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.

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.

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.

Reading the Comics, November 19, 2016: Thought I Featured This Already Edition

For the second half of last week Comic Strip Master Command sent me a couple comics I would have sworn I showed off here before.

Jason Poland’s Robbie and Bobby for the 16th I would have sworn I’d featured around here before. I still think it’s a rerun but apparently I haven’t written it up. It’s a pun, I suppose, playing on the use of “power” to mean both exponentials and the thing knowledge is. I’m curious why Polard used 10 for the new exponent. Normally if there isn’t an exponent explicitly written we take that to be “1”, and incrementing 1 would give 2. Possibly that would have made a less-clear illustration. Or possibly the idea of sleeping squared lacked the Brobdingnagian excess of sleeping to the tenth power.

Exponentials have been written as a small number elevated from the baseline since 1636. James Hume then published an edition of François Viète’s text on algebra. Hume used a Roman numeral in the superscript — xⁱⁱ instead of x² — but apart from that it’s the scheme we use today. The scheme was in the air, though. Renée Descartes also used the notation, but with Arabic numerals throughout, from 1637. (With quirks; he would write “xx” instead of “x²”, possibly because it’s the same number of characters to write.) And Pierre Hérigone just wrote the exponent after the variable: x2, like you see in bad character-recognition texts. That isn’t a bad scheme, particularly since it’s so easy to type, although we would add a caret: x^2. (I draw all this history, as ever, from Florian Cajori’s A History of Mathematical Notations, particularly sections 297 through 299).

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 16th has a fun concept about statisticians running wild and causing chaos. I appreciate a good healthy prank myself. It does point out something valuable, though. People in general have gotten to understand the idea that there are correlations between things. An event happening and some effect happening seem to go together. This is sometimes because the event causes the effect. Sometimes they’re both caused by some other factor; the event and effect are spuriously linked. Sometimes there’s just no meaningful connection. Coincidences do happen. But there’s really no good linking of how strong effects can be. And that’s not just a pop culture thing. For example, doing anything other than driving while driving increases the risk of crashing. But by how much? It’s easy to take something with the shape of a fact. Suppose it’s “looking at a text quadruples your risk of crashing”. (I don’t know what the risk increase is. Pretend it’s quadruple for the sake of this.) That’s easy to remember. But what’s my risk of crashing? Suppose it’s a clear, dry day, no winds, and I’m on a limited-access highway with light traffic. What’s the risk of crashing? Can’t be very high, considering how long I’ve done that without a crash. Quadruple that risk? That doesn’t seem terrifying. But I don’t know what that is, or how to express it in a way that helps make decisions. It’s not just newscasters who have this weakness.

Mark Anderson’s Andertoons for the 18th is the soothing appearance of Andertoons for this essay. And while it’s the familiar form of the student protesting the assignment the kid does have a point. There are times an estimate is all we need, and there’s times an exact answer is necessary. When are those times? That’s another skill that people have to develop.

Arthur C Clarke, in his semi-memoir Astounding Days, wrote of how his early-40s civil service job had him auditing schoolteacher pension contributions. He worked out that he really didn’t need to get the answers exactly. If the contribution was within about one percent of right it wasn’t worth his time to track it down more precisely. I’m not sure that his supervisors would take the same attitude. But the war soon took everyone to other matters without clarifying just how exactly he was supposed to audit.

Mark Anderson’s Mr Lowe rerun for the 18th is another I would have sworn I’ve brought up before. The strip was short-lived and this is at least its second time through. But then mathematics is only mentioned here as a dull things students must suffer through. It might not have seemed interesting enough for me to mention before.

Rick Detorie’s One Big Happy rerun for the 19th is another sort of pun. At least it plays on the multiple meanings of “negative”. And I suspect that negative numbers acquired a name with, er, negative connotations because the numbers were suspicious. It took centuries for mathematicians to move them from “obvious nonsense” to “convenient but meaningless tools for useful calculations” to “acceptable things” to “essential stuff”. Non-mathematicians can be forgiven for needing time to work through that progression. Also I’m not sure I didn’t show this one off here when it was first-run. Might be wrong.

Saturday Morning Breakfast Cereal pops back into my attention for the 19th. That’s with a bit about Dad messing with his kid’s head. Not much to say about that so let me bury the whimsy with my earnestness. The strip does point out that what we name stuff is arbitrary. We would say that 4 and 12 and 6 are “composite numbers”, while 2 and 3 are “prime numbers”. But if we all decided one day to swap the meanings of the terms around we wouldn’t be making any mathematics wrong. Or linguistics either. We would probably want to clarify what “a really good factor” is, but all the comic really does is mess with the labels of groups of numbers we’re already interested in.