Reading the Comics, July 27, 2019: July 27, 2019 Edition


Last week was busy enough in mathematically themed comic strips. Some of these are pretty slight topics. But including them lets me do one of my favorite things, to have an essay that’s all comics from a single day. It’s my blog, I can use it to amuse myself.

Marcus Hamilton and Ron Ferdinand’s Dennis the Menace for the 27th shows the kind of slightness I’m dealing with. ‘Statistic’ has some nasty connotations in this sense. It suggests something dehumanizing has happened. But the word was maybe doomed to that. The word came about in the 18th century, to describe the systematic collection and study of information about whole populations. They started out being the gathering of information about the state.

Dennis, walking in to his parents: 'Mr Wilson told me not to become a 'statistic'. What church do they go to?'
Marcus Hamilton and Ron Ferdinand’s Dennis the Menace for the 27th of July, 2019. I have a few essays mentioning Dennis the Menace at this link.

But gathering information about a whole state implies, first, that the thing one finds interesting about a people are some measured and recorded aspect. Not the whole of their person-hood. Second, it implies that you wish to approximate the diversity of a whole people with some smaller set of numbers. There’s compelling reasons for a state to want to have statistics. They make it more plausible to know what the state can do. They make it plausible to forecast the results of a policy. Ideally, this encourages wisdom in policy-making. If the tools are used well.

Val, at the store: 'I admit, change is hard. Nobody really *likes* change. But we all have to know how to deal with it.' Cashier, fumbling over work: 'But they didn't *teach* us this in math class.'
Jan Eliot’s Stone Soup Classics for the 27th of July, 2019. The comic originally ran the 18th of September, 1999. Stone Soup has joined those comic strips which are offer only new material on Sundays. However, GoComics offers both the current-syndication-offering and reprints of the strip from its beginning, this “Classics” run. Essays mentioning either current Stone Strip comics or their twenty-year-old reprints are at this link. Or at least they will be: it turns out this is a new tag. I would have sworn I’d discussed this comic before.

Jan Eliot’s Stone Soup Classics for the 27th is the slightest of the comic strips I’m featuring this week. Really it should have been just a mention, but I wanted to have at least three comics shown for today’s essay. Making and counting change is constantly held up as the supreme purpose of teaching arithmetic. This though most any shop has a cash register that will calculate change faster and more accurately than even someone skilled in arithmetic will. I understand the crankiness of people who give the cashier $15.13 for their $12.38 bill, and get the thirteen cents handed back to them before it’s rung up. It’s not evidence that civilization is collapsing. It’s loose change.

Thatababay drawing on figures: Circular. A circle with an ice skater drifting inside it. Rectangular: soccer player kicking a ball to a net at the right edge of the field. Triangular: frame and figure drawn underneath so it's a person hang-gliding. Tubular: skateboarder on top.
Paul Trap’s Thatababy for the 27th of July, 2019. This is another of those comics that wants to be the next Andertoons. Essays featuring Thatababy in their discussion are here.

Paul Trap’s Thatababy for the 27th continues the strip’s thread of turning geometry figures into jokes. This one is less useful than the comic featured Tuesday, which might help one remember what a scalene triangle or a rhombus looks like. Still might be fun.


And with that, last week’s mathematically-themed comic strips are fully discussed. This week’s comics will get discussion at an essay linked from here. Please visit soon and we’ll see what I have to say, and about what.

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Reading the Comics, May 4, 2019: Wednesday Looks A Lot Like Tuesday Edition


I didn’t get this published on Tuesday, owing to circumstances beyond my control, such as my not writing it Monday. I have hopes of catching up on all the writing I want to do. Someday, I might.

Marcus Hamilton and Scott Ketcham’s Dennis the Menace for the 2nd hardly seems like Dennis lives up to his “Menace” title. It seems more like he’s discovered wordplay. This is usually no worse than “mildly annoying”. Joey seems alarmed, but I must tell you, reader, he’s easily alarmed. But I think there is some depth here.

Dennis, sitting beside some papers and crayons and his friend: 'When it comes to numbers, Joey ... there's always *one more*.'
Marcus Hamilton and Scott Ketcham’s Dennis the Menace for the 2nd of May, 2019. This is twice in three months that this venerable comic’s made an appearance here. Who saw that coming? This and past appearances of Dennis the Menace are at this link. Future appearances should be, too, if they happen.

One is that, as we’ve thought of counting numbers, there is always “one more”. This doesn’t have to be. We could work with perfectly good number systems that have a largest number. We do, in fact. Every computer programming language has some largest integer that it will deal with. If you need a larger number, you have to do something clever. Your clever idea will let you address some range of bigger numbers, but it too will have a maximum. We’ve set those limits large enough that, usually, they’re not an inconvenience. They’re still there.

But those limits are forced on us by the many failings of matter. What when we get just past Plato’s line’s division, into the reasoning of pure mathematics? There we can set up counting numbers. The standard way to do this is to suppose there is a number “1”. And to suppose that, for any counting number we have, there is a successor, a number one-plus-that. If Joey were to ask why there has to be, all Dennis could do is shrug. This makes an axiom out of there always being one more. If you don’t like it, make some other arithmetic. Anyway we only understand any of this using fallible matter, so good luck.

This progression can be heady, though. The counting numbers are probably the most understandable infinitely large set there is. Thinking about them seriously can induce the sort of dizzy awe that pondering Deep Time or the vastness of space can do. That seems a bit above Dennis’s age level, but some people are stricken with the infinite sooner than others are.

Charlie Brown: 'You think I'm dumb, don't you? Well, ask me a question! Ask me anything!' Patty: 'All right, how much is two and two?' Charlie Brown: 'Hmmm ... Why don't you ask me something more practical?'
Charles Schulz’s Peanuts Begins rerun for the 2nd of May, 2019. The strip originally ran the 23rd of March, 1951. When I have reason to discuss Peanuts, either the current-newspaper-reruns or these early-50s reruns, the essays should appear here.

Charles Schulz’s Peanuts Begins rerun for the 2nd has Charlie Brown dismiss arithmetic as impractical. It fits the motif of mathematics as an unworldly subject. There’s the common joke that pure mathematics even dreams of being of no use to anyone. Arithmetic, though, has always been a practical subject. It introduces us to many abstract ideas, particularly group theory. This subject looks at what we can do with systems that work like arithmetic without necessarily having numbers, or anything that works with numbers.

Venn diagram labelled 'Caffeine Routine'. One circle, beside a cup of coffee, is labelled 'me'. The second circle, beside a travel mug of coffee, is labelled 'also me'. The intersection is labelled 'too much coffee'.
John Atkinson’s Wrong Hands for the 3rd of May, 2019. Other essays featuring by Wrong Hands are at this link.

John Atkinson’s Wrong Hands for the 3rd is the Venn Diagram joke for the week. I’m not sure the logic of the joke quite holds up, but it’s funny at a glance and that’s as much as it needs to do.

Several geometric figures lay on the beach. A triangle, wearing sunglasses, says to an un-worn hat and pair of glasses beside it: 'Ahh, this is the life, eh, Vera? ... Vera?' Caption: 'Bermuda Triangles'.
Scott Hilburn’s The Argyle Sweater for the 4th of May, 2019. The many essays discussing The Argyle Sweater appear at this link.

Scott Hilburn’s The Argyle Sweater for the 4th is the anthropomorphic geometric figures joke for the week.


And a couple of comic strips mentioned mathematics, although in too slight a way to discuss. Dana Simpson’s Phoebe and her Unicorn on the 30th of April started a sequence in which doodles on Phoebe’s homework came to life. That it’s mathematics homework was mostly incidental. I’m open to the argument that mathematics encourages doodling in a way that, say, spelling does not. I’d also be open to the argument you aren’t doing geometry if you don’t doodle. Anyway. Dan Thompson’s Brevity for the 2nd of May features Sesame Street’s Count von Count. It’s a bit of wordplay on the use of “numbers” for songs. And, of course, the folkloric tradition of vampires as compulsive counters.


With that, I’m temporarily caught up on my comics. I’m falling behind almost every week, though. Come Sunday, the next essay should appear here.

Reading the Comics, March 2, 2019: Process Edition


There were a handful of comic strips from last week which I didn’t already discuss. Two of them inspire me to write about how we know how to do things. That makes a good theme.

Marcus Hamilton and Scott Ketcham’s Dennis the Menace for the 27th gets into deep territory. How does we could count to a million? Maybe some determined soul has actually done it. But it would take the better part of a month. Things improve some if we allow that anything a computing machine can do, a person could do. This seems reasonable enough. It’s heady to imagine that all the computing done to support, say, a game of Roller Coaster Tycoon could be done by one person working alone with a sheet of paper. Anyway, a computer could show counting up to a million, a billion, a trillion, although then we start asking whether anyone’s checked that it hasn’t skipped some numbers. (Don’t laugh. The New York Times print edition includes an issue number, today at 58,258, at the top of the front page. It’s meant to list the number of published daily editions since the paper started. They mis-counted once, in 1898, and nobody noticed until 1999.)

Dennis, to Margaret: 'How do you know you can count to a million if you've never done it?'
Marcus Hamilton and Scott Ketcham’s Dennis the Menace for the 27th of February, 2019. I’m not quite confident that I have the credits right here, but if I am parsing Wikipedia’s entry correctly Hamilton and Ketcham work on the daily comics and Ron Ferdinand and Ketcham work on the Sunday strips. And I would have thought this was a new tag but it turns out I have several Dennis the Menace-based essays at this link.

Anyway, allow that. Nobody doubts that, if we put enough time and effort into it, we could count up to any positive whole number, or as they say in the trade, “counting number”. But … there is some largest number that we could possibly count to, even if we put every possible resource and all the time left in the universe to that counting. So how do we know we “could” count to a number bigger than that? What does it mean to say we “could” if the circumstances of the universe are such that we literally could not?

Counting up to a number seems uncontroversial enough. If I wanted to prove it I’d say something like “if we can count to the whole number with value N, then we can count to the whole number with value N + 1 by … going one higher.” And “We can count to the whole number 1”, proving that by enunciating as clearly as I can. The induction follows. Fine enough. That’s a nice little induction proof.

But … what if we needed to do more work? What if we needed to do a lot of work? There is a corner of logic which considers infinitely long proofs, or infinitely long statements. They’re not part of the usual deductive logic that any mathematician knows and relies on. We’re used to, at least in principle, being able to go through and check every step of a proof. If that becomes impossible is that still a proof? It’s not my field, so I feel comfortable not saying what’s right and what’s wrong. But it is one of those lectures in your Mathematical Logic course that leaves you hanging your jaw open.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 27th is a joke about algorithms. These are the processes by which we know how to do a thing. Here, Hansel and Gretel are shown using what’s termed a “greedy algorithm” to follow pebbles back home. This kind of thing reflects trying to find an acceptable solution, in this case, finding a path somewhere. What makes it “greedy” is each step. You’re at a pebble. You can see other pebbles nearby. Which one do you go to? Go to some extreme one; in this case, the nearest. It could instead have been the biggest, or the shiniest, the one at the greatest altitude, the one nearest a water source. Doesn’t matter. You choose your summum bonum and, at each step, take the move that maximizes that.

During the great famine, Hansel and Gretel's mother decided to leave them in the woods. Overhearing the conversation, Hansel had an idea. `I will take these bright pebbles and leave them along our path, then we can follow them home.` Little did they know, their mother overheard *their* conversation. That night she created loops of shiny pebbles at various points in the woods. The following evening she left them in the forest. Gretel: `Just always go to the nearest pebble, keep doing that until you are home.` On the path they encountered a loop which caused them to go in an endless cycle until they passed out from exhaustion. The moral of this story? There are arts far darker than witchcraft. (Shows the wicked stepmother reading Introduction to Algorithms.)
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 27th of February, 2019. There’s no mistaking this for a new tag. Saturday Morning Breakfast Cereal inspires many discussions at this link.

The wicked mother knows something about this sort of algorithm, one that promises merely a solution and not the best solution. And that is that all these solutions can be broken. You can set up a problem that the algorithm can’t solve. Greedy algorithms are particularly vulnerable to this. They’re called “local maximums”. You find the best answer of the ones nearby, but not the best one you possibly could locate.

Why use an algorithm like this, that can be broken so? That’s because we often want to do problems like finding a path through the woods. There are so many possible paths that it’s hard to find one of the acceptable ones. But there are processes that will, typically, find an acceptable answer. Maybe processes that will let us take an acceptable answer and improve it to a good answer. And this is getting into my field.

Actual persons encountering one of these pebble rings would (probably) notice they were caught in a loop. And what they’d do, then, is suspend the greedy rule: instead of going to the nearest pebble they could find, they’d pick something else. Maybe simply the nearest pebble they hadn’t recently visited. Maybe the second-nearest pebble. Maybe they’d give up and strike out in a random direction, trusting they’ll find some more pebbles. This can lead them out of the local maximum they don’t want toward the “global maximum”, the path home, that they do. There’s no reason they can’t get trapped again — this is why the wicked mother made many loops — and no reason they might not get caught in a loop of loops again. Every algorithm like this can get broken by some problem, after all. But sometimes taking the not-the-best steps can lead you to a better solution. That’s the insight at the heart of “Metropolis-Hastings” algorithms, which was my field before I just read comic strips all the time.

Father Figure Eight. A big 8, wearing ice skates and holding a tiny 8's hand, says, 'Son, I'll show you how to skate in the shape of a right-side-up infinity symbol!'
Dan Thompson’s Brevity for the 28th of February, 2019. This is another strip that’s inspired a host of essays. Brevity panels get shown off at this link.

Dan Thompson’s Brevity for the 28th is a nice simple anthropomorphic figures joke. It would’ve been a good match for the strips I talked about Sunday. I’m just normally reluctant to sort these comic strips other than by publication date.


And there were some comic strips I didn’t think worth making paragraphs about. Chris Giarrusso’s G-Man Webcomics for the 25th of February mentioned negative numbers and built a joke on the … negative … connotations of that word. (And inaugurates a tag for that comic strip. This fact will certainly come back to baffle me some later day.) Art Sansom and Chip Sansom’s The Born Loser for the 2nd of March has a bad mathematics report card. Tony Rubino and Gary Markstein’s Daddy’s Home for the 2nd has geometry be the subject parents don’t understand. Bill Amend’s FoxTrot Classics for the 2nd has a mathematics-anxiety dream.


And this closes out my mathematics comics for the week. Come Sunday I should have a fresh post with more comics, and I thank you for considering reading that.

Reading the Comics, September 17, 2018: Hard To Credit Edition


Two of the four comic strips I mean to feature here have credits that feel unsatisfying to me. One of them is someone’s pseudonym and, yeah, that’s their business. One is Dennis the Menace, for which I find an in-strip signature that doesn’t match the credentials on Comics Kingdom’s web site, never mind Wikipedia. I’ll go with what’s signed in the comic as probably authoritative. But I don’t like it.

R Ferdinand and S Ketcham’s Dennis the Menace for the 16th is about calculation. One eternally surprising little thing about calculators and computers is that they don’t do anything you can’t do by hand. Or, for that matter, in your head. They do it faster, typically, and more reliably. They can seem magical. But the only difference between what they do and what we do is the quantity with which they do this work. You can take this as humbling or as inspirational, as fits your worldview.

Dad: 'The battery in my calculator is dead!' Dennis: 'Here! Use my chalkboard!' Dad: 'Uhhh ... thanks, but ... ' Denis: 'There's no batteries, so you can always COUNT on it! Well! Go ahead, Dad!' Dad: 'Okay! Okay! .. Let's see here ... just a give me a minute ... and carry the one ... ' (Dennis looks at the reader.)
R Ferdinand and S Ketcham’s Dennis the Menace for the 16th of September, 2018. I know it’s a standard bit of Dennis the Menace snarking to rate Dennis’s actual menacing nature. But forcing his father to show that he’s lost his proficiency at arithmetic in the guise of helping him? … It’s kind of a long-game bit of menace, I suppose.

Ham’s Life on Earth for the 16th is a joke about the magical powers we attribute to mathematics. It’s also built on one of our underlying assumptions of the world, that it must be logically consistent. If one has an irrefutable logical argument that something isn’t so, then that thing must not be so. It’s hard to imagine how an illogical world would work. But it is hard not to wonder if there’s some arrogance involved in supposing the world has to square with the rules of logic that we find sensible. And to wonder whether we perceive world consistent with that logic because our expectations frame what we’re able to perceive.

Man at chalkboard writing out the 'Mathematical Proof That I Don't Exist'. As he finishes it, he disappears.
Ham’s Life on Earth for the 16th of September, 2018. Raise your hand if you’ve been there. Hah! You’re fibbing.

In any case, as we frame logic, an argument’s validity shouldn’t depend on the person making the argument. Or even whether the argument has been made. So it’s hard to see how simply voicing the argument that one doesn’t exist could have that effect. Except that mathematics has got magical connotations, and vice-versa. That’ll be good for building jokes for a while yet.

Wavehead responding to the blackboard question 36 / 6: 'It's not that I can't divide that, but I've always fancied myself more of a uniter.'
Mark Anderson’s Andertoons for the 17th of September, 2018. So is this a substitute or does Wavehead just have a new mathematics teacher?

Mark Anderson’s Andertoons for the 17th is the Mark Anderson’s Andertoons for the week. It’s wordplay, built on the connotation that division is a bad thing. It seems less dire if we think of division as learning how to equally share something that’s been held in common, though. Or if we think of it as learning what to multiply a thing by to get a particular value. Most mathematical operations can be taken to mean many things. Surely division has some constructive and happy interpretations.

Poncho, the dog, looking over his owner's laptop: 'They say if you let an infinite number of cats walk on an infinite number of keyboards, they'll eventually type all the great works of Shakespeare.' The cat walks across the laptop, connecting to their owner's bank site and entering the correct password. Poncho: 'I'll take it.'
Paul Gilligan’s Pooch Cafe for the 17th of September, 2018. For my money the cat hasn’t walked across the keyboard right if it hasn’t got you Freakazoid powers.

Paul Gilligan’s Pooch Cafe for the 17th is a variation of the monkeys-on-keyboards joke. If what you need is a string of nonsense characters then … well, a cat on the keys is at least famous for producing some gibberish. It’s likely not going to be truly random, though. If a cat’s paw has stepped on, say, the ‘O’, there’s a good chance the cat is also stepping on ‘P’ or ‘9’. It also suggests that if the cat starts from the right, they’re more likely to have a character like ‘O’ early in the string of characters and less likely at the end. A completely random string would be as likely to have an ‘O’ at the start as at the end of the string.

And even if a cat on the keyboard did produce good-quality randomness, well. How likely a randomly-generated string of characters is to match a thing depends on the length of the thing. If the meaning of the symbols doesn’t matter, then ‘Penny Lane’ is as good as ‘*2ft,2igFIt’. This is not to say you can just use, say, ‘asdfghjkl’ as your password, at least not for anything that would hurt you if it were cracked. If everyone picked all passwords with no regard for what the symbols meant, these would be. But passwords that seem easy to think get used more often than they should be. It’s not that they’re easier to guess, but that guessing them is more likely to be correct.


Later this week I’ll host this month’s Playful Mathematics Blog Carnival! If you know of any mathematics that teaches or delights or both please share it with me, and we’ll let the world know. Also this week I should finally start my 2018 Mathematics A To Z, explaining words from mathematics one at a time.

And there’ll be another Reading the Comics Post before next Sunday. It and all my other Reading the Comics posts should be at this tag. Other appearances of Dennis the Menace should be at this link. This and other essays mentioning Life On Earth are at this link. The many appearances of Andertoons are at this link And other essays with Pooch Cafe should be at this link. Thanks for reading along.

Reading the Comics, September 8, 2017: First Split Week Edition, Part 1


It was looking like another slow week for something so early in the (United States) school year. Then Comic Strip Master Commend sent a flood of strips in for Friday and Saturday, so I’m splitting the load. It’s not a heavy one, as back-to-school jokes are on people’s minds. But here goes.

Marcus Hamilton and Scott Ketcham’s Dennis the Menace for the 3rd of September, 2017 is a fair strip for this early in the school year. It’s an old joke about making subtraction understandable.

Dennis's Mom: 'How was school today?' Dennis: 'Not great. We just learned how to add and they're expecting us to subtract!' Mom: 'Let me see if I can help. If you have five pieces of candy, and you give Margaret there pieces of candy, what do you have?' Dennis: 'TEMPORARY INSANITY!!'
Marcus Hamilton and Scott Ketcham’s Dennis the Menace for the 3rd of September, 2017. The joke pretty well explains itself, but I would like to point out the great use of color for highlighting here. The different shades are done in a way very consistent with the mid-century stylings of the characters, but are subtler than could have been done when Hank Ketcham started the comic in the 1950s. For that matter, it’s subtler than could have been printed until quite recently in the newspaper industry. It’s worth noticing.

Mark Anderson’s Andertoons for the 3rd is the Mark Anderson installment for this week, so I’m glad to have that. It’s a good old classic cranky-students setup and it reminds me that “unlike fractions” is a thing. I’m not quibbling with the term, especially not after the whole long-division mess a couple weeks back. I just hadn’t thought in a long while about how different denominators do make adding fractions harder.

Jeff Harris’s Shortcuts informational feature for the 3rd I couldn’t remember why I put on the list of mathematically-themed comic strips. The reason’s in there. There’s a Pi Joke. But my interest was more in learning that strawberries are a hybrid created in France from a North American and a Chilean breed. Isn’t that intriguing stuff?

Mom-type showing a flashcard, '5 x 7 = ?', to two kids. Boy: 'Isn't there an app for this sort of thing?'
Bill Abbott’s Specktickles for the 8th of September, 2017. I confess that I don’t know whether this comic is running in any newspapers. But I could find it easily enough so that’s why I read it and look for panels that touch on mathematics topics.

Bill Abbott’s Specktickles for the 8th uses arithmetic — multiplication flash cards — as emblem of stuff to study. About all I can say for that.