Reading the Comics, November 9, 2018: Standing For Things Edition

There was something in common in two of the last five comic strips worth attention from last week. That’s good enough to give the essay its name.

Greg Cravens’s The Buckets for the 8th showcases Toby discovering the point of letters in algebra. It’s easy to laugh at him being ignorant. But the use of letters this way is something it’s easy to miss. You need first to realize that we don’t need to have a single way to represent a number. Which is implicit in learning, say, that you can write ‘7’ as the Roman numeral ‘VII’ or so, but I’m not sure that’s always clear. And realizing that you could use any symbol to write out ‘7’ if you agree that’s what the symbol means? That’s an abstraction tossed onto people who often aren’t really up for that kind of abstraction. And that we can have a symbol for “a number whose identity we don’t yet know”? Or even “a number whose identity we don’t care about”? Don’t blame someone for rearing back in confusion at this.

Friend 1: 'That algebra test was awful.' Friend 2: 'Toby just gave up and handed his paper in!' Toby: 'No, I finished. My mom said as long as I studied I didn't have to do any chores.' Friend 1: 'That'd eat up all your gaming hours!' Toby: 'Yep. Hey, did you know algebra letters stand for things?'
Greg Cravens’s The Buckets for the 8th of November, 2018. I’m sorry I can’t figure out the names of Toby’s friends here. Character lists, cartoonists, please.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th talks about vectors and scalars. And about the little ways that instructors in one subject can sabotage one another. In grad school I was witness to the mathematics department feeling quite put-upon by the engineering departments, who thought we were giving their students inadequate calculus training. Meanwhile we couldn’t figure out what they were telling students about calculus except that it was screwing up their understanding.

Funtime Activity: Ruining students forever. Teacher: 'Physics students must learn the difference between vectors and scalars is that scalars don't exist.' Student: 'What about 'amount of apples'?' Teacher: 'Huh? Oh, you're referring to 'distance in apple-space'.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th of November, 2018. Also, shouldn’t that be “displacement in apple-space”?

To a physicist, a vector is a size and a direction together. (At least until they get seriously into mathematical physics when they need a more abstract idea.) A scalar is a number. Like, a real-valued number such as ‘4’. Maybe a complex-valued number such as ‘4 + 6i’. Vectors are great because a lot of physics problems become easier when thought of in terms of directions and amounts in that direction.

A mathematician would start out with vectors and scalars like that. But then she’d move into a more abstract idea. A vector, to a mathematician, is a thing you can add to another vector and get a vector out. A scalar is something that’s not a vector but that, multiplied by a vector, gets you a vector out. This sounds circular. But by defining ‘vector’ and ‘scalar’ in how they interact with each other we get a really sweet flexibility. We can use the same reasoning — and the same proofs — for lots of things. Directions, yes. But also matrices, and continuous functions, and probabilities of events, and more. That’s a bit much to give the engineering student who’s trying to work out some problem about … I don’t know. Whatever they do over in that department. Truss bridges or electrical circuits or something.

Billy: 'On the 80s station I think I just heard my favorite song ever! It's about carrying a laser down some road. I think it's called 'Carry a laser' and it's all about lasers!' Cow: 'Actually, it's 'Kyrie Eleison'. It means 'Lord, have Mercy'. It has nothing at all to do with lasers.' Billy: 'Right, and 'Hip to b^2' has nothing to do with algebra.' Cow: 'That I don't know.'s
Mark Leiknes’s Cow and Boy rerun for the 9th of November, 2018. It first ran the 19th of March, 2012.

Mark Leiknes’s Cow and Boy for the 9th is really about misheard song lyrics, a subject that will never die now that we don’t have the space to print lyrics in the album lining anymore, or album linings. But it has a joke resonant with that of The Buckets, in supposing that algebra is just some bunch of letters mixed up with numbers. And Cow and Boy was always a strip I loved, as baffling as it might be to a casual reader. It had a staggering number of running jokes, although not in this installment.

Brad: 'I think I've got this worked out. It takes 500 half-inch hairs to make a good moustache. If I grow one hair a week, and each new hair grows 1/8 inch per month, I can grow a perfect moustache in ... ' Luann: '225 years, not bad!'
Greg Evans’s Luann Againn for the 9th of November, 2018. It first ran the 9th of November, 1990.

Greg Evans’s Luann Againn for the 9th shows Brad happy to work out arithmetic when it’s for something he’d like to know. The figure Luan gives is ridiculously high, though. If he needs 500 hairs, and one new hair grows in each week, then that’s a little under ten years’ worth of growth. Nine years and a bit over seven months to be exact. If a moustache hair needs to be a half-inch long, and it grows at 1/8th of an inch per month, then it takes four months to be sufficiently long. So in the slowest possible state it’d be nine years, eleven months. I can chalk Luann’s answer up to being snidely pessimistic about his hair growth. But his calculator seems to agree and that suggests something went wrong along the way.

Test Question: 'Mr Gray drove 55 mph to a city 80 miles away. He made two stops: one for 20 minutes, and one for 5. How long did it take Mr Gray to reach the city?' Student's answer: 'This made my head hurt, so I'm just going to say 'the whole trip'. You can't argue that.'
John Zakour and Scott Roberts’s Maria’s Day for the 9th of November, 2018. Again, character lists. I don’t know which of the characters this is except that he’s either very small or has an enormous pencil.

John Zakour and Scott Roberts’s Maria’s Day for the 9th is a story problem joke. It looks to me like a reasonable story problem, too: the distance travelled and the speed are reasonable, and give sensible numbers. The two stops add a bit of complication that doesn’t seem out of line. And the kid’s confusion is fair enough. It takes some experience to realize that the problem splits into an easy part, a hard part, and an easy part. The first easy part is how long the stops take all together. That’s 25 minutes. The hard part is realizing that if you want to know the total travel time it doesn’t matter when the stops are. You can find the total travel time by adding together the time spent stopped with the time spent driving. And the other easy part is working out how long it takes to go 80 miles if you travel at 55 miles per hour. That’s just a division. So find that and add to it the 25 minutes spent at the two stops.

The various Reading the Comics posts should all be at this link. Essays which discuss The Buckets are at this link. The incredibly many essays mentioning Saturday Morning Breakfast Cereal are at this link. Essays which mention Cow and Boy are at this link. Essays inspired in part by Luann, both the current-day and the vintage 1990 run, are at this link. The credibly many essays mentioning Maria’s Day are at this link.

And through the end of December my Fall 2018 Mathematics A-To-Z should have two new posts a week. You might like some of them.


Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

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