Reading the Comics, 16 May 2013

It’s a good time for another round of comic strip reading, particularly I haven’t had the time to think in detail about all the news in number theory that’s come out this past week, and that I’m not sure whether I should go into explaining arc lengths after I trapped at least one friend into trying to work out the circumference of an ellipse (you can’t do it either, but there are a lot of curves you could). I also notice I’m approaching that precious 10,000th blog hit here, so I can get back to work verifying that law about random data starting with the digit 1.

Berkeley Breathed’s Bloom County (May 2, rerun) throws up a bunch of mathematical symbols with the intention of producing a baffling result, so that Milo can make a clean getaway from Freida. The splendid thing to me, though, is that Milo’s answer — “log 10 times 10 to the derivative of 10,000” — actually does parse, if you read it a bit charitably. The “log 10” bit we can safely suppose to mean the logarithm base 10, because the strip originally ran in 1981 or so when there was still some use for the common logarithm. These days, we have calculators, and “log” is moving over to be the “natural logarithm”, base e, what was formerly denoted as “ln”.

But log 10 — or the log of any number, in that base — is another way of saying 1. So the formula can be simplified to “1 times 10 to the derivative of 10,000”. The term “derivative of 10,000” feels a little bit incomplete, since we usually talk about the derivative of one thing with respect to another — how much the “one thing” changes for a tiny change in the “another”. However, 10,000 is a constant: it doesn’t change, regardless of whatever else changes. So while your calculus instructor would probably mark you down and think you a worse person for saying “the derivative of 10,000”, your fellow mathematician would probably accept it as the zero that’s intended. (Or you would be writing in some context where the derivative with respect to what is clear.) So, if the derivative of 10,000 is zero, then, 10 to that power — ten to the zeroth power — is 1. So the formula is 1 times 1, just as promised.

I tend to think of it as a sign that a humorist is working hard when throwaway bits like this — which could have been replaced with total gibberish since nobody needs to actually work it out — actually do parse, and better, parse correctly. So it’s probably not surprising that Berkeley Breathed, growing into such a dominant voice of cartooning in the 80s, put that effort in to the joke.

John Zakour and Scott Roberts’s Maria’s Day (May 5) plays out a math-anxiety joke drawn in a rather literal-minded fashion. Zakour and Roberts, oddly, choose a string of fractions that’s actually not getting closer to 1, but seems to be settling around one-half. Of course, what the fractions are don’t matter, and even if they were a string getting closer and closer to 1, that would open the sequence up to the argument that since the fractions approach but never equal 1, Maria could be safely out of range.

Mark Tatulli’s Lio (May 6) does the sort of “anthropomorphized numerals” joke that I expect more from Scott Hilburn and The Argyle Sweater, as he got to on May 10th. This one also tosses in a joke about an “expression” to see if the readers are paying attention.

Bill Amend’s Fox Trot (Classics) (May 8, rerun) is technically set with Peter Fox talking to his physics teacher, but Peter throws in a homework-avoidance excuse based on extrapolation: why not estimate his performance on the skipped questions from the ones he does give? I suppose there’s a sense in which any homework or test is itself a kind of extrapolation, though: using the performance of the student on a couple of data points the students’ ability in a whole field is evaluated.

The pedant might argue that, since Peter does problems 1, 5, 10, 15, and 20, and asks that his performance on the skipped questions be worked out, this is more properly interpolation than extrapolation. This is why we don’t ask pedants to sit beside us.

Dan Thompson’s Brevity (May 10) carries on Thompson’s efforts to appeal to the nerd set with a pun on Euclid’s name. I grant this is maybe a reach to include in a collection of mathematics-themed strips but, heck, I grinned, and Tom Thaves could probably do the same joke in Frank and Ernest and get away with it.

Ed Allison’s Unstrange Phenomena (May 13) riffs on the famous old attitude that there wasn’t any need for people to have personal computers by looking at an older computing technology, complete with the giant size the older units had. I’m certainly amused.

Daniel Shelton’s Ben (May 16) puts out as something “too many to count without a calculator” an estimate of how many diapers two parents have changed over eight years of raising young kids. And yet, as my faithful readers surely remember, it’s far from an intractable bit of mental arithmetic. He estimates changing “four diapers a day, 365 days a year, times, well, eight years”. This isn’t too hard to get right in one’s head, or near enough right.

Remember that 3 times 365 is pretty nearly 1100. We don’t see a 3 times 365 anywhere in here, but that just means we have to find it: 4 times 365 times 8 is the same as 4 times 8 times 365, or 32 times 365. Where this is any better is that 32 is pretty near 33, which is 11 times 3. And so, 11 times 3 times 365 is about 11 times 1100, or 12,100. If we want to be a little more exact — since 32 is 33 minus 1 — we can subtract 1 times 365 from that 12,100, and that gives us 11,735. The exact number is actually 11,680; for working this out in one’s head — and considering that “four diapers a day” is a rough average, this has to count as being dead-on right. At least that’s how I make it out in my head.

Tom Toles’s Randolph Itch, 2 am, May 16 (rerun) is again not really mathematical, but does that artistic trick of building a figure out of numerals. It’s cute.

Doug Savage’s Savage Chickens (May 16, rerun) offers a “sudoku for beginners” puzzle which would seem to be the simplest possible puzzle. While the actual solving of particular sudoku puzzles is only lightly mathematical — it’s essentially a long string of reducto ad absurdum reasoning, ruling numbers into or out of position on the grounds of what contradicts other information in the puzzle — there is quite a bit of mathematics to be done in exploring what are valid sudoku puzzles. The one I remember interesting me was the puzzle of how little information one can start with — how many of the initial cells have to be filled out — while still having a solvable puzzle. Somehow I missed the announcement last year that there aren’t any valid puzzles with just 16 given numbers, but there are ones with 17.