Reading the Comics, November 2, 2019: Eugene the Jeep Edition

I knew by Thursday this would be a brief week. The number of mathematically-themed comic strips has been tiny. I’m not upset, as the days turned surprisingly full on me once again. At some point I would have to stop being surprised that every week is busier than I expect, right?

Anyway, the week gives me plenty of chances to look back to 1936, which is great fun for people who didn’t have to live through 1936.

Elzie Segar’s Thimble Theatre rerun for the 28th of October is part of the story introducing Eugene the Jeep. The Jeep has astounding powers which, here, are finally explained as being due to it being a fourth-dimensional creature. Or at least able to move into the fourth dimension. This is amazing for how it shows off the fourth dimension being something you could hang a comic strip plot on, back in the day. (Also back in the day, humor strips with ongoing plots that might run for months were very common. The only syndicated strips like it today are Gasoline Alley, Alley Oop, the current storyline in Safe Havens where they’ve just gone and terraformed Mars, and Popeye, rerunning old daily stories.) The Jeep has many astounding powers, including that he can’t be kept inside — or outside — anywhere against his will, and he’s able to forecast the future.

Elzie Segar’s Thimble Theatre rerun for the 28th of October, 2019. It originally ran the 28th of May, 1936. Essays that have some inspiration in things that turn up in Popeye (current syndication strips) or Thimble Theatre (the 1930s reprints) or Popeye’s Cartoon Club (a special Sunday event for this year) should be at this link. Also I know that these 1930s strips are great massive heaps of words, but they are worth looking at. There’s a bunch of funny stuff going on in here, including Professor Gipf addressing Olive Oyl and Popeye as “Lady and Gentleman”, or his declaration that of course all mysteries are simple when solved. And there is a great puckish glee in Elzie Segar’s final panel, urging kids everywhere to ask their parents to explain “in detail” about the fourth dimension.

Could there be a fourth-dimensional animal? I dunno, I’m not a dimensional biologist. It seems like we need a rich chemistry for life to exist. Lots of compounds, many of them long and complicated ones. Can those exist in four dimensions? I don’t know the quantum mechanics of chemical formation well enough to say. I think there’s obvious problems. Electrical attraction and repulsion would fall off much more rapidly with distance than they do in three-dimensional space. This seems like it argues chemical bonds would be weaker things, which generically makes for weaker chemical compounds. So probably a simpler chemistry. On the other hand, what’s interesting in organic chemistry is shapes of molecules, and four dimensions of space offer plenty of room for neat shapes to form. So maybe that compensates for the chemical bonds. I don’t know.

But if we take the premise as given, that there is a four-dimensional animal? With some minor extra assumptions then yeah, the Jeep’s powers fit well enough. Not being able to be enclosed follows almost naturally. You, a three-dimensional being, can’t be held against your will by someone tracing a line on the floor around you. The Jeep — if the fourth dimension is as easy to move through as the third — has the same ability.

Forecasting the future, though? We have a long history of treating time as “the” fourth dimension. There’s ways that this makes good organizational sense. But we do have to treat time as somehow different from space, even to make, for example, general relativity work out. If the Jeep can see and move through time? Well, yeah, then if he wants he can check on something for you, at least if it’s something whose outcome he can witness. If it’s not, though? Well, maybe the flow of events from the fourth dimension is more obvious than it is from a mere three, in the way that maybe you can spot something coming down the creek easily, from above, in a way that people on the water can’t tell.

Olive Oyl and Popeye use the Jeep to tease one another, asking for definite answers about whether the other is cute or not. This seems outside the realm of things that the fourth dimension could explain. In the 1960s cartoons he even picks up the power to electrically shock offenders; I don’t remember if this was in the comic strips at all.

Elzie Segar’s Thimble Theatre rerun for the 29th of October, 2019. It originally ran the 29th of May, 1936. Also wait, where did Wimpy pick up all this talk about the fourth dimension? I guess if you’re going to let a line of smooth patter take the place of working you have to be on top of anything that might come up, but it still seems like a lot of work he’s gone to here to use the Jeep to win horse races.

Elzie Segar’s Thimble Theatre rerun for the 29th of October has Wimpy doing his best to explain the fourth dimension. I think there’s a warning here for mathematician popularizers here. He gets off to a fair start and then it all turns into a muddle. Explaining the fourth dimension in terms of the three dimensions we’re familiar with seems like a good start. Appealing to our intuition to understand something we have to reason about has a long and usually successful history. But then Wimpy goes into a lot of talk about the mystery of things, and it feels like it’s all an appeal to the strangeness of the fourth dimension. I don’t blame Popeye for not feeling it’s cleared anything up. Segar would come back, in this storyline, to several other attempted explanations of the Jeep’s powers, although they do come back around to, y’know, it’s a magical animal. They’re all over the place in the Popeye comic universe.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th of October, 2019. Those occasional times I do think to discuss Saturday Morning Breakfast Cereal are gathered at this link.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th of October is a riff on predictability and encryption. Good encryption schemes rely on randomness. Concealing the content of a message means matching it to an alternate message. Each of the alternate messages should be equally likely to be transmitted. This way, someone who hasn’t got the key would not be able to tell what’s being sent. The catch is that computers do not truly do randomness. They mostly rely on quasirandom schemes that could, in principle, be detected and spoiled. There are ways to get randomness, mostly involving putting in something from the real world. Sensors that detect tiny fluctuations in temperature, for example, or radio detectors. I recall one company going for style and using a wall of lava lamps, so that the rise and fall of lumps were in some way encoded into unpredictable numbers.

Robb Armstrong’s JumpStart for the 2nd of November, 2019. When I have an essay inspired by something in JumpStart it appears at this link.

Robb Armstrong’s JumpStart for the 2nd of November is a riff on the Birthday “Paradox”, the thing where you’re surprised to find someone shares a birthday with you. (I have one small circle of friends featuring two people who share my birthday, neatly enough.) Paradox is in quotes because it defies only intuition, not logic. The logic is clear that you need only a couple dozen people before some pair will probably share a birthday. Marcie goes overboard in trying to guess how many people at her workplace would share their birthday on top of that. Birthdays are nearly uniformly spread across all days of the year. There are slight variations; September birthdays are a little more likely than, say, April ones; the 13th of any month is a less likely birthday than the 12th or the 24th are. But this is a minor correction, aptly ignored when you’re doing a rough calculation. With 615 birthdays spread out over the year you’d expect the average day to be the birthday of about 1.7 people. (To be not silly about this, a ten-day span should see about 17 birthdays.) However, there are going to be “clumps”, days where three or even four people have birthdays. There will be gaps, days nobody has a birthday, or even streaks of days where nobody has a birthday. If there weren’t a fair number of days with a lot of birthdays, and days with none, we’d have to suspect birthdays weren’t random here.

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There were also a handful of comic strips just mentioning mathematics, that I can’t make anything in depth about. Here’s two.

T Shepherd’s Snow Sez for the 1st of November nominally talks about how counting can be a good way to meditate. It can also become a compulsion, with hazards, though.

Terri Libenson’s The Pajama Diaries for the 2nd of November uses mathematics as the sort of indisputably safe topic that someone can discuss in place of something awkward.

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And that is all I have to say for last week’s comics. Tuesday I should publish the next Fall 2019 A to Z essay. I also figure to open the end of the alphabet up to nominations this week. My next planned Reading the Comic post should be Sunday. Thanks for reading.

By the way, Thimble Theatre is trying to explain the fourth dimension

I hope to have proper comment about it in the usual Sunday Reading the Comics post. But the “current” storyline in Elzie Segar’s Thimble Theatre comic strip — Popeye to normal people — is the 1936 introduction of Eugene the Jeep. If you’ve looked at my user icon here you know I like Eugene.

Anyway, Eugene the Jeep has wondrous powers. These include the power of prophecy and the power to disappear from even enclosed spaces. Segar’s explanation for this was that the Jeep can turn into the fourth dimension and so do things we can’t hope to do. Which is a fun premise, yes. More, though, it’s got to be a pretty early use of the fourth or other high dimensions in pop culture. Yes, there were some things normal people might know that talk about higher dimensions. H G Wells’s The Time Machine starts with talk about time as a dimension like space. Edwin Abbott’s Flatland is explicitly about two- and three-dimensions, although Square thinks of whether there could be four- or more-dimensional spaces.

Elzie Segar’s Thimble Theatre (Popeye) for the 25th of October, 2019. It originally ran the 26th of May, 1936. Fun fact: that last panel shows the extension strip in the living room where we have the TV, DVR, Blu-Ray, Switch, and record player plugged in.

Wikipedia helps me find a few pieces of literature mentioning the fourth dimension before Eugene the Jeep. And a few pieces of visual art as well. No mention of earlier comic strips, although there’s no mention of Eugene the Jeep in either. So, all I can say is this is an early pop cultural appearance of the fourth dimension. I can’t say it’s the first, even among major comic strips.

Do not try to use this to pass your geometry quals.

Reading the Comics, September 24, 2019: I Make Something Of This Edition

I trust nobody’s too upset that I postponed the big Reading the Comics posts of this week a day. There’s enough comics from last week to split them into two essays. Please enjoy.

Scott Shaw! and Stan Sakai’s Popeye’s Cartoon Club for the 22nd is one of a yearlong series of Sunday strips, each by different cartoonists, celebrating the 90th year of Popeye’s existence as a character. And, I’m a Popeye fan from all the way back when Popeye was still a part of the pop culture. So that’s why I’m bringing such focus to a strip that, really, just mentions the existence of algebra teachers and that they might present a fearsome appearance to people.

Scott Shaw! and Stan Sakai’s Popeye’s Cartoon Club for the 22nd of September, 2019. This is the first (and likely last) time Popeye’s Cartoon Club has gotten a mention here. But appearances by this and by the regular Popeye comic strip (Thimble Theatre, if you prefer) should be gathered at this link.

Lincoln Pierce’s Big Nate for the 22nd has Nate seeking an omen for his mathematics test. This too seems marginal. But I can bring it back to mathematics. One of the fascinating things about having data is finding correlations between things. Sometimes we’ll find two things that seem to go together, including apparently disparate things like basketball success and test-taking scores. This can be an avenue for further research. One of these things might cause the other, or at least encourage it. Or the link may be spurious, both things caused by the same common factor. (Superstition can be one of those things: doing a thing ritually, in a competitive event, can help you perform better, even if you don’t believe in superstitions. Psychology is weird.)

Lincoln Pierce’s Big Nate for the 22nd of September, 2019. Essays inspired by something in Big Nate, either new-run or the Big Nate: First Class vintage strips, are at this link.

But there are dangers too. Nate shows off here the danger of selecting the data set to give the result one wants. Even people with honest intentions can fall prey to this. Any real data set will have some points that just do not make sense, and look like a fluke or some error in data-gathering. Often the obvious nonsense can be safely disregarded, but you do need to think carefully to see that you are disregarding it for safe reasons. The other danger is that while two things do correlate, it’s all coincidence. Have enough pieces of data and sometimes they will seem to match up.

Norm Feuti’s Gil rerun for the 22nd has Gil practicing multiplication. It’s really about the difficulties of any kind of educational reform, especially in arithmetic. Gil’s mother is horrified by the appearance of this long multiplication. She dubs it both inefficient and harder than the way she learned. She doesn’t say the way she learned, but I’m guessing it’s the way that I learned too, which would have these problems done in three rows beneath the horizontal equals sign, with a bunch of little carry notes dotting above.

Norm Feuti’s Gil rerun for the 22nd of September, 2019. Essays inspired by either the rerun or the new Sunday Gil strips should be gathered at this link.

Gil’s Mother is horrified for bad reasons. Gil is doing exactly the same work that she was doing. The components of it are just written out differently. The only part of this that’s less “efficient” is that it fills out a little more paper. To me, who has no shortage of paper, this efficiency doens’t seem worth pursuing. I also like this way of writing things out, as it separates cleanly the partial products from the summations done with them. It also means that the carries from, say, multiplying the top number by the first digit of the lower can’t get in the way of carries from multiplying by the second digits. This seems likely to make it easier to avoid arithmetic errors, or to detect errors once suspected. I’d like to think that Gil’s Mom, having this pointed out, would drop her suspicions of this different way of writing things down. But people get very attached to the way they learned things, and will give that up only reluctantly. I include myself in this; there’s things I do for little better reason than inertia.

People will get hung up on the number of “steps” involved in a mathematical process. They shouldn’t. Whether, say, “37 x 2” is done in one step, two steps, or three steps is a matter of how you’re keeping the books. Even if we agree on how much computation is one step, we’re left with value judgements. Like, is it better to do many small steps, or few big steps? My own inclination is towards reliability. I’d rather take more steps than strictly necessary, if they can all be done more surely. If you want speed, my experience is, it’s better off aiming for reliability and consistency. Speed will follow from experience.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 22nd of September, 2019. Essays which go into some aspect of Saturday Morning Breakfast Cereal turn up all the time, such as at this link.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 22nd builds on mathematical physics. Lagrangian mechanics offers great, powerful tools for solving physics problems. It also offers a philosophically challenging interpretation of physics problems. Look at the space made up of all the possible configurations of the system. Take one point to represent the way the system starts. Take another point to represent the way the system ends. Grant that the system gets from that starting point to that ending point. How does it do that? What is the path in this configuration space that goes in-between this start and this end?

We can find the path by using the Lagrangian. Particularly, integrate the Lagrangian over every possible curve that connects the starting point and the ending point. This is every possible way to match start and end. The path that the system actually follows will be an extremum. The actual path will be one that minimizes (or maximizes) this integral, compared to all the other paths nearby that it might follow. Yes, that’s bizarre. How would the particle even know about those other paths?

This seems bad enough. But we can ignore the problem in classical mechanics. The extremum turns out to always match the path that we’d get from taking derivatives of the Lagrangian. Those derivatives look like calculating forces and stuff, like normal.

Then in quantum mechanics the problem reappears and we can’t just ignore it. In the quantum mechanics view no particle follows “a” “path”. It instead is found more likely in some configurations than in others. The most likely configurations correspond to extreme values of this integral. But we can’t just pretend that only the best-possible path “exists”.

Thus the strip’s point. We can represent mechanics quite well. We do this by pretending there are designated starting and ending conditions. And pretending that the system selects the best of every imaginable alternative. The incautious pop physics writer, eager to find exciting stuff about quantum mechanics, will describe this as a particle “exploring” or “considering” all its options before “selecting” one. This is true in the same way that we can say a weight “wants” to roll down the hill, or two magnets “try” to match north and south poles together. We should not mistake it for thinking that electrons go out planning their days, though. Newtonian mechanics gets us used to the idea that if we knew the positions and momentums and forces between everything in the universe perfectly well, we could forecast the future and retrodict the past perfectly. Lagrangian mechanics seems to invite us to imagine a world where everything “perceives” its future and all its possible options. It would be amazing if this did not capture our imaginations.

Bil Keane and Jeff Keane’s Family Circus for the 24th of September, 2019. I’m surprised there are not more appearance of this comic strip here. But Family Circus panels inspire essays at these links.

Bil Keane and Jeff Keane’s Family Circus for the 24th has young Billy amazed by the prospect of algebra, of doing mathematics with both numbers and letters. I’m assuming Billy’s awestruck by the idea of letters representing numbers. Geometry also uses quite a few letters, mostly as labels for the parts of shapes. But that seems like a less fascinating use of letters.

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The second half of last week’s comics I hope to post here on Wednesday. Stick around and we’ll see how close I come to making it. Thank you.

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.

Art by Thomas K Dye, creator of the web comics Newshounds, Something Happens, and Infinity Refugees. His current project is Projection Edge. And you can get Projection Edge six months ahead of public publication by subscribing to his Patreon. And he’s on Twitter as @Newshoundscomic.

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 3x<sup>2</sup> + 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 , 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.

Elzie Segar’s Thimble Theater from the 14th of September, 1929. Rerun on ComicsKingdom on the 26th of February, 2016. That’s Bernice, the magical Whiffle Hen, as the strange birdlike creature in the last panel there.

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.”

Bill Amend’s FoxTrot Classics for the 23rd of May, 2018. It originally ran the 29th of May, 1996.

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.

John Rose’s Barney Google and Snuffy Smith for the 12th of February, 2016.

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.

Terri Libenson’s Pajama Diaries for the 16th of November, 2016. I was never one for buying too much of the bakery aisle, myself, but then I also haven’t got teenagers. And I did go through so much of my life figuring there was no reason I shouldn’t eat another bagel again.

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.”

Don Trachte’s Henry for the 6th of September, 2015.

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.

Scott Hilburn’s The Argyle Sweater for the 9th of May, 2018. I like the shout-out to Archimedes in the background art, too. Archimedes, though, didn’t use fractions in the way we’d recognize them. He’d write out a number as a combination of ratios of some reference number. So he might estimate the length of something being as to the length of something else as 19 is to 7, or something like that. This seems like a longwinded and cumbersome way to write out numbers, or much of anything, and makes one appreciate his indefatigability as much as his insight.

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.

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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, January 16, 2017: Better Workflow Edition

So one little secret of my Reading the Comics posts is I haven’t been writing them in a way that makes sense to me. To me, I should take each day’s sufficiently relevant comics, describe them in a paragraph or two, and then have a nice pile of text all ready for the posting Sunday and, if need be, later. I haven’t been doing that. I’ve let links pile up until Friday or Saturday, and then try to process them all, and if you’ve ever wondered why the first comic of the week gets 400 words about some subtlety while the last gets “this is a comic that exists”, there you go. This time around, let me try doing each day’s strips per day and see how that messes things up.

Jef Mallett’s Frazz for the 14th of January is another iteration of the “when will we ever use mathematics” complaint. The answer of “you’ll use it on the test” is unsatisfactory. But somehow, the answer of “you’ll use it to think deeply about something you had never considered before” also doesn’t satisfy. Anyway I’d like to see the idea that education is job-training abolished; I think it should be about making a person conversant with the history of human thought. That can’t be done perfectly, and we might ask whether factoring 32 is that important a piece, but it should certainly be striven for.

Ham’s Life on Earth for the 14th is a Gary Larsonesque riff on that great moment of calculus and physics history, Newton’s supposition that gravity has to follow a universally true law. I’m not sure this would have made my cut if I reviewed a week’s worth of strips at a time. Hm.

Mason Mastroianni’s B.C. for the 15th is a joke about story problem construction, and how the numbers in a story problem might be obvious nonsense. It’s also a cheap shot at animal hoarders, I suppose, but that falls outside my territory here.

Anthony Blades’s Bewley rerun for the 15th riffs on the natural number sense we all have. And we do have a number sense, remarkably. We might not be able to work out 9 times 6 instantly. But asked to pick from a list of possible values, we’re more likely to think that 58 is credible than that 78 or 38 are. It’s quite imprecise, but isn’t it amazing that it’s there at all?

Bill Amend’s FoxTrot Classics for the 15th is a story problem joke, in this case, creating one with a strong motivation for its solution to be found. The strip originally ran the 22nd of January, 1996.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 16th is maybe marginal to include, too. It’s about the kinds of logic puzzles that mathematicians grow up reading and like to pass around. And the way you can fake out someone by presenting a problem with too obvious a solution. It’s not just professors who’ll be stymied by having the answer look too obvious, by the way. Everyone’s similarly vulnerable. To see anything, including an abstract thing like the answer to a puzzle, you need some idea of what you are looking at. If you don’t think the answer could be something that simple, you won’t see it there.

Gordon Bess’s Redeye for the 6th of September, 1971. That’s the sort of punch line that really brings out the comically-anachronistic Old West theme.

Gordon Bess’s Redeye for the 6th of September, 1971, was reprinted the 17th. It’s about the fun of teaching a subject you aren’t all that good on yourself. The mathematics is a name-drop here, but the joke wouldn’t make sense if it were about social studies.

Elzie Segar’s Thimble Theatre for the 10th of August, 1931. Not listed: the rate of exchange for paczki, which reappeared this week.

Elzie Segar’s Thimble Theatre for the 10th of August, 1931, was also reprinted the 17th. It’s an old gag, even back when it was first run. But I suppose there’s some numerical-conversion mathematics to wring out of it. Given the rate of exchange, a pezozee would seem to be 2⁴ pazimees. I’m not sure we need so many units in-between the pazimee and the pezozee, but perhaps King Blozo’s land set its units in a time when fractions were less familiar to the public. The punch line depends on the pazimee being worth nothing and, taken literally, that has sad implications for the pezozee too. If you take the King as speaking roughly, though, sixteen times a small amount is … at least a less small amount. It wouldn’t take many doublings to go from an infinitesimally tiny sum to a respectable one.

And it turns out there were enough comic strips I need to split this into two segments. So I should schedule that to appear. It’s already written and everything.

Reading the Comics, January 9, 2018: Be Squared Edition

It wasn’t just another busy week from Comic Strip Master Command. And a week busy enough for me to split the mathematics comics into two essays. It was one where I recognized one of the panels as one I’d featured before. Multiple times. Some of the comics I feature are in perpetual reruns and don’t have your classic, deep, Peanuts-style decades of archives to draw from. I don’t usually go checking my archives to see if I’ve mentioned a comic before, not unless something about it stands out. So for me to notice I’ve seen this strip repeatedly can mean only one thing: there was something a little bit annoying about it. Recognize it yet? You will.

Hy Eisman’s Popeye for the 7th of January, 2018 is an odd place for mathematics to come in. J Wellington Wimpy regales Popeye with all the intellectual topics he tried to impress his first love with, and “Euclidean postulates in the original Greek” made the cut. And, fair enough. Euclid’s books are that rare thing that’s of important mathematics (or scientific) merit and that a lay person can just pick up and read, even for pleasure. These days we’re more likely to see a division between mathematics writing that’s accessible but unimportant (you know, like, me) or that’s important but takes years of training to understand. Doing it in the original Greek is some arrogant showing-off, though. Can’t blame Carolyn for bailing on someone pulling that stunt.

Hy Eisman’s Popeye for the 7th of January, 2018. Why does Wimpy’s shirt have a belly button?

Mark O’Hare’s Citizen Dog rerun for the 7th continues last essay’s storyline about Fergus taking Maggie’s place at school. He’s having trouble understanding the story within a story problem. I sympathize.

John Hambrock’s The Brilliant Mind of Edison Lee for the 8th is set in mathematics class. And Edison tries to use a pile of mathematically-tinged words to explain why it’s okay to read a Star Wars book instead of paying attention. Or at least to provide a response the teacher won’t answer. Maybe we can make something out of this by allowing the monetary value of something to be related to its relevance. But if we allow that then Edison’s messed up. I don’t know what quantity is measured by multiplying “every Star Wars book ever written” by “all the movies and merchandise”. But dividing that by the value of the franchise gets … some modest number in peculiar units divided by a large number of dollars. The number value is going to be small. And the dimensions are obviously crazy. Edison needs to pay better attention to the mathematics.

John Hambrock’s The Brilliant Mind of Edison Lee for the 8th of January, 2018. No, I haven’t got any idea how the third panel leads to the fourth. I mean, I know what should lead from there to there — a moment of Edison realizing he’s said something so impolitic he can’t carry on — but that moment isn’t there. The teacher seems to just shrug the whole nonsense off. Something went wrong in the composing of the joke.

Johnny Hart’s B.C. for the 14th of July, 1960 shows off the famous equation of the 20th century. All part of the comic’s anachronism-comedy chic. The strip reran the 9th of January. “E = mc²” is, correctly, associated with Albert Einstein and some of his important publications of 1905. But the expression does have some curious precursors, people who had worked out the relationship (or something close to it) before Einstein and who didn’t quite know what they had. A short piece from Scientific American a couple years back describes pre-Einstein expressions of the equation from Oliver Heaviside, Henri Poincaré, and Fritz Hasenöhrl. I’m not surprised Poincaré had something close to this; it seems like he spent twenty years almost discovering Relativity. That’s all right; he did enough in dynamical systems that mathematicians aren’t going to forget him.

Tim Lachowski’s Get A Life for the 9th is at least the fourth time I’ve seen this panel since I started doing Reading the Comics posts regularly. (Previous times: the 5th of November, 2012 and the 10th of March, 2015 and the 14th of July, 2016.) I’m like this close to concluding the strip’s in perpetual rerun and I can drop it from my daily reading.

Jason Chatfield’s Ginger Meggs for the 9th draws my eye just because the blackboard lists “Prime Numbers”. Fair enough place setting, although what’s listed are 1, 3, 5, and 7. These days mathematicians don’t tend to list 1 as a prime number; it’s inconvenient. (A lot of proofs depend on their being exactly one way to factorize a number. But you can always multiply a number by ‘1’ a couple more times without changing its value. So ‘6’ is 3 times 2, but it’s also 3 times 2 times 1, or 3 times 2 times 1 times 1, or 3 times 2 times 1^{145,388,434,247}. You can write around that, but it’s easier to define ‘1’ as not a prime.) But it could be defended. I can’t think any reason to leave ‘2’ off a list of prime numbers, though. I think Chatfield conflated odd and prime numbers. If he’d had a bit more blackboard space we could’ve seen whether the next item was 9 or 11 and that would prove the matter.

Paul Trap’s Thatababy for the 9th uses arithmetic — square roots — as the kind of thing to test whether a computer’s working. Everyone has their little tests like this. My love’s father likes to test whether the computer knows of the band Walk The Moon or of Christine Korsgaard (a prominent philosopher in my love’s specialty). I’ve got a couple words I like to check dictionaries for. Of course the test is only any good if you know what the answer should be, and what’s the actual square root of 3,278? Goodness knows. It’s got to be between 50 (50 squared is 25 hundred) and 60 (60 squared is 36 hundred). Since 3,278 is so much closer 3,600 than 2,500 its square root should be closer to 60 than to 50. So 57-point-something is plausible. Unfortunately square roots don’t lend themselves to the same sorts of tricks from reading the last digit that cube roots do. And 3,278 isn’t a perfect square anyway. Alexa is right on this one. Also about the specific gravity of cobalt, at least if Wikipedia is right and not conspiring with the artificial intelligences on this one. Catch you in 2021.

Charles Schulz’s Peanuts for the 8th of October, 1953, is about practical uses of mathematics. It got rerun on the 9th of January.

Reading the Comics, December 16, 2017: Andertoons Drought Ended Edition

And now, finally, we get what we’ve been waiting so long for: my having enough energy and time to finish up last week’s comics. And I make excuses to go all fanboy over Elzie Segar’s great Thimble Theatre. Also more attention to Zach Weinersmith. You’ve been warned.

Mark Anderson’s Andertoons for the 13th is finally a breath of Mark Anderson’s Andertoons around here. Been far too long. Anyway it’s an algebra joke about x’s search for identity. And as often happens I’m sympathetic here. It’s not all that weird to think of ‘x’ as a label for some number. Knowing whether it means “a number whose value we haven’t found yet” or “a number whose value we don’t care about” is one trick, though. It’s not something you get used to from learning about, like, ‘6’. And knowing whether we can expect ‘x’ to have held whatever value it represented before, or whether we can expect it to be something different, is another trick.

Doug Bratton’s Pop Culture Shock Therapy for the 13th I feel almost sure has come up here before. Have I got the energy to find where? Oh, yes. It ran the 5th of September, 2015.

David Gilbert’s Buckles for the 14th of December, 2017. I quite like Buckles’s little off-put look in the final panel. It’s very dog considering the situation.

David Gilbert’s Buckles for the 14th is a joke on animals’ number sense. In fairness, after that start I wouldn’t know whether to go for four or five barks myself.

Bud Blake’s Tiger for the 15th of December, 2017. One of my love’s favorite recurring motifs in Peanuts is when Sally works out some ridiculous string of not-quite-reasoning and Charlie Brown just sits and watches and kind of stares at the reader through it. Tiger is definitely doing that same “… what?” look as Hugo figures out his strategy.

Bud Blake’s Tiger for the 15th is a bit of kid logic about how to make a long column of numbers easier to add. I endorse the plan of making the column shorter, although I’d do that by trying to pair up numbers that, say, add to 10 or 20 or something else easy to work with. Partial sums can make the overall work so much easier. And probably avoid mistakes.

Elzie Segar’s Thimble Theatre for the 8th of July, 1931, and rerun the 15th of December, 2017. If I’m not missing, this week has included Popeye’s first claims about spinach providing him with superior strength. And I know you’re looking at the referee there and thinking J Wellington Wimpy. I’m not sure, since I haven’t checked the complete collection to read ahead in the story, but I think this is merely a proto-Wimpy. (Mind, the Wikipedia entry on this is a complete mess. Bud Sagendorf’s Popeye: The First Fifty Years says Wimpy was derived from a minor character in Segar’s earlier The Five-Fifteen strip, which would itself turn into Sappo. But that proto-Wimpy didn’t have much personality or even a name.)

Elzie Segar’s Thimble Theatre for the 8th of July, 1931, is my most marginal inclusion yet. It was either that strip or the previous day’s worth including. I’m throwing it in here because Segar’s Thimble Theatre keeps being surprisingly good. And, heck, slowing a count by going into fractions is viable way to do it. As the clobbered General Bunzo points out, you can drag this out longer by going into hundredths. Or smaller units. There is no largest real number less than ten; if it weren’t incredibly against the rules, boxers could make use of that.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is about those mathematics problems with clear and easy-to-understand statements whose answers defy intuition. Weinersmith is completely correct about all of this. I’m surprised he doesn’t mention the one about how you could divide an orange into five pieces, reassemble the pieces, and get back two spheres each the size of a sun.

Reading the Comics, October 7, 2017: Rerun Comics Edition

The most interesting mathematically-themed comic strips from last week were also reruns. So be it; at least I have an excuse to show a 1931-vintage comic. Also, after discovering my old theme didn’t show the category of essay I was posting, I did literally minutes of search for a new theme that did. And that showed tags. And that didn’t put a weird color behind LaTeX inline equations. So I’m using the same theme as my humor blog does, albeit with a different typeface, and we’ll hope that means I don’t post stuff to the wrong blog. As it is I start posting something to the wrong place about once every twenty times. All I want is a WordPress theme with all the good traits of the themes I look at and none of the drawbacks; why is that so hard to get?

Elzie Segar’s Thimble Theatre rerun for the 25th of April, 1931, and rerun the 5th of October, 2017. No, Kabibble Kabaret is not actually a joke and yes, it’s always like that, and no, I have no idea why Comics Kingdom includes these footers. I find them fascinating in their badness, but, yeah.

Elzie Segar’s Thimble Theatre rerun for the 5th originally ran the 25th of April, 1931. It’s just a joke about Popeye not being good at bookkeeping. In the story, Popeye’s taking the $50,000 reward from his last adventure and opened a One-Way Bank, giving people whatever money they say they need. And now you understand how the first panel of the last row has several jokes in it. The strip is partly a joke about Popeye being better with stuff he can hit than anything else, of course. I wonder if there’s an old stereotype of sailors being bad at arithmetic. I remember reading about pirate crews that, for example, not-as-canny-as-they-think sailors would demand a fortieth or a fiftieth of the prizes as their pay, instead of a mere thirtieth. But it’s so hard to tell what really happened and what’s just a story about the stupidity of people. Marginal? Maybe, but I’m a Popeye fan and this is my blog, so there.

Bill Rechin’s Crock rerun(?) from the 6th must have come before. I don’t know when. Anyway it’s a joke about mathematics being way above everybody’s head.

Bill Rechin’s Crock from the 6th of October, 2017. Yeah, I don’t exactly get the vulture as a pack animal either, but it’s kind of a cute idea. Or I’m a soft touch for cartoon and comic strip vultures. I would like to identify the characters but I forget their names and Wikipedia and the official Comics Kingdom site don’t give me any help.

Norm Feuti’s Gil rerun for the 6th is a subverted word problem joke. And it’s a reminder of how hard story problems can be. You need something that has a mathematics question on point. And the question has to be framed as asking something someone would actually care to learn. Plus the story has to make sense. Much easier when you’re teaching calculus, I think.

Jason Chatfield’s Ginger Meggs for the 6th is a playing-stupid joke built in percentages. Cute enough for the time it takes to read.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 6th is a parent-can’t-help-with-homework joke, done with arithmetic since it’s hard to figure another subject that would make the joke possible. I suppose a spelling assignment could be made to work. But that would be hard to write so it didn’t seem contrived.

Thaves’ Frank and Ernest for the 7th feels like it’s a riff on the old saw about Plato’s Academy. (The young royal sent home with a coin because he asked what the use of this instruction was, and since he must get something from everything, here’s his drachma.) Maybe. Or it’s just the joke that you make if you have “division” and “royals” in mind.

Mark Tatulli’s Lio for the 7th is not quite the anthropomorphic symbols joke for this past week. It’s circling that territory, though.

Reading the Comics, October 22, 2015: Foundations Edition

I am, yes, saddened to hear that Apartment 3-G is apparently shuffling off to a farm upstate. There it will be visited by a horrifying kangaroo-deer-fox-demon. And an endless series of shots of two talking heads saying they should go outside, when they’re already outside. But there are still many comic strips running, on Gocomics.com and on Comics Kingdom. They’ll continue to get into mathematically themed subjects. And best of all I can use a Popeye strip to talk about the logical foundations of mathematics and what computers can do for them.

Jef Mallett’s Frazz for the 18th of October carries on the strange vendetta against “showing your work”. If you do read through the blackboard-of-text you’ll get some fun little jokes. I like the explanation of how “obscure calculus symbols” could be used, “And a Venn diagram!” Physics majors might notice the graph on the center-right, to the right of the DNA strand. That could show many things, but the one most plausible to me is a plot of the velocity and the position of an object undergoing simple harmonic motion.

Still, I do wonder what work Caulfield would show if the problem were to say what fraction were green apples, if there were 57 green and 912 red apples. There are levels where “well, duh” will not cut it. In case “well, duh” does cut it, then a mathematician might say the answer is “obvious”. But she may want to avoid the word “obvious”, which has a history of being dangerously flexible. She might then say “by inspection”. That means, basically, look at it and yeah, of course that’s right.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 18th of October uses mathematics as the quick way to establish “really smart”. It doesn’t take many symbols this time around, curiously. Superstar Equation E = mc² appears in a misquoted form. At first that seems obvious, since if there were an equals sign in the denominator the whole expression would not parse. Then, though, you notice: if E and m and c mean what they usually do in the Superstar Equation, then, “E – mc²” is equal to zero. It shouldn’t be in the denominator anyway. So, the big guy has to be the egghead.

Peter Maresca’s Origins of the Sunday Comics for the 18th of October reprints one of Windsor McCay’s Dreams of the Rarebit Fiend strips. As normal for Dreams and so much of McCay’s best work, it’s a dream-to-nightmare strip. And this one gives a wonderful abundance of numerals, and the odd letter, to play with. Mathematical? Maybe not. But it is so merrily playful it’d be a shame not to include.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 20th of October is a joke soundly in set theory. It also feels like it’s playing with a set-theory-paradox problem but I can’t pin down which one exactly. It feels most like the paradox of “find the smallest uninteresting counting number”. But being the smallest uninteresting counting number would be an interesting property to have. So any candidate number has to count as interesting. It also feels like it’s circling around the heap paradox. Take a heap of sand and remove one grain, and you still have a heap of sand. But if you keep doing that, at some point, you have just one piece of sand from the original pile, and that is no heap. When does the heap move away?

Daniel Shelton’s Ben for the 21st of October is a teaching-arithmetic problem, using jellybeans. And fractions. Well, real objects can do wonders in connecting a mathematical abstraction to something one has an intuition for. One just has to avoid unwanted connotations and punching.

Doug Savage’s Savage Chickens for the 21st of October uses “mathematics homework” as the emblem of the hardest kind of homework there might ever be. I saw the punch line coming a long while off, but still laughed.

Bud Sagendorf’s Popeye for the 22nd of October, 2015. The strip originally ran sometime in 1981. This would be only a few years after the Four-Color Theorem was solved by computer. The computer did this by trying out all the possibilities and reporting everything was OK.

Bud Sagendorf’s Popeye began what it billed as a new story, “Science Vs Sorcery”, on Monday the 19th. I believe it’s properly a continuation of the previous story, though, “Back-Room Pest!” which began the 13th of July. “Back-Room Pest!”, according to my records, originally ran from the 27th of July, 1981, through to the 23rd of January, 1982. So there’s obviously time missing. And this story, like “Back-Room Pest”, features nutty inventor Professor O G Wotasnozzle. I know, I know, you’re all deeply interested in working out correct story guides for this.

Anyway, the Sea Hag in arguing against scientists claims “they can’t even think! They have to use machines to tell them what two plus two is!! And another machine to prove the first one was right!” It’s a funny line and remarkably pointed for an early-80s Popeye comic. The complaint that computers leave one unable to do even simple reasoning is an old one, of course. The complaint has been brought against every device or technique that promises to lighten a required mental effort. It seems to me similar to the way new kinds of weapons are accused of making war too monstrous and too unchivalrous, too easily done by cowards. I suppose it’s also the way a fable like the story of John Henry hold up human muscle against the indignity of mechanical work.

The crack about needing another machine to prove the first was right is less usual, though. Sagendorf may have meant to be whimsically funny, but he hit on something true. One of the great projects of late 19th and early 20th century mathematics was the attempt to place its foundations on strict logic, independent of all human intuition. (Intuition can be a great guide, but it can lead one astray.) Out of this came a study of proofs as objects, as mathematical constructs which must themselves follow certain rules.

And here we reach a spooky borderland between mathematics and sorcery. We can create a proof system that is, in a way, a language with a grammar. A string of symbols that satisfies all the grammatical rules is itself a proof, a valid argument following from the axioms of the system. (The axioms are some basic set of statements which we declare to be true by assumption.) And it does not matter how the symbols are assembled: by mathematician, by undergrad student worker, by monkey at a specialized typewriter, by a computer stringing things together. Once a grammatically valid string of symbols is done, that string of symbols is a theorem, with its proof written out. The proof is the string of symbols that is the theorem written out. If it were not for the modesty of what is claimed to be done — proofs about arithmetic or geometry or the like — one might think we had left behind mathematics and were now summoning demons by declaring their True Names. Or risk the stars overhead going out, one by one.

So it is possible to create a machine that simply grinds out proofs. Or, since this is the 21st century, a computer that does that. If the computer is given no guidance it may spit out all sorts of theorems that are true but boring. But we can set up a system by which the computer, by itself, works out whether a given theorem does follow from the axioms of mathematics. More, this has been done. It’s a bit of a pain, because any proofs that are complicated enough to really need checking involve an incredible number of steps. But for a challenging enough proof it is worth doing, and automated proof checking is one of the tools mathematicians can now draw on.

Of course, then we have the problem of knowing that the computer is carrying out its automatic-proof programming correctly. I’m not stepping into that kind of trouble.

The attempt to divorce mathematics from all human intuition was a fruitful one. The most awe-inspiring discovery to come from it is surely that of incompleteness. Any mathematical system interesting enough will contain within it statements that are true, but can’t be proven true from the axioms.

Georgia Dunn’s Breaking Cat News for the 22nd of October features a Venn Diagram. It’s part of how cats attempt to understand toddlers. My understanding is that their work is correct.

How May 2015 Treated My Mathematics Blog

For May 2015 I tried a new WordPress theme — P2 Classic — and I find I rather like it. Unfortunately it seems to be rubbish on mobile devices and I’m not WordPress Theme-equipped-enough to figure out how to fix that. I’m sorry, mobile readers. I’m honestly curious whether the theme change affected my readership, which was down appreciably over May.

According to WordPress, the number of pages viewed here dropped to 936 in May, down just over ten percent from April’s 1047 and also below March’s 1022. Perhaps the less-mobile-friendly theme was shooing people away. Maybe not, though: in March and April I’d posted 14 articles each, while in May there were a mere twelve. The number of views per post increased steadily, from 73 in March to just under 75 in April to 78 in May. I’m curious if this signifies anything. I may get some better idea next month. June should have at least 13 posts from the Mathematics A To Z gimmick, plus this statistics post, and there’ll surely be at least two Reading The Comics posts, or at least sixteen posts. And who knows what else I’ll feel like throwing in? It’ll be an interesting experiment at least.

Anyway, the number of unique visitors rose to 415 in May, up from April’s 389 but still below March’s 468. The number of views per visitor dropped to 2.26, far below April’s 2.68, but closer in line with March’s 2.18. And 2.26 is close to the normal count for this sort of thing.

The number of likes on posts dropped to 259. In April it was 296 likes and in March 265. That may just reflect the lower number of posts, though. Divide the number of likes by the number of posts and March saw an average of 18.9, April 21.14, and May 21.58. That’s all at least consistent, although there’s not much reason to suppose that only things from the current month were liked.

The number of comments recovered also. May saw 83 comments, up from April’s 64, but not quite back to March’s 93. That comes to, for May, 6.9 comments for each post, but that’s got to be counting links to other posts, including pingbacks and maybe the occasional reblogging. I’ve been getting chattier with folks around here, but not seven comments per post chatty.

June starts at 24,820 views, and 485 people following specifically through WordPress.

I’ve got a healthy number of popular posts the past month; all of these got at least 37 page views each. I cut off at 37 because that’s where the Trapezoids one came in and we already know that’s popular. More popular than that were:

• Reading the Comics, April 20, 2015: History of Mathematics Edition
• Reading the Comics, May 9, 2015: Trapezoid Edition
• Reading The Comics, May 22, 2015: Might Be Giving Up Mickey Mouse Edition
• Reading the Comics, May 4, 2015: Hatless Aliens Edition
• Reading the Comics, May 14, 2015: At The Cash Register Edition
• Calculating Pi Less Terribly
• Playful Mathematics: Sweet Add-A-Line

I have the suspicion that comics fans are catching on, quietly, to all this stuff.

Now the countries report. The nations sending me at least twenty page views were the United States (476), the United Kingdom (85), Canada (65), Italy (53), and Austria (20).

Sending just a single reader were Belgium, Bulgaria, Colombia, Nigeria, Norway, Pakistan, Romania, and Vietnam. Romania is on a three-month single-reader streak; Vietnam, two. India sent me a mere two readers, down from six last month. The European Union sent me three.

And among the interesting search terms this past month were:

• origin is the gateway to your entire gaming universe.
• how to do a cube box (the cube is easy enough, it’s getting the boxing gloves on that’s hard)
• popeye “computer king” (Remember that comic?)
• google can you show me in 1 trapezoid how many cat how many can you make of 2 (?, although I like the way Google is named at the start of the query, like someone on Next Generation summoning the computer)
• plato “divided line” “arthur cayley” (I believe that mathematics comes in on the lower side of the upper half of Plato’s divided line)
• where did negative numbers originate from

Someday I must work out that “origin is the gateway” thing.

20,000: My Math Blog’s Statistics

I reached my 20,000th view around here sometime on the final day of 2014, which is an appealingly tidy coincidence. I’m glad for it. It also gives me a starting point to review the blog’s statistics, as gathered by WordPress, which is trying to move us to a new and perfectly awful statistics page that shows less information more inconveniently.

The total number of page views grew from 625 in October to 674 in November all the way to 831 in December 2014, which just ties my record number of viewers from back in January 2013. The number of unique visitors grew from October’s 323 to November’s 366 up to 424 total, which comes in second-place to January 2013’s 473. I don’t know what I was doing in January 2013 that I’m only gradually getting back up to these days. The number of views per visitor went from 1.93, to 1.84, back up to 1.96, which is probably just a meaningless fluctuation. January 2013 had 1.76.

My most popular articles — with 25 views or more each — were Reading The Comics posts, mostly, with the exceptions being two things almost designed to be clickbait, although I mean them sincerely:

1. Reading the Comics, December 14, 2014: Pictures Gone Again? Edition, in which I work out one of the calculus-y expressions and find it isn’t all that interesting.
2. Reading the Comics, December 5, 2014: Good Questions Edition, in which I figured out a Dark Side Of The Horse comic was using a page of symbols from orbital perturbation problems.
3. Reading the Comics, December 27, 2014: Last of the Year Edition?, which it wasn’t, and which let me talk about how Sally Brown is going to discover rational numbers if Charlie Brown doesn’t over-instruct her.
4. Reading The Comics, December 22, 2015: National Mathematics Day Edition, which celebrated Srinivasa Ramanujan’s birth by showing a formula that Leonhard Euler discovered, but Euler’s formula is much more comic-strip-readable than any of Ramanujan’s.
5. What Do I Need To Pass This Class? (December 2014 Edition), which gathered and reposted for general accessibility the formula and the charts so people can figure out what the subject line says. Also what you need to get a B, or A, or any other desired grade. (Mostly, you needed to start caring about your grade earlier.)
6. How Many Trapezoids I Can Draw, my life’s crowning achievement. (Six. If you find a seventh please let me know and I’ll do a follow-up post.)

The country sending me the most readers was, as ever, Bangladesh with 535 viewers. Well, two viewers, but it’s boring just listing the United States up front every time. The United Kingdom (37) and Canada (33) came up next, then Argentina (17), which surprises me every month by having a healthy number of readers there, Australia (12), Austria (11), and the Netherlands (10), proving that people in countries that don’t start with ‘A’ can still kind of like me too. The single-reader countries this month were the Czech Republic, Greece, Macedonia, Mexico, Romania, and South Africa. That’s far fewer than last month; of November’s 17 single-reader countries only Romania is a repeat.

Among search terms that brought people here were popeye comic computer king — I don’t know just how that’s going to end up either, folks, but I’m guessing “not that satisfyingly”, since Bud Sagendorf was fond of shaggy-dog non-endings to tales — and which reindeer was in arthur christmas (they were descendants of the “Original” canonical eight, though Grand-Santa forgets some of the names), daily press, “the dinette set” answer for december 11, 2014, and solution to the comic puzzle, “the dinette set”. in the daily press, december 12, 2014, and answer to the comic puzzle, “the dinette set”. in the daily press, december 12, 2014, which suggests maybe I should ditch the pop-math racket and just get into explaining The Dinette Set, which is admittedly kind of a complicated panel strip. There’s multiple riffs around the central joke in each panel, but if you don’t get the main joke then the riffs look like they’re part of the main joke, and they aren’t, so the whole thing becomes confusing. And the artist includes a “Find-It” bit in every panel, usually hiding something like a triangle or a star or something in the craggly details of the art and that can be hard to find. Mostly, though, the joke is: these people are genially and obliviously obnoxious people who you might love but you’d still find annoying. That’s it, nearly every panel. I hope that helps.