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.
nebusresearch 