I have only a couple strips this time, and from this week. I’m not sure when I’ll return to full-time comics reading, but I do want to share strips that inspire something.
Carol Lay’s Lay Lines for the 24th of May riffs on Hilbert’s Hotel. This is a metaphor often used in pop mathematics treatments of infinity. So often, in fact, a friend snarked that he wished for any YouTube mathematics channel that didn’t do the same three math theorems. Hilbert’s Hotel was among them. I think I’ve never written a piece specifically about Hilbert’s Hotel. In part because every pop mathematics blog has one, so there are better expositions available. I have a similar restraint against a detailed exploration of the different sizes of infinity, or of the Monty Hall Problem.
Hilbert’s Hotel is named for David Hilbert, of Hilbert problems fame. It’s a thought experiment to explore weird consequences of our modern understanding of infinite sets. It presents various cases about matching elements of a set to the whole numbers, by making it about guests in hotel rooms. And then translates things we accept in set theory, like combining two infinitely large sets, into material terms. In material terms, the operations seem ridiculous. So the set of thought experiments get labelled “paradoxes”. This is not in the logician sense of being things both true and false, but in the ordinary sense that we are asked to reconcile our logic with our intuition.
So the Hotel serves a curious role. It doesn’t make a complex idea understandable, the way many demonstrations do. It instead draws attention to the weirdness in something a mathematics student might otherwise nod through. It does serve some role, or it wouldn’t be so popular now.
Anyway, Carol Lay does an great job making a story of it.
Leigh Rubin’s Rubes for the 25th of May I’ll toss in here too. It’s a riff on the art convention of a blackboard equation being meaningless. Normally, of course, the content of the equation doesn’t matter. So it gets simplified and abstracted, for the same reason one draws a brick wall as four separate patches of two or three bricks together. It sometimes happens that a cartoonist makes the equation meaningful. That’s because they’re a recovering physics major like Bill Amend of FoxTrot. Or it’s because the content of the blackboard supports the joke. Which, in this case, it does.
Doug Savage’s Savage Chickens for the 26th uses a blackboard of mathematics (as part of “understanding of particle physics”) as symbolic of intelligence. I’m not versed enough in particle physics to say whether the expressions make sense. I’m inclined toward it, since the first line has an integral of the reciprocal of the distance between a point x and a point x’. That looks to me like a calculation of some potential energy-related stuff.
Dana Simpson’s Phoebe and her Unicorn for the 27th uses “memorizing multiplication tables” as the sort of challenging and tedious task that a friend would not put another one through. The strip surprised me; I would have thought Phoebe the sort of kid who’d find multiplication tables, with their symmetry and teasing hints of structure (compare any number on the upper-left-to-lower-right diagonal to the numbers just up-and-right or down-and-left to it, for example), fascinating enough to memorize on their own.
Leigh Rubin’s Rubes for the 27th has a rat-or-mouse showing off one of those exciting calculations about how many rats-or-mice could breed in a year if absolutely nothing limited their growth. These sorts of calculations are fun for getting to big numbers in pretty little time. They’re only the first, loosest pieces of a model for anything’s population, though.
Pab Sungenis’s New Adventures of Queen Victoria for the 28th gets into the question about whether the new decade starts in 2020 or 2021. I wasn’t aware people were asking the question until a few weeks ago, when my father asked me for an authoritative answer. He respects my credentials as a mathematician and a calendar freak. The only answer I can defend, though, is to say of course a new decade starts in 2020. A new decade also starts in 2021. There’s also a decade starting in 2022. There’s a new decade starting five minutes from the moment you read this sentence. If you hurry you just might make it.
If you want to make any claims about “the” new decade, you have to say what you pick “the” to signify. Complete decades from the (proleptically defined) 1st of January, 1, is a compelling choice. “Years starting the 1st of January, 2020” is also a compelling choice. Decide your preference and you’ll decide your answer.
Thank you for reading, this essay and this whole year. 2020 is, of course, a leap year, or “bissextile year” if you want to establish your reputation as a calendar freak. Good luck.
I’d like to open today’s installment with a trifle from Thomas K Dye. He’s a friend, and the cartoonist behind the long-running web comic Newshounds, its new spinoff Infinity Refugees, and some other projects.
Q: Have you read the story of Solidus and Virgule? A: Nah, I'm not into slash fiction.
Dye also has a Patreon, most recently featuring a subscribers-only web comic. And he’s good enough to do the occasional bit of spot art to spruce up my work here.
Henry Scarpelli and Craig Boldman’s Archie rerun for the 9th of April, 2018 is, for me, relatable. I think I’ve read off this anecdote before. The first time I took Real Analysis I was completely lost. Getting me slightly less lost was borrowing a library book on Real Analysis from the mathematics library. The book was in French, a language I can only dimly read. But the different presentation and, probably, the time I had to spend parsing each sentence helped me get a basic understanding of the topic. So maybe trying algebra upside-down isn’t a ridiculous idea.
Lincoln Pierce’s Big Nate rerun for the 9th presents an arithmetic sequence, which is always exciting to work with, if you’re into sequences. I had thought Nate was talking about mathematics quizzes but I see that’s not specified. Could be anything. … And yes, there is something cool in finding a pattern. Much of mathematics is driven by noticing, or looking for, patterns in things and then describing the rules by which new patterns can be made. There’s many easy side questions to be built from this. When would quizzes reach a particular value? When would the total number of points gathered reach some threshold? When would the average quiz score reach some number? What kinds of patterns would match the 70-68-66-64 progression but then do something besides reach 62 next? Or 60 after that? There’s some fun to be had. I promise.
Dave Whamond’s Reality Check for the 10th similarly doesn’t depend on what the question is. It happens to be arithmetic, but it could as easily be identifying George Washington or picking out the noun in a sentence.
Leigh Rubin’s Rubes for the 10th riffs on randomness. In this case it’s riffing on the unpredictability and arbitrariness of random things. Random variables are very interesting in certain fields of mathematics. What makes them interesting is that any specific value — the next number you generate — is unpredictable. But aggregate information about the values is predictable, often with great precision. For example, consider normal distributions. (A lot of stuff turns out to be normal.) In that case we can be confident that the values that come up most often are going to be close to the arithmetic mean of a bunch of values. And that there’ll be about as many values greater than the mean as there are less than the mean. And this will be only loosely true if you’ve looked at a handful of values, at ten or twenty or even two hundred of them. But if you looked at, oh, a hundred thousand values, these truths would be dead-on. It’s wonderful and it seems to defy intuition. It just works.
John Atkinson’s Wrong Hands for the 10th is the anthropomorphic numerals joke for the week. It’s easy to think of division as just making numbers smaller: 4 divided by 6 is less than either 4 or 6. 1 divided by 4 is less than either 1 or 4. But this is a bad intuition, drawn from looking at the counting numbers that don’t look boring. But 4 divided by 1 isn’t less than either 1 or 4. Same with 6 divided by 1. And then when we look past counting numbers we realize that’s not always so. 6 divided by ½ gives 12, greater than either of those numbers, and I don’t envy the teachers trying to explain this to an understandably confused student. And whether 6 divided by -1 gives you something smaller than 6 or smaller than -1 is probably good for an argument in an arithmetic class.
Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 11th has an argument about predicting humans mathematically. It’s so very tempting to think people can be. Some aspects of people can. In the founding lore of statistics is the astonishment at how one could predict how many people would die, and from what causes, over a time. No person’s death could be forecast, but their aggregations could be. This unsettles people. It should: it seems to defy reason. It seems to me even people who embrace a deterministic universe suppose that while, yes, a sufficiently knowledgeable creature might forecast their actions accurately, mere humans shouldn’t be sufficiently knowledgeable.
No strips are tagged for the first time this essay. Just noticing.
And now to wrap up last week’s mathematically-themed comic strips. It’s not a set that let me get into any really deep topics however hard I tried overthinking it. Maybe something will turn up for Sunday.
Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. for the 7th tries setting arithmetic versus celebrity trivia. It’s for the old joke about what everyone should know versus what everyone does know. One might question whether Kardashian pet eating habits are actually things everyone knows. But the joke needs some hyperbole in it to have any vitality and that’s the only available spot for it. It’s easy also to rate stuff like arithmetic as trivia since, you know, calculators. But it is worth knowing that seven squared is pretty close to 50. It comes up when you do a lot of estimates of calculations in your head. The square root of 10 is pretty near 3. The square root of 50 is near 7. The cube root of 10 is a little more than 2. The cube root of 50 a little more than three and a half. The cube root of 100 is a little more than four and a half. When you see ways to rewrite a calculation in estimates like this, suddenly, a lot of amazing tricks become possible.
Leigh Rubin’s Rubes for the 7th is a “mathematics in the real world” joke. It could be done with any mythological animals, although I suppose unicorns have the advantage of being relatively easy to draw recognizably. Mermaids would do well too. Dragons would also read well, but they’re more complicated to draw.
Mark Pett’s Mr Lowe rerun for the 8th has the kid resisting the mathematics book. Quentin’s grounds are that how can he know a dated book is still relevant. There’s truth to Quentin’s excuse. A mathematical truth may be universal. Whether we find it interesting is a matter of culture and even fashion. There are many ways to present any fact, and the question of why we want to know this fact has as many potential answers as it has people pondering the question.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th is a paean to one of the joys of numbers. There is something wonderful in counting, in measuring, in tracking. I suspect it’s nearly universal. We see it reflected in people passing around, say, the number of rivets used in the Chrysler Building or how long a person’s nervous system would reach if stretched out into a line or ever-more-fanciful measures of stuff. Is it properly mathematics? It’s delightful, isn’t that enough?
Bill Rechin’s Crock rerun for the 11th is a name-drop of mathematics. Really anybody’s homework would be sufficiently boring for the joke. But I suppose mathematics adds the connotation that whatever you’re working on hasn’t got a human story behind it, the way English or History might, and that it hasn’t got the potential to eat, explode, or knock a steel ball into you the way Biology, Chemistry, or Physics have. Fair enough.