Reading the Comics, March 17, 2018: Pi Day 2018 Edition


So today I am trying out including images for all the mathematically-themed comic strips here. This is because of my discovery that some links even on GoComics.com vanish without warning. I’m curious how long I can keep doing this. Not for legal reasons. Including comics for the purpose of an educational essay about topics raised by the strips is almost the most fair use imaginable. Just because it’s a hassle copying the images and putting them up on WordPress.com and that’s even before I think about how much image space I have there. We’ll see. I might try to figure out a better scheme.

Also in this batch of comics are the various Pi Day strips. There was a healthy number of mathematically-themed comics on the 14th of March. Many of those were just coincidence, though, with no Pi content. I’ll group the Pi Day strips together.

Counselor: 'Come in Funky! What seems to be troubling you?' Funky: 'We're nothing but computer numbers at this school, Mr Fairgood! Nobody cares about us as persons! I'm tired of being just a number! I want a chance to make some of my own decisions!' Counselor: 'Okay! What would you like to be, odd or even?'
Tom Batiuk’s Funky Winkerbean for the 2nd of April, 1972 and rerun the 11th of March, 2018. Maybe I’m just overbalancing for the depression porn that Funky Winkerbean has become, but I find this a funny bordering-on-existential joke.

Tom Batiuk’s Funky Winkerbean for the 2nd of April, 1972 is, I think, the first appearance of Funky Winkerbean around here. Comics Kingdom just started running the strip, as well as Bud Blake’s Tiger and Bill Hoest’s Lockhorns, from the beginning as part of its Vintage Comics roster. And this strip really belonged in Sunday’s essay, but I noticed the vintage comics only after that installment went to press. Anyway, this strip — possibly the first Sunday Funky Winkerbean — plays off a then-contemporary fear of people being reduced to numbers in the face of a computerized society. If you can imagine people ever worrying about something like that. The early 1970s were a time in American society when people first paid attention to the existence of, like, credit reporting agencies. Just what they did and how they did it drew a lot of critical examination. Josh Lauer’s recently published Creditworthy: a History of Consumer Surveillance and Financial Identity in America gets into this.

Bear: 'Can I come in?' Molly: 'Sure.' Bear: 'What happened?' Molly: 'I got an F on my math test.' Bear: 'But you're a genius at math.' Molly: 'I didn't have time to study.' Bear: 'Is it because I distracted you with my troubles yesterday?' Molly: 'No. Well, maybe. Not really. Okay, sure. Yes. I don't know. ARRGHHHH!!!'
Bob Scott’s Bear With Me for the 14th of March, 2018. Every conversation with a high-need, low-self-esteem friend.

Bob Scott’s Bear With Me for the 14th sees Molly struggling with failure on a mathematics test. Could be any subject and the story would go as well, but I suppose mathematics gets a connotation of the subject everybody has to study for, even the geniuses. (The strip used to be called Molly and the Bear. In either name this seems to be the first time I’ve tagged it, although I only started tagging strips by name recently.)

Jeff: 'Next November you and I will have appeared in this comic strip for 45 years!' Mutt: 'Mmm. 45 years! That's 540 months or 2,340 weeks! So, the boss drew us 1,436 times ... one each day of the year! Now, 16,436 until I'm 90 ... ' Jeff: 'What have you been working on?' Mutt: 'Oh, I'm just calculating what we'll be doing during the next 45 years!' (Jeff leaves having clobbered Mutt.) Mutt: 'No! Not this!'
Bud Fisher’s Mutt and Jeff rerun for the 14th of March, 2018. The comic strip ended the 26th of June, 1983 — I remember the announcement of its ending in the (Perth Amboy) News-Tribune, our evening paper, and thinking it seemed illicit that an ancient comic strip like that could end. It was a few months from being 76 years old then.

Bud Fisher’s Mutt and Jeff rerun for the 14th is a rerun from sometime in 1952. I’m tickled by the problem of figuring out how many times Fisher and his uncredited assistants drew Mutt and Jeff. Mutt saying that the boss “drew us 14,436 times” is the number of days in 45 years, so that makes sense if he’s counting the number of strips drawn. The number of times that Mutt and Jeff were drawn is … probably impossible to calculate. There’s so many panels each strip, especially going back to earlier and earlier times. And how many panels don’t have Mutt or don’t have Jeff or don’t have either in them? Jeff didn’t appear in the strip until March of 1908, for example, four months after the comic began. (With a different title, so the comic wasn’t just dangling loose all that while.)

Diagram: Pie Chart, Donut Chart (pie chart with the center missing), Tart Charts (several small pie charts), Shepherd's Pie Chart (multiple-curve plot with different areas colored differently), Tiramisu Chart (multiple-curve plot with all areas colored the same), and Lobster Thermidor Chart (lobster with chunks labelled).
Doug Savage’s Savage Chickens for the 14th of March, 2018. Yeah, William Playfair invented all these too.

Doug Savage’s Savage Chickens for the 14th is a collection of charts. Not all pie charts. And yes, it ran the 14th but avoids the pun it could make. I really like the tart charts, myself.

And now for the Pi Day strips proper.

[PI sces ] Guy at bar talking to Pi: 'Wow, so you were born on March 14th at 1:59, 26 seconds? What're the odds?'
Scott Hilburn’s The Argyle Sweater for the 14th of March, 2018. Also a free probability question, if you’re going to assume that every second of the year is equally likely to be the time of birth.

Scott Hilburn’s The Argyle Sweater for the 14th starts the Pi Day off, of course, with a pun and some extension of what makes 3/14 get its attention. And until Hilburn brought it up I’d never thought about the zodiac sign for someone born the 14th of March, so that’s something.

Pi figure, wearing glasses, reading The Neverending Story.
Mark Parisi’s Off The Mark for the 14th of March, 2018. Really the book seems a little short for that.

Mark Parisi’s Off The Mark for the 14th riffs on one of the interesting features of π, that it’s an irrational number. Well, that its decimal representation goes on forever. Rational numbers do that too, yes, but they all end in the infinite repetition of finitely many digits. And for a lot of them, that digit is ‘0’. Irrational numbers keep going on with more complicated patterns. π sure seems like it’s a normal number. So we could expect that any finite string of digits appears somewhere in its decimal expansion. This would include a string of digits that encodes any story you like, The Neverending Story included. This does not mean we might ever find where that string is.

[ How ancient mathematicians amused themselves, AKA how to celebrate Pi Day today; third annual Pi-Easting Contest. Emcee: 'And HERE he is, our defending champ, that father of conic sections --- ARCHIMEDES!' They're all eating cakes shaped like pi.
Michael Cavna’s Warped for the 14th of March, 2018. Yes, but have you seen Pythagoras and his golden thigh?

Michael Cavna’s Warped for the 14th combines the two major joke threads for Pi Day. Specifically naming Archimedes is a good choice. One of the many things Archimedes is famous for is finding an approximation for π. He’d worked out that π has to be larger than 310/71 but smaller than 3 1/7. Archimedes used an ingenious approach: we might not know the precise area of a circle given only its radius. But we can know the area of a triangle if we know the lengths of its legs. And we can draw a series of triangles that are enclosed by a circle. The area of the circle has to be larger than the sum of the areas of those triangles. We can draw a series of triangles that enclose a circle. The area of the circle has to be less than the sum of the areas of those triangles. If we use a few triangles these bounds are going to be very loose. If we use a lot of triangles these bounds can be tight. In principle, we could make the bounds as close together as we could possibly need. We can see this, now, as a forerunner to calculus. They didn’t see it as such at the time, though. And it’s a demonstration of what amazing results can be found, even without calculus, but with clever specific reasoning. Here’s a run-through of the process.

[ To Stephen Hawking, Thanks for making the Universe a little easier for the rest of us to understand ] Jay: 'I suppose it's only appropriate that he'd go on Pi Day.' Roy: 'Not to mention, Einstein's birthday.' Katherine: 'I'll bet they're off in some far reach of the universe right now playing backgammon.'
John Zakour and Scott Roberts’s Working Daze for the 15th of March, 2018. No, you should never read the comments, but here, really, don’t read the comments.

John Zakour and Scott Roberts’s Working Daze for the 15th is a response to Dr Stephen Hawking’s death. The coincidence that he did die on the 14th of March made for an irresistibly interesting bit of trivia. Zakour and Roberts could get there first, thanks to working on a web comic and being quick on the draw. (I’m curious whether they replaced a strip that was ready to go for the 15th, or whether they normally work one day ahead of publication. It’s an exciting but dangerous way to go.)

Reading the Comics, June 25, 2015: Not Making A Habit Of This Edition


I admit I did this recently, and am doing it again. But I don’t mean to make it a habit. I ran across a few comic strips that I can’t, even with a stretch, call mathematically-themed, but I liked them too much to ignore them either. So they’re at the end of this post. I really don’t intend to make this a regular thing in Reading the Comics posts.

Justin Boyd’s engagingly silly Invisible Bread (June 22) names the tuning “two steps below A”. He dubs this “negative C#”. This is probably an even funnier joke if you know music theory. The repetition of the notes in a musical scale could be used as an example of cyclic or modular arithmetic. Really, that the note above G is A of the next higher octave, and the note below A is G of the next lower octave, probably explains the idea already.

If we felt like, we could match the notes of a scale to the counting numbers. Match A to 0, B to 1, C to 2 and so on. Work out sharps and flats as you like. Then we could think of transposing a note from one key to another as adding or subtracting numbers. (Warning: do not try to pass your music theory class using this information! Transposition of keys is a much more subtle process than I am describing.) If the number gets above some maximum, it wraps back around to 0; if the number would go below zero, it wraps back around to that maximum. Relabeling the things in a group might make them easier or harder to understand. But it doesn’t change the way the things relate to one another. And that’s why we might call something F or negative C#, as we like and as we hope to be understood.

After a blackboard full of work the mathematician must conclude 'the solution is not in this piece of chalk'.
Hilary Price’s Rhymes With Orange for the 23rd of June, 2015.

Hilary Price’s Rhymes With Orange (June 23) reminds us how important it is to pick the correct piece of chalk. The mathematical symbols on the board don’t mean anything. A couple of the odder bits of notation might be meant as shorthand. Often in the rush of working out a problem some of the details will get written as borderline nonsense. The mathematician is probably more interested in getting the insight down. She’ll leave the details for later reflection.

Jason Poland’s Robbie and Bobby (June 23) uses “calculating obscure digits of pi” as computer fun. Calculating digits of pi is hard, at least in decimals, which is all anyone cares about. If you wish to know the 5,673,299,925th decimal digit of pi, you need to work out all 5,673,299,924 digits that go before it. There are formulas to work out a binary (or hexadecimal) digit of pi without working out all the digits that go before. This saves quite some time if you need to explore the nether-realms of pi’s digits.

The comic strip also uses Stephen Hawking as the icon for most-incredibly-smart-person. It’s the role that Albert Einstein used to have, and still shares. I am curious whether Hawking is going to permanently displace Einstein as the go-to reference for incredible brilliance. His pop culture celebrity might be a transient thing. I suspect it’s going to last, though. Hawking’s life has a tortured-genius edge to it that gives it Romantic appeal, likely to stay popular.

Paul Trap’s Thatababy (June 23) presents confusing brand-new letters and numbers. Letters are obviously human inventions though. They’ve been added to and removed from alphabets for thousands of years. It’s only a few centuries since “i” and “j” became (in English) understood as separate letters. They had been seen as different ways of writing the same letter, or the vowel and consonant forms of the same letter. If enough people found a proposed letter useful it would work its way into the alphabet. Occasionally the ampersand & has come near being a letter. (The ampersand has a fascinating history. Honestly.) And conversely, if we collectively found cause to toss one aside we could remove it from the alphabet. English hasn’t lost any letters since yogh (the Old English letter that looks like a 3 written half a line off) was dropped in favor of “gh”, about five centuries ago, but there’s no reason that it couldn’t shed another.

Numbers are less obviously human inventions. But the numbers we use are, or at least work like they are. Arabic numerals are barely eight centuries old in Western European use. Their introduction was controversial. People feared shopkeepers and moneylenders could easily cheat people unfamiliar with these crazy new symbols. Decimals, instead of fractions, were similarly suspect. Negative numbers took centuries to understand and to accept as numbers. Irrational numbers too. Imaginary numbers also. Indeed, look at the connotations of those names: negative numbers. Irrational numbers. Imaginary numbers. We can add complex numbers to that roster. Each name at least sounds suspicious of the innovation.

There are more kinds of numbers. In the 19th century William Rowan Hamilton developed quaternions. These are 4-tuples of numbers that work kind of like complex numbers. They’re strange creatures, admittedly, not very popular these days. Their greatest strength is in representing rotations in three-dimensional space well. There are also octonions, 8-tuples of numbers. They’re more exotic than quaternions and have fewer good uses. We might find more, in time.

Beside an Escher-esque house a woman says, 'The extra dimensions are wonderful, but oy, the property taxes.'
Rina Piccolo’s entry in Six Chix for the 24th of June, 2015.

Rina Piccolo’s entry in Six Chix this week (June 24) draws a house with extra dimensions. An extra dimension is a great way to add volume, or hypervolume, to a place. A cube that’s 20 feet on a side has a volume of 203 or 8,000 cubic feet, after all. A four-dimensional hypercube 20 feet on each side has a hypervolume of 160,000 hybercubic feet. This seems like it should be enough for people who don’t collect books.

Morrie Turner’s Wee Pals (June 24, rerun) is just a bit of wordplay. It’s built on the idea kids might not understand the difference between the words “ratio” and “racial”.

Tom Toles’s Randolph Itch, 2 am (June 25, rerun) inspires me to wonder if anybody’s ever sold novelty 4-D glasses. Probably they have, sometime.


Now for the comics that I just can’t really make mathematics but that I like anyway:

Phil Dunlap’s Ink Pen (June 23, rerun) is aimed at the folks still lingering in grad school. Please be advised that most doctoral theses do not, in fact, end in supervillainy.

Darby Conley’s Get Fuzzy (June 25, rerun) tickles me. But Albert Einstein did after all say many things in his life, and not everything was as punchy as that line about God and dice.

What We Mean By x


[ Oh, wow. Yesterday’s entry had way fewer hits than average. I also put an equation out right up front where everyone could see it. I wonder if this might be a test of Stephen Hawking’s dictum about equations and sales. Or maybe I was just boring yesterday. I’d ask, but apparently, nobody found me interesting enough yesterday to know for comparison. ]

It shouldn’t be too hard to translate the the idea “I want to know the population of Charlotte at some particular time” into a polynomial. The polynomial ought to look something like y equals some pile of numbers times x’s raised to powers, and x somehow has to do with the particular time, and y has something to do with the population. And it’s not hard to do that translating, but I want to talk about some deeper issues. It’s probably better explaining them on the simple problem, where we know what we want things to mean, than it would be explaining them for a complicated problem.

Continue reading “What We Mean By x”