Reading the Comics, May 12, 2018: New Nancy Artist Edition

And now, closer to deadline than I like, let me wrap up last week’s mathematically-themed comic strips. I had a lot happening, that’s all I can say.

Glenn McCoy and Gary McCoy’s The Flying McCoys for the 10th is another tragic moment in the mathematics department. I’m amused that white lab coats are taken to read as “mathematician”. There are mathematicians who work in laboratories, naturally. Many interesting problems are about real-world things that can be modelled and tested and played with. It’s hardly the mathematics-department uniform, but then, I’m not sure mathematicians have a uniform. We just look like academics is all.

A wall of the Mathematics Department has fallen in. A guy in lab coat says, 'Quick --- someone call the square root of 829,921!!'
Glenn McCoy and Gary McCoy’s The Flying McCoys for the 10th of May, 2018. I suppose the piece of chalk serves as a mathematician’s professional badge, but it would be odd for a person walking in to the room to happen to have a piece. I mean, there’s good reason he might, since there’s never enough chalk in the right places and it has to be stolen from somewhere. But that’s a bit too much backstory for a panel like this.

It also shows off that motif of mathematicians as doing anything with numbers in a more complicated way than necessary. I can’t imagine anyone in an emergency trying to evoke 9-1-1 by solving any kind of puzzle. But comic strip characters are expected to do things at least a bit ridiculously. I suppose.

Mark Litzler’s Joe Vanilla for the 11th is about random numbers. We need random numbers; they do so much good. Getting them is hard. People are pretty lousy at picking random numbers in their head. We can say what “lousy” random numbers look like. They look wrong. There’s digits that don’t get used as much as the others do. There’s strings of digits that don’t get used as much as other strings of the same length do. There are patterns, and they can be subtle ones, that just don’t look right.

Person beside a sign, with the numbers 629510, 787921 and 864370 crossed out and 221473 at the bottom. Caption: 'Performance Art: Random Number Generator'.
Mark Litzler’s Joe Vanilla for the 11th of May, 2018. Bonus: depending on how you want to group a string of six numbers there’s as many as eleven random numbers to select there.

And yet we have a terrible time trying to say what good random numbers look like. Suppose we want to have a string of random zeroes and ones: is 101010 better or worse than 110101? Or 000111? Well, for a string of digits that short there’s no telling. It’s in big batches that we should expect to see no big patterns. … Except that occasionally randomness should produce patterns. How often should we expect patterns, and of what size? This seems to depend on what patterns we’ve found interesting enough to look for. But how can the cultural quirks that make something seem interesting be a substantial mathematical property?

Nancy: 'Don't you hate when you sit down at a computer and can't remember what you were going to do. For the life of me I can't recall what I wanted to do when I sat down.' Teacher: 'Nice try, Nancy, but you still have to take the countywide math test.' (Two other rows of students are on similar computers.)
Olivia Jaimes’s Nancy for the 11th of May, 2018. … Or has the Internet moved on from talking about Nancy already? Bear in mind, I still post to Usenet, so that’s how out of touch I am.

Olivia Jaimes’s Nancy for the 11th uses mathematics-assessment tests for its joke. It’s of marginal relevance, yes, but it does give me a decent pretext to include the new artist’s work here. I don’t know how long the Internet is going to be interested in Nancy. I have to get what attention I can while it lasts.

Scott Hilburn’s The Argyle Sweater for the 12th is the anthropomorphic-geometry joke for the week. Unless there was one I already did Sunday that I already forgot. Oh, no, that was anthropomorphic-numerals. It’s easy to see why a circle might be labelled irrational: either its radius or its area has to be. Both can be. The triangle, though …

Marriage Counsellor: 'She says you're very close-minded.' Triangle: 'It's called 'rational'. But she's all 'pi this' and 'pi that'. Circle: 'It's a constant struggle, doctor.'
Scott Hilburn’s The Argyle Sweater for the 12th of May, 2018. Will admit that I hadn’t heard of Heronian Triangles before I started poking around this, and I started to speculate whether it was even possible for all three legs of a triangle to be rational and the area also be rational. So you can imagine what I felt like when I did some searching and found the 5-12-13 right triangle, since that’s just the other Pythagorean Triplet you learn after the 3-4-5 one. Oh, I guess also the 3-4-5 one.

Well, that’s got me thinking. Obviously all the sides of a triangle can be rational, and so its perimeter can be too. But … the area of an equilateral triangle is \frac{1}{2}\sqrt{3} times the square of the length of any side. It can have a rational side and an irrational area, or vice-versa. Just as the circle has. If it’s not an equilateral triangle?

Can you have a triangle that has three rational sides and a rational area? And yes, you can. Take the right triangle that has sides of length 5, 12, and 13. Or any scaling of that, larger or smaller. There is indeed a whole family of triangles, the Heronian Triangles. All their sides are integers, and their areas are integers too. (Sides and areas rational are just as good as sides and areas integers. If you don’t see why, now you see why.) So there’s that at least. The name derives from Heron/Hero, the ancient Greek mathematician whom we credit with that snappy formula that tells us, based on the lengths of the three sides, what the area of the triangle is. Not the Pythagorean formula, although you can get the Pythagorean formula from it.

Still, I’m going to bet that there’s some key measure of even a Heronian Triangle that ends up being irrational. Interior angles, most likely. And there are many ways to measure triangles; they can’t all end up being rational at once. There are over two thousand ways to define a “center” of a triangle, for example. The odds of hitting a rational number on all of them at once? (Granted, most of these triangle centers are unknown except to the center’s discoverer/definer and that discoverer’s proud but baffled parents.)

Paul: 'Claire, this online business program looks good.' Claire: 'Yeah, I saw that one. But I think it's too intense. I mean, look at this. They make you take two courses in statistics and probability. What are the odds I'd ever need that? ... Oh, wait ... '
Carla Ventresca and Henry Beckett’s On A Claire Day rerun for the 12th of May, 2018. If I make it out right this originally ran the 14th of May, 2010. I forget whether I’ve featured this here already. Likely will drop it from repeats given how hard it is to write much about it. Shame, too, as I’ve just now added that tag to the roster here.

Carla Ventresca and Henry Beckett’s On A Claire Day for the 12th mentions taking classes in probability and statistics. They’re the classes nobody doubts are useful in the real world. It’s easy to figure probability is more likely to be needed than functional analysis on some ordinary day outside the university. I can’t even compose that last sentence without the language of probability.

I’d kind of agree with calling the courses intense, though. Well, “intense” might not be the right word. But challenging. Not that you’re asked to prove anything deep. The opposite, really. An introductory course in either provides a lot of tools. Many of them require no harder arithmetic work than multiplication, division, and the occasional square root. But you do need to learn which tool to use in which scenario. And there’s often not the sorts of proofs that make it easy to understand which tool does what. Doing the proofs would require too much fussing around. Many of them demand settling finicky little technical points that take you far from the original questions. But that leaves the course as this archipelago of small subjects, each easy in themselves. But the connections between them are obscured. Is that better or worse? It must depend on the person hoping to learn.


Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

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