Reading the Comics, April 4, 2020: Ruling Things Out Edition


This little essay should let me wrap up the rest of the comic strips from the past week. Most of them were casual mentions. At least I thought they were when I gathered them. But let’s see what happens when I actually write my paragraphs about them.

Darrin Bell and Theron Heir’s Rudy Park rerun for the 1st of April uses arithmetic as emblematic of things which we know with certainty to be true.

Thaves’s Frank and Ernest for the 2nd is a bit of wordplay, having Euclid and Galileo talking about parallel universes. I’m not sure that Galileo is the best fit for this, but I’m also not sure there’s another person connected who could be named. It’d have to be a name familiar to an average reader as having something to do with geometry. Pythagoras would seem obvious, but the joke is stronger if it’s two people who definitely did not live at the same time. Did Euclid and Pythagoras live at the same time? I am a mathematics Ph.D. and have been doing pop mathematics blogging for nearly a decade now, and I have not once considered the question until right now. Let me look it up.

It doesn’t make any difference. The comic strip has to read quickly. It might be better grounded to post Euclid meeting Gauss or Lobachevsky or Euler (although the similarity in names would be confusing) but being understood is better than being precise.

Stephan Pastis’s Pearls Before Swine for the 2nd is a strip about the foolhardiness of playing the lottery. And it is foolish to think that even a $100 purchase of lottery tickets will get one a win. But it is possible to buy enough lottery tickets as to assure a win, even if it is maybe shared with someone else. It’s neat that an action can be foolish if done in a small quantity, but sensible if done in enough bulk.

Chalkboard problem 10 - 7, with answers given and crossed out of 0, 5, 7, 4, 17, 9, 1, 2, and 70. Wavehead, to teacher: 'OK, the good news is we've ruled these out.'
Mark Anderson’s Andertoons for the 3rd of April, 2020. This is actually the first time I’ve mentioned this strip in two months. But any time I discuss a topic raised by Andertoons should appear at this link.

Mark Anderson’s Andertoons for the 3rd is the Mark Anderson’s Andertoons for the week. Wavehead has made a bunch of failed attempts at subtracting seven from ten, but claims it’s at least progress that some thing have been ruled out. I’ll go along with him that there is some good in ruling out wrong answers. The tricky part is in how you rule them out. For example, obvious to my eye is that the correct answer can’t be more than ten; the problem is 10 minus a positive number. And it can’t be less than zero; it’s ten minus a number less than ten. It’s got to be a whole number. If I’m feeling confident about five and five making ten, then I’d rule out any answer that isn’t between 1 and 4 right away. I’ve got the answer down to four guesses and all I’ve really needed to know is that 7 is greater than five but less than ten. That it’s an even number minus an odd means the result has to be odd; so, it’s either one or three. Knowing that the next whole number higher than 7 is an 8 says that we can rule out 1 as the answer. So there’s the answer, done wholly by thinking of what we can rule out. Of course, knowing what to rule out takes some experience.

Mark Parisi’s Off The Mark for the 4th is roughly the anthropomorphic numerals joke for the week. It’s a dumb one, but, that’s what sketchbooks are for.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th is the Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th for the week. It shows in joking but not wrong fashion a mathematical physicist’s encounters with orbital mechanics. Orbital mechanics are a great first physics problem. It’s obvious what they’re about, and why they might be interesting. And the mathematics of it is challenging in ways that masses on springs or balls shot from cannons aren’t.

How To Learn Orbital Mechanics. Step 1: Gauge Difficulty. Person reading a text: 'It's Newtonian! Piece of cake. Just a bunch of circles and dots.' Step 2: Correction. 'OK, *ellipses* and dots.' Step 3: Concern. 'Oh, Christ, sometimes there are more than two dots.' Step 4: Pick an easier subject. 'I'm gonna go study quantum computing.' The textbook is in the trash.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th of April, 2020. This is actually the first time I’ve mentioned this strip ina week. But any time I discuss a topic raised in Saturday Morning Breakfast Cereal should appear at this link.

A few problems are very easy, like, one thing in circular orbit of another. A few problems are not bad, like, one thing in an elliptical or hyperbolic orbit of another. All our good luck runs out once we suppose the universe has three things in it. You’re left with problems that are doable if you suppose that one of the things moving is so tiny that it barely exists. This is near enough true for, for example, a satellite orbiting a planet. Or by supposing that we have a series of two-thing problems. Which is again near enough true for, for example, a satellite travelling from one planet to another. But these is all work that finds approximate solutions, often after considerable hard work. It feels like much more labor to smaller reward than we get for masses on springs or balls shot from cannons. Walking off to a presumably easier field is understandable. Unfortunately, none of the other fields is actually easier.

Pythagoras died somewhere around 495 BC. Euclid was born sometime around 325 BC. That’s 170 years apart. So Pythagoras was as far in Euclid’s past as, oh, Maria Gaetana Agnesi is to mine.

I did a little series looking into orbital mechanics, not necessarily ones that look like planetary orbits, a couple years ago. You might enjoy that. And I figure to have more mathematically-themed comic strips in the near future. Thanks for reading.

Why Stuff Can Orbit: Why It’s Waiting


I can’t imagine people are going to be surprised to hear this. But I have to put the “Why Stuff Can Orbit” series. It’s about central forces and what circumstances make it possible for something to have a stable orbit. I mean to get back to it. It’s just that the Theorem Thursday posts take up a lot of thinking on my part. They end up running quite long and detailed. I figure to get back to it once I’ve exhausted the Theorem Thursday topics I have in mind, which should be shortly into August.

It happens I’d run across a WordPress blog that contained the whole of the stable-central-orbits argument, in terse but legitimate terms. I wanted to link to that now but the site’s been deleted for reasons I won’t presume to guess. I have guesses. Sorry.

But for some other interesting reading, here’s a bit about Immanuel Kant:

I have long understood, and passed on, that Immanuel Kant had the insight that the laws of physics tell us things about the geometry of space and vice-versa. I haven’t had the chance yet to read Francisco Caruso and Roberto Moreira Xavier’s On Kant’s First Insight into the Problem of Space Dimensionality and its Physical Foundations. But the abstract promises “a conclusion that does not match the usually accepted interpretation of Kant’s reasoning”. I would imagine this to be an interesting introduction to the question, then, and to what might be controversial about Kant and the number of dimensions space should have. Also we need to use the word “tridimensionality” more.