## 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.

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.

• #### Matthew Wright 6:55 pm on Tuesday, 29 November, 2016 Permalink | Reply

‘Rhomboid’ is a wonderful word. Always makes me think of British First World War tanks.

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• #### Joseph Nebus 9:30 pm on Wednesday, 30 November, 2016 Permalink | Reply

It is a great word and you’re right; it’s perfectly captured by British First World War tanks.

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• #### Matthew Wright 6:09 am on Thursday, 1 December, 2016 Permalink | Reply

A triumph of mathematics on the part of Sir Eustace Tennyson-d’Eyncourt and his colleagues – as I understand it the shape was calculated to match the diameter of a 60-foot wheel as a trench-crossing mechanism, but without the radius (well, a triumph of geometry, which isn’t exactly mathematical in the pure sense…). I probably should stop making appalling puns now…

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• #### Joseph Nebus 4:46 pm on Friday, 9 December, 2016 Permalink | Reply

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• #### davekingsbury 5:35 pm on Wednesday, 30 November, 2016 Permalink | Reply

Your comments about tossing a coin suggests to me than working out probability is probably an inherited instinct, which is probably why it’s so tempting to enter a betting shop. (Do you guys have betting shops over the Pond?)

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• #### Joseph Nebus 9:40 pm on Wednesday, 30 November, 2016 Permalink | Reply

I think we don’t have any instinct for probability. There’s maybe a vague idea but it’s just awful for any but the simplest problems. Which is fair enough; for most of our existence probability questions were relatively straightforward things. But it took a generation of mathematicians to work out whether you were more likely to roll a 9 or a 10 on tossing three dice.

There are some betting parlors in the United States, mostly under the name Off-Track Betting shops. I don’t think there’s really a culture of them, though, at least not away from the major horse-racing tracks. I may be mistaken though; it’s not a hobby I’ve been interested in. I believe they’re all limited to horse- and greyhound-racing, though. There are many places that sell state-sponsored lotteries but that isn’t really what I understand betting shops to be about. And lottery tickets are just sidelines from some more reputable concern like being a convenience store.

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• #### davekingsbury 1:37 am on Thursday, 1 December, 2016 Permalink | Reply

Our betting shops are plentiful, several on every high street, and they are full of FOBTs – fixed odds betting terminals – which are a prime source of problem gambling in poorer communities. Looking this up, I’ve just watched a worrying clip of somebody gambling while convincing themselves erroneously that they’re on the verge of a big win … it’s been described as the crack cocaine of gambling and there are 35,000 machines in the UK. If we have any instinct for probability, it’s being abused …

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• #### Joseph Nebus 4:45 pm on Friday, 9 December, 2016 Permalink | Reply

I suspect the fixed odds betting terminals translate in the United States to ordinary slot machines. They’ve been creeping over the United States as Native American nations realize they can license casinos as they are, theoretically, sovereigns on the territory reserved to them. (The state and federal governments get very upset when Native Americans do anything that brings them too much prosperity, though, so casinos get a lot of scrutiny.) But they similarly are all about having a lot of machines, making a lot of noise, and making a huge payout seem imminent and making a small payout seem huge.

Of course, my favorite hobby is pinball, which uses nearly all the same tricks and is the nearly-reputable cousin of slot machines. Pinball machines were banned in many United States municipalities for decades as gambling machines, and it’s a fair cop. Occasionally there’ll be a bit a human-interest news about a city getting around to repealing its pinball-machine ban, and everybody thinks it a hilarious quaint bit about how square, say, Oakland, California, used to be. But the ban was for legitimate reasons, even if they’re now obsolete.

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• #### davekingsbury 8:00 pm on Friday, 9 December, 2016 Permalink | Reply

Fascinating historical perspectives here and I’m completely with you on the thrills of pinball – the virtual versions don’t have the physicality of the real machines, do they, especially that bit where you jerk the machine to wrench back control? My favourite was table football, though, which helped me waste hours as an undergraduate – my defence game was pretty nigh impossible to get round! Of course, it’s all gone downhill since …

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• #### Joseph Nebus 5:33 am on Saturday, 17 December, 2016 Permalink | Reply

The virtual machines have gotten to be really, really good. But yes, there’s this lack of physicality that’s important. Part of it is just the table getting worn and dirty and a little unresponsive, which is so key to actual play and competitive play. The app for Zaccaria Pinball machines allow you to include simulated grime on the playfield, making things play less well and more realistically; it’s a great addition. But the abstraction of nudging really makes a difference. Giving the table just the right shove is one of the big, essential skills on a pinball game and I just haven’t seen anything that gets the physics of it right.

We have table football and several of the bars with pinball machines where we play, but almost never see anyone using them. The nearest hipster bar even had a bumper pool table for months, but since nobody ever knew what the rules of bumper pool were it didn’t get much use. I printed out a set of rules I found on the Internet somewhere and left it on the table, but failed to laminate it or anything and the rules were discarded or lost after about a month. A relatively busy month for game play, too.

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• #### davekingsbury 11:21 am on Saturday, 17 December, 2016 Permalink | Reply

If one wanted a reason to reject the virtual world altogether, it could be the ‘clean’ aspect of the experience – perhaps we could throw in photography while we’re at it, and its dubious relationship with truth … or am I just being a grumpy old fart? Lifting the table in table football was a key tactic, as I recall …

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• #### Joseph Nebus 6:35 am on Wednesday, 21 December, 2016 Permalink | Reply

The clean aspect is a fair reason, yes. Part of the fun of real-world things is that while they can be predictable they’re never perfectly consistent. And there is some definite skill in recovering from stuff that isn’t working quite right.

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• #### davekingsbury 3:56 pm on Wednesday, 21 December, 2016 Permalink | Reply

And learning to grin and bear it when the recovery doesn’t occur!!

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• #### Joseph Nebus 5:02 am on Thursday, 5 January, 2017 Permalink | Reply

Oh, my yes. Learning what to do when recovery isn’t working is a big challenge.

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• #### davekingsbury 9:50 am on Thursday, 5 January, 2017 Permalink | Reply

Character-forming … 67 and still waiting! ;)

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## Reading the Comics, June 21, 2015: Blatantly Padded Edition, Part 2

I said yesterday I was padding one mathematics-comics post into two for silly reasons. And I was. But there were enough Sunday comics on point that splitting one entry into two has turned out to be legitimate. Nice how that works out sometimes.

Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. (June 19) uses mathematics as something to heap upon a person until they yield to your argument. It’s a fallacious way to argue, but it does work. Even at a mathematical conference the terror produced by a screen full of symbols can chase follow-up questions away. On the 21st, they present mathematics as a more obviously useful thing. Well, mathematics with a bit of physics.

Nate Frakes’s Break Of Day (June 19) is this week’s anthropomorphic algebra joke.

Niklas Eriksson’s Carpe Diem for the 20th of June, 2015.

Niklas Eriksson’s Carpe Diem (June 20) is captioned “Life at the Quantum Level”. And it’s built on the idea that quantum particles could be in multiple places at once. Whether something can be in two places at once depends on coming up with a clear idea about what you mean by “thing” and “places” and for that matter “at once”; when you try to pin the ideas down they prove to be slippery. But the mathematics of quantum mechanics is fascinating. It cries out for treating things we would like to know about, such as positions and momentums and energies of particles, as distributions instead of fixed values. That is, we know how likely it is a particle is in some region of space compared to how likely it is somewhere else. In statistical mechanics we resort to this because we want to study so many particles, or so many interactions, that it’s impractical to keep track of them all. In quantum mechanics we need to resort to this because it appears this is just how the world works.

(It’s even less on point, but Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 21st of June has a bit of riffing on Schrödinger’s Cat.)

Brian and Ron Boychuk’s Chuckle Brothers (June 20) name-drops algebra as the kind of mathematics kids still living with their parents have trouble with. That’s probably required by the desire to make a joking definition of “aftermath”, so that some specific subject has to be named. And it needs parents to still be watching closely over their kids, something that doesn’t quite fit for college-level classes like Intro to Differential Equations. So algebra, geometry, or trigonometry it must be. I am curious whether algebra reads as the funniest of that set of words, or if it just fits better in the space available. ‘Geometry’ is as long a word as ‘algebra’, but it may not have the same connotation of being an impossibly hard class.

Jimmy Hatlo’s Little Iodine for the 18th of April, 1954, and rerun the 18th of June, 2015.

And from the world of vintage comic strips, Jimmy Hatlo’s Little Iodine (June 21, originally run the 18th of April, 1954) reminds us that anybody can do any amount of arithmetic if it’s something they really want to calculate.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney (June 21) is another strip using the idea of mathematics — and particularly word problems — to signify great intelligence. I suppose it’s easier to recognize the form of a word problem than it is to recognize a good paper on the humanities if you only have two dozen words to show it in.

Juba’s Viivi and Wagner (June 21) is a timely reminder that while sudokus may be fun logic puzzles, they are ultimately the puzzle you decide to make of them.

• #### ivasallay 1:08 am on Thursday, 25 June, 2015 Permalink | Reply

They’re corny, but I did like Break of Day and Chuckle Brothers a lot.

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• #### Joseph Nebus 3:50 am on Thursday, 25 June, 2015 Permalink | Reply

They are corny, yeah, but fun. I think Break of Day the better of that pair because it’s more character-based.

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• #### BunKaryudo 3:27 pm on Monday, 30 November, 2015 Permalink | Reply

I love that Life at the Quantum Level cartoon. :)

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• #### Joseph Nebus 9:43 pm on Thursday, 3 December, 2015 Permalink | Reply

I’m tickled by it myself.

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• #### BunKaryudo 1:48 pm on Friday, 4 December, 2015 Permalink | Reply

It is funny. :)

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## Reading the Comics, June 11, 2015: Bonus Education Edition

The coming US summer vacation suggests Comic Strip Master Command will slow down production of mathematics-themed comic strips. But they haven’t quite yet. And this week I also found a couple comics that, while not about mathematics, amused me enough that I want to include them anyway. So those bonus strips I’ll run at the end of my regular business here.

Bill Hinds’s Tank McNamara (June 6) does a pi pun. The pithon mathematical-snake idea is fun enough and I’d be interested in a character design. I think the strip’s unjustifiably snotty about tattoos. But comic strips have a strange tendency to get snotty about other forms of art.

A friend happened to mention one problem with tattoos that require straight lines or regular shapes is that human skin has a non-flat Gaussian curvature. Yes, that’s how the friend talks. Gaussian curvature is, well, a measure of how curved a surface is. That sounds obvious enough, but there are surprises: a circular cylinder, such as the label of a can, has the same curvature as a flat sheet of paper. You can see that by how easy it is to wrap a sheet of paper around a can. But a ball hasn’t, and you see that by how you can’t neatly wrap a sheet of paper around a ball without crumpling or tearing the paper. Human skin is kind of cylindrical in many places, but not perfectly so, and it changes as the body moves. So any design that looks good on paper requires some artistic imagination to adapt to the skin.

Bill Amend’s FoxTrot (June 7) sets Jason and Marcus working on their summer tans. It’s a good strip for adding to the cover of a trigonometry test as part of the cheat-sheet.

Dana Simpson’s Phoebe and her Unicorn (June 8) makes what I think is its first appearance in my Reading the Comics series. The strip, as a web comic, had been named Heavenly Nostrils. Then it got the vanishingly rare chance to run as a syndicated newspaper comic strip. And newspaper comics page editors don’t find the word “nostril” too inherently funny to pass up. Thus the more marketable name. After that interesting background I’m sad to say Simpson delivers a bog-standard “kids not understanding fractions” joke. I can’t say much about that.

Ruben Bolling’s Super Fun-Pak Comix (June 10, rerun) is an installment of everyone’s favorite literary device model of infinite probabilities. A Million Monkeys At A Million Typewriters subverts the model. A monkey thinking about the text destroys the randomness that it depends upon. This one’s my favorite of the mathematics strips this time around.

And Dan Thompson’s traditional Brevity appearance is the June 11th strip, an Anthropomorphic Numerals joke combining a traditional schoolyard gag with a pun I didn’t notice the first time I read the panel.

And now here’s a couple strips that aren’t mathematical but that I just liked too much to ignore. Also this lets Mark Anderson’s Andertoons get back on my page. The June 10th strip is a funny bit of grammar play.

Percy Crosby’s Skippy (June 6, rerun from sometime in 1928) tickles me for its point about what you get at the top and the bottom of the class. Although tutorials and office hours and extracurricular help, and automated teaching tools, do customize things a bit, teaching is ultimately a performance given to an audience. Some will be perfectly in tune with the performance, and some won’t. Audiences are like that.

• #### poetry and chocolate and books 9:29 pm on Thursday, 11 June, 2015 Permalink | Reply

Hey! I have nominated you for the quote challenge :) Check it here, please:
https://poetryandchocolateandbooks.wordpress.com/2015/06/11/if-you-are-a-quote-lover-day-1/

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• #### Joseph Nebus 4:14 am on Saturday, 13 June, 2015 Permalink | Reply

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• #### poetry and chocolate and books 6:35 am on Saturday, 13 June, 2015 Permalink | Reply

Okay! No problem :)

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• #### l1lyl4u 4:18 pm on Friday, 12 June, 2015 Permalink | Reply

I especially love Skippy! Thanks for these :)

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• #### ivasallay 2:24 pm on Saturday, 13 June, 2015 Permalink | Reply

I always enjoy Fox Trot especially when it has something to do with mathematics. That Andertoons strip was definitely worth sharing, too.

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• #### Joseph Nebus 2:19 am on Tuesday, 16 June, 2015 Permalink | Reply

FoxTrot is almost the leader in comic strips that are made for successful newspaper production while being as nerdy and mathematical as fans would like. It’s easy to suspect that Amend does that partly out of training — he was a physics major — although it’s just as easy to suppose he simply likes getting the mathematical stuff right because it makes the joke stronger.

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## Reading the Comics, May 9, 2015: Trapezoid Edition

And now I get caught up again, if briefly, to the mathematically-themed comic strips I can find. I’ve dubbed this one the trapezoid edition because one happens to mention the post that will outlive me.

Todd Clark’s Lola (May 4) is a straightforward joke. Monty’s given his chance of passing mathematics and doesn’t understand the prospect is grim.

Joe Martin’s Willy and Ethel for the 4th of May, 2015. The link will likely expire in early June.

Joe Martin’s Willy and Ethel (May 4) shows an astounding feat of mind-reading, or of luck. How amazing it is to draw a number at random from a range depends on many things. It’s less impressive to pick the right number if there are only three possible answers than it is to pick the right number out of ten million possibilities. When we ask someone to pick a number we usually mean a range of the counting numbers. My experience suggests it’s “one to ten” unless some other range is specified. But the other thing affecting how amazing it is is the distribution. There might be ten million possible responses, but if only a few of them are likely then the feat is much less impressive.

The distribution of a random number is the interesting thing about it. The number has some value, yes, and we may not know what it is, but we know how likely it is to be any of the possible values. And good mathematics can be done knowing the distribution of a value of something. The whole field of statistical mechanics is an example of that. James Clerk Maxwell, famous for the equations which describe electromagnetism, used such random variables to explain how the rings of Saturn could exist. It isn’t easy to start solving problems with distributions instead of particular values — I’m not sure I’ve seen a good introduction, and I’d be glad to pass one on if someone can suggest it — but the power it offers is amazing.

• #### sheldonk2014 10:32 pm on Saturday, 9 May, 2015 Permalink | Reply

I love the Stan Drake strip
As always Sheldon

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• #### Joseph Nebus 3:36 am on Monday, 11 May, 2015 Permalink | Reply

Glad you like it. I’ve been intrigued by The Heart of Juliet Jones as a great example of the romance/soap-opera strip and for being occasionally very funny in how it hews to the genre conventions.

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• #### ivasallay 1:11 am on Sunday, 10 May, 2015 Permalink | Reply

Thanks for introducing me to that classic strip Skippy.

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• #### Joseph Nebus 3:37 am on Monday, 11 May, 2015 Permalink | Reply

Happy to. It’s one of the underrated gems of 20th century American comics.

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• #### elkement 7:51 am on Tuesday, 12 May, 2015 Permalink | Reply

Yes, the E=mc2 joke hurts a bit – thinking about units ;-)

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• #### Joseph Nebus 4:05 pm on Friday, 15 May, 2015 Permalink | Reply

Aw, all unit problems can be worked out by just not paying attention to them.

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• #### chattykerry 9:31 pm on Tuesday, 12 May, 2015 Permalink | Reply

I feel like Penny in the Big Bang Theory when reading your site… Clearly, only the left side of my brain works. :) Thank you for enjoying my guest blog on Jumbled Writer.

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• #### Joseph Nebus 4:07 pm on Friday, 15 May, 2015 Permalink | Reply

Aw, goodness, don’t be hard on yourself. Everyone can do mathematics and ought to feel like they’re welcome to.

I promise: if something I write seems unclear, tell me. I’ll do my best to be more understandable.

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## Reading the Comics, April 10, 2015: Getting Into The Story Problem Edition

I know it’s been like forever, or four days, since the last time I had a half-dozen or so mathematically themed comic strips to write about, but if Comic Strip Master Command is going to order cartoonists to give me stuff to write about I’m not going to turn them away. Several seemed to me about the struggle to get someone to buy into a story — the thing being asked after in a word problem, perhaps, or about the ways mathematics is worth knowing, or just how the mathematics in a joke’s setup are presented — and how skepticism about these things can turn up. So I’ll declare that the theme of this collection.

Steve Sicula’s Home And Away started a sequence on April 7th about “is math really important?”, with the father trying to argue that it’s so very useful. I’m not sure anyone’s ever really been convinced by the argument that “this is useful, therefore it’s important, therefore it’s interesting”. Lots of things are useful or important while staying fantastically dull to all but a select few souls. I would like to think a better argument for learning mathematics is that it’s beautiful, and astounding, and it allows you to discover new ways of studying the world; it can offer all the joy of any art, even as it has a practical side. Anyway, the sequence goes on for several days, and while I can’t say the arguments get very convincing on any side, they do allow for a little play with the fourth wall that I usually find amusing in comics which don’t do that much.

• #### Chiaroscuro 3:05 pm on Saturday, 11 April, 2015 Permalink | Reply

I think the Frazz joke is that a 96-story building would be “96 Tiers”, which would perfectly reference “96 Tears”, by Question Mark and the Mysterians.

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• #### Joseph Nebus 4:00 am on Friday, 17 April, 2015 Permalink | Reply

Oh, a good thought. I didn’t think of the reference and I even have its album. (And this considering the Mysterians come up fairly often, because my love talks philosophy with me, and Mysterianism is one of the names given to a particular theory of mind.)

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• #### ivasallay 7:43 am on Sunday, 12 April, 2015 Permalink | Reply

My favorite was a little play with the fourth wall.

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• #### Joseph Nebus 4:04 am on Friday, 17 April, 2015 Permalink | Reply

Light play with the fourth wall always seems to go well, I think.

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Jef Mallet’s Frazz: there are basic forces at which parabolic curves hold up all the time, but a cubic polynomial? I’m no mathematician, let alone a JPL scientist, but I’d think the spaceship would have to be guided by a computer to make a cubic curve in motion…roughly.

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• #### Joseph Nebus 4:16 am on Friday, 17 April, 2015 Permalink | Reply

Well, an unpowered — ballistic — rocket would normally follow either something pretty close to a parabola or something pretty close to an ellipse in its patterns. A rocket that’s under power will have a more complicated shape, especially if it was coming in for a landing. But the problem as presented in the textbook described something going in free space along a classic S-curve cubic, with something being tossed overboard at some point and moving thus in a tangent line. Not in free fall, no; that doesn’t make sense.

There is a famous anecdote about the Apollo lunar module computer, which was designed to have the capability of landing by itself without human intervention. Supposedly in development, the computer would allow the module to crash into the lunar ‘surface’, since it could project a path that sank to a negative height and then came back up to touch down at surface level. Numerically, of course, there’s nothing particularly objectionable about negative heights; it’s just that they have a real-world meaning that’s kind of important in this context.

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…Okay, just about all of that went over my head (no pun intended). I get that kept in orbit, an ellipsoid would amount, but distance from surface would still fit into an acceleration model with adjusted constants—still parabolic, to hover around an intended constant result. That’s all I understand, thinking about it (no textbooks). Again, I’m no JPL scientist…

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• #### Joseph Nebus 10:42 pm on Wednesday, 22 April, 2015 Permalink | Reply

It’d be paraboloid when the rocket’s out of orbit, and when it’s between firings of the engines. But while the engine is burning, well, a great number of shapes are possible. For example, if you had enough fuel, you might fire the rocket just strongly to exactly balance gravity and have the rocket hover for as long as the fuel holds out. That sounds daft, but it’s a fair way to approach a landing on unfamiliar territory, like the surface of the moon.

Or, in a launch from Earth, the goal is to go upwards as quickly as possible, getting through the thick lower atmosphere, and then roll over to nearly horizontal, building the orbital speed needed.

You can approximate these shapes with parabolas, and get the approximations as exact as you need, but they aren’t going to be exactly any ordinary shape.

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• #### Joseph Nebus 8:00 pm on Saturday, 17 January, 2015 Permalink | Reply Tags: accounting ( 8 ), answers, anthropomorphism, chaos ( 9 ), KenKen ( 2 ), navigation ( 4 ), pi ( 40 ), robert benchley ( 4 ), textbooks ( 2 )

This week’s collection of mathematics-themed comic strips includes one of the best examples of using mathematics in real life, because it describes how to find your position if you’re lost in, in this case, an uncharted island. I’m only saddened that I couldn’t find a natural way to work in how to use an analog watch as a makeshift compass, so I’m shoehorning it in up here, as well as pointing out that if you don’t have an analog clock to use, you can still approximate it by drawing the hands of the clock on a sheet of paper and using that as a pretend watch, and there is something awesome about using a sheet of paper with the time drawn on it as a way to finding north.

Dave Whamond’s Reality Check (January 12) is a guru-on-the-mountain joke, explaining that the answers to life are in the back of the math book. It’s certainly convention for a mathematics book, at least up through about Intro Differential Equations, to include answers to the problems, or at least a selection of problems, in the back, and on reflection it’s a bit of an odd convention. You don’t see that in, say, a history book even where the questions can be reduced to picking out trivia from the main text. I suppose the math-answers convention reflects an idea that there’s a correct way to go about solving a problem, and therefore, you can check whether you picked the correct way and followed it correctly with no more answer than a printed “15/2” as guide. In this way, I suppose, a mathematics textbook can be self-teaching — at least, the eager student can do some of her own pass/fail grading — which was probably invaluable back in the days when finding a skilled mathematics teacher was so much harder than it is today.

• #### ivasallay 7:32 pm on Monday, 19 January, 2015 Permalink | Reply

I love that the answers to all of the questions of the universe are in the back of a math book, but I suspect it’s only the odd questions.
Kids learning about division would probably enjoy the Maria’s Day strip if their teacher showed it to them.
Thanks for reading so many comics and sharing these with us!

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• #### Joseph Nebus 10:01 pm on Tuesday, 20 January, 2015 Permalink | Reply

Happy to serve.

I wonder how it is that it’s most often the odd problems that have answers. I’ve seen some books in which the even-numbered problems have the given answers, and the occasional freak case in which there’s no obvious pattern, but it seems to me that odd is more popular. Although I probably should actually check some books and report back before declaring it’s so.

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