Here’s an assortment of 35 cartoons I’ve posted to Twitter and Facebook in the last year. Hope you enjoy!

**Which Ratio is Truly Golden?**

I find it troubling that the golden ratio has so little in common with the golden rule.

Like, if you did unto others 1.618 times what you’d have them do unto you, then we’d all wind up exhausted.

And if you’re only doing 1/1.618 times unto them, then isn’t that a bit lazy?

**A Puzzle About Rates**

I’ve always enjoyed those puzzles like, “If 3 chickens can lay 3 eggs in 3 days, then how long will it take 100 chickens to lay 100 eggs?” They’re counter-intuitive (e.g., in my example, each chicken lays 1 egg per 3 days, so the answer is also 3 days), yet deal only with simple constant rates.

So what if the rates weren’t constant? Like in, say, a bureaucracy, where 20 times more people will accomplish only 1/20th as much?

(Sorry for putting the answer upside down. It reads: “Please complete the attached form (Z302: Aggregate Task Completion Rate Information Request) and we’ll process your inquiry in 4-6 weeks.”)

In this case, “a mathematician” refers specifically to Matt Parker, whose excellent book Humble Pi discusses the first two of these mistakes.

**The Asymptote of Happiness**

Lots of poets have found asymptotes a convenient literary symbol – the idea of eternal striving is a resonant one (even beyond the eternal striving of the struggling algebra student).

I love me some Raymond Smullyan.

Sorry again for putting the answer upside down. I dunno why I thought that was a clever idea. Mostly just forces you to turn off the auto-rotate setting on your phone.

Anyway, it reads: “Ask anything. You should already know not to buy lowfat yogurt.”)

**Proving a New Theorem**

Not that I’ve ever felt this myself. I’m just speculating.

**P-R-E-N-A-T-A-L**

What is parenting, if not a neat LARP?

(LARP = Live-Action Role-Playing Game, for those of you with less geeky acumen than I anticipate my audience to have.)

By the way, my friend Rayleen once described to me a brilliant comic, where one person asks, “When’s the baby due?” and the other person is drawn with a small horizontal stick figure emerging from their stick torso. (See? It’s such a good comic, I can just *describe* it.)

**The Sales Pitch for Math**

I think a lot about the different arguments for math, and the ways that they support or contradict each other. Is it a beautiful art? An urgent set of universal civic skills? Key preparation for technical professions?

The answer is yes to all three. But not for all math, and not all at once – and attempting to blend the purposes can lead to a muddle.

**The Meaning of “Let”**

It’s always tickled me that the mathematician’s verb “let,” which sounds so chill and laissez-faire, is actually a binding command.

**“All Happy Families Are Alike;**

Every Unhappy Family is Unhappy In Its Own Way”

Every Unhappy Family is Unhappy In Its Own Way”

I wrote a bunch of these a few years ago. This one has the benefit of being true: all circles are geometrically similar, but not all ellipses are.

(The same is true, by the way, of parabolas and hyperbolas. The former are all the same basic shape, just zoomed in or zoomed out, whereas the latter constitute a whole family of different shapes.)

(Chew on that, Tolstoy.)

**The Court-Appointed Translator**

I wrote this little dialogue after listening to a great episode of The Allusionist, before it turned out that *Game of Thrones* would suffer the worst collapse in storytelling that I have ever experienced.

Oh well!

As my wife said, “At least this way we’ll never have to bargain with our daughter about when she’s old enough to watch *Game of Thrones*. The ending is so bad, in 10 or 15 years no one will be watching it anymore.”

**Identity Politics**

This is a really dumb pun.

Also one of the more popular cartoons in this list.

Go figure.

**Another Dumb Pun**

This one is inspired by that time Malcolm Gladwell referred to eigenvectors as “igon vectors,” and Steven Pinker blasted him for it, at which point Gladwell blasted Pinker for something else, and eventually we all lost the thread and just went about our days.

And if you want more godawful matrix puns, I’ve got ’em.

I don’t know what day you’re reading this, but guess what? It’s also a bad approximation of pi! So go ahead and celebrate!

(Though if you want some very clever alternative pi days, check out Evelyn Lamb’s page-a-day calendar, which includes a Pi Day each month, and not where you’d expect!)

**Uncountably Many Wishes**

After I posted this, there was a bunch of discussion on Twitter about whether I’d mischaracterized the Axiom of Choice, which is totally possible, in which case, oops.

Also, some folks pointed out that it’s pretty greedy to wish for uncountably many wishes, when you could just as easily wish for countably many.

To which I say: What’s the point of a magic lamp, if not to have greed be your undoing?

**Maximization vs. Minimization**

For lots of optimization problems, maximizing makes sense, but minimizing doesn’t. (Or vice versa.) An example: What’s the largest rectangle you can make from 4 feet of wire?

It’s the 1-by-1 square, with an area of 1 square foot.

But what’s the *smallest* rectangle you can make (in terms of area)? Well, you could make the 1.9999 by 0.0001 rectangle, which has a very tiny area…

Or you could make the 1.999999 by 0.000001 rectangle, which has an even smaller area…

Or the 1.99999999999999 by 0.000000000000001 rectangle, whose area is microscopic…

…and so on.

I hope that was worth it! And I suspect it wasn’t! Anyway, moving on.

More thoughts here.

**The Villainous Mathematician Explains His Plan**

Clearly this villain should be assigning more group work.

Anyway, I for one am curious to know how a complex-valued currency might work. I’d pay a hefty fee for an accountant or tax attorney who can turn imaginary assets into real ones, or real debts into imaginary ones.

**The Cat on the Bed**

I found it very hard to draw a decent space-filling curve.

Also, to draw a decent cat.

**Only Slept Four Hours**

This is how I feel about anyone who sleeps less than 7 hours in a given night.

**Axioms of Life**

This is my version of that xkcd about kitties.

Also pretty well summarizes parenthood. I still enjoy a cerebral geek-out, as I always have; but I also really enjoy holding my daughter in my arms and calling her the world’s best monkey over and over.

**How Many Stars?**

I would totally read a graphic novel about the dating life of Georg Cantor.

The problem is that no one is going to write this graphic novel except for me.

Oh well. I’m under contract for two more books at the moment, but after that will come TRANSFINITE LOVE: THE ROMANTIC ESCAPADES OF A SET THEORIST.

**Quick-Draw Answers**

Drawn from an actual experience, in my first week teaching 7th grade. I hadn’t really figured out how to tee up a problem-solving experience yet.

**Twenty Questions**

Drew this one for a Jim Propp essay. Recommended as always!

**A New Proof**

A teaching friend of mine had a whole list of proofs that 1 = 0, which he busted out at various developmentally appropriate points in grades 6 through 12.

I love that. Curious how far you could get writing a book of proofs that 1 = 0, each introducing a key idea in mathematics…

Maybe that’ll be my next project after the George Cantor romance novel.

**E = mc**

Philosophical question: Is this a pun?

The case against: “A pun is a joke that plays on words that sound similar but mean different things. This isn’t doing that.”

The case for: “A pun is a joke that plays on linguistic expressions with similar surface features, but different deep meanings. This is doing exactly that: the premise of the joke is that an exponent and a footnote are both denoted with a superscript, yet mean very different things.”

So I guess this has a deep resemblance to puns, but lacks a surface resemblance… which is itself, not very pun-like.

Ruling: Not a pun!

**“The Exception Proves the Rule”**

I guess you hear this inane phrase less often these days. But there was a time, kiddos, when people could hear a devastating counterexample to what they were arguing, and then blithely say “the exception proves the rule” with a straight face.

**The Math Sequence**

I’m pretty agnostic on the math sequence. But I have strong intuitions that Star Wars should be screened in the order: IV, V, I, II, III, VI, and so on. (I view the sequels as pretty optional. Prequels too, for that matter, but if you limit yourself to the original trilogy, it’s a boring problem.)

**The “Same” Age**

A lot of people on Facebook seemed to read this as though the right-hand character was creeping on Ariana Grande. Not my intention at all! I just wanted to pick a mid-20s celebrity. Could’ve just as easily been Bieber.

(My primary association with Ariana Grande, by the way, is her performance in the short-lived bar mitzvah-themed Broadway musical Thirteen.)

**Lemniskate**

I’m not sure there’s a joke here.

I’m fond of this drawing anyway.

**Linear Child**

Michael Pershan, the internet’s most relentlessly analytical math educator, inexplicably loved this joke, so I call it a win.

Someone on social media speculated about the position by which this linear combination had been “conceived,” which I found quite vulgar and upsetting (but which I also sort of invited by drawing a comic about procreating vectors).

**If P, then Q**

Where do we draw the line between logical succession, and outright stalking? I leave that to the courts.

**Loons and Lunes**

Sometimes I just want to do a cute drawing that has no joke in it, okay?

**The Vertical Line Test**

I’m actually skeptical that the phrase “vertical line test” has any value. To me it feels like a fancy name for a fact that doesn’t need a fancy name. And, as in the two-column-proof version of geometry, giving fancy names to facts that students should be reasoning out for themselves can become obfuscatory rather than clarifying.

**Whose Fractal is Whose?**

Please join me in making “Patricia gasket” a thing! E.g., “Did you know Copley Square in Boston is the approximate shape of the mathematical figure known as a Patricia Gasket?”

Funny as always!

Just got Change is the Only Constant for my birthday and it was great.

What surprises people looking up at the sky, I think, is how few

visiblestars there are. If the Earth were transparent, we’d see about 6000, but in fact only about 2000 are visible at any given moment.If Earth was transparent, then it would be a lens that would “shrink” our view of the stars on that side.

Imaginary currency reminds me of a joke from my college time. It goes like this: “I have -3i dollars. Meaning, I owe 3 that I’m never going to pay back.”

I have a couple of concerns about this otherwise excellent stream of consciousness and both involve conflict between (your) math and language.

1. “Every circle is alike” is not equivalent to “all circles are geometrically similar” and has the same linguistic problem as asking, “What’s the difference between a duck?”

2. “The Exception Proves the Rule” makes perfect sense if you use definition 2 for “to prove”, namely “to test”, and that’s what speakers used to have in mind, in the Goode Olde days, when using that phrase. And another common example is “the proof is in the pudding”, where we mean the best way to test how good a cook is, is to taste their pudding.

Perhaps: “Math with Bad Drawings and Occasionally Questionable Grammar”?

Occasionally? Always!

1. You’re quite right; I should’ve said “All circles are alike.”

2. I’ve heard two nice explanations of “the exception proves the rule,” the other being that the careful carving out of an exception demonstrates the existence of a rule that otherwise holds (e.g., “Parking Allowed on Sundays” suggests that it isn’t allowed on other days). I suspect yours is the historically accurate one, though I like both.

“What’s the difference between a duck?”

One of its hind legs are both the same.

THIS IS MY FAVORITE JOKE

It makes zero sense but is still completely funny

I don’t think that’s what linguists sound like. They’d be more likely to say “we asked a bunch of native speakers of Mathematical English, and they said 1 isn’t prime (98%/2%, n=1002, p=2.3e-4).”

Lol – I like that.

Probably should have said “armchair etymologists.”

If you only knew how many of my fractals came out as the Patricia Gasket.

Puns galore. I loved this

The Exception Proves the Rule” makes perfect sense if you use definition 2 for “to prove”, namely “to test”, and that’s what speakers used to have in mind, in the Good Old days, when using that phrase. And another common example is “the proof is in the pudding”, where we mean the best way to test how good a cook is, is to taste their pudding.

ornaments

Yes, I like that interpretation of “the exception proves the rule.”

The other version I’ve heard is that “by stating an exception, you imply the existence of a rule.” E.g., “no parking on Sundays” suggests that the general rule is you CAN park.

I think the Star Wars movies should be screened in this order:

IV, V.