## Reading the Comics, August 16, 2019: The Comments Drive Me Crazy Edition

Last week was another light week of work from Comic Strip Master Command. One could fairly argue that nothing is worth my attention. Except … one comic strip got onto the calendar. And that, my friends, is demanding I pay attention. Because the comic strip got multiple things wrong. And then the comments on GoComics got it more wrong. Got things wrong to the point that I could not be sure people weren’t trolling each other. I know how nerds work. They do this. It’s not pretty. So since I have the responsibility to correct strangers online I’ll focus a bit on that.

Robb Armstrong’s JumpStart for the 13th starts off all right. The early Roman calendar had ten months, December the tenth of them. This was a calendar that didn’t try to cover the whole year. It just started in spring and ran into early winter and that was it. This may seem baffling to us moderns, but it is, I promise you, the least confusing aspect of the Roman calendar. This may seem less strange if you think of the Roman calendar as like a sports team’s calendar, or a playhouse’s schedule of shows, or a timeline for a particular complicated event. There are just some fallow months that don’t need mention.

Things go wrong with Rob’s claim that December will have five Saturdays, five Sundays, and five Mondays. December 2019 will have no such thing. It has four Saturdays. There are five Sundays, Mondays, and Tuesdays. From Crunchy’s response it sounds like Joe’s run across some Internet Dubious Science Folklore. You know, where you see a claim that (like) Saturn will be larger in the sky than anytime since the glaciers receded or something. And as you’d expect, it’s gotten a bit out of date. December 2018 had five Saturdays, Sundays, and Mondays. So did December 2012. And December 2007.

And as this shows, that’s not a rare thing. Any month with 31 days will have five of some three days in the week. August 2019, for example, has five Thursdays, Fridays, and Saturdays. October 2019 will have five Tuesdays, Wednesdays, and Thursdays. This we can show by the pigeonhole principle. And there are seven months each with 31 days in every year.

It’s not every year that has some month with five Saturdays, Sundays, and Mondays in it. 2024 will not, for example. But a lot of years do. I’m not sure why December gets singled out for attention here. From the setup about December having long ago been the tenth month, I guess it’s some attempt to link the fives of the weekend days to the ten of the month number. But we get this kind of December about every five or six years.

This 823 years stuff, now that’s just gibberish. The Gregorian calendar has its wonders and mysteries yes. None of them have anything to do with 823 years. Here, people in the comments got really bad at explaining what was going on.

So. There are fourteen different … let me call them year plans, available to the Gregorian calendar. January can start on a Sunday when it is a leap year. Or January can start on a Sunday when it is not a leap year. January can start on a Monday when it is a leap year. January can start on a Monday when it is not a leap year. And so on. So there are fourteen possible arrangements of the twelve months of the year, what days of the week the twentieth of January and the thirtieth of December can occur on. The incautious might think this means there’s a period of fourteen years in the calendar. This comes from misapplying the pigeonhole principle.

Here’s the trouble. January 2019 started on a Tuesday. This implies that January 2020 starts on a Wednesday. January 2025 also starts on a Wednesday. But January 2024 starts on a Monday. You start to see the pattern. If this is not a leap year, the next year starts one day of the week later than this one. If this is a leap year, the next year starts two days of the week later. This is all a slightly annoying pattern, but it means that, typically, it takes 28 years to get back where you started. January 2019 started on Tuesday; January 2020 on Wednesday, and January 2021 on Friday. the same will hold for January 2047 and 2048 and 2049. There are other successive years that will start on Tuesday and Wednesday and Friday before that.

Except.

The important difference between the Julian and the Gregorian calendars is century years. 1900. 2000. 2100. These are all leap years by the Julian calendar reckoning. Most of them are not, by the Gregorian. Only century years divisible by 400 are. 2000 was a leap year; 2400 will be. 1900 was not; 2100 will not be, by the Gregorian scheme.

These exceptions to the leap-year-every-four-years pattern mess things up. The 28-year-period does not work if it stretches across a non-leap-year century year. By the way, if you have a friend who’s a programmer who has to deal with calendars? That friend hates being a programmer who has to deal with calendars.

There is still a period. It’s just a longer period. Happily the Gregorian calendar has a period of 400 years. The whole sequence of year patterns from 2000 through 2019 will reappear, 2400 through 2419. 2800 through 2819. 3200 through 3219.

(Whether they were also the year patterns for 1600 through 1619 depends on where you are. Countries which adopted the Gregorian calendar promptly? Yes. Countries which held out against it, such as Turkey or the United Kingdom? No. Other places? Other, possibly quite complicated, stories. If you ask your computer for the 1619 calendar it may well look nothing like 2019’s, and that’s because it is showing the Julian rather than Gregorian calendar.)

Except.

This is all in reference to the days of the week. The date of Easter, and all of the movable holidays tied to Easter, is on a completely different cycle. Easter is set by … oh, dear. Well, it’s supposed to be a simple enough idea: the Sunday after the first spring full moon. It uses a notional moon that’s less difficult to predict than the real one. It’s still a bit of a mess. The date of Easter is periodic again, yes. But the period is crazy long. It would take 5,700,000 years to complete its cycle on the Gregorian calendar. It never will. Never try to predict Easter. It won’t go well. Don’t believe anything amazing you read about Easter online.

Michael Jantze’s The Norm (Classics) for the 15th is much less trouble. It uses some mathematics to represent things being easy and things being hard. Easy’s represented with arithmetic. Hard is represented with the calculations of quantum mechanics. Which, oddly, look very much like arithmetic. $\phi = BA$ even has fewer symbols than $1 + 1 = 2$ has. But the symbols mean different abstract things. In a quantum mechanics context, ‘A’ and ‘B’ represent — well, possibly matrices. More likely operators. Operators work a lot like functions and I’m going to skip discussing the ways they don’t. Multiplying operators together — B times A, here — works by using the range of one function as the domain of the other. Like, imagine ‘B’ means ‘take the square of’ and ‘A’ means ‘take the sine of’. Then ‘BA’ would mean ‘take the square of the sine of’ (something). The fun part is the ‘AB’ would mean ‘take the sine of the square of’ (something). Which is fun because most of the time, those won’t have the same value. We accept that, mathematically. It turns out to work well for some quantum mechanics properties, even though it doesn’t work like regular arithmetic. So $\phi = BA$ holds complexity, or at least strangeness, in its few symbols.

Henry Scarpelli and Craig Boldman’s Archie for the 16th is a joke about doing arithmetic on your fingers and toes. That’s enough for me.

There were some more comic strips which just mentioned mathematics in passing.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers rerun for the 11th has a blackboard of mathematics used to represent deep thinking. Also, it I think, the colorist didn’t realize that they were standing in front of a blackboard. You can see mathematicians doing work in several colors, either to convey information in shorthand or because they had several colors of chalk. Not this way, though.

Mark Leiknes’s Cow and Boy rerun for the 16th mentions “being good at math” as something to respect cows for. The comic’s just this past week started over from its beginning. If you’re interested in deeply weird and long-since cancelled comics this is as good a chance to jump on as you can get.

And Stephen ‘s Herb and Jamaal rerun for the 16th has a kid worried about a mathematics test.

That’s the mathematically-themed comic strips for last week. All my Reading the Comics essays should be at this link. I’ve traditionally run at least one essay a week on Sunday. But recently that’s moved to Tuesday for no truly compelling reason. That seems like it’s working for me, though. I may stick with it. If you do have an opinion about Sunday versus Tuesday please let me know.

Don’t let me know on Twitter. I continue to have this problem where Twitter won’t load on Safari. I don’t know why. I’m this close to trying it out on a different web browser.

And, again, I’m planning a fresh A To Z sequence. It’s never to early to think of mathematics topics that I might explain. I should probably have already started writing some. But you’ll know the official announcement when it comes. It’ll have art and everything.

## Reading the Comics, August 9, 2019: Venn Diagrams Edition

Thanks for sticking around as I finally got to the past week’s comic strips. There were just enough for me to divide them into two chunks and not feel like I’m cheating anyone of my sparkling prose.

Sandra Bell-Lundy’s Between Friends for the 4th is another entry in this strip’s string of not-quite-Venn-Diagram jokes. As will happen, the point of the diagram seems clear enough even if it doesn’t quite parse. And it isn’t a proper Venn diagram, of course; a Venn diagram for five propositions has to have 31 regions, representing all the possible ways five things can combine or be excluded. They can be beautiful to look at, but start losing their value as ways to organize thought. This is again a Euclid diagram, which doesn’t need to show every possible overlap.

Michael Jantze’s The Norm 4.0 for the 5th is the other Venn Diagram joke for the week. Again properly the first one, showing the complete lack of overlap between two positions, is an Euler rather than a Venn diagram. The second, the “Amity Venn diagram on planet X”, is a Venn diagram and showing the intersection of blue and yellow regions as green is a nice way to show that. (I’m not fond of the gender stereotyping here, nor of the conflation of gender and chromosomes. But the comic strip does have to rely on shorthands or there’s just not going to be the space to compose a joke.)

Harry Bliss’s Bliss for the 6th name-checks tetrahedrons. These are the shapes the rest of us would probably call pyramids or perhaps d4. It’s a bit silly to suppose a hairball should be a tetrahedron. But natural processes will form particular shapes. The obvious example is the hexagonal prisms of honeycombs, which come about for reasons … I’m not sure biologists are completely agreed on. Hexagons do seem to be efficient ways to encompass a lot of volume with a minimum of material, at least. But even the classic hairball looks like that for reasons, related to how it’s created and how it’s expelled from the cat. They just don’t usually have corners.

Niklas Eriksson’s Carpe Diem for the 9th has you common blackboard full of symbols to represent mathematical work. It also evokes a well-worn joke that defines a mathematician as a mechanism for turning coffee into theorems. The explosion of creativity though is true to mathematicians, though. When inspiration is flowing the notes will get abundant and start going in many different wild directions. The symbols in the comic strip don’t mean anything. But that’s not inauthentic. The notes written during an inspired burst will be nonsensical. The great idea needs to be preserved. It can be cleaned up and, one hopes, made presentable later.

This and other Reading the Comics posts are at this link. I should have a fresh one on Thursday, wrapping up the past week.

## Reading the Comics, May 31, 2017: Feast Week Edition

You know we’re getting near the end of the (United States) school year when Comic Strip Master Command orders everyone to clear out their mathematics jokes. I’m assuming that’s what happened here. Or else a lot of cartoonists had word problems on their minds eight weeks ago. Also eight weeks ago plus whenever they originally drew the comics, for those that are deep in reruns. It was busy enough to split this week’s load into two pieces and might have been worth splitting into three, if I thought I had publishing dates free for all that.

Larry Wright’s Motley Classics for the 28th of May, a rerun from 1989, is a joke about using algebra. Occasionally mathematicians try to use the the ability of people to catch things in midair as evidence of the sorts of differential equations solution that we all can do, if imperfectly, in our heads. But I’m not aware of evidence that anyone does anything that sophisticated. I would be stunned if we didn’t really work by a process of making a guess of where the thing should be and refining it as time allows, with experience helping us make better guesses. There’s good stuff to learn in modeling how to catch stuff, though.

Michael Jantze’s The Norm Classics rerun for the 28th opines about why in algebra you had to not just have an answer but explain why that was the answer. I suppose mathematicians get trained to stop thinking about individual problems and instead look to classes of problems. Is it possible to work out a scheme that works for many cases instead of one? If it isn’t, can we at least say something interesting about why it’s not? And perhaps that’s part of what makes algebra classes hard. To think about a collection of things is usually harder than to think about one, and maybe instructors aren’t always clear about how to turn the specific into the general.

Also I want to say some very good words about Jantze’s graphical design. The mock textbook cover for the title panel on the left is so spot-on for a particular era in mathematics textbooks it’s uncanny. The all-caps Helvetica, the use of two slightly different tans, the minimalist cover art … I know shelves stuffed full in the university mathematics library where every book looks like that. Plus, “[Mathematics Thing] And Their Applications” is one of the roughly four standard approved mathematics book titles. He paid good attention to his references.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 28th deploys a big old whiteboard full of equations for the “secret” of the universe. This makes a neat change from finding the “meaning” of the universe, or of life. The equations themselves look mostly like gibberish to me, but Wise and Aldrich make good uses of their symbols. The symbol $\vec{B}$, a vector-valued quantity named B, turns up a lot. This symbol we often use to represent magnetic flux. The B without a little arrow above it would represent the intensity of the magnetic field. Similarly an $\vec{H}$ turns up. This we often use for magnetic field strength. While I didn’t spot a $\vec{E}$ — electric field — which would be the natural partner to all this, there are plenty of bare E symbols. Those would represent electric potential. And many of the other symbols are what would naturally turn up if you were trying to model how something is tossed around by a magnetic field. Q, for example, is often the electric charge. ω is a common symbol for how fast an electromagnetic wave oscillates. (It’s not the frequency, but it’s related to the frequency.) The uses of symbols is consistent enough, in fact, I wonder if Wise and Aldrich did use a legitimate sprawl of equations and I’m missing the referenced problem.

John Graziano’s Ripley’s Believe It Or Not for the 28th mentions how many symbols are needed to write out the numbers from 1 to 100. Is this properly mathematics? … Oh, who knows. It’s just neat to know.

Mark O’Hare’s Citizen Dog rerun for the 29th has the dog Fergus struggle against a word problem. Ordinary setup and everything, but I love the way O’Hare draws Fergus in that outfit and thinking hard.

The Eric the Circle rerun for the 29th by ACE10203040 is a mistimed Pi Day joke.

Bill Amend’s FoxTrot Classicfor the 31st, a rerun from the 7th of June, 2006, shows the conflation of “genius” and “good at mathematics” in everyday use. Amend has picked a quixotic but in-character thing for Jason Fox to try doing. Euclid’s Fifth Postulate is one of the classic obsessions of mathematicians throughout history. Euclid admitted the thing — a confusing-reading mess of propositions — as a postulate because … well, there’s interesting geometry you can’t do without it, and there doesn’t seem any way to prove it from the rest of his geometric postulates. So it must be assumed to be true.

There isn’t a way to prove it from the rest of the geometric postulates, but it took mathematicians over two thousand years of work at that to be convinced of the fact. But I know I went through a time of wanting to try finding a proof myself. It was a mercifully short-lived time that ended in my humbly understanding that as smart as I figured I was, I wasn’t that smart. We can suppose Euclid’s Fifth Postulate to be false and get interesting geometries out of that, particularly the geometries of the surface of the sphere, and the geometry of general relativity. Jason will surely sometime learn.