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  • Joseph Nebus 12:22 am on Sunday, 30 April, 2017 Permalink | Reply
    Tags: , Calvin and Hobbes, , Doonesbury, , , , , , ,   

    Reading the Comics, April 24, 2017: Reruns Edition 


    I went a little wild explaining the first of last week’s mathematically-themed comic strips. So let me split the week between the strips that I know to have been reruns and the ones I’m not so sure were.

    Bill Amend’s FoxTrot for the 23rd — not a rerun; the strip is still new on Sundays — is a probability question. And a joke about story problems with relevance. Anyway, the question uses the binomial distribution. I know that because the question is about doing a bunch of things, homework questions, each of which can turn out one of two ways, right or wrong. It’s supposed to be equally likely to get the question right or wrong. It’s a little tedious but not hard to work out the chance of getting exactly six problems right, or exactly seven, or exactly eight, or so on. To work out the chance of getting six or more questions right — the problem given — there’s two ways to go about it.

    One is the conceptually easy but tedious way. Work out the chance of getting exactly six questions right. Work out the chance of getting exactly seven questions right. Exactly eight questions. Exactly nine. All ten. Add these chances up. You’ll get to a number slightly below 0.377. That is, Mary Lou would have just under a 37.7 percent chance of passing. The answer’s right and it’s easy to understand how it’s right. The only drawback is it’s a lot of calculating to get there.

    So here’s the conceptually harder but faster way. It works because the problem says Mary Lou is as likely to get a problem wrong as right. So she’s as likely to get exactly ten questions right as exactly ten wrong. And as likely to get at least nine questions right as at least nine wrong. To get at least eight questions right as at least eight wrong. You see where this is going: she’s as likely to get at least six right as to get at least six wrong.

    There’s exactly three possibilities for a ten-question assignment like this. She can get four or fewer questions right (six or more wrong). She can get exactly five questions right. She can get six or more questions right. The chance of the first case and the chance of the last have to be the same.

    So, take 1 — the chance that one of the three possibilities will happen — and subtract the chance she gets exactly five problems right, which is a touch over 24.6 percent. So there’s just under a 75.4 percent chance she does not get exactly five questions right. It’s equally likely to be four or fewer, or six or more. Just-under-75.4 divided by two is just under 37.7 percent, which is the chance she’ll pass as the problem’s given. It’s trickier to see why that’s right, but it’s a lot less calculating to do. That’s a common trade-off.

    Ruben Bolling’s Super-Fun-Pax Comix rerun for the 23rd is an aptly titled installment of A Million Monkeys At A Million Typewriters. It reminds me that I don’t remember if I’d retired the monkeys-at-typewriters motif from Reading the Comics collections. If I haven’t I probably should, at least after making a proper essay explaining what the monkeys-at-typewriters thing is all about.

    'This new math teacher keeps shakin' us down every morning, man ... what's she looking for, anyway?' 'Pocket calculators.'

    Ted Shearer’s Quincy from the 28th of February, 1978. So, that FoxTrot problem I did? The conceptually-easy-but-tedious way is not too hard to do if you have a calculator. It’s a buch of typing but nothing more. If you don’t have a calculator, though, the desire not to do a whole bunch of calculating could drive you to the conceptually-harder-but-less-work answer. Is that a good thing? I suppose; insight is a good thing to bring. But the less-work answer only works because of a quirk in the problem, that Mary Lou is supposed to have a 50 percent chance of getting a question right. The low-insight-but-tedious problem will aways work. Why skip on having something to do the tedious part?

    Ted Shearer’s Quincy from the 28th of February, 1978 reveals to me that pocket calculators were a thing much earlier than I realized. Well, I was too young to be allowed near stuff like that in 1978. I don’t think my parents got their first credit-card-sized, solar-powered calculator that kind of worked for another couple years after that. Kids, ask about them. They looked like good ideas, but you could use them for maybe five minutes before the things came apart. Your cell phone is so much better.

    Bil Watterson’s Calvin and Hobbes rerun for the 24th can be classed as a resisting-the-word-problem joke. It’s so not about that, but who am I to slow you down from reading a Calvin and Hobbes story?

    Garry Trudeau’s Doonesbury rerun for the 24th started a story about high school kids and their bad geography skills. I rate it as qualifying for inclusion here because it’s a mathematics teacher deciding to include more geography in his course. I was amused by the week’s jokes anyway. There’s no hint given what mathematics Gil teaches, but given the links between geometry, navigation, and geography there is surely something that could be relevant. It might not help with geographic points like which states are in New England and where they are, though.

    Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 24th is built on a plot point from Carl Sagan’s science fiction novel Contact. In it, a particular “message” is found in the digits of π. (By “message” I mean a string of digits that are interesting to us. I’m not sure that you can properly call something a message if it hasn’t got any sender and if there’s not obviously some intended receiver.) In the book this is an astounding thing because the message can’t be; any reasonable explanation for how it should be there is impossible. But short “messages” are going to turn up in π also, as per the comic strips.

    I assume the peer review would correct the cartoon mathematicians’ unfortunate spelling of understanding.

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  • Joseph Nebus 6:00 pm on Sunday, 16 April, 2017 Permalink | Reply
    Tags: Amanda the Great, , , , Calvin and Hobbes, , , , , , Skin Horse, , ,   

    Reading the Comics, April 15, 2017: Extended Week Edition 


    It turns out last Saturday only had the one comic strip that was even remotely on point for me. And it wasn’t very on point either, but since it’s one of the Creators.com strips I’ve got the strip to show. That’s enough for me.

    Henry Scarpelli and Craig Boldman’s Archie for the 8th is just about how algebra hurts. Some days I agree.

    'Ugh! Achey head! All blocked up! Throbbing! Completely stuffed!' 'Sounds like sinuses!' 'No. Too much algebra!'

    Henry Scarpelli and Craig Boldman’s Archie for the 8th of April, 2017. Do you suppose Archie knew that Dilton was listening there, or was he just emoting his fatigue to himself?

    Ruben Bolling’s Super-Fun-Pak Comix for the 8th is an installation of They Came From The Third Dimension. “Dimension” is one of those oft-used words that’s come loose of any technical definition. We use it in mathematics all the time, at least once we get into Introduction to Linear Algebra. That’s the course that talks about how blocks of space can be stretched and squashed and twisted into each other. You’d expect this to be a warmup act to geometry, and I guess it’s relevant. But where it really pays off is in studying differential equations and how systems of stuff changes over time. When you get introduced to dimensions in linear algebra they describe degrees of freedom, or how much information you need about a problem to pin down exactly one solution.

    It does give mathematicians cause to talk about “dimensions of space”, though, and these are intuitively at least like the two- and three-dimensional spaces that, you know, stuff moves in. That there could be more dimensions of space, ordinarily inaccessible, is an old enough idea we don’t really notice it. Perhaps it’s hidden somewhere too.

    Amanda El-Dweek’s Amanda the Great of the 9th started a story with the adult Becky needing to take a mathematics qualification exam. It seems to be prerequisite to enrolling in some new classes. It’s a typical set of mathematics anxiety jokes in the service of a story comic. One might tsk Becky for going through university without ever having a proper mathematics class, but then, I got through university without ever taking a philosophy class that really challenged me. Not that I didn’t take the classes seriously, but that I took stuff like Intro to Logic that I was already conversant in. We all cut corners. It’s a shame not to use chances like that, but there’s always so much to do.

    Mark Anderson’s Andertoons for the 10th relieves the worry that Mark Anderson’s Andertoons might not have got in an appearance this week. It’s your common kid at the chalkboard sort of problem, this one a kid with no idea where to put the decimal. As always happens I’m sympathetic. The rules about where to move decimals in this kind of multiplication come out really weird if the last digit, or worse, digits in the product are zeroes.

    Mel Henze’s Gentle Creatures is in reruns. The strip from the 10th is part of a story I’m so sure I’ve featured here before that I’m not even going to look up when it aired. But it uses your standard story problem to stand in for science-fiction gadget mathematics calculation.

    Dave Blazek’s Loose Parts for the 12th is the natural extension of sleep numbers. Yes, I’m relieved to see Dave Blazek’s Loose Parts around here again too. Feels weird when it’s not.

    Bill Watterson’s Calvin and Hobbes rerun for the 13th is a resisting-the-story-problem joke. But Calvin resists so very well.

    John Deering’s Strange Brew for the 13th is a “math club” joke featuring horses. Oh, it’s a big silly one, but who doesn’t like those too?

    Dan Thompson’s Brevity for the 14th is one of the small set of punning jokes you can make using mathematician names. Good for the wall of a mathematics teacher’s classroom.

    Shaenon K Garrity and Jefferey C Wells’s Skin Horse for the 14th is set inside a virtual reality game. (This is why there’s talk about duplicating objects.) Within the game, the characters are playing that game where you start with a set number (in this case 20) tokens and take turn removing a couple of them. The “rigged” part of it is that the house can, by perfect play, force a win every time. It’s a bit of game theory that creeps into recreational mathematics books and that I imagine is imprinted in the minds of people who grow up to design games.

     
  • Joseph Nebus 5:47 pm on Tuesday, 7 July, 2015 Permalink | Reply
    Tags: Calvin and Hobbes, , , , tongue twisters,   

    Reading the Comics, July 7, 2015: Carrying On The Streak Edition 


    I admit I’ve been a little unnerved lately. Between the A To Z project and the flood of mathematics-themed jokes from Comic Strip Master Command — and miscellaneous follies like my WordPress statistics-reading issues — I’ve had a post a day for several weeks now. The streak has to end sometime, surely, right? So it must, but not today. I admit the bunch of comics mentioning mathematical topics the past couple days was more one of continuing well-explored jokes rather than breaking new territory. But every comic strip is somebody’s first, isn’t it? (That’s an intimidating thought.)

    Mickey Mouse promises to help a nephew with his mathematics homework. The word problem is also a tongue-twister. It haunts Mickey all night.

    Disney’s Mickey Mouse rerun the 6th of July, 2015. Probably rerun many more times, too.

    Disney’s Mickey Mouse (June 6, rerun from who knows when) is another example of the word problem that even adults can’t do. I think it’s an interesting one for being also a tongue-twister. I tend to think of this sort of problem as a calculus question, but that’s surely just that I spend more time with calculus than with algebra or simpler arithmetic.

    Donald keeps his nephews awake by counting sheep all night. They all get to sleep when he counts sheep by fours.

    Disney’s Donald Duck for the 6th of July, 2015. Also probably rerun many times.

    And then Disney’s Donald Duck (June 6 also, but probably a rerun from some other date) is a joke built on counting sheep. Might help someone practice their four-times table, too. I like the internal logic of this one. Maybe I just like sheep in comic strips.

    Eric Teitelbaum and Bill Teitelbaum’s Bottomliners (June 6) is a bit of wordplay based on the idiom that figures will “add up” if they’re correct. There are so many things one can do with figures, though, aren’t there? Surely something will be right.

    Justin Thompson’s Mythtickle (June 6, again a rerun) is about the curious way that objects are mostly empty space. The first panel shows on the alien’s chalkboard legitimate equations from quantum mechanics. The first line describes (in part) a function called psi that describes where a particle is likely to be found over time. The second and third lines describe how the probability distribution — where a particle is likely to be found — changes over time.

    Doug Bratton’s Pop Culture Shock Therapy (July 7) just name-drops mathematics as something a kid will do badly in. In this case the kid is Calvin, from Calvin and Hobbes. While it’s true he did badly in mathematics I suspect that’s because it’s so easy to fit an elementary-school arithmetic question and a wrong answer in a single panel.

    The idea of mathematics as a way to bludgeon people into accepting your arguments must have caught someone’s imagination over at the Parker studios. Jeff Parker’s The Wizard of Id for July 7 uses this joke, just as Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. did back on June 19th. (Both comic strips were created by the prolific Johnny Hart. I was surprised to learn they’re not still drawn and written by the same teams.) As I mentioned at the time, smothering people beneath mathematical symbols is logically fallacious. This is not to say it doesn’t work.

     
    • Dawn 10:01 pm on Wednesday, 8 July, 2015 Permalink | Reply

      About Mickey’s math problem: Sam should shear six sheep in sixty-six seconds (assuming the sheep take the same amount of time to shear). But we don’t know anything about Shelley… is she an expert sheep-shearer like Sam? If she’s as bad as I am, it might take 6 hours… or never get done. How could calculus tell us?

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      • Joseph Nebus 6:04 am on Friday, 10 July, 2015 Permalink | Reply

        Yeah, there’s a gap in how to relate Sam’s and Shelly’s rates. I can imagine plausible relations, like, “Shelley shears sheep six seconds slower than Sam”, or such. But that problem shouldn’t take Mickey all night.

        There’s some missing piece of data. Maybe the teacher was trying to see what students would say “the problem can’t be answered like this. If we added this information, then we could answer it.” That would be a good thing to teach.

        I have sometimes given the instruction, “if a problem seems to be unsolvable because some information is missing, say what you need”. If it’s homework I go farther and say “make up a reasonable-sounding bit of information, say what that is, and continue with the problem”. It’s meant as a catch in case I mess up in writing the problem, but I have thought about putting out problems specifically like that.

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    • ivasallay 2:32 pm on Thursday, 9 July, 2015 Permalink | Reply

      Regardless of any variation in skill, shouldn’t Mickey just have to keep the tongue twister going and answer that Shelly should shear sixty-six sheep in six seconds?

      I really enjoyed both of these sheep comics, too.

      Like

  • Joseph Nebus 11:47 pm on Saturday, 24 January, 2015 Permalink | Reply
    Tags: , airlines, , , Calvin and Hobbes, , polls, , ,   

    Reading the Comics, January 24, 2015: Many, But Not Complicated Edition 


    I’m sorry to have fallen behind on my mathematics-comics posts, but I’ve been very busy wielding a cudgel at Microsoft IIS all week in the service of my day job. And since I telecommute it’s quite hard to convincingly threaten the server, however much it deserves it. Sorry. Comic Strip Master Command decided to send me three hundred billion gazillion strips, too, so this is going to be a bit of a long post.

    Jenny Campbell’s Flo and Friends (January 19) is almost a perfect example of the use of calculus as a signifier of “something really intelligent people think of”. Which is flattening to mathematicians, certainly, although I worry that attitude does make people freeze up in panic when they hear that they have to take calculus.

    The Amazing Yet Tautological feature of Ruben Bolling’s Super-Fun-Pak Comix (January 19) lives up to its title, at least provided we are all in agreement about what “average” means. From context this seems to be the arithmetic mean — that’s usually what people, mathematicians included mean by “average” if they don’t specify otherwise — although you can produce logical mischief by slipping in an alternate average, such as the “median” — the amount that half the results are less than and half are greater than — or the “mode” — the most common result. There are other averages too, but they’re not so often useful. On the 21st Super-Fun-Pak Comix returned with another installation of Chaos Butterfly, by the way.

    (More …)

     
    • The Chaos Realm 11:43 pm on Sunday, 25 January, 2015 Permalink | Reply

      …somewhat off the mark, but do you know how many times I catch the spelling of “discrete” substituted for “discreet” as in “She tried to be discreet in her actions…” LOL Maybe they are meant to be mathematicians, not writers :-)

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      • Joseph Nebus 10:01 pm on Tuesday, 27 January, 2015 Permalink | Reply

        Oh, I worry excessively about the difference between ‘discrete’ and ‘discreet’ and every time I have to use one of the words I over-think whether I’ve picked out the right one. Sometimes I rework the whole sentence so I can avoid the question.

        Still, there was that time back in grad school when the homework papers for Discrete and for Vector Calculus were put into separate piles labelled “Discrete” and “Flamboyant”.

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    • ivasallay 8:02 am on Monday, 26 January, 2015 Permalink | Reply

      I think the funniest thing was that Bob Newhart was an accountant. That previously unknown-to-me fact fired up my imagination the most!

      Like

      • Joseph Nebus 10:02 pm on Tuesday, 27 January, 2015 Permalink | Reply

        And it’s even true! He mentions it in passing in the start of his “Retirement Party” routine, and in his biography mentions how this led him to working in the Unemployment Office, until he found that he did better per hour without a job, collecting unemployment rather than working for what they would pay him.

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    • Aquileana 11:15 pm on Saturday, 31 January, 2015 Permalink | Reply

      Stunning deliver… I much enjoyed your post Nebus!… All my best wishes, Aquileana :D

      Like

  • Joseph Nebus 12:39 am on Tuesday, 16 September, 2014 Permalink | Reply
    Tags: , Calvin and Hobbes, , , , ,   

    Reading the Comics, September 15, 2014: Are You Trying To Overload Me Edition 


    One of the little challenges in writing about mathematics-themed comics is one of pacing: how often should I do a roundup? Posting weekly, say, helps figure out a reasonable posting schedule for those rare moments when I’m working ahead of deadline, but that leaves the problem of weeks that just don’t have anything. Waiting for a certain number of comics before writing about them seems more reasonable, but then I have to figure how many comics are enough. I’ve settled into five-to-six as my threshold for a new post, but that can mean I have weeks where it seems like I’m doing nothing but comic strips posts. And then there’s conditions like this one where Comic Strip Master Command had its cartoonists put up just enough that I’d started composing a fresh post, and then tossed in a whole bunch more the next day. It’s like they’re trying to shake me by having too many strips to write about. I’d have though they’d be flattered to have me writing about them so.

    Tiger studied times tables today. Studied it, not learned it.

    Bud Blake’s _Tiger_ for the 11th of September, 2014.

    Bud Blake’s Tiger (September 11, rerun) mentions Tiger as studying the times tables and points out the difference between studying a thing and learning it.

    Marc Anderson’s Andertoons (September 12) belongs to that vein of humor about using technology words to explain stuff to kids. I admit I’m vague enough on the concept of mashups that I can accept that it might be a way of explaining addition, but it feels like it might also be a way of describing multiplication or for that matter the composition of functions. I suppose the kids would be drawn as older in those cases, though.

    Bill Amend’s FoxTrot (September 13, rerun) does a word problem joke, but it does have the nice beat in the penultimate panel of Paige running a sanity check and telling at a glance that “two dollars” can’t possibly be the right answer. Sanity checks are nice things to have; they don’t guarantee against making mistakes, but they at least provide some protection against the easiest mistakes, and having some idea of what an answer could plausibly be might help in working out the answer. For example, if Paige had absolutely no idea how to set up equations for this problem, she could reason that the apple and the orange have to cost something from 1 to 29 cents, and could try out prices until finding something that satisfies both requirements. This is an exhausting method, but it would eventually work, too, and sometimes “working eventually” is better than “working cleverly”.

    Bill Schorr’s The Grizzwells (September 13) starts out by playing on the fact that “yard” has multiple meanings; it also circles around one of those things that distinguishes word problems from normal mathematics. A word problem, by convention, normally contains exactly the information needed to solve what’s being asked — there’s neither useless information included nor necessary information omitted, except if the question-writer has made a mistake. In a real world application, figuring out what you need, and what you don’t need, is part of the work, possibly the most important part of the work. So to answer how many feet are in a yard, Gunther (the bear) is right to ask more questions about how big the yard is, as a start.

    Ed would rather snack bars came in 100-calorie forms, rather than 70-calorie ones.

    Steve Kelly and Jeff Parker’s _Dustin_ for the 14th of September, 2014.

    Steve Kelley and Jeff Parker’s Dustin (September 14) is about one of the applications for mental arithmetic that people find awfully practical: counting the number of food calories that you eat. Ed’s point about it being convenient to have food servings be nice round numbers, as they’re easier to work with, is a pretty good one, and it’s already kind of accounted for in food labelling: it’s permitted (in the United States) to round off calorie counts to the nearest ten or so, on the rather sure grounds that if you are counting calories you’d rather add 70 to the daily total than 68 or 73. Don’t read the comments thread, which includes the usual whining about the Common Core and the wild idea that mental arithmetic might be well done by working out a calculation that’s close to the one you want but easier to do and then refining it to get the accuracy you need.

    Mac and Bill King’s Magic In A Minute kids activity panel (September 14) presents a magic trick that depends on a bit of mental arithmetic. It’s a nice stunt, although it is certainly going to require kids to practice things because, besides dividing numbers by 4, it also requires adding 6, and that’s an annoying number to deal with. There’s also a nice little high school algebra problem to be done in explaining why the trick works.

    Bill Watterson’s Calvin and Hobbes (September 15, rerun) includes one of Hobbes’s brilliant explanations of how arithmetic works, and if I haven’t wasted the time spent memorizing the strips where Calvin tries to do arithmetic homework then Hobbes follows up tomorrow with imaginary numbers. Can’t wait.

    Jef Mallet’s Frazz (September 15) expresses skepticism about a projection being made for the year 2040. Extrapolations and interpolations are a big part of numerical mathematics and there’s fair grounds to be skeptical: even having a model of whatever your phenomenon is that accurately matches past data isn’t a guarantee that there isn’t some important factor that’s been trivial so far but will become important and will make the reality very different from the calculations. But that hardly makes extrapolations useless: for one, the fact that there might be something unknown which becomes important is hardly a guarantee that there is. If the modelling is good and the reasoning sound, what else are you supposed to use for a plan? And of course you should watch for evidence that the model and the reality aren’t too very different as time goes on.

    Gary Wise and Lance Aldrich’s Real Life Adventures (September 15) describes mathematics as “insufferable and enigmatic”, which is a shame, as mathematics hasn’t said anything nasty about them, now has it?

     
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