Updates from March, 2017 Toggle Comment Threads | Keyboard Shortcuts

  • Joseph Nebus 6:00 pm on Sunday, 19 March, 2017 Permalink | Reply
    Tags: 2 Cows And A Chicken, Archie, , Arlo and Janis, Lard's World Peace Tips, , Off The Mark, , , , Working Daze   

    Reading the Comics, March 18, 2017: Pi Day Edition 

    No surprise what the recurring theme for this set of mathematics-mentioning comic strips is. Look at the date range. But here goes.

    Henry Scarpelli and Craig Boldman’s Archie rerun for the 13th uses algebra as the thing that will stun a class into silence. I know the silence. As a grad student you get whole minutes of instructions on how to teach a course before being sent out as recitation section leader for some professor. And what you do get told is the importance of asking students their thoughts and their ideas. This maybe works in courses that are obviously friendly to opinions or partially formed ideas. But in Freshman Calculus? It’s just deadly. Even if you can draw someone into offering an idea how we might start calculating a limit (say), they’re either going to be exactly right or they’re going to need a lot of help coaxing the idea into something usable. I’d like to have more chatty classes, but some subjects are just hard to chat about.

    Mr Weatherby walks past a silent class. 'What a well-behaved class! ... Flutesnoot, how do you get them to be so quiet and still?' 'I just asked for a volunteer to solve an algebra problem!'

    Henry Scarpelli and Craig Boldman’s Archie rerun for the 13th of March, 2017. I didn’t know the mathematics teacher’s name and suppose that “Flutesnoot” is as plausible as anything. Anyway, I admire his ability to stand in front of a dead-silent class. The stage fright the scenario produces is powerful. At least when I was taught how to teach we got nothing about stage presence or how to remain confident during awkward pauses. What I know I learned from a half-year Drama course in high school.

    Steve Skelton’s 2 Cows And A Chicken for the 13th includes some casual talk about probability. As normally happens, they figure the chances are about 50-50. I think that’s a default estimate of the probability of something. If you have no evidence to suppose one outcome is more likely than the other, then that is a reason to suppose the chance of something is 50 percent. This is the Bayesian approach to probability, in which we rate things as more or less likely based on what information we have about how often they turn out. It’s a practical way of saying what we mean by the probability of something. It’s terrible if we don’t have much reliable information, though. We need to fall back on reasoning about what is likely and what is not to save us in that case.

    Scott Hilburn’s The Argyle Sweater lead off the Pi Day jokes with an anthropomorphic numerals panel. This is because I read most of the daily comics in alphabetical order by title. It is also because The Argyle Sweater is The Argyle Sweater. Among π’s famous traits is that it goes on forever, in decimal representations, yes. That’s not by itself extraordinary; dull numbers like one-third do that too. (Arguably, even a number like ‘2’ does, if you write all the zeroes in past the decimal point.) π gets to be interesting because it goes on forever without repeating, and without having a pattern easily describable. Also because it’s probably a normal number but we don’t actually know that for sure yet.

    Mark Parisi’s Off The Mark panel for the 14th is another anthropomorphic numerals joke and nearly the same joke as above. The answer, dear numeral, is “chained tweets”. I do not know that there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. But there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. If there isn’t, there is now.

    John Zakour and Scott Roberts’s Working Daze for the 14th is your basic Pi Day Wordplay panel. I think there were a few more along these lines but I didn’t record all of them. This strip will serve for them all, since it’s drawn from an appealing camera angle to give the joke life.

    Dave Blazek’s Loose Parts for the 14th is a mathematics wordplay panel but it hasn’t got anything to do with π. I suspect he lost track of what days he was working on, back six or so weeks when his deadline arrived.

    Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 15th is some sort of joke about the probability of the world being like what it seems to be. I’m not sure precisely what anyone is hoping to express here or how it ties in to world peace. But the world does seem to be extremely well described by techniques that suppose it to be random and unpredictable in detail. It is extremely well predictable in the main, which shows something weird about the workings of the world. It seems to be doing all right for itself.

    Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is built on the staggering idea that the Earth might be the only place with life in the universe. The cosmos is a good stand-in for infinitely large things. It might be better as a way to understand the infinitely large than actual infinity would be. Somehow thinking of the number of stars (or whatnot) in the universe and writing out a representable number inspires an understanding for bigness that the word “infinity” or the symbols we have for it somehow don’t seem to, at least to me.

    Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 17th gives us valuable information about how long ahead of time the comic strips are working. Arithmetic is probably the easiest thing to use if one needs an example of a fact. But even “2 + 2 = 4” is a fact only if we accept certain ideas about what we mean by “2” and “+” and “=” and “4”. That we use those definitions instead of others is a reflection of what we find interesting or useful or attractive. There is cultural artifice behind the labelling of this equation as a fact.

    Jimmy Johnson’s Arlo and Janis for the 18th capped off a week of trying to explain some point about the compression and dilution of time in comic strips. Comic strips use space and time to suggest more complete stories than they actually tell. They’re much like every other medium in this way. So, to symbolize deep thinking on a subject we get once again a panel full of mathematics. Yes, I noticed the misquoting of “E = mc2” there. I am not sure what Arlo means by “Remember the boat?” although thinking on it I think he did have a running daydream about living on a boat. Arlo and Janis isn’t a strongly story-driven comic strip, but Johnson is comfortable letting the setting evolve. Perhaps all this is forewarning that we’re going to jump ahead to a time in Arlo’s life when he has, or has had, a boat. I don’t know.

  • Joseph Nebus 6:00 pm on Sunday, 26 February, 2017 Permalink | Reply
    Tags: , , Flo and Friends, , , , Promises Promises, , , , Tiger   

    Reading the Comics, February 23, 2017: The Week At Once Edition 

    For the first time in ages there aren’t enough mathematically-themed comic strips to justify my cutting the week’s roundup in two. No, I have no idea what I’m going to write about for Thursday. Let’s find out together.

    Jenny Campbell’s Flo and Friends for the 19th faintly irritates me. Flo wants to make sure her granddaughter understands that just because it takes people on average 14 minutes to fall asleep doesn’t mean that anyone actually does, by listing all sorts of reasons that a person might need more than fourteen minutes to sleep. It makes me think of a behavior John Allen Paulos notes in Innumeracy, wherein the statistically wise points out that someone has, say, a one-in-a-hundred-million chance of being killed by a terrorist (or whatever) and is answered, “ah, but what if you’re that one?” That is, it’s a response that has the form of wisdom without the substance. I notice Flo doesn’t mention the many reasons someone might fall asleep in less than fourteen minutes.

    But there is something wise in there nevertheless. For most stuff, the average is the most common value. By “the average” I mean the arithmetic mean, because that is what anyone means by “the average” unless they’re being difficult. (Mathematicians acknowledge the existence of an average called the mode, which is the most common value (or values), and that’s most common by definition.) But just because something is the most common result does not mean that it must be common. Toss a coin fairly a hundred times and it’s most likely to come up tails 50 times. But you shouldn’t be surprised if it actually turns up tails 51 or 49 or 45 times. This doesn’t make 50 a poor estimate for the average number of times something will happen. It just means that it’s not a guarantee.

    Gary Wise and Lance Aldrich’s Real Life Adventures for the 19th shows off an unusually dynamic camera angle. It’s in service for a class of problem you get in freshman calculus: find the longest pole that can fit around a corner. Oh, a box-spring mattress up a stairwell is a little different, what with box-spring mattresses being three-dimensional objects. It’s the same kind of problem. I want to say the most astounding furniture-moving event I’ve ever seen was when I moved a fold-out couch down one and a half flights of stairs single-handed. But that overlooks the caged mouse we had one winter, who moved a Chinese finger-trap full of crinkle paper up the tight curved plastic to his nest by sheer determination. The trap was far longer than could possibly be curved around the tube. We have no idea how he managed it.

    J R Faulkner’s Promises, Promises for the 20th jokes that one could use Roman numerals to obscure calculations. So you could. Roman numerals are terrible things for doing arithmetic, at least past addition and subtraction. This is why accountants and mathematicians abandoned them pretty soon after learning there were alternatives.

    Mark Anderson’s Andertoons for the 21st is the Mark Anderson’s Andertoons for the week. Probably anything would do for the blackboard problem, but something geometry reads very well.

    Jef Mallett’s Frazz for the 21st makes some comedy out of the sort of arithmetic error we all make. It’s so easy to pair up, like, 7 and 3 make 10 and 8 and 2 make 10. It takes a moment, or experience, to realize 78 and 32 will not make 100. Forgive casual mistakes.

    Bud Fisher’s Mutt and Jeff rerun for the 22nd is a similar-in-tone joke built on arithmetic errors. It’s got the form of vaudeville-style sketch compressed way down, which is probably why the third panel could be made into a satisfying final panel too.

    'How did you do on the math test?' 'Terrible.' 'Will your mom be mad?' 'Maybe. But at least she'll know I didn't cheat!'

    Bud Blake’s Tiger for the 23rd of February, 2017. I want to blame the colorists for making Hugo’s baby tooth look so weird in the second and third panels, but the coloring is such a faint thing at that point I can’t. I’m sorry to bring it to your attention if you didn’t notice and weren’t bothered by it before.

    Bud Blake’s Tiger rerun for the 23rd just name-drops mathematics; it could be any subject. But I need some kind of picture around here, don’t I?

    Mike Baldwin’s Cornered for the 23rd is the anthropomorphic numerals joke for the week.

  • Joseph Nebus 6:00 pm on Thursday, 26 January, 2017 Permalink | Reply
    Tags: , Clear Blue Water, Hi and Lois, , , One Big Family, ,   

    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.

    'Anne has six nickels. Sue has 41 pennies. Who has more money?' 'That's not going to be easy to figure out. It all depends on how they're dressed!'

    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.

    'Uh, Fi? Have you looked at the non-compete clause in your contract?' 'I wouldn't go to one of Fastrack's competitors.' 'No, but, um ... you'd better read this.' 'I COULDN'T USE NUMBERS FOR TWO YEARS???' 'Roman numerals would be okay.'

    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.

    'I hope our kids are smart enough to win scholarships for college.' 'We can't count on that. We'll just have to save the money!' 'Do you know it costs about $10,000 to send one child through college?!' 'That's $40,000 we'd have to save!' Lois reads to the kids: (d^2/dx^2)y = 6x - 2.

    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?


      • 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.


  • Joseph Nebus 6:00 pm on Sunday, 18 December, 2016 Permalink | Reply
    Tags: , dinosaurs,   

    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.

    'Dadburnit! I ain't never gonna git geometry!' 'Bah! Don't fret, Jughaid --- I never understood it neither! But I still manage to work all th' angles!'

    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.

    'Teacher! Todd just passed out! But he's waring one of those medic alert bracelets! ... Do not expose the wearer of this bracelet to anything mathematical, especially x's and y's, fractions, or anything that he should remember for a test!' 'Amazing how much writing they were able to fit on a little ol' T-Rex wrist!'

    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.

  • Joseph Nebus 6:00 pm on Tuesday, 13 December, 2016 Permalink | Reply
    Tags: , , , MacArthur Genius Grants, , ,   

    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.

    People contorted to look like a 4, a 2, and a 7 bounce past Dethany's desk. She ponders: 'Performance review time ... when the company reduces people to numbers.' Wendy, previous star of the strip, tells Dethany 'You're next.' Wendy's hair is curled into an 8.

    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.

    Sarge demands to know who left this algebra book on his desk; Zero says not him. Sarge ignores him and asks 'Who's been figuring all over my desk pad?' Zero also unnecessarily denies it. 'Come on, whose is it?!' Zero reflects, 'Gee, he *never* picks on *me*!'

    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.

  • Joseph Nebus 6:00 pm on Sunday, 11 December, 2016 Permalink | Reply
    Tags: , , , pranks, , titles   

    Reading the Comics, December 5, 2016: Cameo Appearances Edition 

    Comic Strip Master Command sent a bunch of strips my way this past week. They’ll get out to your way over this week. The first bunch are all on Gocomics.com, so I don’t feel quite fair including the strips themselves. This set also happens to be a bunch in which mathematics gets a passing mention, or is just used because they need some subject and mathematics is easy to draw into a joke. That’s all right.

    Jef Mallet’s Frazz for the 4th uses blackboard arithmetic and the iconic minor error of arithmetic. It’s also strikingly well-composed; look at the art from a little farther away. Forgetting to carry the one is maybe a perfect minor error for this sort of thing. Everyone does it, experienced mathematicians included. It’s very gradable. When someone’s learning arithmetic making this mistake is considered evidence that someone doesn’t know how to add. When someone’s learned it, making the mistake isn’t considered evidence the person doesn’t know how to add. A lot of mistakes work that way, somehow.

    Rick Stromoski’s Soup to Nutz for the 4th name-drops Fundamentals of Algebra as a devilish, ban-worthy book. Everyone feels that way. Mathematics majors get that way around two months in to their Introduction To Not That Kind Of Algebra course too. I doubt Stromoski has any particular algebra book in mind, but it doesn’t matter. The convention in mathematics books is to make titles that are ruthlessly descriptive, with not a touch of poetry to them. Among the mathematics books I have on my nearest shelf are Resnikoff and Wells’s Mathematics in Civilization; Koks’ Explorations in Mathematical Physics: The Concepts Behind An Elegant Language; Enderton’s A Mathematical Introduction To Logic; Courant, Robbins, and Stewart’s What Is Mathematics?; Murasagi’s Knot Theory And Its Applications; Nishimori’s Statistical Physics of Spin Glasses and Information Processing; Brush’s The Kind Of Motion We Call Heat, and so on. Only the Brush title has the slightest poetry to it, and it’s a history (of thermodynamics and statistical mechanics). The Courant/Robbins/Stewart has a title you could imagine on a bookstore shelf, but it’s also in part a popularization.

    It’s the convention, and it’s all right in its domain. If you are deep in the library stacks and don’t know what a books is about, the spine will tell you what the subject is. You might not know what level or depth the book is in, but you’ll know what the book is. The down side is if you remember having liked a book but not who wrote it you’re lost. Methods of Functional Analysis? Techniques in Modern Functional Analysis? … You could probably make a bingo game out of mathematics titles.

    Johnny Hart’s Back to B.C. for the 5th, a rerun from 1959, plays on the dawn of mathematics and the first thoughts of parallel lines. If parallel lines stir feelings in people they’re complicated feelings. One’s either awed at the resolute and reliable nature of the lines’ interaction, or is heartbroken that the things will never come together (or, I suppose, break apart). I can feel both sides of it.

    Dave Blazek’s Loose Parts for the 5th features the arithmetic blackboard as inspiration for a prank. It’s the sort of thing harder to do with someone’s notes for an English essay. But, to spoil the fun, I have to say in my experience something fiddled with in the middle of a board wouldn’t even register. In much the way people will read over typos, their minds seeing what should be there instead of what is, a minor mathematical error will often not be seen. The mathematician will carry on with what she thought should be there. Especially if the error is a few lines back of the latest work. Not always, though, and when it doesn’t it’s a heck of a problem. (And here I am thinking of the week, the week, I once spent stymied by a problem because I was differentiating the function ex wrong. The hilarious thing here is it is impossible to find something easier to differentiate than ex. After you differentiate it correctly you get ex. An advanced squirrel could do it right, and here I was in grad school doing it wrong.)

    Nate Creekmore’s Maintaining for the 5th has mathematics appear as the sort of homework one does. And a word problem that uses coins for whatever work it does. Coins should be good bases for word problems. They’re familiar enough and people do think about them, and if all else fails someone could in principle get enough dimes and quarters and just work it out by hand.

    Sam Hepburn’s Questionable Quotebook for the 5th uses a blackboard full of mathematics to signify a monkey’s extreme intelligence. There’s a little bit of calculus in there, an appearance of “\frac{df}{dx} ” and a mention of the limit. These are things you get right up front of a calculus course. They’ll turn up in all sorts of problems you try to do.

    Charles Schulz’s Peanuts for the 5th is not really about mathematics. Peppermint Patty just mentions it on the way to explaining the depths of her not-understanding stuff. But it’s always been one of my favorite declarations of not knowing what’s going on so I do want to share it. The strip originally ran the 8th of December, 1969.

  • Joseph Nebus 6:00 pm on Saturday, 10 December, 2016 Permalink | Reply
    Tags: , , ,   

    What Do I Need To Pass This Class? (December 2016 Edition) 

    Chatting with friends made me aware some schools have already started finals. So I’m sorry to be late with this. But for those who need it here’s my ancient post on how to calculate the minimum score you need on the final to get the grade you want in the class. And for those who see my old prose style and recoil in horror I’m sorry. I was less experienced back then. Don’t look smug; you were too. But here’s a set of tables for common grade distributions, so you don’t have to do any calculations yourself. Just look up numbers instead.

    With that information delivered, let me say once more: what you really need is to start preparing early, and consistently. Talk with your instructor about stuff you don’t understand, and stuff you think you understand, early on. Don’t give a line about the grade you need; that puts an inappropriate pressure on the instructor to grade you incorrectly. Study because it’s worth studying. Even if you don’t see why the subject is interesting, it is something that people smarter than you have spent a lot of time thinking about. It’s worth figuring out something of what they know that you don’t yet.

    • davekingsbury 11:13 pm on Sunday, 11 December, 2016 Permalink | Reply

      Have you got any tables with the answers? ;)


      • Joseph Nebus 6:06 am on Saturday, 17 December, 2016 Permalink | Reply

        So there’s this old joke about the professor hoping to draw students to the review session ahead of the exam, which is to be the classic blend of true-or-false questions, multiple-choice questions, short-answer questions, major problems. To get students in she promises that she’ll give the answer to one of the questions during the review. The review session comes and gets pretty good attendance. As she’s dismissing the class one of the students reminds her of the promise for one of the answers. And she says, ‘Very well. One of the answers is true.’

        There is sometimes a temptation to do something playful or weird with true-false questions, particularly. I remember once giving in to the temptation to make all the questions in the true-or-false section ‘true’, partly to see if students would be unnerved by too long a series of identical answers. It was a dumb idea. I don’t think most students even noticed. And if they were unnerved by too many identical answers in a row, then, I would now say, that was me screwing up. If there is a point to tests it is whether students can demonstrate mastery of a concept. It’s fair to test someone on how well they’ve understood the subtleties of the concept. Head games the teacher might be playing have absolutely nothing to do with the concept, though, so it’s poor form to mark someone down — or up! — for mastering me instead.

        Liked by 1 person

    • davekingsbury 11:32 am on Saturday, 17 December, 2016 Permalink | Reply

      Nice answer to my question! I agree that tests should give students a chance to use what they’ve learned – a much higher-order skill than box-ticking.


      • Joseph Nebus 6:44 am on Wednesday, 21 December, 2016 Permalink | Reply

        Well, I’ve come to see tests as having a couple purposes. And there is some value in box-ticking. We need to be able to think deeply about stuff, but we also need to have mastery of boring little facts o that we’re thinking about the right stuff. Multiple-choice or true/false questions are pretty good about straightening out whether someone has got definitions and basic concepts and all that. In (say) an essay it can be hard to tell whether the thing’s gone wrong because a good argument was built on bad understandings, or because the argument was lousy yet the basic concepts understood perfectly.

        Liked by 1 person

        • davekingsbury 4:00 pm on Wednesday, 21 December, 2016 Permalink | Reply

          Yes, horses for courses, as they say … I preferred doing essays probably because I could waffle for England!


          • Joseph Nebus 5:09 am on Thursday, 5 January, 2017 Permalink | Reply

            There is that. A competent essay is such a blessing in the midst of a pile of exams. They stand out from the incompetent or the incoherent pieces. Once they pass the plagiarism check.


            • davekingsbury 9:54 am on Thursday, 5 January, 2017 Permalink | Reply

              Ah plagiarism – killed coursework, unfortunately – though I think people should be allowed to quote as long as they refute or develop the ideas themselves.


  • Joseph Nebus 6:00 pm on Tuesday, 29 November, 2016 Permalink | Reply
    Tags: , , , , , ,   

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

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

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

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

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

    'Can you help me with my math, Grandma?' 'Let me see.' 'It's pre-algebra.' 'Oh, darn!' 'What's wrong?' 'I'm post-algebra.'

    Rick Kirkman and Jerry Scott’s Baby Blues for the 26th of November, 2016. I suppose Kirkman and Scott know their characters better than I do but isn’t Zoe like nine or ten? Isn’t pre-algebra more a 7th or 8th grade thing? I can’t argue Grandma being post-algebra but I feel like the punch line was written and then retrofitted onto the characters.

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

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

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

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

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

    • 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.


      • 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.

        Liked by 1 person

        • 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…


    • 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?)


      • 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.


    • 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 …


      • 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.

        Liked by 1 person

    • 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 …


      • 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.

        Liked by 1 person

    • 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 …


      • 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.


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

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


          • 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.


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

      Character-forming … 67 and still waiting! ;)


  • Joseph Nebus 6:00 pm on Sunday, 13 November, 2016 Permalink | Reply
    Tags: , , complexity, , , , , ,   

    Reading the Comics, November 12, 2016: Frazz and Monkeys Edition 

    Two things made repeat appearances in the mathematically-themed comics this week. They’re the comic strip Frazz and the idea of having infinitely many monkeys typing. Well, silly answers to word problems also turned up, but that’s hard to say many different things about. Here’s what I make the week in comics out to be.

    'An infinite number of monkeys sitting at an infinite number of typewriters will eventually reproduce the works of Shakespeare. ... Justy sayin' ... a four digit pin number is statistically sooo much better.'

    Sandra Bell-Lundy’s Between Friends for the 6th of November, 2016. I’m surprised Bell-Lundy used the broader space of a Sunday strip for a joke that doesn’t need that much illustration, but I understand sometimes you just have to go with the joke that you have. And it isn’t as though Sunday comics get that much space anymore either. Anyway, I suppose we have all been there, although for me that’s more often because I used to have a six-digit pin, and a six-digit library card pin, and those were just close enough to each other that I could never convince myself I was remembering the right one in context, so I would guess wrong.

    Sandra Bell-Lundy’s Between Friends for the 6th introduces the infinite monkeys problem. I wonder sometimes why the monkeys-on-typewriters thing has so caught the public imagination. And then I remember it encourages us to stare directly into infinity and its intuition-destroying nature from the comfortable furniture of the mundane — typewriters, or keyboards, for goodness’ sake — with that childish comic dose of monkeys. Given that it’s a wonder we ever talk about anything else, really.

    Monkeys writing Shakespeare has for over a century stood as a marker for what’s possible but incredibly improbable. I haven’t seen it compared to finding a four-digit PIN. It has got me wondering about the chance that four randomly picked letters will be a legitimate English word. I’m sure the chance is more than the one-in-a-thousand chance someone would guess a randomly drawn PIN correctly on one try. More than one in a hundred? I’m less sure. The easy-to-imagine thing to do is set a computer to try out all 456,976 possible sets of four letters and check them against a dictionary. The number of hits divided by the number of possibilities would be the chance of drawing a legitimate word. If I had a less capable computer, or were checking even longer words, I might instead draw some set number of words, never minding that I didn’t get every possibility. The fraction of successful words in my sample would be something close to the chance of drawing any legitimate word.

    If I thought a little deeper about the problem, though, I’d just count how many four-letter words are already in my dictionary and divide that into 456,976. It’s always a mistake to start programming before you’ve thought the problem out. The trouble is not being able to tell when that thinking-out is done.

    Richard Thompson’s Poor Richard’s Almanac for the 7th is the other comic strip to mention infinite monkeys. Well, chimpanzees in this case. But for the mathematical problem they’re not different. I’ve featured this particular strip before. But I’m a Thompson fan. And goodness but look at the face on the T S Eliot fan in the lower left corner there.

    Jeff Mallet’s Frazz for the 6th gives Caulfield one of those flashes of insight that seems like it should be something but doesn’t mean much. He’s had several of these lately, as mentioned here last week. As before this is a fun discovery about Roman Numerals, but it doesn’t seem like it leads to much. Perhaps a discussion of how the subtractive principle — that you can write “four” as “IV” instead of “IIII” — evolved over time. But then there isn’t much point to learning Roman Numerals at all. It’s got some value in showing how much mathematics depends on culture. Not just that stuff can be expressed in different ways, but that those different expressions make different things easier or harder to do. But I suspect that isn’t the objective of lessons about Roman Numerals.

    Frazz got my attention again the 12th. This time it just uses arithmetic, and a real bear of an arithmetic problem, as signifier for “a big pile of hard work”. This particular problem would be — well, I have to call it tedious, rather than hard. doing it is just a long string of adding together two numbers. But to do that over and over, by my count, at least 47 times for this one problem? Hardly any point to doing that much for one result.

    Patrick Roberts’s Todd the Dinosaur for the 7th calls out fractions, and arithmetic generally, as the stuff that ruins a child’s dreams. (Well, a dinosaur child’s dreams.) Still, it’s nice to see someone reminding mathematicians that a lot of their field is mostly used by accountants. Actuaries we know about; mathematics departments like to point out that majors can get jobs as actuaries. I don’t know of anyone I went to school with who chose to become one or expressed a desire to be an actuary. But I admit not asking either.

    Todd declares that after hearing one speak to his class he wants to be an accountant when he grows up. Trent, Todd's caretaker, says that's great but he'll need to do stuff that involves 'carrying the one and probably some fractions.' Todd panics. 'AAAGH! Not 'carrying the one' and that other word you said!'

    Patrick Roberts’s Todd the Dinosaur for the 7th of November, 2016. I don’t remember being talked to by classmates’ parents about what they where, but that might just be that it’s been a long time since I was in elementary school and everybody had the normal sorts of jobs that kids don’t understand. I guess we talked about what our parents did but that should make a weaker impression.

    Mike Thompson’s Grand Avenue started off a week of students-resisting-the-test-question jokes on the 7th. Most of them are hoary old word problem jokes. But, hey, I signed up to talk about it when a comic strip touches a mathematics topic and word problems do count.

    Zach Weinersmith’s Saturday Morning Breakfast Cereal reprinted the 7th is a higher level of mathematical joke. It’s from the genre of nonsense calculation. This one starts off with what’s almost a cliche, at least for mathematics and physics majors. The equation it starts with, e^{i Pi} = -1 , is true. And famous. It should be. It links exponentiation, imaginary numbers, π, and negative numbers. Nobody would have seen it coming. And from there is the sort of typical gibberish reasoning, like writing “Pi” instead of π so that it can be thought of as “P times i”, to draw to the silly conclusion that P = 0. That much work is legitimate.

    From there it sidelines into “P = NP”, which is another equation famous to mathematicians and computer scientists. It’s a shorthand expression of a problem about how long it takes to find solutions. That is, how many steps it takes. How much time it would take a computer to solve a problem. You can see why it’s important to have some study of how long it takes to do a problem. It would be poor form to tie up your computer on a problem that won’t be finished before the computer dies of old age. Or just take too long to be practical.

    Most problems have some sense of size. You can look for a solution in a small problem or in a big one. You expect searching for the solution in a big problem to take longer. The question is how much longer? Some methods of solving problems take a length of time that grows only slowly as the size of the problem grows. Some take a length of time that grows crazy fast as the size of the problem grows. And there are different kinds of time growth. One kind is called Polynomial, because everything is polynomials. But there’s a polynomial in the problem’s size that describes how long it takes to solve. We call this kind of problem P. Another is called Non-Deterministic Polynomial, for problems that … can’t. We assume. We don’t know. But we know some problems that look like they should be NP (“NP Complete”, to be exact).

    It’s an open question whether P and NP are the same thing. It’s possible that everything we think might be NP actually can be solved by a P-class algorithm we just haven’t thought of yet. It would be a revolution in our understanding of how to find solutions if it were. Most people who study algorithms think P is not NP. But that’s mostly (as I understand it) because it seems like if P were NP then we’d have some leads on proving that by now. You see how this falls short of being rigorous. But it is part of expertise to get a feel for what seems to make sense in light of everything else we know. We may be surprised. But it would be inhuman not to have any expectations of a problem like this.

    Mark Anderson’s Andertoons for the 8th gives us the Andertoons content for the week. It’s a fair question why a right triangle might have three sides, three angles, three vertices, and just the one hypotenuse. The word’s origin, from Greek, meaning “stretching under” or “stretching between”. It’s unobjectionable that we might say this is the stretch from one leg of the right triangle to another. But that leaves unanswered why there’s just the one hypothenuse, since the other two legs also stretch from the end of one leg to another. Dr Sarah on The Math Forum suggests we need to think of circles. Draw a circle and a diameter line on it. Now pick any point on the circle other than where the diameter cuts it. Draw a line from one end of the diameter to your point. And from your point to the other end of the diameter. You have a right triangle! And the hypothenuse is the leg stretching under the other two. Yes, I’m assuming you picked a point above the diameter. You did, though, didn’t you? Humans do that sort of thing.

    I don’t know if Dr Sarah’s explanation is right. It sounds plausible and sensible. But those are weak pins to hang an etymology on. But I have no reason to think she’s mistaken. And the explanation might help people accept there is the one hypothenuse and there’s something interesting about it.

    The first (and as I write this only) commenter, Kristiaan, has a good if cheap joke there.

    • davekingsbury 10:38 pm on Monday, 14 November, 2016 Permalink | Reply

      I reckon it was Bob Newhart’s sketch about it that made the monkey idea so popular. Best bit, something like, hey one of them has something over here er to be or not to be that is the … gezoinebplatf!


      • Joseph Nebus 3:35 am on Sunday, 20 November, 2016 Permalink | Reply

        I like to think that helped. I fear that that particular routine’s been forgotten, though. I was surprised back in the 90s when I was getting his albums and ran across that bit, as I’d never heard it before. But it might’ve been important in feeding the idea to other funny people. There’s probably a good essay to be written tracing the monkeys at typewriters through pop culture.

        Liked by 1 person

  • Joseph Nebus 6:00 pm on Sunday, 6 November, 2016 Permalink | Reply
    Tags: , , Halloween, , , ,   

    Reading the Comics, November 5, 2016: Surprisingly Few Halloween Costumes Edition 

    Comic Strip Master Command gave me a light load this week, which suit me fine. I’ve been trying to get the End 2016 Mathematics A To Z comfortably under way instead. It does strike me that there were fewer Halloween-themed jokes than I’d have expected. For all the jokes there are to make about Halloween I’d imagine some with some mathematical relevance would come up. But they didn’t and, huh. So it goes. The one big exception is the one I’d have guessed would be the exception.

    Bill Amend’s FoxTrot for the 30th — a new strip — plays with the scariness of mathematics. Trigonometry specifically. Trig is probably second only to algebra for the scariest mathematics normal people encounter. And that’s probably more because people get to algebra before they might get to trigonometry. Which is madness, in its way. Trigonometry is about how we can relate angles, arcs, and linear distances. It’s about stuff anyone would like to know, like how to go from an easy-to-make observation of the angle spanned by a thing to how big the thing must be. But the field does require a bunch of exotic new functions like sine and tangent and novelty acts like “arc-cosecant”. And the numbers involved can be terrible things. The sine of an angle, for example, is almost always going to be some irrational number. For common angles we use a lot it’ll be an irrational number with an easy-to-understand form. For example the sine of 45 degrees, mentioned here, is “one-half the square root of two”. Anyone not trying to be intimidating will use that instead. But the sine of, say, 50 degrees? I don’t know what that is either except that it’s some never-ending sequence of digits. People love to have digits, but when they’re asked to do something with them, they get afraid and I don’t blame them.

    Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 30th uses sudoku as shorthand for “genius thinking”. I am aware some complain sudoku isn’t mathematics. It’s certainly logic, though, and if we’re going to rule out logic puzzles from mathematics we’re going to lose a lot of fun fields. One of the commenters provided what I suppose the solution to be. (I haven’t checked.) If wish to do the puzzle be careful about scrolling.

    In Jef Mallet’s Frazz for the 2nd Caulfield notices something cute about 100. A perfect square is a familiar enough idea; it’s a whole number that’s the square of another whole number. The “roundest of round numbers” is a value judgement I’m not sure I can get behind. It’s a good round number, anyway, at least for stuff that’s sensibly between about 50 and 150. Or maybe between 50 and 500 if you’re just interested in about how big something might be. An irrational number, well, you know where that joke’s going.

    Mrs Olsen doesn’t seem impressed by Caulfield’s discovery, although in fairness we don’t see the actual aftermath. Sometimes you notice stuff like that and it is only good for a “huh”. But sometimes you get into some good recreational mathematics. It’s the sort of thinking that leads to discovering magic squares and amicable numbers and palindromic prime numbers and the like. Do they lead to important mathematics? Some of them do. Or at least into interesting mathematics. Sometimes they’re just passingly amusing.

    Greg Curfman’s Meg rerun for the 12th quotes Einstein’s famous equation as the sort of thing you could just expect would be asked in school. I’m not sure I ever had a class where knowing E = mc2 was the right answer to a question, though. Maybe as I got into physics since we did spend a bit of time on special relativity and E = mc2 turns up naturally there. Maybe I’ve been out of elementary school too long to remember.

    Mark Tatulli’s Heart of the City for the 4th has Heart and Dean talking about postapocalyptic society. Heart doubts that postapocalyptic society would need people like him, “with long-division experience”. Ah, but, grant the loss of computing devices. People will still need to compute. Before the days of electrical, and practical mechanical, computing people who could compute accurately were in demand. The example mathematicians learn to remember is Zacharias Dase, a German mental calculator. He was able to do astounding work and in his head. But he didn’t earn so much money as pro-mental-arithmetic propaganda would like us to believe. And why work entirely in your head if you don’t need to?

    Larry Wright’s Motley Classics rerun for the 5th is a word problem joke. And it’s mixed with labor relations humor for the sake of … I’m not quite sure, actually. Anyway I would have sworn I’d featured this strip in a long-ago Reading The Comics post, but I don’t see it on a casual search. So, go figure.

  • Joseph Nebus 6:00 pm on Sunday, 30 October, 2016 Permalink | Reply
    Tags: , , fingers, , ,   

    Reading the Comics, October 29, 2016: Rerun Comics Edition 

    There were a couple of rerun comics in this week’s roundup, so I’ll go with that theme. And I’ll put in one more appeal for subjects for my End of 2016 Mathematics A To Z. Have a mathematics term you’d like to see me go on about? Just ask! Much of the alphabet is still available.

    John Kovaleski’s Bo Nanas rerun the 24th is about probability. There’s something wondrous and strange that happens when we talk about the probability of things like birth days. They are, if they’re in the past, determined and fixed things. The current day is also a known, determined, fixed thing. But we do mean something when we say there’s a 1-in-365 (or 366, or 365.25 if you like) chance of today being your birthday. It seems to me this is probability based on ignorance. If you don’t know when my birthday is then your best guess is to suppose there’s a one-in-365 (or so) chance that it’s today. But I know when my birthday is; to me, with this information, the chance today is my birthday is either 0 or 1. But what are the chances that today is a day when the chance it’s my birthday is 1? At this point I realize I need much more training in the philosophy of mathematics, and the philosophy of probability. If someone is aware of a good introductory book about it, or a web site or blog that goes into these problems in a way a lay reader will understand, I’d love to hear of it.

    I’ve featured this installment of Poor Richard’s Almanac before. I’ll surely feature it again. I like Richard Thompson’s sense of humor. The first panel mentions non-Euclidean geometry, using the connotation that it does have. Non-Euclidean geometries are treated as these magic things — more, these sinister magic things — that defy all reason. They can’t defy reason, of course. And at least some of them are even sensible if we imagine we’re drawing things on the surface of the Earth, or at least the surface of a balloon. (There are non-Euclidean geometries that don’t look like surfaces of spheres.) They don’t work exactly like the geometry of stuff we draw on paper, or the way we fit things in rooms. But they’re not magic, not most of them.

    Stephen Bentley’s Herb and Jamaal for the 25th I believe is a rerun. I admit I’m not certain, but it feels like one. (Bentley runs a lot of unannounced reruns.) Anyway I’m refreshed to see a teacher giving a student permission to count on fingers if that’s what she needs to work out the problem. Sometimes we have to fall back on the non-elegant ways to get comfortable with a method.

    Dave Whamond’s Reality Check for the 25th name-drops Einstein and one of the three equations that has any pop-culture currency.

    Guy Gilchrist’s Today’s Dogg for the 27th is your basic mathematical-symbols joke. We need a certain number of these.

    Berkeley Breathed’s Bloom County for the 28th is another rerun, from 1981. And it’s been featured here before too. As mentioned then, Milo is using calculus and logarithms correctly in his rather needless insult of Freida. 10,000 is a constant number, and as mentioned a few weeks back its derivative must be zero. Ten to the power of zero is 1. The log of 10, if we’re using logarithms base ten, is also 1. There are many kinds of logarithms but back in 1981, the default if someone said “log” would be the logarithm base ten. Today the default is more muddled; a normal person would mean the base-ten logarithm by “log”. A mathematician might mean the natural logarithm, base ‘e’, by “log”. But why would a normal person mention logarithms at all anymore?

    Jef Mallett’s Frazz for the 28th is mostly a bit of wordplay on evens and odds. It’s marginal, but I do want to point out some comics that aren’t reruns in this batch.

  • Joseph Nebus 6:00 pm on Tuesday, 11 October, 2016 Permalink | Reply
    Tags: , , ,   

    Reading the Comics, October 8, 2016: Split Week Edition Part 2 

    And now I can finish off last week’s comics. It was a busy week. The first few days of this week have been pretty busy too. Meanwhile, Dave Kingsbury has recently read a biography of Lewis Carroll, and been inspired to form a haiku/tanka project. You might enjoy.

    Susan Camilleri Konar is a new cartoonist for the Six Chix collective. Her first strip to get mentioned around these parts is from the 5th. It’s a casual mention of the Fibonacci sequence, which is one of the few sequences that a normal audience would recognize as something going on forever. And yes, I noticed the spiral in the background. That’s one of the common visual representations of the Fibonacci sequence: it starts from the center. The rectangles inside have dimensions 1 by 2, then 2 by 3, then 3 by 5, then 5 by 8, and so on; the spiral connects vertices of these rectangles. It’s an attractive spiral and you can derive the overrated Golden Ratio from the dimensions of larger rectangles. This doesn’t make the Golden Ratio important or anything, but it is there.

    'It seems like Fibonacci's been entering his password for days now.'

    Susan Camilleri Konar ‘s Six Chix for the 5th of October, 2016. And yet what distracts me is both how much food Fibonacci has on his desk and how much of it is hidden behind his computer where he can’t get at it. He’s going to end up spilling his coffee on something important fiddling around like that. And that’s not even getting at his computer being this weird angle relative to the walls.

    Ryan North’s Dinosaur Comics for the 6th is part of a story about T-Rex looking for certain truth. Mathematics could hardly avoid coming up. And it does offer what look like universal truths: given the way deductive logic works, and some starting axioms, various things must follow. “1 + 1 = 2” is among them. But there are limits to how much that tells us. If we accept the rules of Monopoly, then owning four railroads means the rent for landing on one is a game-useful $200. But if nobody around you cares about Monopoly, so what? And so it is with mathematics. Utahraptor and Dromiceiomimus point out that the mathematics we know is built on premises we have selected because we find them interesting or useful. We can’t know that the mathematics we’ve deduced has any particular relevance to reality. Indeed, it’s worse than North points out: How do we know whether an argument is valid? Because we believe that its conclusions follow from its premises according to our rules of deduction. We rely on our possibly deceptive senses to tell us what the argument even was. We rely on a mind possibly upset by an undigested bit of beef, a crumb of cheese, or a fragment of an underdone potato to tell us the rules are satisfied. Mathematics seems to offer us absolute truths, but it’s hard to see how we can get there.

    Rick Stromoskis Soup to Nutz for the 6th has a mathematics cameo in a student-resisting-class-questions problem. But the teacher’s question is related to the figure that made my first fame around these parts.

    Mark Anderson’s Andertoons for the 7th is the long-awaited Andertoon for last week. It is hard getting education in through all the overhead.

    Bill Watterson’s Calvin and Hobbes rerun for the 7th is a basic joke about Calvin’s lousy student work. Fun enough. Calvin does show off one of those important skills mathematicians learn, though. He does do a sanity check. He may not know what 12 + 7 and 3 + 4 are, but he does notice that 12 + 7 has to be something larger than 3 + 4. That’s a starting point. It’s often helpful before starting work on a problem to have some idea of what you think the answer should be.

    • davekingsbury 5:57 pm on Wednesday, 12 October, 2016 Permalink | Reply

      Thank you for the mention. Good advice about starting work on a problem knowing roughly what the answer is … though my post demonstrated the opposite!


      • Joseph Nebus 3:43 am on Saturday, 15 October, 2016 Permalink | Reply

        Quite welcome. And, well, usually having an idea what answer you expect helps. Sometimes it misfires, I admit. But all rules of thumb sometimes misfire. If your expectation misfires it’s probably because you expect the answer to be something that’s not just wrong, but wrong in a significant way. That is, not wrong because you’re thinking 12 when it should be 14, but rather wrong because you’re thinking 12 when you should be thinking of doughnut shapes. But figuring that out is another big learning experience.

        Liked by 1 person

  • Joseph Nebus 6:00 pm on Sunday, 18 September, 2016 Permalink | Reply
    Tags: , , , , , ,   

    Reading the Comics, September 17, 2016: Show Your Work Edition 

    As though to reinforce how nothing was basically wrong, Comic Strip Master Command sent a normal number of mathematically themed comics around this past week. They bunched the strips up in the first half of the week, but that will happen. It was a fun set of strips in any event.

    Rob Harrell’s Adam @ Home for the 11th tells of a teacher explaining division through violent means. I’m all for visualization tools and if we are going to use them, the more dramatic the better. But I suspect Mrs Clark’s students will end up confused about what exactly they’ve learned. If a doll is torn into five parts, is that communicating that one divided by five is five? If the students were supposed to identify the mass of the parts of the torn-up dolls as the result of dividing one by five, was that made clear to them? Maybe it was. But there’s always the risk in a dramatic presentation that the audience will misunderstand the point. The showier the drama the greater the risk, it seems to me. But I did only get the demonstration secondhand; who knows how well it was done?

    Greg Cravens’ The Buckets for the 11th has the kid, Toby, struggling to turn a shirt backwards and inside-out without taking it off. As the commenters note this is the sort of problem we get into all the time in topology. The field is about what can we say about shapes when we don’t worry about distance? If all we know about a shape is the ways it’s connected, the number of holes it has, whether we can distinguish one side from another, what else can we conclude? I believe Gocomics.com commenter Mike is right: take one hand out the bottom of the shirt and slide it into the other sleeve from the outside end, and proceed from there. But I have not tried it myself. I haven’t yet started wearing long-sleeve shirts for the season.

    Bill Amend’s FoxTrot for the 11th — a new strip — does a story problem featuring pizzas cut into some improbable numbers of slices. I don’t say it’s unrealistic someone might get this homework problem. Just that the story writer should really ask whether they’ve ever seen a pizza cut into sevenths. I have a faint memory of being served a pizza cut into tenths by same daft pizza shop, which implies fifths is at least possible. Sevenths I refuse, though.

    Mark Tatulli’s Heart of the City for the 12th plays on the show-your-work directive many mathematics assignments carry. I like Heart’s showiness. But the point of showing your work is because nobody cares what (say) 224 divided by 14 is. What’s worth teaching is the ability to recognize what approaches are likely to solve what problems. What’s tested is whether someone can identify a way to solve the problem that’s likely to succeed, and whether that can be carried out successfully. This is why it’s always a good idea, if you are stumped on a problem, to write out how you think this problem should be solved. Writing out what you mean to do can clarify the steps you should take. And it can guide your instructor to whether you’re misunderstanding something fundamental, or whether you just missed something small, or whether you just had a bad day.

    Norm Feuti’s Gil for the 12th, another rerun, has another fanciful depiction of showing your work. The teacher’s got a fair complaint in the note. We moved away from tally marks as a way to denote numbers for reasons. Twelve depictions of apples are harder to read than the number 12. And they’re terrible if we need to depict numbers like one-half or one-third. Might be an interesting side lesson in that.

    Brian Basset’s Red and Rover for the 14th is a rerun and one I’ve mentioned in these parts before. I understand Red getting fired up to be an animator by the movie. It’s been a while since I watched Donald Duck in Mathmagic Land but my recollection is that while it was breathtaking and visually inventive it didn’t really get at mathematics. I mean, not at noticing interesting little oddities and working out whether they might be true always, or sometimes, or almost never. There is a lot of play in mathematics, especially in the exciting early stages where one looks for a thing to prove. But it’s also in seeing how an ingenious method lets you get just what you wanted to know. I don’t know that the short demonstrates enough of that.

    Punkinhead: 'Can you answer an arithmetic question for me, Julian?' Julian: 'Sure.' Punkinhead: 'What is it?'

    Bud Blake’s Tiger rerun for the 15th of September, 2016. I don’t get to talking about the art of the comics here, but, I quite like Julian’s expressions here. And Bud Blake drew fantastic rumpled clothes.

    Bud Blake’s Tiger rerun for the 15th gives Punkinhead the chance to ask a question. And it’s a great question. I’m not sure what I’d say arithmetic is, not if I’m going to be careful. Offhand I’d say arithmetic is a set of rules we apply to a set of things we call numbers. The rules are mostly about how we can take two numbers and a rule and replace them with a single number. And these turn out to correspond uncannily well with the sorts of things we do with counting, combining, separating, and doing some other stuff with real-world objects. That it’s so useful is why, I believe, arithmetic and geometry were the first mathematics humans learned. But much of geometry we can see. We can look at objects and see how they fit together. Arithmetic we have to infer from the way the stuff we like to count works. And that’s probably why it’s harder to do when we start school.

    What’s not good about that as an answer is that it actually applies to a lot of mathematical constructs, including those crazy exotic ones you sometimes see in science press. You know, the ones where there’s this impossibly complicated tangle with ribbons of every color and a headline about “It’s Revolutionary. It’s 46-Dimensional. It’s Breaking The Rules Of Geometry. Is It The Shape That Finally Quantizes Gravity?” or something like that. Well, describe a thing vaguely and it’ll match a lot of other things. But also when we look to new mathematical structures, we tend to look for things that resemble arithmetic. Group theory, for example, is one of the cornerstones of modern mathematical thought. It’s built around having a set of things on which we can do something that looks like addition. So it shouldn’t be a surprise that many groups have a passing resemblance to arithmetic. Mathematics may produce universal truths. But the ones we see are also ones we are readied to see by our common experience. Arithmetic is part of that common experience.

    'Dude, you have something on your face.' 'Food? Ink? Zit? What??' 'I think it's math.' 'Oh, yeah. I fell asleep on my Calculus book.'

    Jerry Scott and Jim Borgman’s Zits for the 14th of September, 2016. Properly speaking that is ink on his face, but I suppose saying it’s calculus pins down where it came from. Just observing.

    Also Jerry Scott and Jim Borgman’s Zits for the 14th I think doesn’t really belong here. It’s just got a cameo appearance by the concept of mathematics. Dave Whamond’s Reality Check for the 17th similarly just mentions the subject. But I did want to reassure any readers worried after last week that Pierce recovered fine. Also that, you know, for not having a stomach for mathematics he’s doing well carrying on. Discipline will carry one far.

    • ivasallay 3:44 am on Monday, 19 September, 2016 Permalink | Reply

      You said, “Twelve depictions of apples are harder to read than the number 12.” It might be a little difficult to see at first, but the twelve apples were arranged to form the numerals 1 and 2. I thought it was rather clever.


  • Joseph Nebus 6:00 pm on Sunday, 28 August, 2016 Permalink | Reply
    Tags: , ,   

    Reading the Comics, August 27, 2016: Calm Before The Term Edition 

    Here in the United States schools are just lurching back into the mode where they have students come in and do stuff all day. Perhaps this is why it was a routine week. Comic Strip Master Command wants to save up a bunch of story problems for us. But here’s what the last seven days sent into my attention.

    Jeff Harris’s Shortcuts educational feature for the 21st is about algebra. It’s got a fair enough blend of historical trivia and definitions and examples and jokes. I don’t remember running across the “number cruncher” joke before.

    Mark Anderson’s Andertoons for the 23rd is your typical student-in-lecture joke. But I do sympathize with students not understanding when a symbol gets used for different meanings. It throws everyone. But sometimes the things important to note clearly in one section are different from the needs in another section. No amount of warning will clear things up for everybody, but we try anyway.

    Tom Thaves’s Frank and Ernest for the 23rd tells a joke about collapsing wave functions, which is why you never see this comic in a newspaper but always see it on a physics teacher’s door. This is properly physics, specifically quantum mechanics. But it has mathematical import. The most practical model of quantum mechanics describes what state a system is in by something called a wave function. And we can turn this wave function into a probability distribution, which describes how likely the system is to be in each of its possible states. “Collapsing” the wave function is a somewhat mysterious and controversial practice. It comes about because if we know nothing about a system then it may have one of many possible values. If we observe, say, the position of something though, then we have one possible value. The wave functions before and after the observation are different. We call it collapsing, reflecting how a universe of possibilities collapsed into a mere fact. But it’s hard to find an explanation for what that is that’s philosophically and physically satisfying. This problem leads us to Schrödinger’s Cat, and to other challenges to our sense of how the world could make sense. So, if you want to make your mark here’s a good problem for you. It’s not going to be easy.

    John Allison’s Bad Machinery for the 24th tosses off a panel full of mathematics symbols as proof of hard thinking. In other routine references John Deering’s Strange Brew for the 26th is just some talk about how hard fractions are.

    While it’s outside the proper bounds of mathematics talk, Tom Toles’s Randolph Itch, 2 am for the 23rd is a delight. My favorite strip of this bunch. Should go on the syllabus.

  • Joseph Nebus 6:00 pm on Thursday, 11 August, 2016 Permalink | Reply
    Tags: alliteration, , , , ,   

    Finally, What I Learned Doing Theorem Thursdays 

    Here’s the index to the stuff I posted on them.

    The biggest thing I learned from my Theorem Thursdays project was: don’t do this for Thursdays. The appeal is obvious. If things were a little different I’d have no problem with Thursdays. But besides being a slightly-read pop-mathematics blogger I’m also a slightly-read humor blogger. And I try to have a major piece, about seven hundred words that are more than simply commentary on how a comic strip’s gone wrong, ready for Thursday evenings my time.

    That’s all my doing. It’s a relic of my thinking that the humor blog should run at least a bit like a professional syndicated columnist’s, with a fixed deadline for bigger pieces. While I should be writing more ahead of deadline than this, what I would do is get to Wednesday realizing I have two major things to write in a day. I’d have an idea for one of them, the mathematics thing, since I would pick a topic the previous Thursday. And once I’ve picked an idea the rest is easy. (Part of the process of picking is realizing whether there’s any way to make seven hundred words about something.) But that’s a lot of work for something that’s supposed to be recreational. Plus Wednesdays are, two weeks a month, a pinball league night.

    So Thursday is right out, unless I get better about having first drafts of stuff done Monday night. So Thursday is right out. This has problems for future appearances of the gimmick. The alliterative pull is strong. The only remotely compelling alternative is Theorems on the Threes, maybe one the 3rd, 13th, and 23rd of the month. That leaves the 30th and 31st unaccounted for, and room for a good squabble about whether they count in an “on the threes” scheme.

    There’s a lot of good stuff to say about the project otherwise. The biggest is that I had fun with it. The Theorem Thursday pieces sprawled into for-me extreme lengths, two to three thousand words. I had space to be chatty and silly and autobiographic in ways that even the A To Z projects don’t allow. Somehow those essays didn’t get nearly as long, possibly because I was writing three of them a week. I didn’t actually write fewer things in July than I did in, say, May. But it was fewer kinds of things; postings were mostly Theorem Thursdays and Reading the Comics posts. Still, overall readership didn’t drop and people seemed to quite like what I did write. It may be fewer but longer-form essays are the way I should go.

    Also I found that people like stranger stuff. There’s an understandable temptation in doing pop-mathematics to look for topics that are automatically more accessible. People are afraid enough of mathematics. They have good reason to be terrified of some topic even mathematics majors don’t encounter until their fourth year. So there’s a drive to simpler topics, or topics that have fewer prerequisites, and that’s why every mathematics blogger has an essay about how the square root of two is irrational and how there’s different sizes to infinitely large sets. And that’s produced some excellent writing about topics like those, which are great topics. They have got the power to inspire awe without requiring any warming up. That’s special.

    But it also means they’re hard to write anything new or compelling about if you’re like me, and in somewhere like the second hundred billion of mathematics bloggers. I can’t write anything better than what’s already gone about that. Liouville’s Theorem? That’s something I can be a good writer about. With that, I can have a blog personality. It’s like having a real personality but less work.

    As I did with the Leap Day 2016 A To Z project, I threw the topics open to requests. I didn’t get many. Possibly the form gave too much freedom. Picking something to match a letter, as in the A to Z, gives a useful structure for choosing something specific. Pick a theorem from anywhere in mathematics? Something from algebra class? Something mentioned in a news report about a major breakthrough the reporter doesn’t understand but had an interesting picture? Something that you overheard the name of once without any context? How should people know what the scope of it is, before they’ve even seen a sample? And possibly people don’t actually remember the names of theorems unless they stay in mathematics or mathematics-related fields. Those folks hardly need explained theorems with names they remember. This is a hard problem to imagine people having, but it’s something I must consider.

    So this is what I take away from the two-month project. There’s a lot of fun digging into the higher-level mathematics stuff. There’s an interest in it, even if it means I write longer and therefore fewer pieces. Take requests, but have a structure for taking them that makes it easy to tell what requests should look like. Definitely don’t commit to doing big things for Thursday, not without a better scheme for getting the humor blog pieces done. Free up some time Wednesday and don’t put up an awful score on Demolition Man like I did last time again. Seriously, I had a better score on The Simpsons Pinball Party than I did on Demolition Man and while you personally might not find this amusing there’s at least two people really into pinball who know how hilarious that is. (The games have wildly different point scorings. This like having a basketball score be lower than a hockey score.) That isn’t so important to mathematics blogging but it’s a good lesson to remember anyway.

    • elkement (Elke Stangl) 6:21 am on Monday, 22 August, 2016 Permalink | Reply

      You are such a prolific writer – kudos! Sorry that I am hardly able to catch up in some months ;-)


      • Joseph Nebus 8:48 pm on Sunday, 28 August, 2016 Permalink | Reply

        Aw, well, thank you, trusting that prolific is a good thing. I doubt I have time to read myself myself, as my problem with comments should prove.

        It happens I’ve gotten into a slow stretch the past few weeks. I’m hoping that with the start of a new season I’ll be able to get to a better balance between twice-a-week and daily.

        Liked by 1 person

  • Joseph Nebus 6:00 pm on Tuesday, 9 August, 2016 Permalink | Reply
    Tags: , teachers,   

    Reading the Comics, August 5, 2016: Word Problems Edition 

    And now to close out the rest of last week’s comics, those from between the 1st and the 6th of the month. It’s a smaller set. Take it up with the traffic division of Comic Strip Master Command.

    Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. for the 2nd is mostly a word problem joke. It’s boosted some by melting into it a teacher complaining about her pay. It does make me think some about what the point of a story problem is. That is, why is the story interesting? Often it isn’t. The story is just an attempt to make a computation problem look like the sort of thing someone might wonder in the real world. This is probably why so many word problems are awful as stories and as incentive to do a calculation. There’s a natural interest that one might have in, say, the total distance travelled by a rubber ball dropped and bouncing until it finally comes to a rest. But that’s only really good for testing how one understands a geometric series. It takes more storytelling to work out why you might want to find a cube root of x2 minus eight.

    Dave Whamond’s Reality Check for the 3rd uses mathematics on the blackboard as symbolic for all the problems one might have. Also a solution, if you call it that. It wouldn’t read so clearly if Ms Haversham had an English problem on the board.

    Mark Anderson’s Andertoons for the 5th keeps getting funnier to me. At first reading I didn’t connect the failed mathematics problem of 2 x 0 with the caption. Once I did, I realized how snugly fit the comic is.

    Greg Curfman’s Meg Classics for the 5th ran originally the 23rd of May, 1998. The application of mathematics to everyday sports was a much less developed thing back then. It’s often worthwhile to methodically study what you do, though, to see what affects the results. Here Mike has found the team apparently makes twelve missed shots for each goal. This might not seem like much of a formula, but these are kids. We shouldn’t expect formulas with a lot of variables under consideration. Since Meg suggests Mike needed to account for “the whiff factor” I have to suppose she doesn’t understand the meaning of the formula. Or perhaps she wonders why missed kicks before getting to the goal don’t matter. Well, every successful model starts out as a very simple thing to which we add complexity, and realism, as we’re able to handle them. If lucky we end up with a good balance between a model that describes what we want to know and yet is simple enough to understand.

  • Joseph Nebus 6:00 pm on Sunday, 7 August, 2016 Permalink | Reply
    Tags: , discovery, divisors, ,   

    Reading the Comics, August 1, 2016: Kalends Edition 

    The last day of July and first day of August saw enough mathematically-themed comic strips to fill a standard-issue entry. The rest of the week wasn’t so well-stocked. But I’ll cover those comics on Tuesday if all goes well. This may be a silly plan, but it is a plan, and I will stick to that.

    Johnny Hart’s Back To BC reprints the venerable and groundbreaking comic strip from its origins. On the 31st of July it reprinted a strip from February 1959 in which Peter discovers mathematics. The work’s elaborate, much more than we would use to solve the problem today. But it’s always like that. Newly-discovered mathematics is much like any new invention or innovation, a rickety set of things that just barely work. With time we learn better how the idea should be developed. And we become comfortable with the cultural assumptions going into the work. So we get more streamlined, faster, easier-to-use mathematics in time.

    The early invention of mathematics reappears the 1st of August, in a strip from earlier in February 1959. In this case it’s the sort of word problem confusion strip that any comic with a student could do. That’s a bit disappointing but Hart had much less space than he’d have for the Sunday strip above. One must do what one can.

    Mac King and Bill King’s Magic in a Minute for the 31st maybe isn’t really mathematics. I guess there’s something in the modular-arithmetic implied by it. But it depends on a neat coincidence. Follow the directions in the comic about picking a number from one to twelve and counting out the letters in the word for that number. And then the letters in the word for the number you’re pointing to, and then once again. It turns out this leads to the same number. I’d never seen this before and it’s neat that it does.

    Rick Detorie’s One Big Happy rerun for the 31st features Ruthie teaching, as she will. She mentions offhand the “friendlier numbers”. By this she undoubtedly means the numbers that are attractive in some way, like being nice to draw. There are “friendly numbers”, though, as number theorists see things. These are sets of numbers. For each number in this set you get the same index if you add together all its divisors (including 1 and the original number) and divide it by the original number. For example, the divisors of six are 1, 2, 3, and 6. Add that together and you get 12; divide that by the original 6 and you get 2. The divisors of 28 are 1, 2, 4, 7, 14, and 28. Add that pile of numbers together and you get 56; divide that by the original 28 and you get 2. So 6 and 28 are friendly numbers, each the friend of the other.

    As often happens with number theory there’s a lot of obvious things we don’t know. For example, we know that 1, 2, 3, 4, and 5 have no friends. But we do not know whether 10 has. Nor 14 nor 20. I do not know if it is proved whether there are infinitely many sets of friendly numbers. Nor do I know if it is proved whether there are infinitely many numbers without friends. Those last two sentences are about my ignorance, though, and don’t reflect what number theory people know. I’m open to hearing from people who know better.

    There are also things called “amicable numbers”, which are easier to explain and to understand than “friendly numbers”. A pair of numbers are amicable if the sum of one number’s divisors is the other number. 220 and 284 are the smallest pair of amicable numbers. Fermat found that 17,296 and 18,416 were an amicable pair; Descartes found that 9,363,584 and 9,437,056 were. Both pairs were known to Arab mathematicians already. Amicable pairs are easy enough to produce. From the tenth century we’ve had Thâbit ibn Kurrah’s rule, which lets you generate sets of numbers. Ruthie wasn’t thinking of any of this, though, and was more thinking how much fun it is to write a 7.

    Terry Border’s Bent Objects for the 1st just missed the anniversary of John Venn’s birthday and all the joke Venn Diagrams that were going around at least if your social media universe looks anything like mine.

    Jon Rosenberg’s Scenes from a Multiverse for the 1st is set in “Mathpinion City”, in the “Numerically Flexible Zones”. And I appreciate it’s a joke about the politicization of science. But science and mathematics are human activities. They are culturally dependent. And especially at the dawn of a new field of study there will be long and bitter disputes about what basic terms should mean. It’s absurd for us to think that the question of whether 1 + 1 should equal 2 or 3 could even arise.

    But we think that because we have absorbed ideas about what we mean by ‘1’, ‘2’, ‘3’, ‘plus’, and ‘equals’ that settle the question. There was, if I understand my mathematics history right — and I’m not happy with my reading on this — a period in which it was debated whether negative numbers should be considered as less than or greater than the positive numbers. Absurd? Thermodynamics allows for the existence of negative temperatures, and those represent extremely high-energy states, things that are hotter than positive temperatures. A thing may get hotter, from 1 Kelvin to 4 Kelvin to a million Kelvin to infinitely many Kelvin to -1000 Kelvin to -6 Kelvin. If there are intuition-defying things to consider about “negative six” then we should at least be open to the proposition that the universal truths of mathematics are understood by subjective processes.

  • Joseph Nebus 6:00 pm on Sunday, 31 July, 2016 Permalink | Reply
    Tags: , , electronics, , mnemonics, rock-paper-scissors   

    Reading the Comics, July 30, 2016: Learning Tools Edition 

    I thank Comic Strip Master Command for the steady pace of mathematically-themed comics this past week. It fit quite nicely with my schedule, which you might get hints about in weeks to come. Depends what I remember to write about. I did have to search a while for any unifying motif of this set. The idea of stuff you use to help learn turned up several times over, and that will do.

    Steve Breen and Mike Thompson’s Grand Avenue threatened on the 24th to resume my least-liked part of reading comics for mathematics themes. This would be Grandma’s habit of forcing the kids to spend their last month of summer vacation doing arithmetic drills. I won’t say that computing numbers isn’t fun because I know what it’s like to work out how many seconds are in 50 years in your head. But that’s never what this sort of drill is about. The strip’s diverted from that subject, but it might come back to spoil the end of summer vacation. (I’m not positive what my least-liked part of the comics overall is. I suspect it might be the weird anti-participation-trophy bias comic strip writers have.)

    Ryan North’s Dinosaur Comics reprint for the 25th is about the end of the universe. We’ve got several competing theories about how the universe is likely to turn out, several trillion years down the road. The difference between them is in the shape of space and how that shape is changing. I’ve mentioned sometimes the wonder of being able to tell something about a whole shape from local information, things we can tell without being far from a single point. The fate of the universe must be the greatest example of this. Considering how large the universe is and how little of it we will ever be able to send an instrument to, we measure the shape of space from a single point. And we can realistically project what will happen in unimaginably distant times. Admittedly, if we get it wrong, we’ll never know, which takes off some of the edge.

    Dinosaur Comics reappears the 28th with some talk about number bases. It’s all fine and accurate enough, except for the suggestion that anyone would use base five for something other than explaining how bases work. I like learning about bases. When I was a kid this concept explained much to me about how our symbols for numbers work. It also helped appreciate that symbols are not these fixed or universal things. They’re our creations and ours to adapt for whatever reason we find convenient. In the past we’ve found bases as high as sixty to be convenient. (The division of angles into 360 degrees each of 60 minutes, each of those of 60 seconds, is an echo of that.) But when I was a kid doing alternate-base problems nobody knew what I was doing or why, except the mathematics teacher who said I might like the optional sections in the book. We only really need base ten, base two, and base sixteen, which might as well be base two written more compactly. The rest are toys, good for instruction and for fun. Sorry, base seven.

    Scott Meyer’s Basic Instructions rerun for the 27th is about everyone’s favorite bit of intransitivity. Rock-Paper-Scissors and its related games are all about systems in which any two results can be decisive but any three might not be. This prospect turns up whenever there are three or more possible outcomes. And it doesn’t require a system to be irrational or random. Chaos and counterintuitive results just happen when there’s three of a thing.

    I remember, and possibly you remember too, learning of a computer system that can consistently beat humans at Rock-Paper-Scissors. It manages to do that by the oldest of game theory exploits, cheating. Its sensors look for the twitches suggesting what a person is going to throw and then it changes its throw to beat that. I don’t know what that’s supposed to prove since anyone who’s played a Sid Meier’s Civilization game knows that computers already know how to cheat.

    Thom Bluemel’s Birdbrains, yes, you can be in my Reading The Comics post this week too. Don’t beg.

    Bill Schorr’s The Grizzwells for the 28th is a resisted word problem joke. It doesn’t use the classic railroad or airplane forms, but it’s the same joke anyway.

    'My drive to solve this [ a pie chart of the relationships between current, voltage, resistance, and power in an electrical circuit ] keeps getting interrupted by my desire to order a PIZZA'.

    Benita Epstein’s Six Chix for the 29th of July, 2016. The pie chart’s valid, in case you need it, in which case you’re doing the mathematics of electric circuits. Current, voltage, resistance, and power all relate to one another in ways the chart makes clear once you know how to read it. Each of the quantities — I, V, R, or P — is equal to each of the expressions outside it. Pizza, meanwhile, is just a naturally funny word and thus appears in comic strips to amuse you.

    Benita Epstein’s Six Chix for the 29th is probably familiar to the folks taking electronics. The chart is a compact map used as a mnemonic for the different relationships between the current (I), the voltage (V), the resistance (R), and the power (P) in a circuit. When I was a student we got this as two separate circles, one for current-voltage-resistance and one for power-current-voltage. Each was laid out like the T-and-O maps which pre-Renaissance Western Europe used to diagram the world. While I now see that as a convenient and useful tool, as a student, I was skeptical that it was any easier to use the mnemonic aid than it was to just remember “voltage equals current times resistance” and “power equals voltage times current”. I’ve always had an irrational suspicion of mnemonic devices. I’m trying to do better.

    Brian Boychuk and Ron Boychuk’s Chuckle Brothers for the 30th is a return of the whiteboard full of symbols to represent deep thinking. The symbols don’t mean anything as equations, though that might be my limited perspective. And that also might represent the sketchy, shorthand way serious work is done. As an idea is sketched out weird bundles of symbols that don’t literally parse do appear. In a publishable paper this is all turned into neatly formatted and standard stuff. Or we introduce symbols with clear explanations of what they mean so that others can learn to read what we write. But for ourselves, in the heat of work, we’ll produce what looks like gibberish to others and that’s all right as long as we don’t forget what the gibberish means. Sometimes we do, but the gibberish typically helps us recapture a lost idea. (I offer the tale of a mathematician with pages of notes for a brilliant insight which she has to reconstruct from a lost memory to would-be short story writers looking for a Romantic hook.)

    • tziviaeadler 9:43 pm on Tuesday, 2 August, 2016 Permalink | Reply

      That image is worse than Venn diagrams for making someone want pizza.
      At least i had some pie on pi day :)


      • Joseph Nebus 7:34 pm on Tuesday, 9 August, 2016 Permalink | Reply

        Ah, well, good. I’m glad you could have some pie. I’ve refrained lately — watching my weight as it goes up against what I wanted to be a hard boundary — but I know that’s just a prelude to me inhaling the Chinese buffet sometime soon.


  • Joseph Nebus 6:00 pm on Wednesday, 20 July, 2016 Permalink | Reply
    Tags: , , intuition, , reruns   

    Reading the Comics, July 16, 2016: More To Life Than Mathematics Edition 

    I know, it’s impolitic for me to say something like my title. But I noticed a particular rerun in this set of mathematically-themed comics. And it left me wondering if I should drop that from my daily routine. There are strips I read more out of a fear of missing out than anything else. Most of them are in perpetual reruns, though some of them are so delightful I wouldn’t dare drop them. (Here I mean Cul de Sac and Peanuts.) An individual comic takes typically little time to read, but add that up and it does take a while, especially on vacation or the like. I won’t actually change anything; I’m too stubborn in lazy ways for that. But it crosses my mind.

    Tim Lachowski’s Get A Life for the 14th is what set me off. Lachowski’s rerun this before, and I’ve mentioned it before, back in March of 2015 and back in November 2012. Given this I wonder if there’s a late-2013 or early-2014 reuse of the strip I failed to note around here. Or just missed, possibly because I was on vacation.

    Nicholas Gurewitch’s Perry Bible Fellowship reprint for the 14th gives me the title for this edition. It uses symbols and diagrams of mathematics for their graphical artistry, the sort of thing I’m surprised doesn’t get done more. Back in college the creative-writing-and-arts editor for the unread leftist weekly asked me to do a page of physics calculations as an aesthetic composition and I was glad to do it. Good notation has a beauty to it; I wonder if people would like mathematics more if they got to spend time at play with its shapes.

    Morrie Turner’s Wee Pals rerun for the 14th name-checks the New Math. The New Math was this attempt to reform mathematics in the 1970s. It was great for me, and my love remembers only liking or understanding mathematics while in New Math-guided classes. But it was an attempt at educational reform that didn’t promise that people at the cash registers would make change fast enough, and so was doomed to failure. (I am being reductive here. Much about the development of New Math went wrong, and it’s unfair to blame it all on the resistance of parents to new teaching methods. But educational reform always crashes hard against parents’ reasonable question, “Why should my child be your test case?”)

    Many of the New Math ideas grew out of the work of Nicholas Bourbaki, and the attempt to explain mathematics on completely rigorous logical foundations, as free from intuition as possible to get. That sounds like an odd thing to do; intuition is a guide to useful ways to spend one’s time and energy. But that supposes the intuition is good.

    Much of late 19th and early 20th century mathematics was spent discovering cases in which intuitive understandings of things were wrong. Deterministic systems can be unpredictable. A curve can be continuous at a single point and nowhere else in space. Infinitely large sets can be bigger or smaller than other sets. A line can wriggle around so much that it has a volume, it fills space. In that context wanting to ditch intuition a a once-useful but now-unreliable guide is not a bad idea.

    I like the New Math. I suppose we always like the way we first learned things. But I still think it’s got a healthy focus. The idea that mathematics is built on rules we agree to use, and that we are free to change if we find they’re not doing things we need, is true. It’s one easy to forget considering mathematics’ primary job, which has always been making trade, accounting, and record-keeping go smoothly. Changing those systems are perilous. But we should know something about how to pick tools to use.

    Zoe Piel’s At The Zoo for the 15th uses the blackboard-full-of-mathematics image to suggest deep thinking. (Toby the lion’s infatuated with the vet, which is why he’s thinking how to get her to visit again.) Really there’s a bunch of iconic cartoon images of deep thinking, including a mid-century-esque big-tin-box computer with reel-to-reel memory tape. Modern computers are vastly more powerful than that sort of 50s/60s contraption, but they’re worthless artistically if you want to suggest any deep thinking going on. You need stuff with moving parts for that, even in a still image.

    Scott Adams’s Dilbert Classics for the 16th originally ran the 21st of May, 1993. And it comes back to a practical use for mathematics and the sort of thing we do need to know how to calculate. It also uses the image of mathematics as obscurant nonsense.

    That tweet’s interesting in itself, although one of the respondents wonders if William meant astrology, often called “mathematics” at the time. That would be a fairer thing to call magic. But it would be only a century after William of Malmesbury’s death that Arabic numerals would become familiar in Europe. They would bring suspicions that merchants and moneylenders were trying to cheat their customers, by using these exotic specialist notations with unrecognizable rules, instead of the traditional and easy-to-follow Roman numerals. If this particular set of mathematics comics were mostly reruns, that’s all right; sometimes life is like that.

  • Joseph Nebus 6:00 pm on Monday, 18 July, 2016 Permalink | Reply
    Tags: , , birds, , ,   

    Reading the Comics, July 13, 2016: Catching Up On Vacation Week Edition 

    I confess I spent the last week on vacation, away from home and without the time to write about the comics. And it was another of those curiously busy weeks that happens when it’s inconvenient. I’ll try to get caught up ahead of the weekend. No promises.

    Art and Chip Samson’s The Born Loser for the 10th talks about the statistics of body measurements. Measuring bodies is one of the foundations of modern statistics. Adolphe Quetelet, in the mid-19th century, found a rough relationship between body mass and the square of a person’s height, used today as the base for the body mass index.Francis Galton spent much of the late 19th century developing the tools of statistics and how they might be used to understand human populations with work I will describe as “problematic” because I don’t have the time to get into how much trouble the right mind at the right idea can be.

    No attempt to measure people’s health with a few simple measurements and derived quantities can be fully successful. Health is too complicated a thing for one or two or even ten quantities to describe. Measures like height-to-waist ratios and body mass indices and the like should be understood as filters, the way temperature and blood pressure are. If one or more of these measurements are in dangerous ranges there’s reason to think there’s a health problem worth investigating here. It doesn’t mean there is; it means there’s reason to think it’s worth spending resources on tests that are more expensive in time and money and energy. And similarly just because all the simple numbers are fine doesn’t mean someone is perfectly healthy. But it suggests that the person is more likely all right than not. They’re guides to setting priorities, easy to understand and requiring no training to use. They’re not a replacement for thought; no guides are.

    Jeff Harris’s Shortcuts educational panel for the 10th is about zero. It’s got a mix of facts and trivia and puzzles with a few jokes on the side.

    I don’t have a strong reason to discuss Ashleigh Brilliant’s Pot-Shots rerun for the 11th. It only mentions odds in a way that doesn’t open up to discussing probability. But I do like Brilliant’s “Embrace-the-Doom” tone and I want to share that when I can.

    John Hambrock’s The Brilliant Mind of Edison Lee for the 13th of July riffs on the world’s leading exporter of statistics, baseball. Organized baseball has always been a statistics-keeping game. The Olympic Ball Club of Philadelphia’s 1837 rules set out what statistics to keep. I’m not sure why the game is so statistics-friendly. It must be in part that the game lends itself to representation as a series of identical events — pitcher throws ball at batter, while runners wait on up to three bases — with so many different outcomes.

    'Edison, let's discuss stats while we wait for the opening pitch.' 'Statistics? I have plenty of those. A hot dog has 400 calories and costs five dollars. A 12-ounce root beer has 38 grams of sugar.' 'I mean *player* stats.' 'Oh'. (To his grandfather instead) 'Did you know the average wait time to buy nachos is eight minutes and six seconds?'

    John Hambrock’s The Brilliant Mind of Edison Lee for the 13th of July, 2016. Properly speaking, the waiting time to buy nachos isn’t a player statistic, but I guess Edison Lee did choose to stop talking to his father for it. Which is strange considering his father’s totally natural and human-like word emission ‘Edison, let’s discuss stats while we wait for the opening pitch’.

    Alan Schwarz’s book The Numbers Game: Baseball’s Lifelong Fascination With Statistics describes much of the sport’s statistics and record-keeping history. The things recorded have varied over time, with the list of things mostly growing. The number of statistics kept have also tended to grow. Sometimes they get dropped. Runs Batted In were first calculated in 1880, then dropped as an inherently unfair statistic to keep; leadoff hitters were necessarily cheated of chances to get someone else home. How people’s idea of what is worth measuring changes is interesting. It speaks to how we change the ways we look at the same event.

    Dana Summers’s Bound And Gagged for the 13th uses the old joke about computers being abacuses and the like. I suppose it’s properly true that anything you could do on a real computer could be done on the abacus, just, with a lot ore time and manual labor involved. At some point it’s not worth it, though.

    Nate Fakes’s Break of Day for the 13th uses the whiteboard full of mathematics to denote intelligence. Cute birds, though. But any animal in eyeglasses looks good. Lab coats are almost as good as eyeglasses.

    LERBE ( O O - O - ), GIRDI ( O O O - - ), TACNAV ( O - O - O - ), ULDNOA ( O O O - O - ). When it came to measuring the Earth's circumference, there was a ( - - - - - - - - ) ( - - - - - ).

    David L Hoyt and Jeff Knurek’s Jumble for the 13th of July, 2016. The link will be gone sometime after mid-August I figure. I hadn’t thought of a student being baffled by using the same formula for an orange and a planet’s circumference because of their enormous difference in size. It feels authentic, though.

    David L Hoyt and Jeff Knurek’s Jumble for the 13th is about one of geometry’s great applications, measuring how large the Earth is. It’s something that can be worked out through ingenuity and a bit of luck. Once you have that, some clever argument lets you work out the distance to the Moon, and its size. And that will let you work out the distance to the Sun, and its size. The Ancient Greeks had worked out all of this reasoning. But they had to make observations with the unaided eye, without good timekeeping — time and position are conjoined ideas — and without photographs or other instantly-made permanent records. So their numbers are, to our eyes, lousy. No matter. The reasoning is brilliant and deserves respect.

Compose new post
Next post/Next comment
Previous post/Previous comment
Show/Hide comments
Go to top
Go to login
Show/Hide help
shift + esc
%d bloggers like this: