rick Detorie’s One Big Happy for the 12th is a story-problem-subversion joke. The joke’s good enough as it is, but the supposition of the problem is that the driving does cover fifty miles in an hour. This may not be the speed the car travels at the whole time of the problem. Mister Green is maybe speeding to make up for all the time spent travelling slower.

Brandon Sheffield and Dami Lee’s Hot Comics for Cool People for the 13th uses a blackboard full of equations to represent the deep thinking being done on a silly subject.

Shannon Wheeler’s Too Much Coffee Man for the 15th also uses a blackboard full of equations to represent the deep thinking being done on a less silly subject. It’s a really good-looking blackboard full of equations, by the way. Beyond the appearance of our old friend E = mc2 there’s a lot of stuff that looks like legitimate quantum mechanics symbols there. They’re at least not obvious nonsense, as best I can tell without the ability to zoom the image in. I wonder if Wheeler didn’t find a textbook and use some problems from it for the feeling of authenticity.

Samson’s Dark Side of the Horse for the 16th is a story-problem subversion joke.

Jef Mallett’s Frazz for the 18th talks about making a bet on the World Series, which wrapped up a couple weeks ago. It raises the question: can you bet on an already known outcome? Well, sure, you can bet on anything you like, given a willing partner. But there does seem to be something fundamentally different between betting on something whose outcome isn’t in principle knowable, such as the winner of the next World Series, and betting on something that could be known but happens not to be, such as the winner of the last. We see this expressed in questions like “is it true the 13th of a month is more likely to be Friday than any other day of the week?” If you know which month and year is under discussion the chance the 13th is Friday is either 1 or 0. But we mean something more like, if we don’t know what month and year it is, what’s the chance this is a month with a Friday the 13th? Something like this is at work in this World Series bet. (The Astros won the recently completed World Series.)

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th is also featured on some underemployed philosopher’s “Reading the Comics” WordPress blog and fair enough. Utilitarianism exists in an odd triple point, somewhere on the borders of ethics, economics, and mathematics. The idea that one could quantize the good or the utility or the happiness of society, and study how actions affect it, is a strong one. It fits very well the modern mindset that holds everything can be quantified even if we don’t know how to do it well just yet. And it appeals strongly to a mathematically-minded person since it sounds like pure reason. It’s not, of course, any more than any ethical scheme can be. But it sounds like the ethics a Vulcan would come up with and that appeals to a certain kind of person. (The comic is built on one of the implications of utilitarianism that makes it seem like the idea’s gone off the rails.)

There’s some mathematics symbols on The Utilitarian’s costume. The capital U on his face is probably too obvious to need explanation. The \sum u on his chest relies on some mathematical convention. For maybe a half-millennium now mathematicians have been using the capital sigma to mean “take a sum of things”. The things are whatever the expression after that symbol is. Usually, the Sigma will have something below and above which carries meaning. It says what the index is for the thing after the symbol, and what the bounds of the index are. Here, it’s not set. This is common enough, though, if this is understood from context. Or if it’s obvious. The small ‘u’ to the right suggests the utility of whatever’s thought about. (“Utility” being the name for the thing measured and maximized; it might be happiness, it might be general well-being, it might be the number of people alive.) So the symbols would suggest “take the sum of all the relevant utilities”. Which is the calculation that would be done in this case.

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Reading the Comics, August 26, 2017: Dragon Edition


It’s another week where everything I have to talk about comes from GoComics.com. So, no pictures. The Comics Kingdom and the Creators.com strips are harder for non-subscribers to read so I feel better including those pictures. There’s not an overarching theme that I can fit to this week’s strips either, so I’m going to name it for the one that was most visually interesting to me.

Charlie Pondrebarac’s CowTown for the 22nd I just knew was a rerun. It turned up the 26th of August, 2015. Back then I described it as also “every graduate students’ thesis defense anxiety dream”. Now I wonder if I have the possessive apostrophe in the right place there. On reflection, if I have “every” there, then “graduate student” has to be singular. If I dropped the “every” then I could talk about “graduate students” in the plural and be sensible. I guess that’s all for a different blog to answer.

Mike Thompson’s Grand Avenue for the 22nd threatened to get me all cranky again, as Grandmom decided the kids needed to do arithmetic worksheets over the summer. The strip earned bad attention from me a few years ago when a week, maybe more, of the strip was focused on making sure the kids drudged their way through times tables. I grant it’s a true attitude that some people figure what kids need is to do a lot of arithmetic problems so they get better at arithmetic problems. But it’s hard enough to convince someone that arithmetic problems are worth doing, and to make them chores isn’t helping.

John Zakour and Scott Roberts’s Maria’s Day for the 22nd name-drops fractions as a worse challenge than dragon-slaying. I’m including it here for the cool partial picture of the fire-breathing dragon. Also I take a skeptical view of the value of slaying the dragons anyway. Have they given enough time for sanctions to work?

Maria’s Day pops back in the 24th. Needs more dragon-slaying.

Eric the Circle for the 24th, this one by Dennill, gets in here by throwing some casual talk about arcs around. That and π. The given formula looks like nonsense to me. \frac{pi}{180}\cdot 94 - sin 94\deg has parts that make sense. The first part will tell you what radian measure corresponds to 94 degrees, and that’s fine. Mathematicians will tend to look for radian measures rather than degrees for serious work. The sine of 94 degrees they might want to know. Subtracting the two? I don’t see the point. I dare to say this might be a bunch of silliness.

Cathy Law’s Claw for the 25th writes off another Powerball lottery loss as being bad at math and how it’s like algebra. Seeing algebra in lottery tickets is a kind of badness at mathematics, yes. It’s probability, after all. Merely playing can be defended mathematically, though, at least for the extremely large jackpots such as the Powerball had last week. If the payout is around 750 million dollars (as it was) and the chance of winning is about one in 250 million (close enough to true), then the expectation value of playing a ticket is about three dollars. If the ticket costs less than three dollars (and it does; I forget if it’s one or two dollars, but it’s certainly not three), then, on average you could expect to come out slightly ahead. Therefore it makes sense to play.

Except that, of course, it doesn’t make sense to play. On average you’ll lose the cost of the ticket. The on-average long-run you need to expect to come out ahead is millions of tickets deep. The chance of any ticket winning is about one in 250 million. You need to play a couple hundred million times to get a good enough chance of the jackpot for it to really be worth it. Therefore it makes no sense to play.

Mathematical logic therefore fails us: we can justify both playing and not playing. We must study lottery tickets as a different thing. They are (for the purposes of this) entertainment, something for a bit of disposable income. Are they worth the dollar or two per ticket? Did you have other plans for the money that would be more enjoyable? That’s not my ruling to make.

Samson’s Dark Side Of The Horse for the 25th just hurts my feelings. Why the harsh word, Samson? Anyway, it’s playing on the typographic similarity between 0 and O, and how we bunch digits together.

Grouping together three decimal digits as a block is as old, in the Western tradition, as decimal digits are. Leonardo of Pisa, in Liber Abbaci, groups the thousands and millions and thousands of millions and such together. By 1228 he had the idea to note this grouping with an arc above the set of digits, like a tie between notes on a sheet of music. This got cut down, part of the struggle in notation to write as little as possible. Johannes de Sacrobosco in 1256 proposed just putting a dot every third digit. In 1636 Thomas Blundeville put a | mark after every third digit. (I take all this, as ever, from Florian Cajori’s A History Of Mathematical Notations, because it’s got like everything in it.) We eventually settled on separating these stanzas of digits with a , or . mark. But that it should be three digits goes as far back as it could.

Reading the Comics, July 29, 2017: Not Really Mathematics Concluded Edition


It was a busy week at Comic Strip Master Command last week, since they wanted to be sure I was overloaded ahead of the start of the Summer 2017 A To Z project. So here’s the couple of comics I didn’t have time to review on Sunday.

Mort (“Addison”) Walker’s Boner’s Ark for the 7th of September, 1971 was rerun the 27th of July. It mentions mathematics but just as a class someone might need more work on. Could be anything, but mathematics has the connotations of something everybody struggles with, and in an American comic strip needs only four letters to write. Most economical use of word balloon space.

Boner: 'Your math could stand a lot more work, Spot.' Aardvark: 'Yeah! Let's get at it, Buddy! Get that old nose to the grindstone!' Spot: 'YOUR nose could use a little time at the grindstone, too, Buddy!'
Mort (“Addison”) Walker’s Boner’s Ark for the 7th of September, 1971 and rerun the 27th of July, 2017. I suppose I’m glad that Boner is making sure his animals get as good an education as possible while they’re stranded on their Ark. I’m just wondering whether Boner’s comment is meant in the parental role of a concerned responsible caretaker figure, or whether he’s serving as a teacher or principal. What exactly is the social-service infrastructure of Boner’s Ark? The world may never know.

Neil Kohney’s The Other End for the 28th also mentions mathematics without having any real mathematics content. Barry tries to make the argument that mathematics has a timeless and universal quality that makes for good aesthetic value. I support this principle. Art has many roles. One is to make us see things which are true which are not about ourselves. This mathematics does. Whether it’s something as instantly accessible as, say, RobertLovesPi‘s illustrations of geometrical structures, or something as involved as the five-color map theorem mathematics gives us something. This isn’t any excuse to slum, though.

Rob Harrell’s Big Top rerun for the 29th features a word problem. It’s cast in terms of what a lion might find interesting. Cultural expectations are inseparable from the mathematics we do, however much we might find universal truths about them. Word problems make the cultural biases more explicit, though. Also, note that Harrell shows an important lesson for artists in the final panel: whenever possible, draw animals wearing glasses.

Samson’s Dark Side Of The Horse for the 29th is another sheep-counting joke. As Samson will often do this includes different representations of numbers before it all turns to chaos in the end. This is why some of us can’t sleep.

Reading the Comics, June 17, 2017: Icons Of Mathematics Edition


Comic Strip Master Command just barely missed being busy enough for me to split the week’s edition. Fine for them, I suppose, although it means I’m going to have to scramble together something for the Tuesday or the Thursday posting slot. Ah well. As befits the comics, there’s a fair bit of mathematics as an icon in the past week’s selections. So let’s discuss.

Mark Anderson’s Andertoons for the 11th is our Mark Anderson’s Andertoons for this essay. Kind of a relief to have that in right away. And while the cartoon shows a real disaster of a student at the chalkboard, there is some truth to the caption. Ruling out plausible-looking wrong answers is progress, usually. So is coming up with plausible-looking answers to work out whether they’re right or wrong. The troubling part here, I’d say, is that the kid came up with pretty poor guesses about what the answer might be. He ought to be able to guess that it’s got to be an odd number, and has to be less than 10, and really ought to be less than 7. If you spot that then you can’t make more than two wrong guesses.

Patrick J Marrin’s Francis for the 12th starts with what sounds like a logical paradox, about whether the Pope could make an infallibly true statement that he was not infallible. Really it sounds like a bit of nonsense. But the limits of what we can know about a logical system will often involve questions of this form. We ask whether something can prove whether it is provable, for example, and come up with a rigorous answer. So that’s the mathematical content which justifies my including this strip here.

Border Collis are, as we know, highly intelligent. The dogs are gathered around a chalkboard full of mathematics. 'I've checked my calculations three times. Even if master's firm and calm and behaves like an alpha male, we *should* be able to whip him.'
Niklas Eriksson’s Carpe Diem for the 13th of June, 2017. Yes, yes, it’s easy to get people excited for the Revolution, but it’ll come to a halt when someone asks about how they get the groceries afterwards.

Niklas Eriksson’s Carpe Diem for the 13th is a traditional use of the blackboard full of mathematics as symbolic of intelligence. Of course ‘E = mc2‘ gets in there. I’m surprised that both π and 3.14 do, too, for as little as we see on the board.

Mark Anderson’s Andertoons for the 14th is a nice bit of reassurance. Maybe the cartoonist was worried this would be a split-week edition. The kid seems to be the same one as the 11th, but the teacher looks different. Anyway there’s a lot you can tell about shapes from their perimeter alone. The one which most startles me comes up in calculus: by doing the right calculation about the lengths and directions of the edge of a shape you can tell how much area is inside the shape. There’s a lot of stuff in this field — multivariable calculus — that’s about swapping between “stuff you know about the boundary of a shape” and “stuff you know about the interior of the shape”. And finding area from tracing the boundary is one of them. It’s still glorious.

Samson’s Dark Side Of The Horse for the 14th is a counting-sheep joke and a Pi Day joke. I suspect the digits of π would be horrible for lulling one to sleep, though. They lack the just-enough-order that something needs for a semiconscious mind to drift off. Horace would probably be better off working out Collatz sequences.

Dana Simpson’s Phoebe and her Unicorn for the 14th mentions mathematics as iconic of what you do at school. Book reports also make the cut.

Dr Zarkov: 'Flash, this is Professor Quita, the inventor of the ... ' Prof Quita: 'Caramba! NO! I am a mere mathematician! With numbers, equations, paper, pencil, I work ... it is my good amigo, Dr Zarkov, who takes my theories and builds ... THAT!!' He points to a bigger TV screen.
Dan Barry’s Flash Gordon for the 31st of July, 1962, rerun the 16th of June, 2017. I am impressed that Dr Zarkov can make a TV set capable of viewing alternate universes. I still literally do not know how it is possible that we have sound for our new TV set, and I labelled and connected every single wire in the thing. Oh, wouldn’t it be a kick if Dr Zarkov has the picture from one alternate universe but the sound from a slightly different other one?

Dan Barry’s Flash Gordon for the 31st of July, 1962 and rerun the 16th I’m including just because I love the old-fashioned image of a mathematician in Professor Quita here. At this point in the comic strip’s run it was set in the far-distant future year of 1972, and the action here is on one of the busy multinational giant space stations. Flash himself is just back from Venus where he’d set up some dolphins as assistants to a fish-farming operation helping to feed that world and ours. And for all that early-60s futurism look at that gorgeous old adding machine he’s still got. (Professor Quinta’s discovery is a way to peer into alternate universes, according to the next day’s strip. I’m kind of hoping this means they’re going to spend a week reading Buck Rogers.)

Reading the Comics, May 27, 2017: Panels Edition


Can’t say this was too fast or too slow a week for mathematically-themed comic strips. A bunch of the strips were panel comics, so that’ll do for my theme.

Norm Feuti’s Retail for the 21st mentions every (not that) algebra teacher’s favorite vague introduction to group theory, the Rubik’s Cube. Well, the ways you can rotate the various sides of the cube do form a group, which is something that acts like arithmetic without necessarily being numbers. And it gets into value judgements. There exist algorithms to solve Rubik’s cubes. Is it a show of intelligence that someone can learn an algorithm and solve any cube? — But then, how is solving a Rubik’s cube, with or without the help of an algorithm, a show of intelligence? At least of any intelligence more than the bit of spatial recognition that’s good for rotating cubes around?

'Rubik's cube, huh? I never could solve one of those.' 'I'm just fidgeting with it. I never bothered learning the algorithm either.' 'What algorithm?' 'The pattern you use to solve it.' 'Wait. All you have to do to solve it is memorize a pattern?' 'Of course. How did you think people solved it?' 'I always thought you had to be super smart to figure it out.' 'Well, memorizing the pattern does take a degree of intelligence.' 'Yeah, but that's not the same thing as solving it on your own.' 'I'm sure some people figured out the algorithm without help.' 'I KNEW Chad Gustafson was a liar! He was no eighth-grade prodigy, he just memorized the pattern!' 'Sounds like you and the CUBE have some unresolved issues.'
Norm Feuti’s Retail for the 21st of May, 2017. A few weeks ago I ran across a book about the world of competitive Rubik’s Cube solving. I haven’t had the chance to read it, but am interested by the ways people form rules for what would seem like a naturally shapeless feature such as solving Rubik’s Cubes. Not featured: the early 80s Saturday morning cartoon that totally existed because somehow that made sense back then.

I don’t see that learning an algorithm for a problem is a lack of intelligence. No more than using a photo reference shows a lack of drawing skill. It’s still something you need to learn, and to apply, and to adapt to the cube as you have it to deal with. Anyway, I never learned any techniques for solving it either. Would just play for the joy of it. Here’s a page with one approach to solving the cube, if you’d like to give it a try yourself. Good luck.

Bob Weber Jr and Jay Stephens’s Oh, Brother! for the 22nd is a word-problem avoidance joke. It’s a slight thing to include, but the artwork is nice.

Brian and Ron Boychuk’s Chuckle Brothers for the 23rd is a very slight thing to include, but it’s looking like a slow week. I need something here. If you don’t see it then things picked up. They similarly tried sprucing things up the 27th, with another joke for taping onto the door.

Nate Fakes’s Break of Day for the 24th features the traditional whiteboard full of mathematics scrawls as a sign of intelligence. The scrawl on the whiteboard looks almost meaningful. The integral, particularly, looks like it might have been copied from a legitimate problem in polar or cylindrical coordinates. I say “almost” because while I think that some of the r symbols there are r’ I’m not positive those aren’t just stray marks. If they are r’ symbols, it’s the sort of integral that comes up when you look at surfaces of spheres. It would be the electric field of a conductive metal ball given some charge, or the gravitational field of a shell. These are tedious integrals to solve, but fortunately after you do them in a couple of introductory physics-for-majors classes you can just look up the answers instead.

Samson’s Dark Side of the Horse for the 26th is the Roman numerals joke for this installment. I feel like it ought to be a pie chart joke too, but I can’t find a way to make it one.

Izzy Ehnes’s The Best Medicine Cartoon for the 27th is the anthropomorphic numerals joke for this paragraph.

Reading the Comics, March 25, 2017: Slow Week Edition


Slow week around here for mathematically-themed comic strips. These happen. I suspect Comic Strip Master Command is warning me to stop doing two-a-week essays on reacting to comic strips and get back to more original content. Message received. If I can get ahead of some projects Monday and Tuesday we’ll get more going.

Patrick Roberts’s Todd the Dinosaur for the 20th is a typical example of mathematics being something one gets in over one’s head about. Of course it’s fractions. Is there anything in elementary school that’s a clearer example of something with strange-looking rules and processes for some purpose students don’t even know what they are? In middle school and high school we get algebra. In high school there’s trigonometry. In high school and college there’s calculus. In grad school there’s grad school. There’s always something.

Teacher: 'Todd, are you wearing water wings? Why, pray tell?' 'So I can make it to the third grade! We're startin' fractions today and YOU said you had a feeling I was gonna get in over my head.' 'Dang!'
Patrick Roberts’s Todd the Dinosaur for the 20th of March, 2017. I’ll allow the kids-say-the-darndest-things setup for the strip. I’m stuck on wondering just how much good water wings that size could do. Yes, he’s limited by his anatomy but aren’t we all?

Jeff Stahler’s Moderately Confused for the 21st is the usual bad-mathematics-of-politicians joke. It may be a little more on point considering the Future Disgraced Former President it names, but the joke is surely as old as politicians and hits all politicians with the same flimsiness.

John Graziano’s Ripley’s Believe It Or Not for the 22nd names Greek mathematician Pythagoras. That’s close enough to on-point to include here, especially considering what a slow week it’s been. It may not be fair to call Pythagoras a mathematician. My understanding is we don’t know that actually did anything in mathematics, significant or otherwise. His cult attributed any of its individuals’ discoveries to him, and may have busied themselves finding other, unrelated work to credit to their founder. But there’s so much rumor and gossip about Pythagoras that it’s probably not fair to automatically dismiss any claim about him. The beans thing I don’t know about. I would be skeptical of anyone who said they were completely sure.

Vic Lee’s Pardon My Planet for the 23rd is the usual sort of not-understanding-mathematics joke. In this case it’s about percentages, which are good for baffling people who otherwise have a fair grasp on fractions. I wonder if people would be better at percentages if they learned to say “percent” as “out of a hundred” instead. I’m sure everyone who teaches percentages teaches that meaning, but that doesn’t mean the warning communicates.

'OK, then let's compromise. I'll be right most of the time - at least 46 percent of the time. And you can be right whenever there is math involved.'
Vic Lee’s Pardon My Planet for the 23rd of March, 2017. Don’t mind me, I’m busy trying to convince myself the back left leg of that park bench is hidden behind the guy’s leg and not missing altogether and it’s still pretty touch-and-go on that.

Stephan Pastis’s Pearls Before Swine for the 24th jams a bunch of angle puns into its six panels. I think it gets most of the basic set in there.

Samson’s Dark Side Of The Horse for the 25th mentions sudokus, and that’s enough for a slow week like this. I thought Horace was reaching for a calculator in the last panel myself, and was going to say that wouldn’t help any. But then I checked the numbers in the boxes and that made it all better.

Reading the Comics, March 4, 2017: Frazz, Christmas Trees, and Weddings Edition


It was another of those curious weeks when Comic Strip Master Command didn’t send quite enough comics my way. Among those they did send were a couple of strips in pairs. I can work with that.

Samson’s Dark Side Of The Horse for the 26th is the Roman Numerals joke for this essay. I apologize to Horace for being so late in writing about Roman Numerals but I did have to wait for Cecil Adams to publish first.

In Jef Mallett’s Frazz for the 26th Caulfield ponders what we know about Pythagoras. It’s hard to say much about the historical figure: he built a cult that sounds outright daft around himself. But it’s hard to say how much of their craziness was actually their craziness, how much was just that any ancient society had a lot of what seems nutty to us, and how much was jokes (or deliberate slander) directed against some weirdos. What does seem certain is that Pythagoras’s followers attributed many of their discoveries to him. And what’s certain is that the Pythagorean Theorem was known, at least a thing that could be used to measure things, long before Pythagoras was on the scene. I’m not sure if it was proved as a theorem or whether it was just known that making triangles with the right relative lengths meant you had a right triangle.

Greg Evans’s Luann Againn for the 28th of February — reprinting the strip from the same day in 1989 — uses a bit of arithmetic as generic homework. It’s an interesting change of pace that the mathematics homework is what keeps one from sleep. I don’t blame Luann or Puddles for not being very interested in this, though. Those sorts of complicated-fraction-manipulation problems, at least when I was in middle school, were always slogs of shuffling stuff around. They rarely got to anything we’d like to know.

Jef Mallett’s Frazz for the 1st of March is one of those little revelations that statistics can give one. Myself, I was always haunted by the line in Carl Sagan’s Cosmos about how, in the future, with the Sun ageing and (presumably) swelling in size and heat, the Earth would see one last perfect day. That there would most likely be quite fine days after that didn’t matter, and that different people might disagree on what made a day perfect didn’t matter. Setting out the idea of a “perfect day” and realizing there would someday be a last gave me chills. It still does.

Richard Thompson’s Poor Richard’s Almanac for the 1st and the 2nd of March have appeared here before. But I like the strip so I’ll reuse them too. They’re from the strip’s guide to types of Christmas trees. The Cubist Fur is described as “so asymmetrical it no longer inhabits Euclidean space”. Properly neither do we, but we can’t tell by eye the difference between our space and a Euclidean space. “Non-Euclidean” has picked up connotations of being so bizarre or even horrifying that we can’t hope to understand it. In practice, it means we have to go a little slower and think about, like, what would it look like if we drew a triangle on a ball instead of a sheet of paper. The Platonic Fir, in the 2nd of March strip, looks like a geometry diagram and I doubt that’s coincidental. It’s very hard to avoid thoughts of Platonic Ideals when one does any mathematics with a diagram. We know our drawings aren’t very good triangles or squares or circles especially. And three-dimensional shapes are worse, as see every ellipsoid ever done on a chalkboard. But we know what we mean by them. And then we can get into a good argument about what we mean by saying “this mathematical construct exists”.

Mark Litzler’s Joe Vanilla for the 3rd uses a chalkboard full of mathematics to represent the deep thinking behind a silly little thing. I can’t make any of the symbols out to mean anything specific, but I do like the way it looks. It’s quite well-done in looking like the shorthand that, especially, physicists would use while roughing out a problem. That there are subscripts with forms like “12” and “22” with a bar over them reinforces that. I would, knowing nothing else, expect this to represent some interaction between particles 1 and 2, and 2 with itself, and that the bar means some kind of complement. This doesn’t mean much to me, but with luck, it means enough to the scientist working it out that it could be turned into a coherent paper.

'Has Carl given you any reason not to trust him?' 'No, not yet. But he might.' 'Fi ... you seek 100% certainty in people, but that doesn't exist. In the end,' and Dethany is drawn as her face on a pi symbol, 'we're *all* irrational numbers.'
Bill Holbrook’s On The Fastrack for the 3rd of March, 2017. Fi’s dress isn’t one of those … kinds with the complicated pattern of holes in it. She got it torn while trying to escape the wedding and falling into the basement.

Bill Holbrook’s On The Fastrack is this week about the wedding of the accounting-minded Fi. And she’s having last-minute doubts, which is why the strip of the 3rd brings in irrational and anthropomorphized numerals. π gets called in to serve as emblematic of the irrational numbers. Can’t fault that. I think the only more famously irrational number is the square root of two, and π anthropomorphizes more easily. Well, you can draw an established character’s face onto π. The square root of 2 is, necessarily, at least two disconnected symbols and you don’t want to raise distracting questions about whether the root sign or the 2 gets the face.

That said, it’s a lot easier to prove that the square root of 2 is irrational. Even the Pythagoreans knew it, and a bright child can follow the proof. A really bright child could create a proof of it. To prove that π is irrational is not at all easy; it took mathematicians until the 19th century. And the best proof I know of the fact does it by a roundabout method. We prove that if a number (other than zero) is rational then the tangent of that number must be irrational, and vice-versa. And the tangent of π/4 is 1, so therefore π/4 must be irrational, so therefore π must be irrational. I know you’ll all trust me on that argument, but I wouldn’t want to sell it to a bright child.

'Fi ... humans are complicated. Like the irrational number pi, we can go on forever. You never get to the bottom of us! But right now, upstairs, there are two variables who *want* you in their lives. Assign values to them.' Carl, Fi's fiancee, is drawn as his face with a y; his kid as a face on an x.
Bill Holbrook’s On The Fastrack for the 4th of March, 2017. I feel bad that I completely forgot Carl had a kid and that the face on the x doesn’t help me remember anything.

Holbrook continues the thread on the 4th, extends the anthropomorphic-mathematics-stuff to call people variables. There’s ways that this is fair. We use a variable for a number whose value we don’t know or don’t care about. A “random variable” is one that could take on any of a set of values. We don’t know which one it does, in any particular case. But we do know — or we can find out — how likely each of the possible values is. We can use this to understand the behavior of systems even if we never actually know what any one of it does. You see how I’m going to defend this metaphor, then, especially if we allow that what people are likely or unlikely to do will depend on context and evolve in time.

Reading the Comics, February 3, 2017: Counting Edition


And now I can close out last week’s mathematically-themed comic strips. Two of them are even about counting, which is enough for me to make that the name of this set.

John Allen’s Nest Heads for the 2nd mentions a probability and statistics class and something it’s supposed to be good for. I would agree that probability and statistics are probably (I can’t find a better way to write this) the most practically useful mathematics one can learn. At least once you’re past arithmetic. They’re practical by birth; humans began studying them because they offer guidance in uncertain situations. And one can use many of their tools without needing more than arithmetic.

I’m not so staunchly anti-lottery as many mathematics people are. I’ll admit I play it myself, when the jackpot is large enough. When the expectation value of the prize gets to be positive, it’s harder to rationalize not playing. This happens only once or twice a year, but it’s fun to watch and see when it happens. I grant it’s a foolish way to use two dollars (two tickets are my limit), but you know? My budget is not so tight I can’t spend four dollars foolishly a year. Besides, I don’t insist on winning one of those half-billion-dollar prizes. I imagine I’d be satisfied if I brought in a mere $10,000.

'Hey, Ruthie's Granny, how old are you?' 'You can't count that high, James.' 'I can too!' 'Fine! Start at one and I'll tell you when you get to my age.' '1, 2, 3, 4, 11, 22, 88, 99, 200, a gazillion!' 'Very good! It's somewhere between 22 and a gazillion!' 'Gazowie!'
Rick Detorie’s One Big Happy for the 3rd of February, 2017. A ‘gazillion’ is actually a surprisingly low number, hovering as it does somewhere around 212. Fun fact!

Rick Detorie’s One Big Happy for the 3rd continues my previous essay’s bit of incompetence at basic mathematics, here, counting. But working out that her age is between 22 an a gazillion may be worth doing. It’s a common mathematical challenge to find a correct number starting from little information about it. Usually we find it by locating bounds: the number must be larger than this and smaller than that. And then get the bounds closer together. Stop when they’re close enough for our needs, if we’re numerical mathematicians. Stop when the bounds are equal to each other, if we’re analytic mathematicians. That can take a lot of work. Many problems in number theory amount to “improve our estimate of the lowest (or highest) number for which this is true”. We have to start somewhere.

Samson’s Dark Side of the Horse for the 3rd is a counting-sheep joke and I was amused that the counting went so awry here. On looking over the strip again for this essay, though, I realize I read it wrong. It’s the fences that are getting counted, not the sheep. Well, it’s a cute little sheep having the same problems counting that Horace has. We don’t tend to do well counting more than around seven things at a glance. We can get a bit farther if we can group things together and spot that, say, we have four groups of four fences each. That works and it’s legitimate; we’re counting and we get the right count out of it. But it does feel like we’re doing something different from how we count, say, three things at a glance.

Mick Mastroianni and Mason MastroianniDogs of C Kennel for the 3rd is about the world’s favorite piece of statistical mechanics, entropy. There’s room for quibbling about what exactly we mean by thermodynamics saying all matter is slowly breaking down. But the gist is fair enough. It’s still mysterious, though. To say that the disorder of things is always increasing forces us to think about what we mean by disorder. It’s easy to think we have an idea what we mean by it. It’s hard to make that a completely satisfying definition. In this way it’s much like randomness, which is another idea often treated as the same as disorder.

Bill Amend’s FoxTrot Classics for the 3rd reprinted the comic from the 10th of February, 2006. Mathematics teachers always want to see how you get your answers. Why? … Well, there are different categories of mistakes someone can make. One can set out trying to solve the wrong problem. One can set out trying to solve the right problem in a wrong way. One can set out solving the right problem in the right way and get lost somewhere in the process. Or one can be doing just fine and somewhere along the line change an addition to a subtraction and get what looks like the wrong answer. Each of these is a different kind of mistake. Knowing what kinds of mistakes people make is key to helping them not make these mistakes. They can get on to making more exciting mistakes.

Reading the Comics, December 30, 2016: New Year’s Eve Week Edition


So last week, for schedule reasons, I skipped the Christmas Eve strips and promised to get to them this week. There weren’t any Christmas Eve mathematically-themed comic strips. Figures. This week, I need to skip New Year’s Eve comic strips for similar schedule reasons. If there are any, I’ll talk about them next week.

Lorie Ransom’s The Daily Drawing for the 28th is a geometry wordplay joke for this installment. Two of them, when you read the caption.

John Graziano’s Ripley’s Believe It or Not for the 28th presents the quite believable claim that Professor Dwight Barkley created a formula to estimate how long it takes a child to ask “are we there yet?” I am skeptical the equation given means all that much. But it’s normal mathematician-type behavior to try modelling stuff. That will usually start with thinking of what one wants to represent, and what things about it could be measured, and how one expects these things might affect one another. There’s usually several plausible-sounding models and one has to select the one or ones that seem likely to be interesting. They have to be simple enough to calculate, but still interesting. They need to have consequences that aren’t obvious. And then there’s the challenge of validating the model. Does its description match the thing we’re interested in well enough to be useful? Or at least instructive?

Len Borozinski’s Speechless for the 28th name-drops Albert Einstein and the theory of relativity. Marginal mathematical content, but it’s a slow week.

John Allison’s Bad Machinery for the 29th mentions higher dimensions. More dimensions. In particular it names ‘ana’ and ‘kata’ as “the weird extra dimensions”. Ana and kata are a pair of directions coined by the mathematician Charles Howard Hinton to give us a way of talking about directions in hyperspace. They echo the up/down, left/right, in/out pairs. I don’t know that any mathematicians besides Rudy Rucker actually use these words, though, and that in his science fiction. I may not read enough four-dimensional geometry to know the working lingo. Hinton also coined the “tesseract”, which has escaped from being a mathematician’s specialist term into something normal people might recognize. Mostly because of Madeline L’Engle, I suppose, but that counts.

Samson’s Dark Side of the Horse for the 29th is Dark Side of the Horse‘s entry this essay. It’s a fun bit of play on counting, especially as a way to get to sleep.

John Graziano’s Ripley’s Believe It or Not for the 29th mentions a little numbers and numerals project. Or at least representations of numbers. Finding other orders for numbers can be fun, and it’s a nice little pastime. I don’t know there’s an important point to this sort of project. But it can be fun to accomplish. Beautiful, even.

Mark Anderson’s Andertoons for the 30th relieves us by having a Mark Anderson strip for this essay. And makes for a good Roman numerals gag.

Ryan Pagelow’s Buni for the 30th can be counted as an anthropomorphic-numerals joke. I know it’s more of a “ugh 2016 was the worst year” joke, but it parses either way.

John Atkinson’s Wrong Hands for the 30th is an Albert Einstein joke. It’s cute as it is, though.

Reading the Comics, July 28, 2012


I intend to be back to regular mathematics-based posts soon. I had a fine idea for a couple posts based on Sunday’s closing of the Diaster Transport roller coaster ride at Cedar Point, actually, although I have to technically write them first. (My bride and I made a trip to the park to get a last ride in before its closing, and that lead to inspiration.) But reviews of math-touching comic strips are always good for my readership, if I’m readin the statistics page here right, so let’s see what’s come up since the last recap, going up to the 14th of July.

Continue reading “Reading the Comics, July 28, 2012”