Reading the Comics, March 9, 2018: Some Old Lines Edition


To close out last week’s comics I got a bunch of strips that were repeats, or that touch on topics I’ve discussed quite a bit around these parts already. I’m pretty sure all the words I have here are new in their specific organization. The words themselves are pretty old.

Maria Scrivan’s Half Full for the 4th is the Rubik’s Cube joke for the week. I ought to write up a proper description of the algebra of Rubik’s Cubes. The real stuff is several books’ worth of material, yes. But a couple hundred words about what’s interesting should be doable. … Or I could just ask folks if they’ve read good descriptions of the group theory that cubes show off. I’m always open to learning other people have said stuff better than me. This is part of why I’ve never published an essay about Cantor’s Diagonal Proof; many people have written such essays and I couldn’t add anything useful to that heap of words.

Partly scrambled Rubik's Cube to a solved one: 'Rough week.'
Maria Scrivan’s Half Full for the 4th of June, 2018. Yeah, uh, it me.

Ryan North’s Dinosaur Comics for the 5th is about the heap paradox. Or the sorites paradox, depending on what book you’ve been reading from. The problem is straightforward enough. As God, in the strip says, a big pile of sand is clearly a heap. One or two grains of sand is clearly not. If you remove grains from the heap, eventually, you lose the heap-ness. T-Rex suggests solving the question of when that happens by statistical survey, finding what people on average find to be the range where things shift over.

God: 'T-Rex let's say you have a giant heap of sand and I remove one grain of it at a time.' T-Rex: 'Ooh, let's!' God: 'Clearly when there's only one grain of sand left it's not a heap anymore!' T-Rex: 'Clearly!' God: 'Aha my friend but when precisely did it switch from heap to non-heap?' T-Rex: 'I dunno! At some fuzzy point if would switch for most observers from 'heap' to, say, 'small pine', and there we can draw the line. Language isn't that precise.' God: 'Listen this is a classic paradox of Eubulides of Miletus came up with over 2000 years ago. You need to have your mind blown now okay.' T-Rex: 'Sounds kinda dumb to me!' Utahraptor: 'What does?' T-Rex: 'The point at which a shrinking heap of sand becomes a non-heap. Clearly I'm supposed to struggle with an arbitrary threshold, because piles on either side of it look much the same. But it's just language! Look at statistical usage of the word 'heap', decide using that average, end of story. Oh, snap, philosophers! Did T-Rex just totally school you with his statistically-based descriptivist approach to semantics? IT APPEARS THAT HE TOTALLY DID! It also appears he's speaking in the third person because he's so impressed with his awesome self!'
Ryan North’s Dinosaur Comics for the 5th of June, 2018. I get that part of the setup of these comics is that T-Rex is nerdy-smart, but I can also imagine the philosophers rolling their eyes at how he’s missed the point. Maybe if he were asked about the density of a single molecule of water he’d understand better why the question can’t be obvious. (And T-Rex does sometimes revisit issues with deeper understanding of the issues. This might have happened between when this strip first appeared on qwantz.com and when it appeared on GoComics.com.

As with many attempts to apply statistical, or experimental, methods to philosophical questions it misses the point. There are properties that things seem to have only as aggregations. Where do they come from? How can there be something true about a collection of things that isn’t true about any part of the thing? This is not just about messy real-world properties either; we can say stuff about groups of mathematical objects that aren’t true about individual objects within the set. For example, suppose we want to draw a real number at random, uniformly, from the continuous interval 0 to 10. There’s a 50% chance we’ll draw a number greater than 5. The chance of drawing any specific number greater than 5, though, is zero. But we can always draw one. Something weird is happening here, as often happens with questions we’ve been trying to answer for thousands of years.

Customer: 'How much will this be at 80% off?' Clerk: 'Ten bucks.' Customer: 'How did you do that in your head so fast?' Clerk: '20% of fifty is ten.' Customer: 'Wow! So you're some kind of super math genius?' Customer: 'Sure.'
Norm Feuti’s Retail for the 6th of June, 2018. This joke, though not this strip, was also run the 26th of June, 2017. There I share my one great retail-mathematics anecdote.

Norm Feuti’s Retail for the 6th is a new strip, although the joke’s appeared before. There’s some arithmetic calculations that are easy to do, or that become easy because you do them a lot. Or because you see them done a lot and learn what the patterns are. A handful of basic tricks — like that 80 percent off is 20 percent of something, or that 20 percent of a thing is one-fifth the original thing — can be stunning. Stage magicians find the same effect.

Rita: 'Tell your group I expect them to give me 110%! Keep in mind, reviews are coming!' Jay: 'Rita --- you should realize that it's impossible to give more than 100%!' Rita: 'No --- not with that kind of attitude!'
John Zakour and Scott Roberts’s Working Daze for the 6th of June, 2018. It ran the 22nd of October, 2014, although that was as part of a “Best Of” week. No idea when it originally ran.

John Zakour and Scott Roberts’s Working Daze for the 6th is another chance for me to talk about the supposed folly of giving 110 percent. Or point you to where I did already. I’m forgiving of the use of the phrase.

Abacus at the bar: 'If you ever find yourself working for Weinstein as a bookkeeper, let me offer you sum advice ... never use the phrase, 'Harvey, you can count on me'.' Hostess: 'Thanks for the tip.'
Bob Shannon’s Tough Town for the 7th of June, 2018. The strip is one about all sorts of odd creatures hanging out in the bar, so, you’re not misunderstanding this.

Bob Shannon’s Tough Town for the 7th is the anthropomorphized abacus joke of the week. Been a while since we had one of those. I suppose an adding machine would be at least as good a representative of the abstract concept of doing arithmetic, but it’s likely harder to draw too. This is just tiring to draw.

Cave-person Father: 'Me have method for knowing how many rocks you have. Called 'counting'. Put up fingers, then say --- ' Cave-person Kid: 'We ever use this in REAL LIFE?' Caption: The First Math Class.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th of June, 2018. Admit I do wonder how often cave people needed to track the number of rocks they had. I mean, how often do we need to count our rocks? Aren’t the rocks themselves an adequate representation of the number of rocks around?

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th presents the old complaint about mathematics’s utility, here in an ancient setting. I’m intereste that the caveman presents counting in terms of matching up other things to his fingers. We use this matching of one set of things to another even today. It gets us to ordinal and cardinal numbers, and the to what we feel pretty sure about with infinitely large sets. An idea can be ancient and basic and still be vital.

Karen: 'Uuuhhhhggghh!!! I hate math!!!' Dad: 'First of all, don't say 'hate'. It's a very strong word. Secondly, you will always need math. Even if you're in sales like me. In fact, I'm using math right now. I'm figuring out where I stand against my quota for this quarter. Observe ... I take this number, add it to that one. Take a percentage of this value and subtract it here. See, that's my number ... ... ... I hate math.'
Steve Sicula’s Home and Away rerun for the 9th of June, 2018. The strip originally ran the 6th of March, 2011. … How does Karen there say “Uuuhhhggghh”?

Steve Sicula’s Home and Away for the 9th is about the hatred people profess for mathematics. Some of that is more hatred of how it’s taught, which is too often as a complicated and apparently pointless activity. Some of that is hatred of how it’s used, since it turns up in a lot of jobs. And for some reason we’ve designed society so that we do jobs we don’t like. I don’t know why we think that’s a good idea. We should work on that.

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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.

Reading the Comics, March 27, 2017: Not The March 26 Edition


My guide for how many comics to include in one of these essays is “at least five, if possible”. Occasionally there’s a day when Comic Strip Master Command sends that many strips at once. Last Sunday was almost but not quite such a day. But the business of that day did mean I had enough strips to again divide the past week’s entries. Look for more comics in a few days, if all goes well here. Thank you.

Mark Anderson’s Andertoons for the 26th reminds me of something I had wholly forgot about: decimals inside fractions. And now that this little horror’s brought back I remember my experience with it. Decimals in fractions aren’t, in meaning, any different from division of decimal numbers. And the decimals are easily enough removed. But I get the kid’s horror. Fractions and decimals are both interesting in the way they represent portions of wholes. They spend so much time standing independently of one another it feels disturbing to have them interact. Well, Andertoons kid, maybe this will comfort you: somewhere along the lines decimals in fractions just stop happening. I’m not sure when. I don’t remember when the last one passed my experience.

Hector Cantu and Carlos Castellanos’s Baldo for the 26th is built on a riddle. It’s one that depends on working in shifting addition from “what everybody means by addition” to “what addition means on a clock”. You can argue — I’m sure Gracie would — that “11 plus 3” does not mean “eleven o’clock plus three hours”. But on what grounds? If it’s eleven o’clock and you know something will happen in three hours, “two o’clock” is exactly what you want. Underlying all of mathematics are definitions about what we mean by stuff like “eleven” and “plus” and “equals”. And underlying the definitions is the idea that “here is a thing we should like to know”.

Addition of hours on a clock face — I never see it done with minutes or seconds — is often used as an introduction to modulo arithmetic. This is arithmetic on a subset of the whole numbers. For example, we might use 0, 1, 2, and 3. Addition starts out working the way it does in normal numbers. But then 1 + 3 we define to be 0. 2 + 3 is 1. 3 + 3 is 2. 2 + 2 is 0. 2 + 3 is 1 again. And so on. We get subtraction the same way. This sort of modulo arithmetic has practical uses. Many cryptography schemes rely on it, for example. And it has pedagogical uses; modulo arithmetic turns up all over a mathematics major’s Introduction to Not That Kind Of Algebra Course. You can use it to learn a lot of group theory with something a little less exotic than rotations and symmetries of polygonal shapes or permutations of lists of items. A clock face doesn’t quite do it, though. We have to pretend the ’12’ at the top is a ‘0’. I’ve grown more skeptical about whether appealing to clocks is useful in introducing modulo arithmetic. But it’s been a while since I’ve needed to discuss the matter at all.

Rob Harrell’s Big Top rerun for the 26th mentions sudoku. Remember when sudoku was threatening to take over the world, or at least the comics page? Also, remember comics pages? Good times. It’s not one of my hobbies, but I get the appeal.

Bob Shannon’s Tough Town I’m not sure if I’ve featured here before. It’s one of those high concept comics. The patrons at a bar are just what you see on the label, and there’s a lot of punning involved. Now that I’ve over-explained the joke please enjoy the joke. There are a couple of strips prior to this one featuring the same characters; they just somehow didn’t mention enough mathematics words for me to bring up here.

Overhearing customers: 'Kids today can't even do basic math. If the computer doesn't tell them how much change to give you, they don't know what to do.' Customer asking: 'How much is 50% off of $49.99 ? Does that mean it's free?' Clerk: Sigh.
Norm Feuti’s Retail for the 27th of March, 2017. Of course customers aren’t generally good at arithmetic either. I’m reminded (once more) of when I worked at Walden Books and a customer wanted to know whether the sticker-promised 10 percent discount on the book was applied to the price before or after the 6 percent sales tax was added to it, or whether it was applied afterwards. I could not speak to the cash register’s programming, but I could promise that the process would come to the same number either way, and I told him what it would be. I think the book had a $14.95 cover price — let’s stipulate it was for the sake of my anecdote — so it would come to $14.26 in the end. He judged me suspiciously and then allowed me to ring it up; the register made it out to be $15.22 and he pounced, saying, see?. Yes: he had somehow found the one freaking book in the store where the UPC bar code price, $15.95, was different from the thing listed as the cover price. I told him why it was and showed him where in the UPC to find the encoded price (it’s in the last stanza of digits underneath the bars) but he was having none of it, even when I manually corrected the error.

Norm Feuti’s Retail for the 27th is about the great concern-troll of mathematics education: can our cashiers make change? I’m being snottily dismissive. Shops, banks, accountants, and tax registries are surely the most common users of mathematics — at least arithmetic — out there. And if people are going to do a thing, ordinarily, they ought to be able to do it well. But, of course, the computer does arithmetic extremely well. Far better, or at least more indefatigably, than any cashier is going to be able to do. The computer will also keep track of the prices of everything, and any applicable sales or discounts, more reliably than the mere human will. The whole point of the Industrial Revolution was to divide tasks up and assign them to parties that could do the separate parts better. Why get worked up about whether you imagine the cashier knows what $22.14 minus $16.89 is?

I will say the time the bookstore where I worked lost power all afternoon and we had to do all the transactions manually we ended up with only a one-cent discrepancy in the till, thank you.