## Reading the Comics, July 7, 2015: Carrying On The Streak Edition

I admit I’ve been a little unnerved lately. Between the A To Z project and the flood of mathematics-themed jokes from Comic Strip Master Command — and miscellaneous follies like my WordPress statistics-reading issues — I’ve had a post a day for several weeks now. The streak has to end sometime, surely, right? So it must, but not today. I admit the bunch of comics mentioning mathematical topics the past couple days was more one of continuing well-explored jokes rather than breaking new territory. But every comic strip is somebody’s first, isn’t it? (That’s an intimidating thought.)

Disney’s Mickey Mouse (June 6, rerun from who knows when) is another example of the word problem that even adults can’t do. I think it’s an interesting one for being also a tongue-twister. I tend to think of this sort of problem as a calculus question, but that’s surely just that I spend more time with calculus than with algebra or simpler arithmetic.

And then Disney’s Donald Duck (June 6 also, but probably a rerun from some other date) is a joke built on counting sheep. Might help someone practice their four-times table, too. I like the internal logic of this one. Maybe I just like sheep in comic strips.

Eric Teitelbaum and Bill Teitelbaum’s Bottomliners (June 6) is a bit of wordplay based on the idiom that figures will “add up” if they’re correct. There are so many things one can do with figures, though, aren’t there? Surely something will be right.

Justin Thompson’s Mythtickle (June 6, again a rerun) is about the curious way that objects are mostly empty space. The first panel shows on the alien’s chalkboard legitimate equations from quantum mechanics. The first line describes (in part) a function called psi that describes where a particle is likely to be found over time. The second and third lines describe how the probability distribution — where a particle is likely to be found — changes over time.

Doug Bratton’s Pop Culture Shock Therapy (July 7) just name-drops mathematics as something a kid will do badly in. In this case the kid is Calvin, from Calvin and Hobbes. While it’s true he did badly in mathematics I suspect that’s because it’s so easy to fit an elementary-school arithmetic question and a wrong answer in a single panel.

The idea of mathematics as a way to bludgeon people into accepting your arguments must have caught someone’s imagination over at the Parker studios. Jeff Parker’s The Wizard of Id for July 7 uses this joke, just as Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. did back on June 19th. (Both comic strips were created by the prolific Johnny Hart. I was surprised to learn they’re not still drawn and written by the same teams.) As I mentioned at the time, smothering people beneath mathematical symbols is logically fallacious. This is not to say it doesn’t work.

## Denominated Mischief

I’ve finally got around to reading one of my Christmas presents, Alfred S Posamentier and Ingmar Lehman’s Magnificent Mistakes in Mathematics, which is about ways that mathematical reasoning can be led astray. A lot, at least in the early pages, is about the ways a calculation can be fowled by a bit of carelessness, especially things like dividing by zero, which seems like such an obvious mistake that who could make it once they’ve passed Algebra II?

They got to a most neat little erroneous calculation, though, and I wanted to share it since the flaw is not immediately obvious although the absurdity of the conclusion drives you to look for it. We begin with a straightforward problem that I think of as Algebra I-grade, though I admit my memories of taking Algebra I are pretty vague these days, so maybe I missed the target grade level by a year or two.

$\frac{3x - 30}{11 - x} = \frac{x + 2}{x - 7} - 4$

Multiply that 4 on the right-hand side by 1 — in this case, by $\frac{x - 7}{x - 7}$ — and combine that into the numerator:

$\frac{3x - 30}{11 - x} = \frac{x + 2 - 4(x - 7)}{x - 7}$

Expand that parentheses and simplify the numerator on the right-hand side:

$\frac{3x - 30}{11 - x} = \frac{3x - 30}{7 - x}$

Since the fractions are equal, and the numerators are equal, therefore their denominators must be equal. Thus, $11 - x = 7 - x$ and therefore, 11 = 7.

Did you spot where the card got palmed there?