I have been reading Pierre-Simon LaPlace, 1749 – 1827, A Life In Exact Science, by Charles Coulson Gillispie with Robert Fox and Ivor Grattan-Guinness. It’s less of a biography than I expected and more a discussion of LaPlace’s considerable body of work. Part of LaPlace’s work was in giving probability a logically coherent, rigorous meaning. Laplace discusses the gambler’s fallacy and the tendency to assign causes to random events. That, for example, if we came across letters from a printer’s font reading out ‘INFINITESIMAL’ we would think that deliberate. We wouldn’t think that for a string of letters in no recognized language. And that brings up this neat quote from Gillispie:
The example may in all probability be adapted from the chapter in the Port-Royal La Logique (1662) on judgement of future events, where Arnauld points out that it would be stupid to bet twenty sous against ten thousand livres that a child playing with printer’s type would arrange the letters to compose the first twenty lines of Virgil’s Aenid.
Although I’m out of the A to Z sequence, I like the habit of posting just the comic strips that name-drop mathematics for the Sunday post. It frees up so much of my Saturday, at the cost of committing my Sunday. So here’s last week’s casual mentions of some mathematics topic.
Bill Holbrook’s On The Fastrack for the 5th has the CEO of Fastrack, Inc, disappointed in what analytics can do. Analytics, here, is the search for statistical correlations, traits that are easy to spot and that indicate greater risks or opportunities. The desire to find these is great and natural. Real data is, though, tantalizingly not quite good enough to answer most interesting questions.
Tauhid Bondia’s Crabgrass for the 6th uses a background panel of calculus work as part of illustrating deep thinking about something, in this case, how to fairly divide chocolate. One of calculus’s traditional strengths is calculating the volumes of interesting figures.
Joe Martin’s Mr Boffo for the 6th is a cute joke on one of the uses of numbers, that of being a convenient and inexhaustible index. The strip ran on Friday and I don’t know how to link to the archives in a stable way. This is why I’ve put the comic up here.
And that’s enough comics for just now. Later this week I’ll get to the comics that inspire me to write more.
So finally I get to the mathematically-themed comic strips of last week. There were four strips which group into natural pairings. So let’s use that as the name for this edition.
Vic Lee’s Pardon My Planet for the 3rd puts forth “cookie and cake charts”, as a riff on pie charts. There’s always room for new useful visual representations of data, certainly, although quite a few of the ones we do use are more than two centuries old now. Pie charts, which we trace to William Playfair’s 1801 Statistical Breviary, were brought to the public renown by Florence Nightingale. She wanted her reports on the causes of death in the Crimean War to communicate well, and illustrations helped greatly.
Wayno and Piraro’s Bizarro for the 9th is another pie chart joke. If I weren’t already going on about pie charts this week I probably would have relegated this to the “casual mentions” heap. I love the look of the pie, though.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 5th jokes about stereotypes of mathematics and English classes. Or exams, anyway. There is some stabbing truth in the presentation of English-as-math-class. Many important pieces of mathematics are definitions or axioms. In an introductory class there’s not much you can usefully say about, oh, why we’d define a limit to be this rather than that. The book surely has its reasons and we’ll avoid confusion by trusting in them.
I dislike the stereotype of English as a subject rewarding longwinded essays that avoid the question. It seems at least unfair to what good academic writing strives for. (If you wish to argue about bad English writing, you have your blog for that, but let’s not pretend mathematics lacks fundamentally bad papers.) And writing an essay about why a thing should be true, or interesting, is certainly worthwhile. I’m reminded of a mathematical logic professor I had, who spoke of a student who somehow could not do a traditional proper-looking proof. But could write a short essay explaining why a thing should be true which convinced the professor that the student deserved an A. The professor was sad that the student was taking the course pass-fail.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th shows off a bit of mathematical modeling. The specific problem is silly, yes. But the approach is dead on: identify the things that affect what you’re interested in, and how they interact. Add to this estimates of the things’ values and you’ll get at least a provisional answer. You can then use that answer to guide the building of a more precise model, if you need one.
This little bugs-on-Superman problem makes note of the units everything’s measured in. Paying attention to the units is often done in dimensional analysis, a great tool for building simple models. I ought to write an essay sequence about that sometime.
Mark Anderson’s Andertoons for the 9th is the Mark Anderson’s Andertoons for the week. This one plays on the use of the same word to measure an angle and a temperature. Degree, etymologically, traces back to “a step”, like you might find in stairs. This, taken to represent a stage of progress, got into English in the 13th century. By the late 14th century “degree” was used to describe this 1/360th slice of a circle. By the 1540s it was a measure of heat. Making the degree the unit of temperature, as on a thermometer, seems to be written down only as far back as the 1720s.
And for a last strip of the week, Gary Wise and Lance Aldrich’s Real Life Adventures for the 7th mentions an advantage of being a cartoonist “instead of an engineer” is how cartooning doesn’t require math. Also I guess this means the regular guy in Real Life Adventures represents one (or both?) of the creators? I guess that makes the name Real Life Adventures make more sense. I just thought he was a generic comic strip male. And, of course, there’s nothing about mathematics that keeps one from being a cartoonist, although I don’t know of any current daily-syndicated cartoonists with strong mathematics backgrounds. Bill Amend, of FoxTrot, and Bud Grade, of The Piranha Club/Ernie, were both physics majors, which is a heavy-mathematics program.
I’m again stepping slightly outside the normal chronological progression of these posts. This is to let me share several days’ worth of Bob Scott’s Bear With Me. It’ll make for cleaner thematic breaks in the week.
Wayno and Piraro’s Bizarro for the 25th is a precision joke. That a proposal might be more than half-baked is reasonable enough. Pinning down its baked-ness to one part in a thousand? Nice gentle absurdity. The panel does showcase two things that connote accuracy, though. Percentages read as confident knowledge: to say something is half-done seems somehow a more uncertain thing than to say something is 50 percent done. And decimal places suggest precision also.
There are different, but not wholly separate, things to value in a measurement. Precision seems like the desirable one. It looks like superior knowledge. But there are other and more important things. One is repeatability: if you measure the same thing again, do you get approximately the same number? If the boss re-read the proposal and judged it to be 24.7 percent baked, would we feel confident in the numbers? And another is whether the measurement corresponds to what we would like to know. The diameter of a person’s head can be measured precisely. And repeatably; the number won’t change very much day to day. But suppose what we really care to know is the person’s intelligence. Does this precision and repeatability matter, given how much intelligence varies for even people of about the same head size?
Amanda El-Dweek’s Amanda the Great for the 25th starts from someone watching a game show. That’s a great way to find casual mathematics problems. Often these involve probability questions, and expectation values. That is, what would be the wisest course if you could play this game thousands or millions or billions of times?
This one dodges that, though, as the strip gets to Gramps shocked by the high price of designer women’s purses. And it features a great bit of mental arithmetic on Amanda’s part. A $2900 purse is more than four hundred times the cost of a $7 wallet. The way I spot that is noticing that 29 is awfully close to 28, but more than it. And 2800 divided by 7 is easy: it’s a hundred times 28 divided by 7. Grant the supposition that cost scales with the wallet or purse’s lifespan. Amanda nails it. If we pretend that more precision would help, she’d be forecasting a nearly 4,143-year lifespan for the purses. I admit that seems to me like an over-engineered purse.
Bob Scott’s Bear With Me for the 25th starts a string of word problem jokes. I like them, not just for liking Bear. I also like the comic motif of the character who’s ordinarily a buffoon but has narrow areas of extreme competence. There was a fun bit on one episode of The Mary Tyler Moore Show in which Ted Baxter was able to do some complex arithmetic in his head just by imagining there was a dollar sign in front of it, for an example close to this one.
Bob Scott’s Bear With Me for the 26th Bear’s arithmetic skills vary with his interest in solving the problem. This is comically exaggerated, yes. It’s something I think is basically true though. I’ve noticed I have an easier time solving problems I’m curious about, for example. I suspect most of us think the sae way, or at least expect people to do so. If we din’t, we wouldn’t worry so about motivating the solving of problems. Molly only has story problems about farmers gathering things because it’s supposed a person would want to know, given this setup, what they might expect to gather.
Bob Scott’s Bear With Me for the 27th shows a hazard in making a story too real-world: someone might want to bring in solutions that fall outside the course material. I don’t think that happens much in mathematics. My love teaches philosophy, though, and there is a streak of students who will not accept the premises of a thought experiment. They’ll insist on disproving that the experiment could happen, or stand on solutions that involve breaking the selection of options.
I’ve got enough new mathematics-themed comic strips to assemble them into a fresh post. It’s a challenge to time these rightly; I don’t want to waste everyone’s time with a set weekly post, particularly since the syndicated comics might just not have anything. On the other hand, waiting until a set number of strips have passed before my eyes seems likely to just encourage me to wonder how marginally a strip can touch mathematics before I include it. Dave Coverly’s Speed Bump, from the 6th of May, is a fine marginal case: there’s a mathematics problem in it, but it’s not at all a mathematics strip. It’s just very easy to put a math problem on the chalkboard and have it be understood the scenario is “student with no idea how to answer”.