## My 2018 Mathematics A To Z: Jokes

For today’s entry, Iva Sallay, of Find The Factors, gave me an irresistible topic. I did not resist.

# Jokes.

What’s purple and commutes?
An Abelian grape.

Whatever else you say about mathematics we are human. We tell jokes. I will tell some here. You may not understand the words in them. That’s all right. From the Abelian grape there, you gather this is some manner of wordplay. A pun, particularly. It’s built on a technical term. “Abelian groups” come from (not high school) Algebra. In an Abelian group, the group multiplication commutes. That is, if ‘a’ and ‘b’ are any things in the group, then their product “ab” is the same as “ba’. That is, the group works like ordinary addition on numbers does. We say “Abelian” in honor of Niels Henrik Abel, who taught us some fascinating stuff about polynomials. Puns are a common kind of humor. So common, they’re almost base. Even a good pun earns less laughter than groans.

But mathematicians make many puns. A typical page of mathematics jokes has a whole section of puns. “What’s yellow and equivalent to the Axiom of Choice? Zorn’s Lemon.” “What’s nonorientable and lives in the sea?” “Möbius Dick.” “One day Jesus said to his disciples, `The Kingdom of Heaven is like 3x2 + 8x – 9′. Thomas looked very confused and asked peter, `What does the teacher mean?’ Peter replied, `Don’t worry. It’s just another one of his parabolas’.” And there are many jokes built on how it is impossible to tell the difference between the sounds of “π” and “pie”.

It shouldn’t surprise that mathematicians make so many puns. Mathematics trains people to know definitions. To think about precisely what we mean. Puns ignore definitions. They build nonsense out of the ways that sounds interact. Mathematicians practice how to make things interact, even if they don’t know or care what the underlying things are. If you’ve gotten used to proving things about $aba^{-1}b^{-1}$, without knowing what ‘a’ or ‘b’ are, it’s difficult to avoid turning “poles on the half-plane” (which matters in some mathematical physics) to a story about Polish people on an aircraft.

If there’s a flaw to this kind of humor it’s that these jokes may sound juvenile. One of the first things that strikes kids as funny is that a thing might have several meanings. Or might sound like another thing. “Why do mathematicians like parks? Because of all the natural logs!”

Jokes can be built tightly around definitions. “What do you get if you cross a mosquito with a mountain climber? Nothing; you can’t cross a vector with a scalar.” “There are 10 kinds of people in the world, those who understand binary mathematics and those who don’t.” “Life is complex; it has real and imaginary parts.”

There are more sophisticated jokes. Many of them are self-deprecating. “A mathematician is a device for turning coffee into theorems.” “An introvert mathematician looks at her shoes while talking to you. An extrovert mathematician looks at your shoes.” “A mathematics professor is someone who talks in someone else’s sleep”. “Two people are adrift in a hot air balloon. Finally they see someone and shout down, `Where are we?’ The person looks up, and studies them, watching the balloon drift away. Finally, when they are barely in shouting range, the person on the ground shouts back, `You are in a balloon!’ The first passenger curses their luck at running across a mathematician. `How do you know that was a mathematician?’ `Because her answer took a long time, was perfectly correct, and absolutely useless!”’ These have the form of being about mathematicians. But they’re not really. It would be the same joke to say “a poet is a device for turning coffee into couplets”, the sleep-talker anyone who teachers, or have the hot-air balloonists discover a lawyer or a consultant.

Some of these jokes get more specific, with mathematics harder to extract from the story. The tale of the nervous flyer who, before going to the conference, sends a postcard that she has a proof of the Riemann hypothesis. She arrives and admits she has no such thing, of course. But she sends that word ahead of every conference. She knows if she died in a plane crash after that, she’d be famous forever, and God would never give her that. (I wonder if Ian Randal Strock’s little joke of a story about Pierre de Fermat was an adaptation of this joke.) You could recast the joke for physicists uniting gravity and quantum mechanics. But I can’t imagine a way to make this joke about an ISO 9000 consultant.

A dairy farmer knew he could be milking his cows better. He could surely get more milk, and faster, if only the operations of his farm were arranged better. So he hired a mathematician to find the optimal way to configure everything. The mathematician toured every part of the pastures, the milking barn, the cows, everything relevant. And then the mathematician set to work devising a plan for the most efficient possible cow-milking operation. The mathematician declared, “First, assume a spherical cow.”

This joke is very mathematical. I know of no important results actually based on spherical cows. But the attitude that tries to make spheres of cows comes from observing mathematicians. To describe any real-world process is to make a model of that thing. A model is a simplification of the real thing. You suppose that things behave more predictably than the real thing. You trust the error made by this supposition is small enough for your needs. A cow is complicated, all those pointy ends and weird contours. A sphere is easy. And, besides, cows are funny. “Spherical cow” is a funny string of sounds, at least in English.

The spherical cows approach parodying the work mathematicians do. Many mathematical jokes are burlesques of deductive logic. Or not even burlesques. Charles Dodgson, known to humans as Lewis Carroll, wrote this in Symbolic Logic:

“No one, who means to go by the train and cannot get a conveyance, and has not enough time to walk to the station, can do without running;
This party of tourists mean to go by the train and cannot get a conveyance, but they have plenty of time to walk to the station.
∴ This party of tourists need not run.”

[ Here is another opportunity, gentle Reader, for playing a trick on your innocent friend. Put the proposed Syllogism before him, and ask him what he thinks of the Conclusion.

He will reply “Why, it’s perfectly correct, of course! And if your precious Logic-book tells you it isn’t, don’t believe it! You don’t mean to tell me those tourists need to run? If I were one of them, and knew the Premises to be true, I should be quite clear that I needn’t run — and I should walk!

And you will reply “But suppose there was a mad bull behind you?”

And then your innocent friend will say “Hum! Ha! I must think that over a bit!” ]

The punch line is diffused by the text being so educational. And by being written in the 19th century, when it was bad form to excise any word from any writing. But you can recognize the joke, and why it should be a joke.

Not every mathematical-reasoning joke features some manner of cattle. Some are legitimate:

Claim. There are no uninteresting whole numbers.
Proof. Suppose there is a smalled uninteresting whole number. Call it N. That N is uninteresting is an interesting fact. Therefore N is not an uninteresting whole number.

Three mathematicians step up to the bar. The bartender asks, “you all want a beer?” The first mathematician says, “I don’t know.” The second mathematician says, “I don’t know.” The third says, “Yes”.

Some mock reasoning uses nonsense methods to get a true conclusion. It’s the fun of watching Mister Magoo walk unharmed through a construction site to find the department store exchange counter:

5095 / 1019 = 5095 / 1019 = 505 / 101 = 55 / 11 = 5

This one includes the thrill of division by zero.

Venn Diagrams are not by themselves jokes (most of the time). But they are a great structure for jokes. And easy to draw, which is great for us who want to be funny but don’t feel sure about their drafting abilities.

And then there are personality jokes. Mathematics encourages people to think obsessively. Obsessive people are often funny people. Alexander Grothendieck was one of the candidates for “greatest 20th century mathematician”. His reputation is that he worked so well on abstract problems that he was incompetent at practical ones. The story goes that he was demonstrating something about prime numbers and his audience begged him to speak about a specific number, that they could follow an example. And that he grumbled a bit and, finally, said, “57”. It’s not a prime number. But if you speak of “Grothendieck’s prime”, many will recognize what you mean, and grin.

There are more outstanding, preposterous personalities. Paul Erdös was prolific, and a restless traveller. The stories go that he would show up at some poor mathematician’s door and stay with them several months. And then co-author a paper with the elevator operator. (Erdös is also credited as the originator of the “coffee into theorems” quip above.) John von Neumann was supposedly presented with this problem:

Two trains are on the same track, 60 miles apart, heading toward each other, each travelling 30 miles per hour. A fly travels 60 miles per hour, leaving one engine flying toward the other. When it reaches the other engine it turns around immediately and flies back to the other engine. This is repeated until the two trains crash. How far does the fly travel before the crash?

The first, hard way to do this is to realize how far the fly travels is a series. The fly starts at, let’s say, the left engine and flies to the right. Add to that the distance from the right to the left train now. Then left to the right again. Right to left. This is a bunch of calculations. Most people give up on that and realize the problem is easier. The trains will crash in one hour. The fly travels 60 miles per hour for an hour. It’ll fly 60 miles total. John von Neumann, say witnesses, had the answer instantly. He recognized the trick? “I summed the series.”

The personalities can be known more remotely, from a handful of facts about who they were or what they did. “Cantor did it diagonally.” Georg Cantor is famous for great thinking about infinitely large sets. His “diagonal proof” shows the set of real numbers must be larger than the set of rational numbers. “Fermat tried to do it in the margin but couldn’t fit it in.” “Galois did it on the night before.” (Évariste Galois wrote out important pieces of group theory the night before a duel. It went badly for him. French politics of the 1830s.) Every field has its celebrities. Mathematicians learn just enough about theirs to know a couple of jokes.

The jokes can attach to a generic mathematician personality. “How can you possibly visualize something that happens in a 12-dimensional space?” “Easy, first visualize it in an N-dimensional space, and then let N go to 12.” Three statisticians go hunting. They spot a deer. One shoots, missing it on the left. The second shoots, missing it on the right. The third leaps up, shouting, “We’ve hit it!” An engineer and a mathematician are sleeping in a hotel room when the fire alarm goes off. The engineer ties the bedsheets into a rope and shimmies out of the room. The mathematician looks at this, unties the bedsheets, sets them back on the bed, declares, “this is a problem already solved” and goes back to sleep. (Engineers and mathematicians pair up a lot in mathematics jokes. I assume in engineering jokes too, but that the engineers make wrong assumptions about who the joke is on. If there’s a third person in the party, she’s a physicist.)

Do I have a favorite mathematics joke? I suppose I must. There are jokes I like better than others, and there are — I assume — finitely many different mathematics jokes. So I must have a favorite. What is it? I don’t know. It must vary with the day and my mood and the last thing I thought about. I know a bit of doggerel keeps popping into my head, unbidden. Let me close by giving it to you.

Integral z-squared dz
From 1 to the cube root of 3
Times the cosine
Of three π over nine
Equals log of the cube root of e.

This may not strike you as very funny. I’m not sure it strikes me as very funny. But it keeps showing up, all the time. That has to add up.

This and other Fall 2018 Mathematics A-To-Z posts can be read at this link. Also, now and then, I talk about comic strips here. You might like that too.

## Reading the Comics, August 5, 2017: Lazy Summer Week Edition

It wasn’t like the week wasn’t busy. Comic Strip Master Command sent out as many mathematically-themed comics as I might be able to use. But they were again ones that don’t leave me much to talk about. I’ll try anyway. It was looking like an anthropomorphic-symboles sort of week, too.

Tom Thaves’s Frank and Ernest for the 30th of July is an anthropomorphic-symbols joke. The tick marks used for counting make an appearance and isn’t that enough? Maybe.

Dan Thompson’s Brevity for the 31st is another entry in the anthropomorphic-symbols joke contest. This one sticks to mathematical symbols, so if the Frank and Ernest makes the cut this week so must this one.

Eric the Circle for the 31st, this installment by “T daug”, gives the slightly anthropomorphic geometric figure a joke that at least mentions a radius, and isn’t that enough? What catches my imagination about this panel particularly is that the “fractured radius” is not just a legitimate pun but also resembles a legitimate geometry drawing. Drawing a diameter line is sensible enough. Drawing some other point on the circle and connecting that to the ends of the diameter is also something we might do.

Scott Hilburn’s The Argyle Sweater for the 1st of August is one of the logical mathematics jokes you could make about snakes. The more canonical one runs like this: God in the Garden of Eden makes all the animals and bids them to be fruitful. And God inspects them all and finds rabbits and doves and oxen and fish and fowl all growing in number. All but a pair of snakes. God asks why they haven’t bred and they say they can’t, not without help. What help? They need some thick tree branches chopped down. The bemused God grants them this. God checks back in some time later and finds an abundance of baby snakes in the Garden. But why the delay? “We’re adders,” explain the snakes, “so we need logs to multiply”. This joke absolutely killed them in the mathematics library up to about 1978. I’m told.

John Deering’s Strange Brew for the 1st is a monkeys-at-typewriters joke. It faintly reminds me that I might have pledged to retire mentions of the monkeys-at-typewriters joke. But I don’t remember so I’ll just have to depend on saying I don’t think I retired the monkeys-at-typewriters jokes and trust that someone will tell me if I’m wrong.

Dana Simpson’s Ozy and Millie rerun for the 2nd name-drops multiplication tables as the sort of thing a nerd child wants to know. They may have fit the available word balloon space better than “know how to diagram sentences” would.

Mark Anderson’s Andertoons for the 3rd is the reassuringly normal appearance of Andertoons for this week. It is a geometry class joke about rays, line segments with one point where there’s an end and … a direction where it just doesn’t. And it riffs on the notion of the existence of mathematical things. At least I can see it that way.

Rick Kirkman and Jerry Scott’s Baby Blues for the 5th is a rounding-up joke that isn’t about herds of 198 cattle.

Stephen Bentley’s Herb and Jamaal for the 5th tosses off a mention of the New Math as something well out of fashion. There are fashions in mathematics, as in all human endeavors. It startles many to learn this.

## Reading the Comics, March 21, 2016: New Math And The NCAA Edition

Terri Libenson’s The Pajama Diaries for the 20th of March mentions, among “reasons for ice cream”, the stress of having “helped with New Math”. It’s a curious reference, to me. I expect it refers to the stress of how they teach arithmetic differently from how it was when you grew up. I expect that feeds any adult’s natural anxiety about having forgot, or never really been good at, arithmetic. Add to that the anxiety of not being able to help your child when you’re called on. And add to that the ever-present fear of looking like a fool. There’s plenty of reason to be anxious.

Still, the reference to “New Math” is curious since, at least in the United States, that refers to a specific era. In the 1960s and 70s mathematics education saw a major revision, called the “New Math”. This revision tried many different approaches, but built around the theory that students should know why mathematics looks like it does. The hope was that in this way students wouldn’t just know what eight times seven was, but would agree that it made sense for this to be 56. The movement is, generally, regarded as a well-meant failure. The reasons are diverse, but many of them amount to it being very hard to explain why mathematics looks like it does. And it’s even harder to explain it to parents, who haven’t gone to school for years and aren’t going to go back to learn eight times seven. And it’s hard for many teachers, who often aren’t specialists in mathematics, to learn eight times seven in a new way either.

Still, the New Math was dead and buried in the United States by the 1980s. And more, Libenson is Canadian. I don’t know what educational fashions, and reform fashions, are like in Canada. I’m curious if Canadian parents or teachers could let me know, what is going on in reforming Canadian mathematics education? Is “New Math” a term of art in Canada now? Or did Libenson pick a term that would communicate efficiently “mathematics but not like I learned it”?

Rudolph Dirk’s The Katzenjammer Kids on the 20th reprinted the strip from the 5th of September, 1943. I mention it here because it contains an example of mathematics talk being used as signifier of great intelligence. The kids expound: “Now, der t’eory uf der twerpsicosis iss dot er sum uf circumvegetatium und der horizontal triggernometry iss equal to der … ” and that’s as far as it needs to go. It isn’t quite mathematics, but it is certainly using a painting of mathematics to make one look bright.

Mark Anderson’s Andertoons got its appearance in here the 20th. It’s got a student resisting the equivalent fractions idea. he kid notes that 1/2 might equal 2/4 and 4/8 and 8/16, but “the ones on the right feel like more bang for your buck”. The kid has a point. These are all the same number. It’s usually easiest to work with the smallest representation that means what you need. But they might convey their meanings differently. I get a different picture, at least, in speaking of “half the class not being done with the assignment” versus “16 of the 32 students aren’t done with the assignment”.

Charlie Podrebarac’s CowTown for the 20th of March claims Charlie could “literally paper the Earth” with losing NCAA brackets. As I make it out, he’s right. There are 263 possible NCAA brackets, because there are 63 matches in the college basketball tournament. All but one of these are losing. If each bracket fits on one sheet of paper — well, how big is a sheet of paper? If each bracket is on a sheet of A4-size paper, then, each page is 1/16th of a square meter. This is easy to work with. Unfortunately, if Charlie cares about the NCAA college basketball tournament, he’s probably in the United States. So he would print out on paper that’s 8 ½ inches by 11 inches. That’s not quite 1/16th of a square meter or any other convenient-to-work-with size. It’s 93.5 square inches but what good is that?

Well, I will pretend that the 8 ½ by 11 inch paper is close enough to A4. It’s going to turn out not to matter. 263 is 9,223,372,036,854,775,808. Subtract one and we have 9,223,372,036,854,775,807. Big difference. Multiply this by one-sixteenth of a square meter and we have about 576,460,752,000,000,000 square meters of paper. I’m rounding off because it is beyond ridiculous that I didn’t before. The surface area of the Earth is about 510,000,000,000,000 square meters. So if Bob picked every possible losing bracket he could indeed literally paper the Earth a thousand times over and have some paper to spare.

T Shepherd’s gentle and sweet Snow Sez for the 21st of March is a bit of humor about addition and the limits of what it can tell us.

Ruben Bolling’s Super-Fun-Pak Comix for the 21st of March is a Guy Walks Into A Bar that depends on non-base-ten arithmetic for its punch line. I’m amused. I learned about different bases as a kid, in the warm glow of the New Math. The different bases and how they changed what arithmetic looked like enchanted me. Today I know there’s not much need for bases besides ten (normal mathematics), two (used by computers), and sixteen (used by people dealing with computers). (Base sixteen converts easily to base two, so people can understand what the computer is actually doing, while being much more compact, so people don’t have to write out prodigiously long sequences of digits.) But for a while there you can play around with base five or base twelve or, as a horse might, base four. It can help you better appreciate how much thought there is behind something as straightforward as “10”.

## How April 2015 Treated My Mathematics Blog

(I apologize if the formatting is messed up. For some reason preview is not working, and I will not be trying the new page for entering posts if I can at all help it. I will fix when I can, if it needs fixing.)

As it’s the start of the month I want to try understanding the readership of my blogs, as WordPress gives me statistics. It’s been a more confusing month than usual, though. One thing is easy to say: the number of pages read was 1,047, an all-time high around these parts for a single month. It’s up from 1,022 in March, and 859 in February. And it’s the second month in a row there’ve been more than a thousand readers. That part’s easy.

The number of visitors has dropped. It was down to 389 in April, from a record 468 in March and still-higher 407 in April. This is, if WordPress doesn’t lead me awry, my fifth-highest number of viewers. This does mean the number of views per visitor was my highest since June of 2013. The blog had 2.69 views per visitor, compared to 2.18 in March and 2.11 in February. It’s one of my highest views-per-visitor on record anyway. Perhaps people quite like what they see and are archive-binging. I approve of this. I’m curious why the number of readers dropped so, though, particularly when I look at my humor blog statistics (to be posted later).

I’m confident the readers are there, though. The number of likes on my mathematics blog was 297, up from March’s 265 and February’s 179. It’s the highest on record far as WordPress will tell me. So readers are more engaged, or else they’re clicking like from the WordPress Reader or an RSS feed. Neither gets counted as a page view or a visitor. That’s another easy part. The number of comments is down to 64, from March’s record 93, but March seems to have been an exceptional month. February had 56 comments so I’m not particularly baffled by April’s drop.

May starts out with 23,884 total views, and 472 people following specifically through WordPress.

It’s a truism that my most popular posts are the trapezoids one and the Reading The Comics posts, but for April that was incredibly true. Most popular the past thirty days were:

I am relieved that I started giving all these Comics posts their own individual “Edition” titles. Otherwise there’d be no way to tell them apart.

The nations sending me the most readers were, as ever, the United States (662), Canada (82), and the United Kingdom (47), with Slovenia once again strikingly high (36). Hong Kong came in with 24 readers, Italy 23, and Austria a mere 18. Elke Stangl’s had a busy month, I know.

This month’s single-reader countries were Czech Republic, Morocco, the Netherlands, Puerto Rico, Romania, Taiwan, and Vietnam. Romania’s the only one that sent me a single reader last month. India bounced back from five readers to six.

Among the search terms bringing people to me were no poems. Among the interesting phrases were:

• what point is driving the area difference between two triangles (A good question!)
• how do you say 1,898,600,000,000,000,000,000,000,000 (I almost never do.)
• is julie larson still drawing the dinette set (Yes, to the best of my knowledge.)
• jpe fast is earth spinning? (About once per day, although the answer can be surprisingly difficult to say! But also figure about 465 times the cosine of your latitude meters per second, roughly.)
• origin is the gateway to your entire gaming universe. (Again, I don’t know what this means, and I’m a little scared to find out.)
• i hate maths 2015 photos (Well, that just hurts.)
• getting old teacher jokes (Again, that hurts, even if it’s not near my birthday.)
• two trapezoids make a (This could be a poem, actually.)
• how to draw 2 trapezoids (I’d never thought about that one. Shall have to consider writing it.)

I don’t know quite what it all means, other than that I need to write about comic strips and trapezoids more somehow.

## Reading the Comics, January 21, 2013

Feast or famine, as I said. It’s not a week since the last comics roundup and I have eight comic strips that have enough mathematical content for me to discuss. Well, they’re fun essays to write, and people seem to quite like them, so why not another so soon?

Well, because I’m overlooking all the King Features Syndicate comics. I’m not actually overlooking them — I’m keeping track of just which ones have something I could write about — but they haven’t had a nice, archive-friendly way to point people to the strips being discussed. (Most newspaper web sites that have King Features comics have links to those pages expire in a measly 28 days.) Based on the surprising number of people who come to my site by searching for Norm Feuti’s Retail comic strip, they certainly deserve to be talked about. I’ll have something worked out about that soon, I promise.

## Cutting Commentary

It might be that one functional definition of a friend is “someone who can say stuff that would be insulting, but you mostly don’t mind”. I had been chatting with a friend who wasn’t aware of my little blogging effort here, and gave the front page URL. My friend claimed to get a headache “from just a casual perusal!”

I know what’s intended: an acknowledgement that the writing I’ve been doing has been at least math-flavored, and that’s got almost universal acclaim as something really hard that stresses the mind to think about, and delivered in the form of a joke. It’s an overused joke, to my tastes, but an overused joke can serve several positive purposes. It can be one of the landmarks that one is in an emotionally comfortable place, or mark that the people sharing it share this in common, or that whatever is being joked about has connections to other times the joke’s been used.

Still, the joke is a bit of a complicated insult too: it insults both the writer, for not being understandable, and the reader, for not understanding. But I know that it’s not meant to insult, and I’m hardly in a position to turn away compliments when I can find them.

All this muttering I mean, largely, to warn that I am working out whether I’m good enough to write a couple pieces towards a question that really is somewhat head-spinning in a way that someone who isn’t a math or physics major would have a hope of following. I might not be; as I do research I realize I’m hitting questions I can’t fully satisfy myself about. If I can, I may go forward and you’ll see what perusal headaches really look like.

## Reading the Comics, January 16, 2013

I was beginning to wonder whether my declaration last time that I’d post a comics review every time I had seven to ten strips to talk about was going to see the extinguishing of math-themed comic strips. It only felt like it. The boom-and-bust cycle continues, though; it took better than two weeks to get six such strips, and then three more came in two days. But that’s the fun of working on relatively rare phenomena. Let me get to the most recent installment of math-themed comics, mostly from Gocomics.com:

## Reading the Comics, November 21, 2012

It’s been long enough since my last roundup of mathematics-themed comics to host a new one. I’m also getting stirred to try tracking how many of these turn up per day, because they certainly feel like they run in a feast-or-famine pattern. There’d be no point to it, besides satisfying my vague feelings that everything can be tracked, but there’s data laying there all ready to be measured, isn’t there?