## Reading the Comics, September 9, 2017: First Split Week Edition, Part 2

I don’t actually like it when a split week has so many more comics one day than the next, but I also don’t like splitting across a day if I can avoid it. This week, I had to do a little of both since there were so many comic strips that were relevant enough on the 8th. But they were dominated by the idea of going back to school, yet.

Randy Glasbergen’s Glasbergen Cartoons rerun for the 8th is another back-to-school gag. And it uses arithmetic as the mathematics at its most basic. Arithmetic might not be the most fundamental mathematics, but it does seem to be one of the parts we understand first. It’s probably last to be forgotten even on a long summer break.

Mark Pett’s Mr Lowe rerun for the 8th is built on the familiar old question of why learn arithmetic when there’s computers. Quentin is unconvinced of this as motive for learning long division. I’ll grant the case could be made better. I admit I’m not sure how, though. I think long division is good as a way to teach, especially, the process of estimating and improving estimates of a calculation. There’s a lot of real mathematics in doing that.

Guy Gilchrist’s Nancy for the 8th is another back-to-school strip. Nancy’s faced with “this much math” so close to summer. Her given problem’s a bit of a mess to me. But it’s mostly teaching whether the student’s got the hang of the order of operations. And the instructor clearly hasn’t got the sense right. People can ask whether we should parse “12 divided by 3 times 4” as “(12 divided by 3) times 4” or as “12 divided by (3 times 4)”, and that does make a major difference. Multiplication commutes; you can do it in any order. Division doesn’t. Leaving ambiguous phrasing is the sort of thing you learn, instinctively, to avoid. Nancy would be justified in refusing to do the problem on the grounds that there is no unambiguous way to evaluate it, and that the instructor surely did not mean for her to evaluate it all four different plausible ways.

By the way, I’ve seen going around Normal Person Twitter this week a comment about how they just discovered the division symbol ÷, the obelus, is “just” the fraction bar with dots above and below where the unknown numbers go. I agree this is a great mnemonic for understanding what is being asked for with the symbol. But I see no evidence that this is where the symbol, historically, comes from. We first see ÷ used for division in the writings of Johann Henrich Rahn, in 1659, and the symbol gained popularity particularly when John Pell picked it up nine years later. But it’s not like Rahn invented the symbol out of nowhere; it had been used for subtraction for over 125 years at that point. There were also a good number of writers using : or / or \ for division. There were some people using a center dot before and after a / mark for this, like the % sign fell on its side. That ÷ gained popularity in English and American writing seems to be a quirk of fate, possibly augmented by it being relatively easy to produce on a standard typewriter. (Florian Cajori notes that the National Committee on Mathematical Requirements recommended dropping ÷ altogether in favor of a symbol that actually has use in non-mathematical life, the / mark. The Committee recommended this in 1923, so you see how well the form agenda is doing.)

Dave Whamond’s Reality Check for the 8th is the anthropomorphic-numerals joke for this week. A week without one is always a bit … peculiar.

Mark Leiknes’s Cow and Boy rerun for the 9th only mentions mathematics, and that as a course that Billy would rather be skipping. But I like the comic strip and want to promote its memory as much as possible. It’s a deeply weird thing, because it has something like 400 running jokes, and it’s hard to get into because the first couple times you see a pastoral conversation interrupted by an orca firing a bazooka at a cat-helicopter while a panda brags of blowing up the moon it seems like pure gibberish. If you can get through that, you realize why this is funny.

Dave Blazek’s Loose Parts for the 9th uses chalkboards full of stuff as the sign of a professor doing serious thinking. Mathematics is will-suited for chalkboards, at least in comic strips. It conveys a lot of thought and doesn’t need much preplanning. Although a joke about the difficulties in planning out blackboard use does take that planning. Yes, there is a particular pain that comes from having more stuff to write down in the quick yet easily collaborative medium of the chalkboard than there is board space to write.

Brian Basset’s Red and Rover for the 9th also really only casually mentions mathematics. But it’s another comic strip I like a good deal so would like to talk up. Anyway, it does show Red discovering he doesn’t mind doing mathematics when he sees the use.

## Reading the Comics, April 6, 2017: Abbreviated Week Edition

I’m writing this a little bit early because I’m not able to include the Saturday strips in the roundup. There won’t be enough to make a split week edition; I’ll just add the Saturday strips to next week’s report. In the meanwhile:

Mac King and Bill King’s Magic in a Minute for the 2nd is a magic trick, as the name suggests. It figures out a card by way of shuffling a (partial) deck and getting three (honest) answers from the other participant. If I’m not counting wrongly, you could do this trick with up to 27 cards and still get the right card after three answers. I feel like there should be a way to explain this that’s grounded in information theory, but I’m not able to put that together. I leave the suggestion here for people who see the obvious before I get to it.

Bil Keane and Jeff Keane’s Family Circus (probable) rerun for the 6th reassured me that this was not going to be a single-strip week. And a dubiously included single strip at that. I’m not sure that lotteries are the best use of the knowledge of numbers, but they’re a practical use anyway.

Bill Bettwy’s Take It From The Tinkersons for the 6th is part of the universe of students resisting class. I can understand the motivation problem in caring about numbers of apples that satisfy some condition. In the role of distinct objects whose number can be counted or deduced cards are as good as apples. In the role of things to gamble on, cards open up a lot of probability questions. Counting cards is even about how the probability of future events changes as information about the system changes. There’s a lot worth learning there. I wouldn’t try teaching it to elementary school students.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 6th uses mathematics as the stuff know-it-alls know. At least I suppose it is; Doctor Know It All speaks of “the pathagorean principle”. I’m assuming that’s meant to be the Pythagorean theorem, although the talk about “in any right triangle the area … ” skews things. You can get to stuf about areas of triangles from the Pythagorean theorem. One of the shorter proofs of it depends on the areas of the squares of the three sides of a right triangle. But it’s not what people typically think of right away. But he wouldn’t be the first know-it-all to start blathering on the assumption that people aren’t really listening. It’s common enough to suppose someone who speaks confidently and at length must know something.

Dave Whamond’s Reality Check for the 6th is a welcome return to anthropomorphic-numerals humor. Been a while.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th builds on the form of a classic puzzle, about a sequence indexed to the squares of a chessboard. The story being riffed on is a bit of mathematical legend. The King offered the inventor of chess any reward. The inventor asked for one grain of wheat for the first square, two grains for the second square, four grains for the third square, eight grains for the fourth square, and so on, through all 64 squares. An extravagant reward, but surely one within the king’s power to grant, right? And of course not: by the 64th doubling the amount of wheat involved is so enormous it’s impossibly great wealth.

The father’s offer is meant to evoke that. But he phrases it in a deceptive way, “one penny for the first square, two for the second, and so on”. That “and so on” is the key. Listing a sequence and ending “and so on” is incomplete. The sequence can go in absolutely any direction after the given examples and not be inconsistent. There is no way to pick a single extrapolation as the only logical choice.

We do it anyway, though. Even mathematicians say “and so on”. This is because we usually stick to a couple popular extrapolations. We suppose things follow a couple common patterns. They’re polynomials. Or they’re exponentials. Or they’re sine waves. If they’re polynomials, they’re lower-order polynomials. Things like that. Most of the time we’re not trying to trick our fellow mathematicians. Or we know we’re modeling things with some physical base and we have reason to expect some particular type of function.

In this case, the \$1.27 total is consistent with getting two cents for every chess square after the first. There are infinitely many other patterns that would work, and the kid would have been wise to ask for what precisely “and so on” meant before choosing.

Berkeley Breathed’s Bloom County 2017 for the 7th is the climax of a little story in which Oliver Wendell Holmes has been annoying people by shoving scientific explanations of things into their otherwise pleasant days. It’s a habit some scientifically-minded folks have, and it’s an annoying one. Many of us outgrow it. Anyway, this strip is about the curious evidence suggesting that the universe is not just expanding, but accelerating its expansion. There are mathematical models which allow this to happen. When developing General Relativity, Albert Einstein included a Cosmological Constant for little reason besides that without it, his model would suggest the universe was of a finite age and had expanded from an infinitesimally small origin. He had grown up without anyone knowing of any evidence that the size of the universe was a thing that could change.

Anyway, the Cosmological Constant is a puzzle. We can find values that seem to match what we observe, but we don’t know of a good reason it should be there. We sciencey types like to have models that match data, but we appreciate more knowing why the models look like that and not anything else. So it’s a good problem some of the cosmologists have been working on. But we’ve been here before. A great deal of physics, especially in the 20th Century, has been driven by looking for reasons behind what look like arbitrary points in a successful model. If Oliver were better-versed in the history of science — something scientifically minded people are often weak on, myself included — he’d be less easily taunted by Opus.

Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 7th thinks that we forgot they ran this same strip back on the 17th of March. I spotted it, though. Nyah.

## Reading the Comics, February 15, 2017: SMBC Does Not Cut In Line Edition

On reflection, that Saturday Morning Breakfast Cereal I was thinking about was not mathematically-inclined enough to be worth including here. Helping make my mind up on that was that I had enough other comic strips to discuss here that I didn’t need to pad my essay. Yes, on a slow week I let even more marginal stuff in. Here’s the comic I don’t figure to talk about. Enjoy!

Jack Pullan’s Boomerangs rerun for the 16th is another strip built around the “algebra is useless in real life” notion. I’m too busy noticing Mom in the first panel saying “what are you doing play [sic] video games?” to respond.

Ruben Bolling’s Super-Fun-Pak Comix excerpt for the 16th is marginal, yeah, but fun. Numeric coincidence and numerology can sneak into compulsions with terrible ease. I can believe easily the need to make the number of steps divisible by some favored number.

Rich Powell’s Wide Open for the 16th is a caveman science joke, and it does rely on a chalkboard full of algebra for flavor. The symbols come tantalizingly close to meaningful. The amount of kinetic energy, K or KE, of a particle of mass m moving at speed v is indeed $K = \frac{1}{2} m v^2$. Both 16 and 32 turn up often in the physics of falling bodies, at least if we’re using feet to measure. $a = -\frac{k}{m} x$ turns up in physics too. It comes from the acceleration of a mass on a spring. But an equation of the same shape turns up whenever you describe things that go through tiny wobbles around the normal value. So the blackboard is gibberish, but it’s a higher grade of gibberish than usual.

Rick Detorie’s One Big Happy rerun for the 17th is a resisting-the-word-problem joke, made fresher by setting it in little Ruthie’s playing at school.

T Lewis and Michael Fry’s Over The Hedge for the 18th mentions the three-body problem. As Verne the turtle says, it’s a problem from physics. The way two objects — sun and planet, planet and moon, pair of planets, whatever — orbit each other if they’re the only things in the universe is easy. You can describe it all perfectly and without using more than freshman physics majors know. Introduce a third body, though, and we don’t know anymore. Chaos can happen.

Emphasis on can. There’s no good way to solve the “general” three-body problem, the one where the star and planets can have any sizes and any starting positions and any starting speeds. We can do well for special cases, though. If you have a sun, a planet, and a satellite — each body negligible compared to the other — we can predict orbits perfectly well. If the bodies have to stay in one plane of motion, instead of moving in three-dimensional space, we can do pretty well. If we know two of the bodies orbit each other tightly and the third is way off in the middle of nowhere we can do pretty well.

But there’s still so many interesting cases for which we just can’t be sure chaos will not break out. Three interacting bodies just offer so much more chance for things to happen. (To mention something surely coincidental, it does seem to be a lot easier to write good comedy, or drama, with three important characters rather than two. Any pair of characters can gang up on the third, after all. I notice how much more energetic Over The Hedge became when Hammy the Squirrel joined RJ and Verne as the core cast.)

Dave Whamond’s Reality Check for the 18th is your basic mathematics-illiteracy joke, done well enough.

## Reading the Comics, February 2, 2017: I Haven’t Got A Jumble Replacement Source Yet

If there was one major theme for this week it was my confidence that there must be another source of Jumble strips out there. I haven’t found it, but I admit not making it a priority either. The official Jumble site says I can play if I activate Flash, but I don’t have enough days in the year to keep up with Flash updates. And that doesn’t help me posting mathematics-relevant puzzles here anyway.

Mark Anderson’s Andertoons for January 29th satisfies my Andertoons need for this week. And it name-drops the one bit of geometry everyone remembers. To be dour and humorless about it, though, I don’t think one could likely apply the Pythagorean Theorem. Typically the horizontal axis and the vertical axis in a graph like this measure different things. Squaring the different kinds of quantities and adding them together wouldn’t mean anything intelligible. What would even be the square root of (say) a squared-dollars-plus-squared-weeks? This is something one learns from dimensional analysis, a corner of mathematics I’ve thought about writing about some. I admit this particular insight isn’t deep, but everything starts somewhere.

Norm Feuti’s Gil rerun for the 30th is a geometry name-drop, listing it as the sort of category Jeopardy! features. Gil shouldn’t quit so soon. The responses for the category are “What is the Pythagorean Theorem?”, “What is acute?”, “What is parallel?”, “What is 180 degrees?” (or, possibly, 360 or 90 degrees), and “What is a pentagon?”.

Terri Libenson’s Pajama Diaries for the 1st of February shows off the other major theme of this past week, which was busy enough that I have to again split the comics post into two pieces. That theme is people getting basic mathematics wrong. Mostly counting. (You’ll see.) I know there’s no controlling what people feel embarrassed about. But I think it’s unfair to conclude you “can no longer” do mathematics in your head because you’re not able to make change right away. It’s normal to be slow or unreliable about something you don’t do often. Inexperience and inability are not the same thing, and it’s unfair to people to conflate them.

Gordon Bess’s Redeye for the 21st of September, 1970, got rerun the 1st of February. And it’s another in the theme of people getting basic mathematics wrong. And even more basic mathematics this time. There’s more problems-with-counting comics coming when I finish the comics from the past week.

Dave Whamond’s Reality Check for the 1st hopes that you won’t notice the label on the door is painted backwards. Just saying. It’s an easy joke to make about algebra, also, that it should put letters in to perfectly good mathematics. Letters are used for good reasons, though. We’ve always wanted to work out the value of numbers we only know descriptions of. But it’s way too wordy to use the whole description of the number every time we might speak of it. Before we started using letters we could use placeholder names like “re”, meaning “thing” (as in “thing we want to calculate”). That works fine, although it crashes horribly when we want to track two or three things at once. It’s hard to find words that are decently noncommittal about their values but that we aren’t going to confuse with each other.

So the alphabet works great for this. An individual letter doesn’t suggest any particular number, as long as we pretend ‘O’ and ‘I’ and ‘l’ don’t look like they do. But we also haven’t got any problem telling ‘x’ from ‘y’ unless our handwriting is bad. They’re quick to write and to say aloud, and they don’t require learning to write any new symbols.

Later, yes, letters do start picking up connotations. And sometimes we need more letters than the Roman alphabet allows. So we import from the Greek alphabet the letters that look different from their Roman analogues. That’s a bit exotic. But at least in a Western-European-based culture they aren’t completely novel. Mathematicians aren’t really trying to make this hard because, after all, they’re the ones who have to deal with the hard parts.

Bu Fisher’s Mutt and Jeff rerun for the 2nd is another of the basic-mathematics-wrong jokes. But it does get there by throwing out a baffling set of story-problem-starter points. Particularly interesting to me is Jeff’s protest in the first panel that they couldn’t have been doing 60 miles an hour as they hadn’t been out an hour. It’s the sort of protest easy to use as introduction to the ideas of average speed and instantaneous speed and, from that, derivatives.

## Reading the Comics, January 21, 2017: Homework Edition

Now to close out what Comic Strip Master Command sent my way through last Saturday. And I’m glad I’ve shifted to a regular schedule for these. They ordered a mass of comics with mathematical themes for Sunday and Monday this current week.

Karen Montague-Reyes’s Clear Blue Water rerun for the 17th describes trick-or-treating as “logarithmic”. The intention is to say that the difficulty in wrangling kids from house to house grows incredibly fast as the number of kids increases. Fair enough, but should it be “logarithmic” or “exponential”? Because the logarithm grows slowly as the number you take the logarithm of grows. It grows all the slower the bigger the number gets. The exponential of a number, though, that grows faster and faster still as the number underlying it grows. So is this mistaken?

I say no. It depends what the logarithm is, and is of. If the number of kids is the logarithm of the difficulty of hauling them around, then the intent and the mathematics are in perfect alignment. Five kids are (let’s say) ten times harder to deal with than four kids. Sensible and, from what I can tell of packs of kids, correct.

Rick Detorie’s One Big Happy for the 17th is a resisting-the-word-problem joke. There’s probably some warning that could be drawn about this in how to write story problems. It’s hard to foresee all the reasonable confounding factors that might get a student to the wrong answer, or to see a problem that isn’t meant to be there.

Bill Holbrook’s On The Fastrack for the 19th continues Fi’s story of considering leaving Fastrack Inc, and finding a non-competition clause that’s of appropriate comical absurdity. As an auditor there’s not even a chance Fi could do without numbers. Were she a pure mathematician … yeah, no. There’s fields of mathematics in which numbers aren’t all that important. But we never do without them entirely. Even if we exclude cases where a number is just used as an index, for which Roman numerals would be almost as good as regular numerals. If nothing else numbers would keep sneaking in by way of polynomials.

Dave Whamond’s Reality Check for the 19th breaks our long dry spell without pie chart jokes.

Mort Walker and Dik Browne’s Vintage Hi and Lois for the 27th of July, 1959 uses calculus as stand-in for what college is all about. Lois’s particular example is about a second derivative. Suppose we have a function named ‘y’ and that depends on a variable named ‘x’. Probably it’s a function with domain and range both real numbers. If complex numbers were involved then the variable would more likely be called ‘z’. The first derivative of a function is about how fast its values change with small changes in the variable. The second derivative is about how fast the values of the first derivative change with small changes in the variable.

The ‘d’ in this equation is more of an instruction than it is a number, which is why it’s a mistake to just divide those out. Instead of writing it as $\frac{d^2 y}{dx^2}$ it’s permitted, and common, to write it as $\frac{d^2}{dx^2} y$. This means the same thing. I like that because, to me at least, it more clearly suggests “do this thing (take the second derivative) to the function we call ‘y’.” That’s a matter of style and what the author thinks needs emphasis.

There are infinitely many possible functions y that would make the equation $\frac{d^2 y}{dx^2} = 6x - 2$ true. They all belong to one family, though. They all look like $y(x) = \frac{1}{6} 6 x^3 - \frac{1}{2} 2 x^2 + C x + D$, where ‘C’ and ‘D’ are some fixed numbers. There’s no way to know, from what Lois has given, what those numbers should be. It might be that the context of the problem gives information to use to say what those numbers should be. It might be that the problem doesn’t care what those numbers should be. Impossible to say without the context.

## Reading the Comics, July 1, 2012

This will be a hastily-written installment since I married just this weekend and have other things occupying me. But there’s still comics mentioning math subjects so let me summarize them for you. The first since my last collection of these, on the 13th of June, came on the 15th, with Dave Whamond’s Reality Check, which goes into one of the minor linguistic quirks that bothers me: the claim that one can’t give “110 percent,” since 100 percent is all there is. I don’t object to phrases like “110 percent”, though, since it seems to me the baseline, the 100 percent, must be to some standard reference performance. For example, the Space Shuttle Main Engines routinely operated at around 104 percent, not because they were exceeding their theoretical limits, but because the original design thrust was found to be not quite enough, and the engines were redesigned to deliver more thrust, and it would have been far too confusing to rewrite all the documentation so that the new design thrust was the new 100 percent. Instead 100 percent was the design capacity of an engine which never flew but which existed in paper form. So I’m forgiving of “110 percent” constructions, is the important thing to me.