Reading the Comics, November 26, 2016: What is Pre-Algebra Edition


Here I’m just closing out last week’s mathematically-themed comics. The new week seems to be bringing some more in at a good pace, too. Should have stuff to talk about come Sunday.

Darrin Bell and Theron Heir’s Rudy Park for the 24th brings out the ancient question, why do people need to do mathematics when we have calculators? As befitting a comic strip (and Sadie’s character) the question goes unanswered. But it shows off the understandable confusion people have between mathematics and calculation. Calculation is a fine and necessary thing. And it’s fun to do, within limits. And someone who doesn’t like to calculate probably won’t be a good mathematician. (Or will become one of those master mathematicians who sees ways to avoid calculations in getting to an answer!) But put aside the obviou that we need mathematics to know what calculations to do, or to tell whether a calculation done makes sense. Much of what’s interesting about mathematics isn’t a calculation. Geometry, for an example that people in primary education will know, doesn’t need more than slight bits of calculation. Group theory swipes a few nice ideas from arithmetic and builds its own structure. Knot theory uses polynomials — everything does — but more as a way of naming structures. There aren’t things to do that a calculator would recognize.

Richard Thompson’s Poor Richard’s Almanac for the 25th I include because I’m a fan, and on the grounds that the Summer Reading includes the names of shapes. And I’ve started to notice how often “rhomboid” is used as a funny word. Those who search for the evolution and development of jokes, take heed.

John Atkinson’s Wrong Hands for the 25th is the awaited anthropomorphic-numerals and symbols joke for this past week. I enjoy the first commenter’s suggestion tha they should have stayed in unknown territory.

'Can you help me with my math, Grandma?' 'Let me see.' 'It's pre-algebra.' 'Oh, darn!' 'What's wrong?' 'I'm post-algebra.'
Rick Kirkman and Jerry Scott’s Baby Blues for the 26th of November, 2016. I suppose Kirkman and Scott know their characters better than I do but isn’t Zoe like nine or ten? Isn’t pre-algebra more a 7th or 8th grade thing? I can’t argue Grandma being post-algebra but I feel like the punch line was written and then retrofitted onto the characters.

Rick Kirkman and Jerry Scott’s Baby Blues for the 26th does a little wordplay built on pre-algebra. I’m not sure that Zoe is quite old enough to take pre-algebra. But I also admit not being quite sure what pre-algebra is. The central idea of (primary school) algebra — that you can do calculations with a number without knowing what the number is — certainly can use some preparatory work. It’s a dazzling idea and needs plenty of introduction. But my dim recollection of taking it was that it was a bit of a subject heap, with some arithmetic, some number theory, some variables, some geometry. It’s all stuff you’ll need once algebra starts. But it is hard to say quickly what belongs in pre-algebra and what doesn’t.

Art Sansom and Chip Sansom’s The Born Loser for the 26th uses two ancient staples of jokes, probabilities and weather forecasting. It’s a hard joke not to make. The prediction for something is that it’s very unlikely, and it happens anyway? We all laugh at people being wrong, which might be our whistling past the graveyard of knowing we will be wrong ourselves. It’s hard to prove that a probability is wrong, though. A fairly tossed die may have only one chance in six of turning up a ‘4’. But there’s no reason to think it won’t, and nothing inherently suspicious in it turning up ‘4’ four times in a row.

We could do it, though. If the die turned up ‘4’ four hundred times in a row we would no longer call it fair. (This even if examination proved the die really was fair after all!) Or if it just turned up a ‘4’ significantly more often than it should; if it turned up two hundred times out of four hundred rolls, say. But one or two events won’t tell us much of anything. Even the unlikely happens sometimes.

Even the impossibly unlikely happens if given enough attempts. If we do not understand that instinctively, we realize it when we ponder that someone wins the lottery most weeks. Presumably the comic’s weather forecaster supposed the chance of snow was so small it could be safely rounded down to zero. But even something with literally zero percent chance of happening might.

Imagine tossing a fair coin. Imagine tossing it infinitely many times. Imagine it coming up tails every single one of those infinitely many times. Impossible: the chance that at least one toss of a fair coin will turn up heads, eventually, is 1. 100 percent. The chance heads never comes up is zero. But why could it not happen? What law of physics or logic would it defy? It challenges our understanding of ideas like “zero” and “probability” and “infinity”. But we’re well-served to test those ideas. They hold surprises for us.

Advertisements

Everything I Know About Trapezoids


The set of posts about the area of a trapezoid seems to form a nearly coherent enough whole that it seems worthwhile to make a convenient reference point so that people searching for “how do you find the area of a trapezoid in the most convoluted and over-explained way possible?” have convenient access to it all. So, this is the path of that whole discussion.

Continue reading “Everything I Know About Trapezoids”