Reading the Comics, February 15, 2017: SMBC Cuts In Line Edition

It’s another busy enough week for mathematically-themed comic strips that I’m dividing the harvest in two. There’s a natural cutting point since there weren’t any comics I could call relevant for the 15th. But I’m moving a Saturday Morning Breakfast Cereal of course from the 16th into this pile. That’s because there’s another Saturday Morning Breakfast Cereal of course from after the 16th that I might include. I’m still deciding if it’s close enough to on topic. We’ll see.

John Graziano’s Ripley’s Believe It Or Not for the 12th mentions the “Futurama Theorem”. The trivia is true, in that writer Ken Keeler did create a theorem for a body-swap plot he had going. The premise was that any two bodies could swap minds at most one time. So, after a couple people had swapped bodies, was there any way to get everyone back to their correct original body? There is, if you bring two more people in to the body-swapping party. It’s clever.

From reading comment threads about the episode I conclude people are really awestruck by the idea of creating a theorem for a TV show episode. The thing is that “a theorem” isn’t necessarily a mind-boggling piece of work. It’s just the name mathematicians give when we have a clearly-defined logical problem and its solution. A theorem and its proof can be a mind-wrenching bit of work, like Fermat’s Last Theorem or the Four-Color Map Theorem are. Or it can be on the verge of obvious. Keeler’s proof isn’t on the obvious side of things. But it is the reasoning one would have to do to solve the body-swap problem the episode posited without cheating. Logic and good story-telling are, as often, good partners.

Teresa Burritt’s Frog Applause is a Dadaist nonsense strip. But for the 13th it hit across some legitimate words, about a 14 percent false-positive rate. This is something run across in hypothesis testing. The hypothesis is something like “is whatever we’re measuring so much above (or so far below) the average that it’s not plausibly just luck?” A false positive is what it sounds like: our analysis said yes, this can’t just be luck, and it turns out that it was. This turns up most notoriously in medical screenings, when we want to know if there’s reason to suspect a health risk, and in forensic analysis, when we want to know if a particular person can be shown to have been a particular place at a particular time. A 14 percent false positive rate doesn’t sound very good — except.

Suppose we are looking for a rare condition. Say, something one person out of 500 will have. A test that’s 99 percent accurate will turn up positives for the one person who has got it and for five of the people who haven’t. It’s not that the test is bad; it’s just there are so many negatives to work through. If you can screen out a good number of the negatives, though, the people who haven’t got the condition, then the good test will turn up fewer false positives. So suppose you have a cheap or easy or quick test that doesn’t miss any true positives but does have a 14 percent false positive rate. That would screen out 430 of the people who haven’t got whatever we’re testing for, leaving only 71 people who need the 99-percent-accurate test. This can make for a more effective use of resources.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 13th is an algebra-in-real-life joke and I can’t make something deeper out of that.

Mike Shiell’s The Wandering Melon for the 13th is a spot of wordplay built around statisticians. Good for taping to the mathematics teacher’s walls.

Eric the Circle for the 14th, this one by “zapaway”, is another bit of wordplay. Tans and tangents.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 16th identifies, aptly, a difference between scientists and science fans. Weinersmith is right that loving trivia is a hallmark of a fan. Expertise — in any field, not just science — is more about recognizing patterns of problems and concepts, ways to bring approaches from one field into another, this sort of thing. And the digits of π are great examples of trivia. There’s no need for anyone to know the 1,681st digit of π. There’s few calculations you could ever do when you needed more than three dozen digits. But if memorizing digits seems like fun then π is a great set to learn. e is the only other number at all compelling.

The thing is, it’s very hard to become an expert in something without first being a fan of it. It’s possible, but if a field doesn’t delight you why would you put that much work into it? So even though the scientist might have long since gotten past caring how many digits of π, it’s awfully hard to get something memorized in the flush of fandom out of your head.

I know you’re curious. I can only remember π out to 3.14158926535787962. I might have gotten farther if I’d tried, but I actually got a digit wrong, inserting a ‘3’ before that last ’62’, and the effort to get that mistake out of my head obliterated any desire to waste more time memorizing digits. For e I can only give you 2.718281828. But there’s almost no hope I’d know that far if it weren’t for how e happens to repeat that 1828 stanza right away.

Reading the Comics, February 11, 2017: Trivia Edition

And now to wrap up last week’s mathematically-themed comic strips. It’s not a set that let me get into any really deep topics however hard I tried overthinking it. Maybe something will turn up for Sunday.

Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. for the 7th tries setting arithmetic versus celebrity trivia. It’s for the old joke about what everyone should know versus what everyone does know. One might question whether Kardashian pet eating habits are actually things everyone knows. But the joke needs some hyperbole in it to have any vitality and that’s the only available spot for it. It’s easy also to rate stuff like arithmetic as trivia since, you know, calculators. But it is worth knowing that seven squared is pretty close to 50. It comes up when you do a lot of estimates of calculations in your head. The square root of 10 is pretty near 3. The square root of 50 is near 7. The cube root of 10 is a little more than 2. The cube root of 50 a little more than three and a half. The cube root of 100 is a little more than four and a half. When you see ways to rewrite a calculation in estimates like this, suddenly, a lot of amazing tricks become possible.

Leigh Rubin’s Rubes for the 7th is a “mathematics in the real world” joke. It could be done with any mythological animals, although I suppose unicorns have the advantage of being relatively easy to draw recognizably. Mermaids would do well too. Dragons would also read well, but they’re more complicated to draw.

Mark Pett’s Mr Lowe rerun for the 8th has the kid resisting the mathematics book. Quentin’s grounds are that how can he know a dated book is still relevant. There’s truth to Quentin’s excuse. A mathematical truth may be universal. Whether we find it interesting is a matter of culture and even fashion. There are many ways to present any fact, and the question of why we want to know this fact has as many potential answers as it has people pondering the question.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th is a paean to one of the joys of numbers. There is something wonderful in counting, in measuring, in tracking. I suspect it’s nearly universal. We see it reflected in people passing around, say, the number of rivets used in the Chrysler Building or how long a person’s nervous system would reach if stretched out into a line or ever-more-fanciful measures of stuff. Is it properly mathematics? It’s delightful, isn’t that enough?

Scott Hilburn’s The Argyle Sweater for the 10th is a Fibonacci Sequence joke. That’s a good one for taping to the walls of a mathematics teacher’s office.

Bill Rechin’s Crock rerun for the 11th of February, 2017. They actually opened a brand-new drive-in theater something like forty minutes away from us a couple years back. We haven’t had the chance to get there. But we did get to one a fair bit farther away where yes, we saw Turbo, that movie about the snail that races in the Indianapolis 500. The movie was everything we hoped for and it’s just a shame Roger Ebert died too young to review it for us.

Bill Rechin’s Crock rerun for the 11th is a name-drop of mathematics. Really anybody’s homework would be sufficiently boring for the joke. But I suppose mathematics adds the connotation that whatever you’re working on hasn’t got a human story behind it, the way English or History might, and that it hasn’t got the potential to eat, explode, or knock a steel ball into you the way Biology, Chemistry, or Physics have. Fair enough.

Reading the Comics, February 6, 2017: Another Pictureless Half-Week Edition

Got another little flood of mathematically-themed comic strips last week and so once again I’ll split them along something that looks kind of middle-ish. Also this is another bunch of GoComics.com-only posts. Since those seem to be accessible to anyone whether or not they’re subscribers indefinitely far into the future I don’t feel like I can put the comics directly up and will trust you all to click on the links that you find interesting. Which is fine; the new GoComics.com design makes it annoyingly hard to download a comic strip. I don’t think that was their intention. But that’s one of the two nagging problems I have with their new design. So you know.

Tony Cochran’s Agnes for the 5th sees a brand-new mathematics. Always dangerous stuff. But mathematicians do invent, or discover, new things in mathematics all the time. Part of the task is naming the things in it. That’s something which takes talent. Some people, such as Leonhard Euler, had the knack a great novelist has for putting names to things. The rest of us muddle along. Often if there’s any real-world inspiration, or resemblance to anything, we’ll rely on that. And we look for terminology that evokes similar ideas in other fields. … And, Agnes would like to know, there is mathematics that’s about approximate answers, being “right around” the desired answer. Unfortunately, that’s hard. (It’s all hard, if you’re going to take it seriously, much like everything else people do.)

Scott Hilburn’s The Argyle Sweater for the 5th is the anthropomorphic numerals joke for this essay.

Carol Lay’s Lay Lines for the 6th depicts the hazards of thinking deeply and hard about the infinitely large and the infinitesimally small. They’re hard. Our intuition seems well-suited to handing a modest bunch of household-sized things. Logic guides us when thinking about the infinitely large or small, but it takes a long time to get truly conversant and comfortable with it all.

Paul Gilligan’s Pooch Cafe for the 6th sees Poncho try to argue there’s thermodynamical reasons for not being kind. Reasoning about why one should be kind (or not) is the business of philosophers and I won’t overstep my expertise. Poncho’s mathematics, that’s something I can write about. He argues “if you give something of yourself, you inherently have less”. That seems to be arguing for a global conservation of self-ness, that the thing can’t be created or lost, merely transferred around. That’s fair enough as a description of what the first law of thermodynamics tells us about energy. The equation he reads off reads, “the change in the internal energy (Δ U) equals the heat added to the system (U) minus the work done by the system (W)”. Conservation laws aren’t unique to thermodynamics. But Poncho may be aware of just how universal and powerful thermodynamics is. I’m open to an argument that it’s the most important field of physics.

Jonathan Lemon’s Rabbits Against Magic for the 6th is another strip Intro to Calculus instructors can use for their presentation on instantaneous versus average velocities. There’s been a bunch of them recently. I wonder if someone at Comic Strip Master Command got a speeding ticket.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th is about numeric bases. They’re fun to learn about. There’s an arbitrariness in the way we represent concepts. I think we can understand better what kinds of problems seem easy and what kinds seem harder if we write them out different ways. But base eleven is only good for jokes.

• davekingsbury 10:01 pm on Monday, 13 February, 2017 Permalink | Reply

He argues “if you give something of yourself, you inherently have less”. That seems to be arguing for a global conservation of self-ness, that the thing can’t be created or lost, merely transferred around.

How, I wonder, to marry that with Juliet’s declaration of love for Juliet?

“My bounty is as boundless as the sea,
My love as deep; the more I give to thee,
The more I have, for both are infinite.”

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• Joseph Nebus 11:08 pm on Thursday, 16 February, 2017 Permalink | Reply

Oh, well, infinities are just trouble no matter what. Anything can happen with them.

I suppose there’s also the question of how the Banach-Tarski Paradox affects love.

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• Downpuppy (@Downpuppy) 12:30 am on Tuesday, 14 February, 2017 Permalink | Reply

Agnes is the first Fuzzy Math reference I’ve seen in about 10 years.

Squirrel Girl counted to 31 on one hand to defeat Count Nefario, but SMBC is more an ASL snub

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• Joseph Nebus 11:12 pm on Thursday, 16 February, 2017 Permalink | Reply

I’m a little surprised fuzzy mathematics doesn’t get used for more comic strips, but I don’t suppose it lends itself to too many different jokes. On the other hand, neither does Pi Day and we’ll see a bunch of those over the coming month.

I had expected, really, Saturday Morning Breakfast Cereal to go with 1,024 as a natural base if you use your hands in a particularly digit-efficient way.

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Reading the Comics, February 3, 2017: Counting Edition

And now I can close out last week’s mathematically-themed comic strips. Two of them are even about counting, which is enough for me to make that the name of this set.

John Allen’s Nest Heads for the 2nd mentions a probability and statistics class and something it’s supposed to be good for. I would agree that probability and statistics are probably (I can’t find a better way to write this) the most practically useful mathematics one can learn. At least once you’re past arithmetic. They’re practical by birth; humans began studying them because they offer guidance in uncertain situations. And one can use many of their tools without needing more than arithmetic.

I’m not so staunchly anti-lottery as many mathematics people are. I’ll admit I play it myself, when the jackpot is large enough. When the expectation value of the prize gets to be positive, it’s harder to rationalize not playing. This happens only once or twice a year, but it’s fun to watch and see when it happens. I grant it’s a foolish way to use two dollars (two tickets are my limit), but you know? My budget is not so tight I can’t spend four dollars foolishly a year. Besides, I don’t insist on winning one of those half-billion-dollar prizes. I imagine I’d be satisfied if I brought in a mere $10,000. Rick Detorie’s One Big Happy for the 3rd of February, 2017. A ‘gazillion’ is actually a surprisingly low number, hovering as it does somewhere around 212. Fun fact! Rick Detorie’s One Big Happy for the 3rd continues my previous essay’s bit of incompetence at basic mathematics, here, counting. But working out that her age is between 22 an a gazillion may be worth doing. It’s a common mathematical challenge to find a correct number starting from little information about it. Usually we find it by locating bounds: the number must be larger than this and smaller than that. And then get the bounds closer together. Stop when they’re close enough for our needs, if we’re numerical mathematicians. Stop when the bounds are equal to each other, if we’re analytic mathematicians. That can take a lot of work. Many problems in number theory amount to “improve our estimate of the lowest (or highest) number for which this is true”. We have to start somewhere. Samson’s Dark Side of the Horse for the 3rd is a counting-sheep joke and I was amused that the counting went so awry here. On looking over the strip again for this essay, though, I realize I read it wrong. It’s the fences that are getting counted, not the sheep. Well, it’s a cute little sheep having the same problems counting that Horace has. We don’t tend to do well counting more than around seven things at a glance. We can get a bit farther if we can group things together and spot that, say, we have four groups of four fences each. That works and it’s legitimate; we’re counting and we get the right count out of it. But it does feel like we’re doing something different from how we count, say, three things at a glance. Mick Mastroianni and Mason MastroianniDogs of C Kennel for the 3rd is about the world’s favorite piece of statistical mechanics, entropy. There’s room for quibbling about what exactly we mean by thermodynamics saying all matter is slowly breaking down. But the gist is fair enough. It’s still mysterious, though. To say that the disorder of things is always increasing forces us to think about what we mean by disorder. It’s easy to think we have an idea what we mean by it. It’s hard to make that a completely satisfying definition. In this way it’s much like randomness, which is another idea often treated as the same as disorder. Bill Amend’s FoxTrot Classics for the 3rd reprinted the comic from the 10th of February, 2006. Mathematics teachers always want to see how you get your answers. Why? … Well, there are different categories of mistakes someone can make. One can set out trying to solve the wrong problem. One can set out trying to solve the right problem in a wrong way. One can set out solving the right problem in the right way and get lost somewhere in the process. Or one can be doing just fine and somewhere along the line change an addition to a subtraction and get what looks like the wrong answer. Each of these is a different kind of mistake. Knowing what kinds of mistakes people make is key to helping them not make these mistakes. They can get on to making more exciting mistakes. • Joseph Nebus 6:00 pm on Sunday, 5 February, 2017 Permalink | Reply Tags: algebra ( 71 ), Andertoons ( 3 ), arithmetic ( 58 ), Gil ( 2 ), jeopardy ( 3 ), Mutt and Jeff ( 3 ), Pajama Diaries, Reality Check ( 3 ), Redeye ( 2 ) 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, 2017. You know even for a fundraising event$17.50 seems a bit much for a hot dog and bottled water. Maybe the friend’s 8-year-old child is way off too.

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.

Gordon Bess’s Redeye for the 21st of September, 1970. Rerun the 1st of February, 2017. I don’t see why they’re so worried about counting bullets if being shot just leaves you a little discombobulated.

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 28, 2017: Chuckle Brothers Edition

The week started out quite busy and I was expecting I’d have to split my essay again. It didn’t turn out that way; Comic Strip Master Command called a big break on mathematically-themed comics from Tuesday on. And then nobody from Comics Kingdom or from Creators.com needed inclusion either. I just have a bunch of GoComics links and a heap of text here. I bet that changes by next week. Still no new Jumble strips.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 22nd was their first anthropomorphic numerals joke of the week.

Kevin Fagan’s Drabble for the 22nd uses arithmetic as the sort of problem it’s easy to get clearly right or clearly wrong. It’s a more economical use of space than (say) knowing how many moons Saturn’s known to have. (More than we thought there were as long ago as Thursday.) I do like that there’s a decent moral to this on the way to the punch line.

Bill Amend’s FoxTrot for the 22nd has Jason stand up for “torus” as a better name for doughnuts. You know how nerdy people will like putting a complicated word onto an ordinary thing. But there are always complications. A torus ordinarily describes the shape made by rotating a circle around an axis that’s in the plane of the circle. The result is a surface, though, the shell of a doughnut and none of the interior. If we’re being fussy. I don’t know of a particular name for the torus with its interior and suspect that, if pressed, a mathematician would just say “torus” or maybe “doughnut”.

We can talk about toruses in two dimensions; those look just like circles. The doughnut-shell shape is a torus in three dimensions. There’s torus shapes made by rotating spheres, or hyperspheres, in four or more dimensions. I’m not going to draw them. And we can also talk about toruses by the number of holes that go through them. If a normal torus is the shape of a ring-shaped pool toy, a double torus is the shape of a two-seater pool toy, a triple torus something I don’t imagine exists in the real world. A quadruple torus could look, I imagine, like some pool toys Roller Coaster Tycoon allows in its water parks. I’m saying nothing about whether they’re edible.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 23rd was their second anthropomorphic numerals joke of the week. I suppose sometimes you just get an idea going.

Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 23rd jokes about mathematics skills versus life. The growth is fine enough; after all, most of us are at, or get to, our best at something while we’re training in it or making regular use of it. So the joke peters out into the usual “I never use mathematics in real life” crack, which, eh. I agree it’s what I feel like my mathematics skills have done ever since I got my degree, at any rate.

Teresa Burritt’s Frog Applause for the 24th describes an extreme condition which hasn’t been a problem for me. I’m not an overindulgey type.

Randy Glasbergen’s Glasbergen Cartoons rerun for the 26th is the pie chart joke for this week.

Michael Fry’s Committed rerun for the 28th just riffs on the escalation of hyperbole, and what sure looks like an exponential growth of hyperbolic numbers. There’s a bit of scientific notation in the last panel. The “1 x” part isn’t necessary. It doesn’t change the value of the expression “1 x 1026”. But it might be convenient to use the “1 x” anyway. Scientific notation is about separating the size of the number from the interesting digits that the number has. Often when you compare numbers you’re interested in the size or else you’re interested in the important digits. Get into that habit and it’s not worth making an exception just because the interesting digits turn out to be boring in this case.

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 of January, 2017. The section was about how the appearance and trappings of wealth matter for more than the actual substance of wealth so everyone’s really up to speed in the course.

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.

Bill Holbrook’s On The Fastrack for the 19th of January, 2017. I feel like someone could write a convoluted story that lets someone do mathematics while avoiding any actual use of any numbers, and that it would probably be Greg Egan who did it.

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.

Mort Walker and Dik Browne’s Vintage Hi and Lois for the 27th of July, 1959. Fortunately Lois discovered the other way to avoid college costs: simply freeze the ages of your children where they are now, so they never face student loans. It’s an appealing plan until you imagine being Trixie.

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.

• Joshua K. 6:26 am on Monday, 30 January, 2017 Permalink | Reply

Why is the function in the Hi & Lois discussion stated as y(x) = (1/6)6x^3 – (1/2)2x^2 + Cx +D? Why not just y(x) = x^3 – x^2 + Cx + D?

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• Joseph Nebus 5:43 pm on Friday, 3 February, 2017 Permalink | Reply

Good question! I actually put a fair bit of thought into this. If I were doing the problem myself I’d have cut right to x^3 – x^2 + Cx + D. But I thought there’s a number of people reading this for whom calculus is a perfect mystery and I thought that if I put an intermediate step it might help spot the pattern at work, that the coefficients in front of the x^3 and x^2 terms don’t vanish without cause.

That said, I probably screwed up by writing them as 1/6 and 1/2. That looks too much like I’m just dividing by what the coefficients are. If I had taken more time to think out the post I should have written 1/(23) and 1/(12). This might’ve given a slightly better chance at connecting the powers of x and the fractions in the denominator. I’m not sure how much help that would give, since I didn’t describe how to take antiderivatives here. But I think it’d be a better presentation and I should remember that in future situations like that.

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Reading the Comics, January 16, 2017: Numerals Edition

Comic Strip Master Command decreed that last week should be busy again. So I’m splitting its strips into two essays. It’s a week that feels like it had more anthropomorphic numerals jokes than usual, but see if I actually count these things.

Mike Peters’s Mother Goose and Grimm for the 15th of January, 2017. I understand that sometimes you just have to use the idea you have instead of waiting for something that can best use the space available, but really, a whole Sunday strip for a single panel? And a panel that’s almost a barren stage?

Mike Peters’s Mother Goose and Grimm for the 15th I figured would be the anthropomorphic numerals joke for the week. Shows what I know. It is an easy joke, but I do appreciate the touch of craft involved in picking the numerals. The joke is just faintly dirty if the numbers don’t add to six. If they were a pair of 3’s, there’d be the unwanted connotations of a pair of twins talking about all this. A 6 and a 0 would make at least one character weirdly obsessed. So it has to be a 4 and a 2, or a 5 and a 1. I imagine Peters knew this instinctively, at this point in his career. It’s one of the things you learn in becoming an expert.

Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. for the 15th is mostly physical comedy, with a touch of — I’m not sure what to call this kind of joke. The one where a little arithmetic error results in bodily harm. In this sort of joke it’s almost always something not being carried that’s the error. I suppose that’s a matter of word economy. “Forgot to carry the (number)” is short, and everybody’s done it. And even if they don’t remember making this error, the phrasing clarifies to people that it’s a little arithmetic mistake. I think in practice mistaking a plus for a minus (or vice-versa) is the more common arithmetic error. But it’s harder to describe that clearly and concisely.

Jef Mallett’s Frazz for the 15th puzzled me. I hadn’t heard this thing the kid says about how if you can “spew ten random lines from a classic movie” to convince people you’ve seen it. (I don’t know the kid’s name; it happens.) I suppose that it would be convincing, though. I certainly know a couple lines from movies I haven’t seen, what with living in pop culture and all that. But ten would be taxing for all but the most over-saturated movies, like any of the Indiana Jones films. (There I’m helped by having played the 90s pinball machine a lot.) Anyway, knowing ten random mathematics things isn’t convincing, especially since you can generate new mathematical things at will just by changing a number. But I would probably be convinced that someone who could describe what’s interesting about ten fields of mathematics had a decent understanding of the subject. That requires remembering more stuff, but then, mathematics is a bigger subject than even a long movie is.

In Bill Holbrook’s On The Fastrack for the 16th Fi speaks of tallying the pluses and minuses of her life. Trying to make life into something that can be counted is an old decision-making technique. I think Benjamin Franklin explained how he found it so useful. It’s not a bad approach if a choice is hard. The challenging part is how to weight each consideration. Getting into fractions seems rather fussy to me, but some things are just like that. There is the connotation here that a fraction is a positive number smaller than 1. But the mathematically-trained (such as Fi) would be comfortable with fractions larger than 1. Or also smaller than zero. “Fraction” is no more bounded than “real number”. So, there’s the room for more sweetness here than might appear to the casual reader.

Bill Holbrook’s On The Fastrack for the 16th of January, 2017. Were I in Dethany’s position I would have asked about being a positive or negative number, but then that would leave Holbrook without a third panel. Dethany knows what her author needs most.

Scott Hilburn’s The Argyle Sweater for the 16th is the next anthropomorphic numerals joke for this week. I’m glad Hilburn want to be in my pages more. 5’s concern about figuring out x might be misplaced. We use variables for several purposes. One of them is as a name to give a number whose value we don’t know but wish to work out, and that’s how we first see them in high school algebra. But a variable might also be a number whose value we don’t particularly care about and will never try to work out. This could be because the variable is a parameter, with a value that’s fixed for a problem but not what we’re interested in. We don’t typically use ‘x’ for that, though; usually parameter are something earlier in the alphabet. That’s merely convention, but it is convention that dates back to René Descartes. Alternatively, we might use ‘x’ as a dummy variable. A dummy variable serves the same role that falsework on a building or a reference for an artistic sketch does. We use dummy variables to organize and carry out work, but we don’t care what its values are and we don’t even see the dummy variable in the final result. A dummy variable can be any name, but ‘x’ and ‘t’ are popular choices.

Terry LaBan and Patty LaBan’s Edge City rerun for the 16th plays on the idea that mathematics people talk in algebra. Funny enough, although, “the opposing defense is a variable of 6”? That’s an idiosyncratic use of “variable”. I’m going to suppose that Charles is just messing with Len’s head because, really, it’s fun doing a bit of that.

Reading the Comics, January 14, 2017: Maybe The Last Jumble? Edition

So now let me get to the other half of last week’s comics. Also, not to spoil things, but this coming week is looking pretty busy so I may have anothe split-week Reading the Comics coming up. The shocking thing this time is that the Houston Chronicle has announced it’s discontinuing its comics page. I don’t know why; I suppose because they’re fed up with people coming loyally to a daily feature. I will try finding alternate sources for the things I had still been reading there, but don’t know if I’ll make it.

I’m saddened by this. Back in the 90s comics were just coming onto the Internet. The Houston Chronicle was one of a couple newspapers that knew what to do with them. It, and the Philadelphia Inquirer and the San Jose Mercury-News, had exactly what we wanted in comics: you could make a page up of all the strips you wanted to read, and read them on a single page. You could even go backwards day by day in case you missed some. The Philadelphia Inquirer was the only page that let you put the comics in the order you wanted, as opposed to alphabetical order by title. But if you were unafraid of opening up URLs you could reorder the Houston Chronicle page you built too.

And those have all faded away. In the interests of whatever interest is served by web site redesigns all these papers did away with their user-buildable comics pages. The Chronicle was the last holdout, but even they abolished their pages a few years ago, with a promise for a while that they’d have a replacement comics-page scheme up soon. It never came and now, I suppose, never will.

Most of the newspapers’ sites had become redundant anyway. Comics Kingdom and GoComics.com offer user-customizable comics pages, with a subscription model that makes it clear that money ought to be going to the cartoonists. I still had the Chronicle for a few holdouts, like Joe Martin’s strips or the Jumble feature. And from that inertia that attaches to long-running Internet associations.

So among the other things January 2017 takes away from us, it is taking the last, faded echo of the days in the 1990s when newspapers saw comics as awesome things that could be made part of their sites.

Lorie Ransom’s The Daily Drawing for the 11th is almost but not quite the anthropomorphized-numerals joke for this installment. It’s certainly the most numerical duck content I’ve got on record.

Tom II Wilson’s Ziggy for the 11th is an Early Pi Day joke. Cosmically there isn’t any reason we couldn’t use π in take-a-number dispensers, after all. Their purpose is to give us some certain order in which to do things. We could use any set of numbers which can be put in order. So the counting numbers work. So do the integers. And the real numbers. But practicality comes into it. Most people have probably heard that π is a bit bigger than 3 and a fair bit smaller than 4. But pity the two people who drew $e^{\pi}$ and $\pi^{e}$ figuring out who gets to go first. Still, I won’t be surprised if some mathematics-oriented place uses a gimmick like this, albeit with numbers that couldn’t be confused. At least not confused by people who go to mathematics-oriented places. That would be for fun rather than cake.

the Jumble for the 11th of January, 2017. This link’s all but sure to die the 1st of February, so, sorry about that. Mesopotamia did have the abacus, although I don’t know that the depiction is anything close to what the actual ones looked like. I’d imagine they do, at least within the limits of what will be an understandable drawing.

I can’t promise that the Jumble for the 11th is the last one I’ll ever feature here. I might find where David L Hoyt and Jeff Knurek keep a linkable reference to their strips and point to them. But just in case of the worst here’s an abacus gag for you to work on.

Corey Pandolph, Phil Frank, and Joe Troise’s The Elderberries for the 12th is, I have to point out, a rerun. So if you’re trying to do the puzzle the reference to “the number of the last president” isn’t what you’re thinking of. It is an example of the conflation of intelligence with skill at arithmetic. It’s also an example the conflation of intelligence with a mastery of trivia. But I think it leans on arithmetic more. I am not sure when this strip first appeared. “The last president” might have been Bill Clinton (42) or George W Bush (43). But this means we’re taking the square root of either 33 or 34. And there’s no doing that in your head. The square root of a whole number is either a whole number — the way the square root of 36 is — or else it’s an irrational number. You can work out the square root of a non-perfect-square by hand. But it’s boring and it’s worse than just writing “$\sqrt{33}$” or “$\sqrt{34}$”. Except in figuring out if that number is larger than or smaller than five or six. It’s good for that.

Dave Blazek’s Loose Parts for the 13th is the actuary joke for this installment. Actuarial studies are built on one of the great wonders of statistics: that it is possible to predict how often things will happen. They can happen to a population, as in forecasts of how many people will be in traffic accidents or fires or will lose their jobs or will move to a new city. We may have no idea to whom any of these will happen, and they may have no way of guessing, but the enormous number of people and great number of things that can combine to make a predictable state of affairs. I suppose it’s imaginable that a group could study its dynamics well enough to identify who screws up the most and most seriously. So they might be able to say what the odds are it is his fault. But I imagine in practice it’s too difficult to define screw-ups or to assign fault consistently enough to get the data needed.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 14th is another multiverse strip, echoing the Dinosaur Comics I featured here Sunday. I’ll echo my comments then. If there is a multiverse — again, there is not evidence for this — then there may be infinitely many versions of every book of the Bible. This suggests, but it does not mandate, that there should be every possible incarnation of the Bible. And a multiverse might be a spendthrift option anyway. Just allow for enough editions, and the chance that any of them will have a misprint at any word or phrase, and we can eventually get infinitely many versions of every book of the Bible. If we wait long enough.

Reading the Comics, January 14, 2017: Redeye and Reruns Edition

So for all I worried about the Gocomics.com redesign it’s not bad. The biggest change is it’s removed a side panel and given the space over to the comics. And while it does show comics you haven’t been reading, it only shows one per day. One week in it apparently sticks with the same comic unless you choose to dismiss that. So I’ve had it showing me The Comic Strip That Has A Finale Every Day as a strip I’m not “reading”. I’m delighted how thisbreaks the logic about what it means to “not read” an “ongoing comic strip”. (That strip was a Super-Fun-Pak Comix offering, as part of Ruben Bolling’s Tom the Dancing Bug. It was turned into a regular Gocomics.com feature by someone who got the joke.)

Comic Strip Master Command responded to the change by sending out a lot of comic strips. I’m going to have to divide this week’s entry into two pieces. There’s not deep things to say about most of these comics, but I’ll make do, surely.

Julie Larson’s Dinette Set rerun for the 8th is about one of the great uses of combinatorics. That use is working out how the number of possible things compares to the number of things there are. What’s always staggering is that the number of possible things grows so very very fast. Here one of Larson’s characters claims a science-type show made an assertion about the number of possible ideas a brain could hold. I don’t know if that’s inspired by some actual bit of pop science. I can imagine someone trying to estimate the number of possible states a brain might have.

And that has to be larger than the number of atoms in the universe. Consider: there’s something less than a googol of atoms in the universe. But a person can certainly have the idea of the number 1, or the idea of the number 2, or the idea of the number 3, or so on. I admit a certain sameness seems to exist between the ideas of the numbers 2,038,412,562,593,604 and 2,038,412,582,593,604. But there is a difference. We can out-number the atoms in the universe even before we consider ideas like rabbits or liberal democracy or jellybeans or board games. The universe never had a chance.

Or did it? Is it possible for a number to be too big for the human brain to ponder? If there are more digits in the number than there are atoms in the universe we can’t form any discrete representation of it, after all. … Except that we kind of can. For example, “the largest prime number less than one googolplex” is perfectly understandable. We can’t write it out in digits, I think. But you now have thought of that number, and while you may not know what its millionth decimal digit is, you also have no reason to care what that digit is. This is stepping into the troubled waters of algorithmic complexity.

Bob Weber Jr’s Slylock Fox and Comics for Kids for the 9th of January, 2017. Not sure why Shady Shrew is selling the circular wands at 50 cents. Sure, I understand wanting a triangle or star or other wand selling at a premium. But then why have the circular wands at such a cheap price? Wouldn’t it be better to put them at like six dollars, so that eight dollars for a fancy wand doesn’t seem that great an extravagance? You have to consider setting an appropriate anchor point for your customer base. But, then, Shady Shrew isn’t supposed to be that smart.

Bob Weber Jr’s Slylock Fox and Comics for Kids for the 9th is built on soap bubbles. The link between the wand and the soap bubble vanishes quickly once the bubble breaks loose of the wand. But soap films that keep adhered to the wand or mesh can be quite strangely shaped. Soap films are a practical example of a kind of partial differential equations problem. Partial differential equations often appear when we want to talk about shapes and surfaces and materials that tug or deform the material near them. The shape of a soap bubble will be the one that minimizes the torsion stresses of the bubble’s surface. It’s a challenge to solve analytically. It’s still a good challenge to solve numerically. But you can do that most wonderful of things and solve a differential equation experimentally, if you must. It’s old-fashioned. The computer tools to do this have gotten so common it’s hard to justify going to the engineering lab and getting soapy water all over a mathematician’s fingers. But the option is there.

Gordon Bess’s Redeye rerun from the 28th of August, 1970, is one of a string of confused-student jokes. (The strip had a Generic Comedic Western Indian setting, putting it in the vein of Hagar the Horrible and other comic-anachronism comics.) But I wonder if there are kids baffled by numbers getting made several different ways. Experience with recipes and assembly instructions and the like might train someone to thinking there’s one correct way to make something. That could build a bad intuition about what additions can work.

Gordon Bess’s Redeye rerun from the 28th of August, 1970. Reprinted the 9th of January, 2017. What makes the strip work is how it’s tied to the personalities of these kids and couldn’t be transplanted into every other comic strip with two kids in it.

Corey Pandolph’s Barkeater Lake rerun for the 9th just name-drops algebra. And that as a word that starts with the “alj” sound. So far as I’m aware there’s not a clear etymological link between Algeria and algebra, despite both being modified Arabic words. Algebra comes from “al-jabr”, about reuniting broken things. Algeria comes from Algiers, which Wikipedia says derives from `al-jaza’ir”, “the Islands [of the Mazghanna tribe]”.

Guy Gilchrist’s Nancy for the 9th is another mathematics-cameo strip. But it was also the first strip I ran across this week that mentioned mathematics and wasn’t a rerun. I’ll take it.

Donna A Lewis’s Reply All for the 9th has Lizzie accuse her boyfriend of cheating by using mathematics in Scrabble. He seems to just be counting tiles, though. I think Lizzie suspects something like Blackjack card-counting is going on. Since there are only so many of each letter available knowing just how many tiles remain could maybe offer some guidance how to play? But I don’t see how. In Blackjack a player gets to decide whether to take more cards or not. Counting cards can suggest whether it’s more likely or less likely that another card will make the player or dealer bust. Scrabble doesn’t offer that choice. One has to refill up to seven tiles until the tile bag hasn’t got enough left. Perhaps I’m overlooking something; I haven’t played much Scrabble since I was a kid.

Perhaps we can take the strip as portraying the folk belief that mathematicians get to know secret, barely-explainable advantages on ordinary folks. That itself reflects a folk belief that experts of any kind are endowed with vaguely cheating knowledge. I’ll admit being able to go up to a blackboard and write with confidence a bunch of integrals feels a bit like magic. This doesn’t help with Scrabble.

Gordon Bess’s Redeye rerun from the 29th of August, 1970. Reprinted the 10th of January, 2017. To be less snarky, I do like the simply-expressed weariness on the girl’s face. It’s hard to communicate feelings with few pen strokes.

Gordon Bess’s Redeye continued the confused-student thread on the 29th of August, 1970. This one’s a much older joke about resisting word problems.

Ryan North’s Dinosaur Comics rerun for the 10th talks about multiverses. If we allow there to be infinitely many possible universes that would suggest infinitely many different Shakespeares writing enormously many variations of everything. It’s an interesting variant on the monkeys-at-typewriters problem. I noticed how T-Rex put Shakespeare at typewriters too. That’ll have many of the same practical problems as monkeys-at-typewriters do, though. There’ll be a lot of variations that are just a few words or a trivial scene different from what we have, for example. Or there’ll be variants that are completely uninteresting, or so different we can barely recognize them as relevant. And that’s if it’s actually possible for there to be an alternate universe with Shakespeare writing his plays differently. That seems like it should be possible, but we lack evidence that it is.

Reading the Comics, January 7, 2016: Just Before GoComics Breaks Everything Edition

Most of the comics I review here are printed on GoComics.com. Well, most of the comics I read online are from there. But even so I think they have more comic strips that mention mathematical themes. Anyway, they’re unleashing a complete web site redesign on Monday. I don’t know just what the final version will look like. I know that the beta versions included the incredibly useful, that is to say dumb, feature where if a particular comic you do read doesn’t have an update for the day — and many of them don’t, as they’re weekly or three-times-a-week or so — then it’ll show some other comic in its place. I mean, the idea of encouraging people to find new comics is a good one. To some extent that’s what I do here. But the beta made no distinction between “comic you don’t read because you never heard of Microcosm” and “comic you don’t read because glancing at it makes your eyes bleed”. And on an idiosyncratic note, I read a lot of comics. I don’t need to see Dude and Dude reruns in fourteen spots on my daily comics page, even if I didn’t mind it to start.

Anyway. I am hoping, desperately hoping, that with the new site all my old links to comics are going to keep working. If they don’t then I suppose I’m just ruined. We’ll see. My suggestion is if you’re at all curious about the comics you read them today (Sunday) just to be safe.

Ashleigh Brilliant’s Pot-Shots is a curious little strip I never knew of until GoComics picked it up a few years ago. Its format is compellingly simple: a little illustration alongside a wry, often despairing, caption. I love it, but I also understand why was the subject of endless queries to the Detroit Free Press (Or Whatever) about why was this thing taking up newspaper space. The strip rerun the 31st of December is a typical example of the strip and amuses me at least. And it uses arithmetic as the way to communicate reasoning, both good and bad. Brilliant’s joke does address something that logicians have to face, too. Whether an argument is logically valid depends entirely on its structure. If the form is correct the reasoning may be excellent. But to be sound an argument has to be correct and must also have its assumptions be true. We can separate whether an argument is right from whether it could ever possibly be right. If you don’t see the value in that, you have never participated in an online debate about where James T Kirk was born and whether Spock was the first Vulcan in Star Fleet.

Thom Bluemel’s Birdbrains for the 2nd of January, 2017, is a loaded-dice joke. Is this truly mathematics? Statistics, at least? Close enough for the start of the year, I suppose. Working out whether a die is loaded is one of the things any gambler would like to know, and that mathematicians might be called upon to identify or exploit. (I had a grandmother unshakably convinced that I would have some natural ability to beat the Atlantic City casinos if she could only sneak the underaged me in. I doubt I could do anything of value there besides see the stage magic show.)

Jack Pullan’s Boomerangs rerun for the 2nd is built on the one bit of statistical mechanics that everybody knows, that something or other about entropy always increasing. It’s not a quantum mechanics rule, but it’s a natural confusion. Quantum mechanics has the reputation as the source of all the most solid, irrefutable laws of the universe’s working. Statistical mechanics and thermodynamics have this musty odor of 19th-century steam engines, no matter how much there is to learn from there. Anyway, the collapse of systems into disorder is not an irrevocable thing. It takes only energy or luck to overcome disorderliness. And in many cases we can substitute time for luck.

Scott Hilburn’s The Argyle Sweater for the 3rd is the anthropomorphic-geometry-figure joke that’s I’ve been waiting for. I had thought Hilburn did this all the time, although a quick review of Reading the Comics posts suggests he’s been more about anthropomorphic numerals the past year. This is why I log even the boring strips: you never know when I’ll need to check the last time Scott Hilburn used “acute” to mean “cute” in reference to triangles.

Mike Thompson’s Grand Avenue uses some arithmetic as the visual cue for “any old kind of schoolwork, really”. Steve Breen’s name seems to have gone entirely from the comic strip. On Usenet group rec.arts.comics.strips Brian Henke found that Breen’s name hasn’t actually been on the comic strip since May, and D D Degg found a July 2014 interview indicating Thompson had mostly taken the strip over from originator Breen.

Mark Anderson’s Andertoons for the 5th is another name-drop that doesn’t have any real mathematics content. But come on, we’re talking Andertoons here. If I skipped it the world might end or something untoward like that.

Ted Shearer’s Quincy for the 14th of November, 1977, and reprinted the 7th of January, 2017. I kind of remember having a lamp like that. I don’t remember ever sitting down to do my mathematics homework with a paintbrush.

Ted Shearer’s Quincy for the 14th of November, 1977, doesn’t have any mathematical content really. Just a mention. But I need some kind of visual appeal for this essay and Shearer is usually good for that.

Corey Pandolph, Phil Frank, and Joe Troise’s The Elderberries rerun for the 7th is also a very marginal mention. But, what the heck, it’s got some of your standard wordplay about angles and it’ll get this week’s essay that much closer to 800 words.

Reading the Comics, December 30, 2016: New Year’s Eve Week Edition

So last week, for schedule reasons, I skipped the Christmas Eve strips and promised to get to them this week. There weren’t any Christmas Eve mathematically-themed comic strips. Figures. This week, I need to skip New Year’s Eve comic strips for similar schedule reasons. If there are any, I’ll talk about them next week.

Lorie Ransom’s The Daily Drawing for the 28th is a geometry wordplay joke for this installment. Two of them, when you read the caption.

John Graziano’s Ripley’s Believe It or Not for the 28th presents the quite believable claim that Professor Dwight Barkley created a formula to estimate how long it takes a child to ask “are we there yet?” I am skeptical the equation given means all that much. But it’s normal mathematician-type behavior to try modelling stuff. That will usually start with thinking of what one wants to represent, and what things about it could be measured, and how one expects these things might affect one another. There’s usually several plausible-sounding models and one has to select the one or ones that seem likely to be interesting. They have to be simple enough to calculate, but still interesting. They need to have consequences that aren’t obvious. And then there’s the challenge of validating the model. Does its description match the thing we’re interested in well enough to be useful? Or at least instructive?

Len Borozinski’s Speechless for the 28th name-drops Albert Einstein and the theory of relativity. Marginal mathematical content, but it’s a slow week.

John Allison’s Bad Machinery for the 29th mentions higher dimensions. More dimensions. In particular it names ‘ana’ and ‘kata’ as “the weird extra dimensions”. Ana and kata are a pair of directions coined by the mathematician Charles Howard Hinton to give us a way of talking about directions in hyperspace. They echo the up/down, left/right, in/out pairs. I don’t know that any mathematicians besides Rudy Rucker actually use these words, though, and that in his science fiction. I may not read enough four-dimensional geometry to know the working lingo. Hinton also coined the “tesseract”, which has escaped from being a mathematician’s specialist term into something normal people might recognize. Mostly because of Madeline L’Engle, I suppose, but that counts.

Samson’s Dark Side of the Horse for the 29th is Dark Side of the Horse‘s entry this essay. It’s a fun bit of play on counting, especially as a way to get to sleep.

John Graziano’s Ripley’s Believe It or Not for the 29th mentions a little numbers and numerals project. Or at least representations of numbers. Finding other orders for numbers can be fun, and it’s a nice little pastime. I don’t know there’s an important point to this sort of project. But it can be fun to accomplish. Beautiful, even.

Mark Anderson’s Andertoons for the 30th relieves us by having a Mark Anderson strip for this essay. And makes for a good Roman numerals gag.

Ryan Pagelow’s Buni for the 30th can be counted as an anthropomorphic-numerals joke. I know it’s more of a “ugh 2016 was the worst year” joke, but it parses either way.

John Atkinson’s Wrong Hands for the 30th is an Albert Einstein joke. It’s cute as it is, though.

Reading the Comics, December 23, 2016: Weak Pretexts Edition

I’ve set the cutoff for the strips this week at Friday because you know how busy the day before Christmas is. If you don’t, then I ask that you trust me: it’s busy. If Comic Strip Master Command sent me anything worthy of comment I’ll report on it next year. I had thought this week’s set of mathematically-themed comics were a weak bunch that I had to strain to justify covering. But on looking at the whole essay … mm. I’m comfortable with it.

Bill Amend’s FoxTrot for the 18th has two mathematical references. Writing “three kings” as “square root of nine kings” is an old sort of joke at least in mathematical circles. It’s about writing a number using some elaborate but valid expression. It’s good fun. A few years back I had a calendar with a mathematics puzzle of the day. And that was fun up until I noticed the correct answer was always the day of the month so that, say, today’s would have an answer of 25. This collapsed the calendar from being about solving problems to just verifying the solution. It’s a little change but it is one that spoiled it for me.

And a few years back an aunt and uncle gave me an “Irrational Watch”, with the dial marked only by irrational numbers — π, for example, a little bit clockwise of where ‘3’ ought to go. The one flaw: it used the Euler-Mascheroni constant, a number that’s about 0.57, to designate that time a little past 12:30. The Euler-Mascheroni constant isn’t actually known to be irrational. It’s the way to bet, but it might just be a rational number after all.

A binary tree, mentioned in the bottom row, is a tree for which every vertex is connected to at most three others. We’ve seen trees recently. And there’s a specially designated vertex known as the root. Each vertex (except the root) is connected to exactly one vertex that’s closer to the root. The structure looks like either the branches or the roots of a tree, depending whether the root is put at the top or bottom. And if you accept a strikingly minimal, Mid-Century Modern style drawing of a (natural) tree.

Ted Shearer’s Quincy for the 26th of October, 1977. Reprinted the 20th of December, 2016. There’s much that’s expressive here, although what most catches my eye is the swoopy curves of the soda straw.

Ted Shearer’s Quincy for the 26th of October, 1977 mentions mathematics. So I’m using that as an excuse to include it. Mostly I like it for the artwork. But the mention of mathematics was strikingly arbitrary; the joke would be the same were it his English homework or Geography or anything else. I suppose mathematics got the nod because it can be written with so few letters. (Art is even more compact, but it would probably distract the reader trying to think of what would be hard to understand about an Art project homework. Difficult, if it were painting or crafting something, sure, but that’s not a challenge in understanding.)

I don’t know what Marty Links’s Emmy Lou for the 20th was getting at. The strip originally ran the 15th of September, 1964. It seems to be referring to some ephemeral trivia passed around the summer of that year. My guess is it refers to some estimation of the unattached male and female populations of some age set and finding that there were very different numbers. That sort of result is typically done by clever definition, sometimes assisted by double-counting and other sleights of hand. It’s legitimate if you accept the definition. But before reacting too much to any surprising claim one should know just what the claim is, and why it’s that.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 20th is mathematics wordplay. Simpson’s Approximation, mentioned here, is a calculus thing. It’s about integrals. We use it to estimate the value of an integral. We find a parabola that resembles the original function. And then the integral of the parabola should be close to the integral of the original function. The advantage of using a parabola is that we know exactly how to integrate that. You may have noticed a lot of calculus is built on finding a problem that we can do that looks enough like the one we want to do. There’s also a Simpson’s 3/8th Approximation. It uses a cubic polynomial instead of a parabola for the approximation. We can integrate cubics exactly too. It’s called the 3/8 Approximation, or the 3/8 Rule, because the formula for it starts off with a 3/8. So now and then a mathematics thing is named appropriately. Simpson’s Approximation is named for Thomas Simpson, an 18th century mathematician and textbook writer who did show the world the 3/8 Approximation. But other people are known to have used Simpson’s non-3/8 Approximation a century or more before Simpson was born .

Jason Poland’s Robbie and Bobby seeks much but slight attention from me this week. The first, from the 21st, riffs on the “randomness” of the random acts of kindness. Robbie strives for a truly random act. Randomness is tricky. We’re pretty sure we know what it ought to look like, but it’s so very hard to ever be sure we have randomness. We have a set of possible outcomes of whatever we’re doing; but, should every one of those outcomes be equally likely? Should some be more likely than others? Should some be almost inevitable but a few have long-shot chances? I suspect that when we say “truly random” we are thinking of a uniform distribution, with every different outcome being equally likely. That isn’t always what fits the situation.

And then on the 23rd the strip names “Zeno’s Paradoxical Pasta”. There are several paradoxes; this surely refers to the one about not being able to cross a distance because one must always get halfway across the distance first. It’s a reliably funny idea. It’s not a paradox by itself, though. What makes the paradox is that Zeno presents several scenarios which ask that we decide whether space and time and movement can be infinitely subdivided or not, and either decision brings up new difficulties.

Reading the Comics, December 17, 2016: Sleepy Week Edition

Comic Strip Master Command sent me a slow week in mathematical comics. I suppose they knew I was on somehow a busier schedule than usual and couldn’t spend all the time I wanted just writing. I appreciate that but don’t want to see another of those weeks when nothing qualifies. Just a warning there.

John Rose’s Barney Google and Snuffy Smith for the 12th of December, 2016. I appreciate the desire to pay attention to continuity that makes Rose draw in the coffee cup both panels, but Snuffy Smith has to swap it from one hand to the other to keep it in view there. Not implausible, just kind of busy. Also I can’t fault Jughaid for looking at two pages full of unillustrated text and feeling lost. That’s some Bourbaki-grade geometry going on there.

John Rose’s Barney Google and Snuffy Smith for the 12th is a bit of mathematical wordplay. It does use geometry as the “hard mathematics we don’t know how to do”. That’s a change from the usual algebra. And that’s odd considering the joke depends on an idiom that is actually used by real people.

Patrick Roberts’s Todd the Dinosaur for the 12th uses mathematics as the classic impossibly hard subject a seven-year-old can’t be expected to understand. The worry about fractions seems age-appropriate. I don’t know whether it’s fashionable to give elementary school students experience thinking of ‘x’ and ‘y’ as numbers. I remember that as a time when we’d get a square or circle and try to figure what number fits in the gap. It wasn’t a 0 or a square often enough.

Patrick Roberts’s Todd the Dinosaur for the 12th of December, 2016. Granting that Todd’s a kid dinosaur and that T-Rexes are not renowned for the hugeness of their arms, wouldn’t that still be enough space for a lot of text to fit around? I would have thought so anyway. I feel like I’m pluralizing ‘T-Rex’ wrong, but what would possibly be right? ‘Ts-rex’? Don’t make me try to spell tyrannosaurus.

Jef Mallett’s Frazz for the 12th uses one of those great questions I think every child has. And it uses it to question how we can learn things from statistical study. This is circling around the “Bayesian” interpretation of probability, of what odds mean. It’s a big idea and I’m not sure I’m competent to explain it. It amounts to asking what explanations would be plausibly consistent with observations. As we get more data we may be able to rule some cases in or out. It can be unsettling. It demands we accept right up front that we may be wrong. But it lets us find reasonably clean conclusions out of the confusing and muddy world of actual data.

Sam Hepburn’s Questionable Quotebook for the 14th illustrates an old observation about the hypnotic power of decimal points. I think Hepburn’s gone overboard in this, though: six digits past the decimal in this percentage is too many. It draws attention to the fakeness of the number. One, two, maybe three digits past the decimal would have a more authentic ring to them. I had thought the John Allen Paulos tweet above was about this comic, but it’s mere coincidence. Funny how that happens.

Reading the Comics, December 10, 2016: E = mc^2 Edition

And now I can finish off last week’s mathematically-themed comic strips. There’s a strong theme to them, for a refreshing change. It would almost be what we’d call a Comics Synchronicity, on Usenet group rec.arts.comics.strips, had they all appeared the same day. Some folks claiming to be open-minded would allow a Synchronicity for strips appearing on subsequent days or close enough in publication, but I won’t have any of that unless it suits my needs at the time.

Ernie Bushmiller’s for the 6th would fit thematically better as a Cameo Edition comic. It mentions arithmetic but only because it’s the sort of thing a student might need a cheat sheet on. I can’t fault Sluggo needing help on adding eight or multiplying by six; they’re hard. Not remembering 4 x 2 is unusual. But everybody has their own hangups. The strip originally ran the 6th of December, 1949.

Bill holbrook’s On The Fastrack for the 7th of December, 2016. Don’t worry about the people in the first three panels; they’re just temps, and weren’t going to appear in the comic again.

Bill holbrook’s On The Fastrack for the 7th seems like it should be the anthropomorphic numerals joke for this essay. It doesn’t seem to quite fit the definition, but, what the heck.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers on the 7th starts off the run of E = mc2 jokes for this essay. This one reminds me of Gary Larson’s Far Side classic with the cleaning woman giving Einstein just that little last bit of inspiration about squaring things away. It shouldn’t surprise anyone that E equalling m times c squared isn’t a matter of what makes an attractive-looking formula. There’s good reasons when one thinks what energy and mass are to realize they’re connected like that. Einstein’s famous, deservedly, for recognizing that link and making it clear.

Mark Pett’s Lucky Cow rerun for the 7th has Claire try to use Einstein’s famous quote to look like a genius. The mathematical content is accidental. It could be anything profound yet easy to express, and it’s hard to beat the economy of “E = mc2” for both. I’d agree that it suggests Claire doesn’t know statistics well to suppose she could get a MacArthur “Genius” Grant by being overheard by a grant nominator. On the other hand, does anybody have a better idea how to get their attention?

Harley Schwadron’s 9 to 5 for the 8th completes the “E = mc2” triptych. Calling a tie with the equation on it a power tie elevates the gag for me. I don’t think of “E = mc2” as something that uses powers, even though it literally does. I suppose what gets me is that “c” is a constant number. It’s the speed of light in a vacuum. So “c2” is also a constant number. In form the equation isn’t different from “E = m times seven”, and nobody thinks of seven as a power.

Morrie Turner’s Wee Pals rerun for the 8th is a bit of mathematics wordplay. It’s also got that weird Morrie Turner thing going on where it feels unquestionably earnest and well-intentioned but prejudiced in that way smart 60s comedies would be.

Mort Walker’s vintage Beetle Bailey for the 18th of May, 1960. Rerun the 9th of December, 2016. For me the really fascinating thing about ancient Beetle Bailey strips is that they could run today with almost no changes and yet they feel like they’re from almost a different cartoon universe from the contemporary comic. I don’t know how that is, or why it is.

Mort Walker’s Beetle Bailey for the 18th of May, 1960 was reprinted on the 9th. It mentions mathematics — algebra specifically — as the sort of thing intelligent people do. I’m going to take a leap and suppose it’s the sort of algebra done in high school about finding values of ‘x’ rather than the mathematics-major sort of algebra, done with groups and rings and fields. I wonder when holding a mop became the signifier of not just low intelligence but low ambition. It’s subverted in Jef Mallet’s Frazz, the title character of which works as a janitor to support his exercise and music habits. But it is a standard prop to signal something.

Reading the Comics, December 3, 2016: Cute Little Jokes Edition

Comic Strip Master Command apparently wanted me to have a bunch of easy little pieces that don’t inspire rambling essays. Message received!

Mark Litzler’s Joe Vanilla for the 27th is a wordplay joke in which any mathematical content is incidental. It could be anything put in a positive light; numbers are just easy things to arrange so. From the prominent appearance of ‘3’ and ‘4’ I supposed Litzler was using the digits of π, but if he is, it’s from some part of π that I don’t recognize. (That would be any part after the seventeenth digit. I’m not obsessive about π digits.)

Samson’s Dark Side Of The Horse is whatever the equivalent of punning is for Roman Numerals. I like Horace blushing.

John Deering’s Strange Brew for the 28th is a paint-by-numbers joke, and one I don’t see done often. And there is beauty in the appearance of mathematics. It’s not appreciated enough. I think looking at the tables of integral formulas on the inside back cover of a calculus book should prove the point, though. All those rows of integral signs and sprawls of symbols after show this abstract beauty. I’ve surely mentioned the time when the creative-arts editor for my undergraduate leftist weekly paper asked for a page of mathematics or physics work to include as an picture, too. I used the problem that inspired my “Why Stuff Can Orbit” sequence over on my mathematics blog. The editor loved the look of it all, even if he didn’t know what most of it meant.

Niklas Eriksson’s Carpe Diem for the 29th of November, 2016. I’m not sure why this has to be worked out in the break room but I guess you work out life where you do. Anyway, I’m glad to see the Grey Aliens allow for Green Aliens representing them on t-shirts.

Niklas Eriksson’s Carpe Diem for the 29th is a joke about life, I suppose. It uses a sprawled blackboard full of symbols to play the part of the proof. It’s gibberish, of course, although I notice how many mathematics cliches get smooshed into it. There’s a 3.1451 — I assume that’s a garbed digits of π — under a square root sign. There’s an “E = mc”, I suppose a garbled bit of Einstein’s Famous Equation in there. There’s a “cos 360”. 360 evokes the number of degrees in a circle, but mathematicians don’t tend to use degrees. There’s analytic reasons why we find it nicer to use radians, for which the equivalent would be “cos 2π”. If we wrote that at all, since the cosine of 2π is one of the few cosines everyone knows. Every mathematician knows. It’s 1. Well, maybe the work just got to that point and it hasn’t been cleaned up.

Eriksson’s Carpe Diem reappears the 30th, with a few blackboards with less mathematics to suggest someone having a creative block. It does happen to us all. My experience is mathematicians don’t tend to say “Eureka” when we do get a good idea, though. It’s more often some vague mutterings and “well what if” while we form the idea. And then giggling or even laughing once we’re sure we’ve got something. This may be just me and my friends. But it is a real rush when we have it.

Dan Collins’s Looks Good On Paper for the 29t tells the Möbius strip joke. It’s a well-rendered one, though; I like that there is a readable strip in there and that it’s distorted to fit the geometry.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 2nd of December tosses off the old gag about not needing mathematics now that we have calculators. It’s not a strip about that, and that’s fine.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 2nd of December, 2016. Now, not to nitpick, but Jughead and Archie don’t declare it *is* a waste of time to learn mathematics or spelling when a computer can do that work. Also, why don’t we have a word like ‘calculator’ for ‘spell-checker’? I mean, yes, ‘spell-checker’ is an acceptable word, but it’s like calling a ‘calculator’ an ‘arithmetic-doer’.

Mark Anderson’s Andertoons finally appeared the 2nd. It’s a resistant-student joke. And a bit of wordplay.

Ruben Bolling’s Super-Fun-Pak Comix from the 2nd featured an installment of Tautological But True. One might point out they’re using “average” here to mean “arithmetic mean”. There probably isn’t enough egg salad consumed to let everyone have a median-sized serving. And I wouldn’t make any guesses about the geometric mean serving. But the default meaning of “average” is the arithmetic mean. Anyone using one of the other averages would say so ahead of time or else is trying to pull something.

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, November 23, 2016: Featuring A Betty Boop Cartoon Edition

I admit to padding this week’s collection of mathematically-themed comic strips. There’s just barely enough to justify my splitting this into a Sunday and a Tuesday installment. I’m including a follow-the-bouncing-ball cartoon to make up for that though. Enjoy!

Jimmy Hatlo’s Little Iodine from the 20th originally ran the 18th of September, 1955. It’s a cute enough bit riffing on realistic word problems. If the problems do reflect stuff ordinary people want to know, after all, then they’re going to be questions people in the relevant fields know how to solve. A limitation is that word problems will tend to pick numbers that make for reasonable calculations, which may be implausible for actual problems. None of the examples Iodine gives seem implausible to me, but what do I know about horses? But I do sometimes encounter problems which have the form but not content of a reasonable question, like an early 80s probability book asking about the chances of one or more defective transistors in a five-transistor radio set. (The problem surely began as one about burned-out vacuum tubes in a radio.)

Daniel Beyer’s Long Story Short for the 21st is another use of Albert Einstein as iconic for superlative first-rate genius. I’m curious how long it did take for people to casually refer to genius as Einstein. The 1930 song Kitty From Kansas City (and its 1931 Screen Songs adaptation, starring Betty Boop) mention Einstein as one of those names any non-stupid person should know. But that isn’t quite the same as being the name for a genius.

My love asked if I’d include Stephen Pastis’s Pearls Before Swine of the 22nd. It has one of the impossibly stupid crocodiles say, poorly, that he was a mathematics major. I admitted it depended how busy the week was. On a slow week I’ll include more marginal stuff.

Is it plausible that the Croc is, for all his stupidity, a mathematics major? Well, sure. Perseverance makes it possible to get any degree. And given Croc’s spent twenty years trying to eat Zebra without getting close clearly perseverance is one of his traits. But are mathematics majors bad at communication?

Certainly we get the reputation for it. Part of that must be that any specialized field — whether mathematics, rocket science, music, or pasta-making — has its own vocabulary and grammar for that vocabulary that outsiders just don’t know. If it were easy to follow it wouldn’t be something people need to be trained in. And a lay audience starts scared of mathematics in a way they’re not afraid of pasta technology; you can’t communicate with people who’ve decided they can’t hear you. And many mathematical constructs just can’t be explained in a few sentences, the way vacuum extrusion of spaghetti noodles could be. And, must be said, it’s often the case a mathematics major (or a major in a similar science or engineering-related field) has English as a second (or third) language. Even a slight accent can make someone hard to follow, and build an undeserved reputation.

The Pearls crocodiles are idiots, though. The main ones, anyway; their wives and children are normal.

Ernie Bushmiller’s Nancy Classics for the 23rd originally appeared the 23rd of November, 1949. It’s just a name-drop of mathematics, though, using it as the sort of problem that can be put on the blackboard easily. And it’s not the most important thing going on here, but I do notice Bushmiller drawing the blackboard as … er … not black. It makes the composition of the last panel easier to read, certainly. And makes the visual link between the paper in the second panel and the blackboard in the last stronger. It seems more common these days to draw a blackboard that’s black. I wonder if that’s so, or if it reflects modern technology making white-on-black-text easier to render. A Photoshop select-and-invert is instantaneous compared to what Bushmiller had to do.

• davekingsbury 11:04 pm on Monday, 28 November, 2016 Permalink | Reply

Where do you find the comics you review, may I ask? It’s extraordinary how many math-related items you find …

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• Joseph Nebus 9:29 pm on Wednesday, 30 November, 2016 Permalink | Reply

Nearly all the comics I read come from two sites. The first is Gocomics.com, and the other is ComicsKingdom.com. I’ve got paid subscriptions to both; the value is fantastic, especially given ComicsKingdom’s vintage selection.

And yeah, I read nearly everything they offer. There’s some comics I don’t read because they’re in perpetual reruns and I’ve seen them all enough times (eg, Berekeley Breathead’s Academica Waltz or the Gocomics slice of Al Capp’s Li’l Abner). And there’s some I don’t read because they’ve irritated or offended me too often. Not many, though; it takes a special knack to be a truly objectionable comic strip.

After that there’s a couple stragglers on Creators.com. Jumble and the various Joe Martin comics I get from the Houston Chronicle’s web site. Those don’t have subscriptions; I just have a tab group for them.

And yeah, this does leave me spending quite some time reading comics each day. It makes a pleasant way to ease into putting off the rest of the morning’s tasks.

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• davekingsbury 12:54 am on Thursday, 1 December, 2016 Permalink | Reply

Thanks for that! You cover the mathematics but there’s also plenty of social history in there, which I also glean from your excellent posts. I’m 67 but I sometimes think I learned most – quickest, anyway – when I was reading comics on a regular basis. My favourite comic strip moment is described in this post, if I may be so bold as to provide a link to it …

https://davekingsbury.wordpress.com/2015/12/01/the-kids-are-all-right/

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• Joseph Nebus 4:39 pm on Friday, 9 December, 2016 Permalink | Reply

I have always loved comic strips, and in maturity I’ve come to appreciate that I still love them, even if a lot of them are honesty pretty bad. Well, ‘bad’ overstates things, but there is a frightful sameness that very many of them have. I did a review of the Gocomics.com strips for a Usenet group a few years back and had no idea how many of them were “three generation and a dog”. Some were great, some were awful, but it’s amazing so many had the same setup.

Anyway, though, thanks for the link. I’m quite ignorant of most non-US comic strips and glad to learn about them, especially comics that people like.

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• davekingsbury 7:49 pm on Friday, 9 December, 2016 Permalink | Reply

By ‘three generation and a dog’, I assume you mean a formulaic family story …

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• Joseph Nebus 5:30 am on Saturday, 17 December, 2016 Permalink | Reply

‘Three Generations And A Dog’ is a setup, and one that’s surprisingly common. I noticed the pattern when I tried reviewing all the Gocomics.com comics for Usenet newsgroup rec.arts.comics.strips, and if I ever get completely hard up for material for my humor blog I’ll start posting those there.

But there’s quite a few comics that have as the central cast three generations of a family: grandparents, parents, and children. And the parents-and-children usually have a pet. Typically that’s a dog, but sometimes it’s a cat. I understand the logic behind this casting. It gives the cartoonist a natural cast of six or seven characters with different backgrounds who have good reason to keep interacting. The focus can shift between them as the story or the cartoonist’s interest varies.

Some are quite good, like Stone Soup (recently gone to Sunday-only) or One Big Happy. Some are steady if not quite first-rate, like Pickles. Some I forget exist, but might be right for people with a different sense of humor than mine, such as Boomerangs or Grand Avenue.

It’s a weird pattern to see once you see that it’s there.

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• davekingsbury 11:12 am on Saturday, 17 December, 2016 Permalink | Reply

Thanks for giving the benefits of your research. I can see why cartoonists would employ such a setting. I suppose it’s the same principle in use in sit-coms, where characters are forced to interact with one another – family, workplace, army, prison, etc.

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• Joseph Nebus 6:30 am on Wednesday, 21 December, 2016 Permalink | Reply

You’re quite welcome. And yes, it is a lot like the process of picking the setup for a sitcom, or a regular drama, for that matter. You need characters who have a reasonable spread of personalities but something to keep them tied together. So families are good starting points. Offices or workplaces too, so it shouldn’t surprise those settings turn up so often. I guess there’s also the desire to have something that doesn’t demand your characters move away, since nobody wants to risk losing a good character, which is probably why there aren’t so many comic strips set in colleges; Watch Your Head is the only one of those that comes to mind. The ones that are set in schools are mostly ones like Frazz that don’t age the characters. (Well, there’s whatever deranged mess Funky Winkerbean is; I suppose that’s nominally set in a high school, but it’s about the faculty rather than the students, when it remembers to do high school stories.)

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Reading the Comics, November 19, 2016: Thought I Featured This Already Edition

For the second half of last week Comic Strip Master Command sent me a couple comics I would have sworn I showed off here before.

Jason Poland’s Robbie and Bobby for the 16th I would have sworn I’d featured around here before. I still think it’s a rerun but apparently I haven’t written it up. It’s a pun, I suppose, playing on the use of “power” to mean both exponentials and the thing knowledge is. I’m curious why Polard used 10 for the new exponent. Normally if there isn’t an exponent explicitly written we take that to be “1”, and incrementing 1 would give 2. Possibly that would have made a less-clear illustration. Or possibly the idea of sleeping squared lacked the Brobdingnagian excess of sleeping to the tenth power.

Exponentials have been written as a small number elevated from the baseline since 1636. James Hume then published an edition of François Viète’s text on algebra. Hume used a Roman numeral in the superscript — xii instead of x2 — but apart from that it’s the scheme we use today. The scheme was in the air, though. Renée Descartes also used the notation, but with Arabic numerals throughout, from 1637. (With quirks; he would write “xx” instead of “x2”, possibly because it’s the same number of characters to write.) And Pierre Hérigone just wrote the exponent after the variable: x2, like you see in bad character-recognition texts. That isn’t a bad scheme, particularly since it’s so easy to type, although we would add a caret: x^2. (I draw all this history, as ever, from Florian Cajori’s A History of Mathematical Notations, particularly sections 297 through 299).

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 16th has a fun concept about statisticians running wild and causing chaos. I appreciate a good healthy prank myself. It does point out something valuable, though. People in general have gotten to understand the idea that there are correlations between things. An event happening and some effect happening seem to go together. This is sometimes because the event causes the effect. Sometimes they’re both caused by some other factor; the event and effect are spuriously linked. Sometimes there’s just no meaningful connection. Coincidences do happen. But there’s really no good linking of how strong effects can be. And that’s not just a pop culture thing. For example, doing anything other than driving while driving increases the risk of crashing. But by how much? It’s easy to take something with the shape of a fact. Suppose it’s “looking at a text quadruples your risk of crashing”. (I don’t know what the risk increase is. Pretend it’s quadruple for the sake of this.) That’s easy to remember. But what’s my risk of crashing? Suppose it’s a clear, dry day, no winds, and I’m on a limited-access highway with light traffic. What’s the risk of crashing? Can’t be very high, considering how long I’ve done that without a crash. Quadruple that risk? That doesn’t seem terrifying. But I don’t know what that is, or how to express it in a way that helps make decisions. It’s not just newscasters who have this weakness.

Mark Anderson’s Andertoons for the 18th is the soothing appearance of Andertoons for this essay. And while it’s the familiar form of the student protesting the assignment the kid does have a point. There are times an estimate is all we need, and there’s times an exact answer is necessary. When are those times? That’s another skill that people have to develop.

Arthur C Clarke, in his semi-memoir Astounding Days, wrote of how his early-40s civil service job had him auditing schoolteacher pension contributions. He worked out that he really didn’t need to get the answers exactly. If the contribution was within about one percent of right it wasn’t worth his time to track it down more precisely. I’m not sure that his supervisors would take the same attitude. But the war soon took everyone to other matters without clarifying just how exactly he was supposed to audit.

Mark Anderson’s Mr Lowe rerun for the 18th is another I would have sworn I’ve brought up before. The strip was short-lived and this is at least its second time through. But then mathematics is only mentioned here as a dull things students must suffer through. It might not have seemed interesting enough for me to mention before.

Rick Detorie’s One Big Happy rerun for the 19th is another sort of pun. At least it plays on the multiple meanings of “negative”. And I suspect that negative numbers acquired a name with, er, negative connotations because the numbers were suspicious. It took centuries for mathematicians to move them from “obvious nonsense” to “convenient but meaningless tools for useful calculations” to “acceptable things” to “essential stuff”. Non-mathematicians can be forgiven for needing time to work through that progression. Also I’m not sure I didn’t show this one off here when it was first-run. Might be wrong.

Saturday Morning Breakfast Cereal pops back into my attention for the 19th. That’s with a bit about Dad messing with his kid’s head. Not much to say about that so let me bury the whimsy with my earnestness. The strip does point out that what we name stuff is arbitrary. We would say that 4 and 12 and 6 are “composite numbers”, while 2 and 3 are “prime numbers”. But if we all decided one day to swap the meanings of the terms around we wouldn’t be making any mathematics wrong. Or linguistics either. We would probably want to clarify what “a really good factor” is, but all the comic really does is mess with the labels of groups of numbers we’re already interested in.

Reading the Comics, November 16, 2016: Seeing the Return of Jokes

Comic Strip Master Command sent out a big mass of comics this past week. Today’s installment will only cover about half of them. This half does feature a number of comics that show off jokes that’ve run here before. I’m sure it was coincidence. Comic Strip Master Command must have heard I was considering alerting cartoonists that I was talking about them. That’s fine for something like last week when I could talk about NP-complete problems or why we call something a “hypotenuse”. It can start a conversation. But “here’s a joke treating numerals as if they were beings”? All they can do is agree, that is what the joke is. If they disagree at that point they’re just trying to start a funny argument.

Scott Metzger’s The Bent Pinky for the 14th sees the return of anthropomorphic numerals humor. I’m a bit surprised Metzger goes so far as to make every numeral either a 3 or a 9. I’d have expected a couple of 2’s and 4’s. I understand not wanting to get into two-digit numbers. The premise of anthropomorphic numerals is troublesome if you need multiple-digit numbers.

Jon Rosenberg’s Goats for the 14th doesn’t directly mention a mathematical topic. But the story has the characters transported to a world with monkeys at typewriters. We know where that is. So we see that return after no time away, really.

Rick Detorie’s One Big Happy rerun for the 14th sees the return of “110 percent”. Happily the joke’s structured so that we can dodge arguing about whether it’s even possible to give 110 percent. I’m inclined to say of course it’s possible. “Giving 100 percent” in the context of playing a sport would mean giving the full reasonable effort. Or it does if we want to insist on idiomatic expressions making sense. It seems late to be insisting on that standard, but some people like it as an idea.

George Herriman’s Krazy Kat for the 22nd of December, 1938. Rerun the 15th of November, 2016. Really though who could sleep when they have a sweet adding machine like that to play with? Someone who noticed that that isn’t machine tape coming out the top, of course, but rather is the punch-cards for a band organ. Curiously low-dialect installment of the comic.

George Herriman’s Krazy Kat for the 22nd of December, 1938, was rerun on Tuesday. And it’s built on counting as a way of soothing the mind into restful sleep. Mathematics as a guide to sleep also appears, in minor form, in Darrin Bell’s Candorville for the 13th. I’m not sure why counting, or mental arithmetic, is able to soothe one into sleep. I suppose it’s just that it’s a task that’s engaging enough the semi-conscious mind can do it without having the emotional charge or complexity to wake someone up. I’ve taken to Collatz Conjecture problems, myself.

Terri Libenson’s Pajama Diaries for the 16th sees the return of Venn Diagram jokes. And it’s a properly-formed Venn Diagram, with the three circles coming together to indicate seven different conditions.

Terri Libenson’s Pajama Diaries for the 16th of November, 2016. I was never one for buying too much of the bakery aisle, myself, but then I also haven’t got teenagers. And I did go through so much of my life figuring there was no reason I shouldn’t eat another bagel again.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 16th just name-drops rhomboids, using them as just a funny word. Geometry is filled with wonderful, funny-sounding words. I’m fond of “icosahedron” myself. But “rhomboid” and its related words are good ones. I think they hit that sweet spot between being uncommon in ordinary language without being so exotic that a reader’s eye trips over it. However funny a “triacontahedron” might be, no writer should expect the reader to forgive that pile of syllables. A rhomboid is a kind of parallelogram, so it’s got four sides. The sides come in two parallel pairs. Both members of a pair have the same length, but the different pairs don’t. They look like the kitchen tiles you’d get for a house you couldn’t really afford, not with tiling like that.

• sheldonk2014 12:08 am on Monday, 21 November, 2016 Permalink | Reply

Hey Joseph I just dropped by to see
How the other half live
Play any pinball lately
Sheldon

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• Joseph Nebus 11:03 pm on Friday, 25 November, 2016 Permalink | Reply

Aw thanks, and glad to see you around. I’ve been pretty well. Played a lot of pinball lately, but the schedule is letting up after a lot of busy weeks. Everyone’s more or less found their place in the state’s championship series and there’s only a few people who can change their positions usefully. Should be a calm month ahead.

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