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  • Joseph Nebus 6:00 pm on Thursday, 9 February, 2017 Permalink | Reply
    Tags: , , , Dogs of C Kennel, , FoxTrot, , Nest Heads,   

    Reading the Comics, February 3, 2017: Counting Edition 

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

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

    I’m not so staunchly anti-lottery as many mathematics people are. I’ll admit I play it myself, when the jackpot is large enough. When the expectation value of the prize gets to be positive, it’s harder to rationalize not playing. This happens only once or twice a year, but it’s fun to watch and see when it happens. I grant it’s a foolish way to use two dollars (two tickets are my limit), but you know? My budget is not so tight I can’t spend four dollars foolishly a year. Besides, I don’t insist on winning one of those half-billion-dollar prizes. I imagine I’d be satisfied if I brought in a mere $10,000.

    'Hey, Ruthie's Granny, how old are you?' 'You can't count that high, James.' 'I can too!' 'Fine! Start at one and I'll tell you when you get to my age.' '1, 2, 3, 4, 11, 22, 88, 99, 200, a gazillion!' 'Very good! It's somewhere between 22 and a gazillion!' 'Gazowie!'

    Rick Detorie’s One Big Happy for the 3rd of February, 2017. A ‘gazillion’ is actually a surprisingly low number, hovering as it does somewhere around 212. Fun fact!

    Rick Detorie’s One Big Happy for the 3rd continues my previous essay’s bit of incompetence at basic mathematics, here, counting. But working out that her age is between 22 an a gazillion may be worth doing. It’s a common mathematical challenge to find a correct number starting from little information about it. Usually we find it by locating bounds: the number must be larger than this and smaller than that. And then get the bounds closer together. Stop when they’re close enough for our needs, if we’re numerical mathematicians. Stop when the bounds are equal to each other, if we’re analytic mathematicians. That can take a lot of work. Many problems in number theory amount to “improve our estimate of the lowest (or highest) number for which this is true”. We have to start somewhere.

    Samson’s Dark Side of the Horse for the 3rd is a counting-sheep joke and I was amused that the counting went so awry here. On looking over the strip again for this essay, though, I realize I read it wrong. It’s the fences that are getting counted, not the sheep. Well, it’s a cute little sheep having the same problems counting that Horace has. We don’t tend to do well counting more than around seven things at a glance. We can get a bit farther if we can group things together and spot that, say, we have four groups of four fences each. That works and it’s legitimate; we’re counting and we get the right count out of it. But it does feel like we’re doing something different from how we count, say, three things at a glance.

    Mick Mastroianni and Mason MastroianniDogs of C Kennel for the 3rd is about the world’s favorite piece of statistical mechanics, entropy. There’s room for quibbling about what exactly we mean by thermodynamics saying all matter is slowly breaking down. But the gist is fair enough. It’s still mysterious, though. To say that the disorder of things is always increasing forces us to think about what we mean by disorder. It’s easy to think we have an idea what we mean by it. It’s hard to make that a completely satisfying definition. In this way it’s much like randomness, which is another idea often treated as the same as disorder.

    Bill Amend’s FoxTrot Classics for the 3rd reprinted the comic from the 10th of February, 2006. Mathematics teachers always want to see how you get your answers. Why? … Well, there are different categories of mistakes someone can make. One can set out trying to solve the wrong problem. One can set out trying to solve the right problem in a wrong way. One can set out solving the right problem in the right way and get lost somewhere in the process. Or one can be doing just fine and somewhere along the line change an addition to a subtraction and get what looks like the wrong answer. Each of these is a different kind of mistake. Knowing what kinds of mistakes people make is key to helping them not make these mistakes. They can get on to making more exciting mistakes.

  • Joseph Nebus 6:00 pm on Sunday, 29 January, 2017 Permalink | Reply
    Tags: , , , , FoxTrot, , , Randy Glasbergen, ,   

    Reading the Comics, January 28, 2017: Chuckle Brothers Edition 

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

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

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

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

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

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

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

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

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

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

  • Joseph Nebus 12:48 am on Thursday, 8 November, 2012 Permalink | Reply
    Tags: , Cantor, , , Fermat, FoxTrot,   

    Dilbert, Infinity, and 17 

    I dreamed recently that I opened the Sunday comics to find Scott Adams’s Dilbert strip turned into a somewhat lengthy, weird illustrated diatribe about how all numbers smaller than infinity were essentially the same, with the exception of the privileged number 17, which was the number of kinds of finite groups sharing some interesting property. Before I carry on I should point out that I have no reason to think that Scott Adams has any particularly crankish mathematical views, and no reason to think that he thinks much about infinity, finite groups, or the number 17. Imagining he has some fixation on them is wholly the creation of my unconscious or semiconscious mind, whatever parts of mind and body create dreams. But there are some points I can talk about from that start.

    (More …)

    • elkement 7:10 pm on Thursday, 8 November, 2012 Permalink | Reply

      Interesting – I would have guessed that math isn’t at all subject to so-called crankery. As for physics, I think many ‘outsider physicists’ try to develop a whole theory of the universe from scratch, including particles and gravity.

      I have read an interesting account of Margaret Wertheim on this recently – http://physicsonthefringe.com . She portrays a typical physics outsider, and this narrative has confirmed my theory: Outsiders(*) sometimes seem to believe or hope that there needs to be an explanation of ‘the world’ that does not require all that advanced math – even if there are already valid explanations in ‘orthodox physics’. That’s why I wondered that there is something as math crankery.

      (*) I am reluctant to use terms like crackpot or cranks – for the same reasons as Wertheim – despite the fact I enjoy dissecting the theories.


      • Joseph Nebus 4:38 am on Friday, 9 November, 2012 Permalink | Reply

        I haven’t read Wertheim’s book, although seeing the cover makes me realize I did consider it at the bookstore. Your foot note raises a fair point; it’s prejudicial to call such things crank work, at least before the work’s been looked at. Mathematics is a field where the amateur or outsider can enter and have a reasonable hope of doing meaningful work.

        But, yeah, mathematics does enjoy a streak of fringe work. The most notorious such work tends to focus on questions that don’t require any mathematics to hear about, such as Fermat’s Last Theorem — there was one person on the Usenet group sci.math who spent an eight-year and utterly compelling odyssey of proving Fermat’s Last Theorem over and over and over again, wrong every time, and eventually spun it out into a factorization algorithm that produced the most hilarious attempted factorization of 15 I imagine I will ever see (several thousand words in it hadn’t got anywhere near three or five) — or whether pi can be written as a rational number.

        Easy as the challenges are to state, these aren’t ones that have easy answers; indeed, just explaining why the answers aren’t easy tends not to be easy. That seems consistent with the idea that there’s a hope for explanations of the world that don’t require advanced math.


      • Geoffrey Brent (@GeoffreyBrent) 2:26 am on Wednesday, 16 January, 2013 Permalink | Reply

        Sorry I missed this discussion when it first appeared…

        Unfortunately, mathematics gets its share of cranks. You can see a selection of amateur cranks over at http://en.wikipedia.org/wiki/Talk:0.999…/Arguments where people argue about whether 0.999999… is equal to 1.

        My reading of this: although we have a rigorous logical framework for mathematics, that’s not really the whole picture. For many people – even sensible mathematicians – mathematical work begins with intuition. Long before we fill in a rigorous proof, intuition is telling us what the answer SHOULD look like, and that directs the process. (If it weren’t so, we’d just be exercising a breadth-first search over the space of all mathematical proofs – and mathematicians would be obsolete, because a computer does that better and faster.)

        Intuition doesn’t always work; even Ramanujan got it wrong occasionally. A good mathematician acknowledges when they can’t find a solid proof to support their intuition, but some bad mathematicians mangle the logic to fit their intuition.

        Topics relating to infinity are popular crank-bait, because there are a lot of non-intuitive results combined with some imprecise terminology. Negative numbers also cause trouble occasionally: e.g. some folk refuse to accept that -1 * -1 = +1, and I suspect this is because they’re attached to an intuitive understanding of a minus sign as “making smaller”.

        And then there are the moral objectors. A lot of people try to view everything in life through a religious/pseudoreligious lens, mathematics included. Georg Cantor’s work on infinite sets is well accepted by modern mathematicians, but in his own day a lot of eminent mathematicians and philosophers took great exception, as some cranks still do. If you’re a monotheist who believes that infinity = God, and then Cantor comes along with a proof that there are many different types of infinity and some are larger than others, that’s a difficult pill to swallow.

        On a side note: I don’t know whether Scott Adams has crankish views about mathematics as such, but he DEFINITELY has crankish views about many other things, including evolution and physics.


        • Joseph Nebus 11:56 pm on Wednesday, 16 January, 2013 Permalink | Reply

          I do think the role of intuition in mathematics is understated, probably as part of a well-meant attempt to highlight how mathematics is utterly logical and reasonable. Thinking over the specification of a problem and concluding, “oh, it must be” and then following that up with “because of symmetries” and maybe later on “because in the limiting case this becomes almost everywhere indistinguishable from a uniform distribution” is a fun narrative but nobody wants to hear about the narrative of your silly little four-page paper on point charge equilibriums.

          You’re probably right about moral objections being part of what attracts certain topics to, to be charitable, nonstandard opinions, particularly from people who haven’t got much experience in the field. I only just learned (or became aware) that Robert Heinlein offered Cantor-as-obscurantist-nonsense sentiments in a couple of his later novels. (Since I haven’t read Number of the Beast or Time Enough For Love, what with their being late-era Robert Heinlein novels and my being able to learn from experience, I can’t say whether they’re offered as opinions of the characters or of the narrator, and I am aware the viewpoint of a book’s narrator is not necessarily the viewpoint of the author, and that an author may advance a contrary view just because it’s interesting.)

          Now that you mention I remember Scott Adams expressing crankish views about evolution (I remember some amusement in rec.arts.comics.strips over it), although I missed any physics points he might have said something dumb about. I feel cynical that I suppose he might have offered opinions regarding climatology which are at considerable variance from the generally accepted understandings of the field.


  • Joseph Nebus 7:39 pm on Sunday, 20 May, 2012 Permalink | Reply
    Tags: , , Bo Nanas, Borel, Bradley Trevor Greive, , Citizen Dog, , , , , denominator, Ed Allison, , FoxTrot, fraction, , Guy Endor-Kaiser, , Jef Mallet, John Kovaleski, Jorge Luis Borges, Kid City, , Latin, , , Mark O'Hare, , numerator, , , , , Rudy Park, Steve McGarry, The Lost Bear, Theron Heir, Unstrange Phenomena   

    Reading The Comics, May 20, 2012 

    Since I suspect that the comics roundup posts are the most popular ones I post, I’m very glad to see there was a bumper crop of strips among the ones I read regularly (from King Features Syndicate and from gocomics.com) this past week. Some of those were from cancelled strips in perpetual reruns, but that’s fine, I think: there aren’t any particular limits on how big an electronic comics page one can have, after all, and while it’s possible to read a short-lived strip long enough that you see all its entries, it takes a couple go-rounds to actually have them all memorized.

    The first entry, and one from one of these cancelled strips, comes from Mark O’Hare’s Citizen Dog, a charmer of a comic set in a world-plus-talking-animals strip. In this case Fergus has taken the place of Maggie, a girl who’s not quite ready to come back from summer vacation. It’s also the sort of series of questions that it feels like come at the start of any class where a homework assignment’s due.

    (More …)

  • Joseph Nebus 1:51 am on Monday, 23 April, 2012 Permalink | Reply
    Tags: , , Dana Simpson, , Fields Medal, FoxTrot, , Heavenly Nostrils, , humorous song, , Lobachevsky, Norm Feuti, Pab Sugenis, Poincare Conjecture, , , Rina Piccolo, , Schrodinger's Equation, Silent E, Six Chix, The Electric Company, Tina's Groove, TMBG, Tom Lehrer,   

    Mid-April 2012 Comics Review 

    I’ve gotten enough comics, I think, to justify a fresh roundup of mathematics appearances in the comic strips. Unfortunately the first mathematics-linked appearance since my most recent entry is also the most badly dated. Pab Sugenis’s The New Adventures of Queen Victoria took (the appropriate) day to celebrate the birthday of Tom Lehrer, but fails to mention his actual greatest contribution to American culture, the “Silent E” song for The Electric Company. He’s also author of the humorous song “Lobachevsky”, which is pretty much the only place to go if you need a mathematics-based song and can’t use They Might Be Giants for some reason. (I regard Lehrer’s “New Math” song as not having a strong enough melody to count.)

    (More …)

    • outofthenormmaths 9:24 am on Monday, 23 April, 2012 Permalink | Reply

      Actually, the maximum number of moves to solve a Rubik’s cube, also known as ‘God’s number’ is now known. The upper and lowers bounds converged on 20 moves. eg. See http://www.cube20.org


      • Joseph Nebus 2:30 am on Tuesday, 24 April, 2012 Permalink | Reply

        I hadn’t heard the news! Thank you.

        I suppose now I can’t feel mildly smug over Joe Martin not having heard about the Poincare conjecture’s proof a couple years back. (I didn’t feel all that smug about it.)


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