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  • Joseph Nebus 6:00 pm on Thursday, 6 April, 2017 Permalink | Reply
    Tags: , , , , , Sticky Comics, Tough Town,   

    Reading the Comics, April 1, 2017: Connotations Edition 


    Last week ended with another little string of mathematically-themed comic strips. Most of them invited, to me, talk about the cultural significance of mathematics and what connotations they have. So, this title for an artless essay.

    Berkeley Breathed’s Bloom County 2017 for the 28th of March uses “two plus two equals” as the definitive, inarguable truth. It always seems to be “two plus two”, doesn’t it? Never “two plus three”, never “three plus three”. I suppose I’ve sometimes seen “one plus one” or “two times two”. It’s easy to see why it should be a simple arithmetic problem, nothing with complicated subtraction or division or numbers as big as six. Maybe the percussive alliteration of those repeated two’s drives the phrase’s success. But then why doesn’t “two times two” show up nearly as often? Maybe the phrase isn’t iambic enough. “Two plus two” allows (to my ear) the “plus” sink in emphasis, while “times” stays a little too prominent. We need a wordsmith in to explore it. (I’m open to other hypotheses, including that “two times two” gets used more than my impression says.)

    Christiann MacAuley’s Sticky Comics for the 28th uses mathematics as the generic “more interesting than people” thing that nerds think about. The thing being thought of there is the Mandelbrot Set. It’s built on complex-valued numbers. Pick a complex number, any you like; that’s called ‘C’. Square the number and add ‘C’ back to itself. This will be some new complex-valued number. Square that new number and add the original ‘C’ back to it again. Square that new number and add the original ‘C’ back once more. And keep at this. There are two things that might happen. These squared numbers might keep growing infinitely large. They might be negative, or imaginary, or (most likely) complex-valued, but their size keeps growing. Or these squared numbers might not grow arbitrarily large. The Mandelbrot Set is the collection of ‘C’ values for which the numbers don’t just keep growing in size. That’s the sort of lumpy kidney bean shape with circles and lightning bolts growing off it that you saw on every pop mathematics book during the Great Fractal Boom of the 80s and 90s. There’s almost no point working it out in your head; the great stuff about fractals almost requires a computer. They take a lot of computation. But if you’re just avoiding conversation, well, anything will do.

    Olivia Walch’s Imogen Quest for the 29th riffs on the universe-as-simulation hypothesis. It’s one of those ideas that catches the mind and is hard to refute as long as we don’t talk to the people in the philosophy department, which we’re secretly scared of. Anyway the comic shows one of the classic uses of statistical modeling: try out a number of variations of a model in the hopes of understanding real-world behavior. This is an often-useful way to balance how the real world has stuff going on that’s important and that we don’t know about, or don’t know how to handle exactly.

    Mason Mastroianni’s The Wizard of Id for the 31st uses a sprawl of arithmetic as symbol of … well, of status, really. The sort of thing that marks someone a white-collar criminal. I suppose it also fits with the suggestion of magic that accompanies huge sprawls of mathematical reasoning. Bundle enough symbols together and it looks like something only the intellectual aristocracy, or at least secret cabal, could hope to read.

    Bob Shannon’s Tough Town for the 1st name-drops arithmetic. And shows off the attitude that anyone we find repulsive must also be stupid, as proven by their being bad at arithmetic. I admit to having no discernable feelings about the Kardashians; but I wouldn’t be so foolish as to conflate intelligence and skill-at-arithmetic.

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    • elkement (Elke Stangl) 3:24 pm on Thursday, 20 April, 2017 Permalink | Reply

      I am replying to the previous post (March statistics) – as nothing happened when I clicked on the reply button at that post. But maybe this is related to what I actually wanted to comment about:

      Your table is displayed at the bottom of the page – below ‘Related’, the comment box, and the previous/next posting links! How did you do this? You totally hacked WordPress ;-)

      Like

      • elkement (Elke Stangl) 3:25 pm on Thursday, 20 April, 2017 Permalink | Reply

        OK – so that reply could be posted. As I said, with your table you confused WordPress a lot :-)

        Like

      • Joseph Nebus 2:43 am on Tuesday, 25 April, 2017 Permalink | Reply

        Huh, and that’s curious. I didn’t realize it and must not have looked close enough at the preview.

        It looks like the fault is that I failed to close the table tag, so WordPress tried to fit the rest of the page in-between the tbody and the end of the table and goodness knows how it worked out that presentation.

        Liked by 1 person

  • Joseph Nebus 6:00 pm on Sunday, 2 April, 2017 Permalink | Reply
    Tags: , , Baldo, , , Tough Town   

    Reading the Comics, March 27, 2017: Not The March 26 Edition 


    My guide for how many comics to include in one of these essays is “at least five, if possible”. Occasionally there’s a day when Comic Strip Master Command sends that many strips at once. Last Sunday was almost but not quite such a day. But the business of that day did mean I had enough strips to again divide the past week’s entries. Look for more comics in a few days, if all goes well here. Thank you.

    Mark Anderson’s Andertoons for the 26th reminds me of something I had wholly forgot about: decimals inside fractions. And now that this little horror’s brought back I remember my experience with it. Decimals in fractions aren’t, in meaning, any different from division of decimal numbers. And the decimals are easily enough removed. But I get the kid’s horror. Fractions and decimals are both interesting in the way they represent portions of wholes. They spend so much time standing independently of one another it feels disturbing to have them interact. Well, Andertoons kid, maybe this will comfort you: somewhere along the lines decimals in fractions just stop happening. I’m not sure when. I don’t remember when the last one passed my experience.

    Hector Cantu and Carlos Castellanos’s Baldo for the 26th is built on a riddle. It’s one that depends on working in shifting addition from “what everybody means by addition” to “what addition means on a clock”. You can argue — I’m sure Gracie would — that “11 plus 3” does not mean “eleven o’clock plus three hours”. But on what grounds? If it’s eleven o’clock and you know something will happen in three hours, “two o’clock” is exactly what you want. Underlying all of mathematics are definitions about what we mean by stuff like “eleven” and “plus” and “equals”. And underlying the definitions is the idea that “here is a thing we should like to know”.

    Addition of hours on a clock face — I never see it done with minutes or seconds — is often used as an introduction to modulo arithmetic. This is arithmetic on a subset of the whole numbers. For example, we might use 0, 1, 2, and 3. Addition starts out working the way it does in normal numbers. But then 1 + 3 we define to be 0. 2 + 3 is 1. 3 + 3 is 2. 2 + 2 is 0. 2 + 3 is 1 again. And so on. We get subtraction the same way. This sort of modulo arithmetic has practical uses. Many cryptography schemes rely on it, for example. And it has pedagogical uses; modulo arithmetic turns up all over a mathematics major’s Introduction to Not That Kind Of Algebra Course. You can use it to learn a lot of group theory with something a little less exotic than rotations and symmetries of polygonal shapes or permutations of lists of items. A clock face doesn’t quite do it, though. We have to pretend the ’12’ at the top is a ‘0’. I’ve grown more skeptical about whether appealing to clocks is useful in introducing modulo arithmetic. But it’s been a while since I’ve needed to discuss the matter at all.

    Rob Harrell’s Big Top rerun for the 26th mentions sudoku. Remember when sudoku was threatening to take over the world, or at least the comics page? Also, remember comics pages? Good times. It’s not one of my hobbies, but I get the appeal.

    Bob Shannon’s Tough Town I’m not sure if I’ve featured here before. It’s one of those high concept comics. The patrons at a bar are just what you see on the label, and there’s a lot of punning involved. Now that I’ve over-explained the joke please enjoy the joke. There are a couple of strips prior to this one featuring the same characters; they just somehow didn’t mention enough mathematics words for me to bring up here.

    Overhearing customers: 'Kids today can't even do basic math. If the computer doesn't tell them how much change to give you, they don't know what to do.' Customer asking: 'How much is 50% off of $49.99 ? Does that mean it's free?' Clerk: Sigh.

    Norm Feuti’s Retail for the 27th of March, 2017. Of course customers aren’t generally good at arithmetic either. I’m reminded (once more) of when I worked at Walden Books and a customer wanted to know whether the sticker-promised 10 percent discount on the book was applied to the price before or after the 6 percent sales tax was added to it, or whether it was applied afterwards. I could not speak to the cash register’s programming, but I could promise that the process would come to the same number either way, and I told him what it would be. I think the book had a $14.95 cover price — let’s stipulate it was for the sake of my anecdote — so it would come to $14.26 in the end. He judged me suspiciously and then allowed me to ring it up; the register made it out to be $15.22 and he pounced, saying, see?. Yes: he had somehow found the one freaking book in the store where the UPC bar code price, $15.95, was different from the thing listed as the cover price. I told him why it was and showed him where in the UPC to find the encoded price (it’s in the last stanza of digits underneath the bars) but he was having none of it, even when I manually corrected the error.

    Norm Feuti’s Retail for the 27th is about the great concern-troll of mathematics education: can our cashiers make change? I’m being snottily dismissive. Shops, banks, accountants, and tax registries are surely the most common users of mathematics — at least arithmetic — out there. And if people are going to do a thing, ordinarily, they ought to be able to do it well. But, of course, the computer does arithmetic extremely well. Far better, or at least more indefatigably, than any cashier is going to be able to do. The computer will also keep track of the prices of everything, and any applicable sales or discounts, more reliably than the mere human will. The whole point of the Industrial Revolution was to divide tasks up and assign them to parties that could do the separate parts better. Why get worked up about whether you imagine the cashier knows what $22.14 minus $16.89 is?

    I will say the time the bookstore where I worked lost power all afternoon and we had to do all the transactions manually we ended up with only a one-cent discrepancy in the till, thank you.

     
    • The Chaos Realm 1:05 pm on Monday, 3 April, 2017 Permalink | Reply

      Forget school-taught math, that’s how I best learned math…as a cashier…

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      • Joseph Nebus 2:18 am on Tuesday, 4 April, 2017 Permalink | Reply

        I shouldn’t be surprised! Doing anything often will encourage people to find more accurate and faster ways to do it. So one speeds up either by just being better at recognizing common operations or by developing useful shortcuts. (The shortcuts can be disastrous if, for example, they accidentally cause some needed safety precaution not to be taken, but that doesn’t tend to apply in cashier work.)

        Liked by 1 person

        • The Chaos Realm 2:29 am on Tuesday, 4 April, 2017 Permalink | Reply

          Yeah, I used to drive my math teachers crazy with my shortcuts. But, I love when I see the light bulb go off in kids when I show them other ways to do math problems (even as a sub, I do sometimes get to teach :-) )
          .

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          • Joseph Nebus 5:23 am on Friday, 14 April, 2017 Permalink | Reply

            There is that. A weird shortcut or novel trick for a problem, even if it doesn’t lead to a generally useful technique, is good to have on the record. It inspires the imagination and lets folks know that there’s almost never just one way to do things.

            Liked by 1 person

    • davekingsbury 9:10 pm on Monday, 3 April, 2017 Permalink | Reply

      Guestimation keeps the common sense in maths I, er … guess. As for Sudoku, is there any other way to do it than listing all possible #s in each box? I see people on buses and trains just staring at it – are they hoping for inspiration or else doing prodigious memory work?

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      • Joseph Nebus 2:23 am on Tuesday, 4 April, 2017 Permalink | Reply

        I’m not an expert sudoku solver. I’d done some for a little while, especially after some students gave me a book of puzzles as a parting gift, but I never caught the bug.

        But when I do them, it is … I wouldn’t say a prodigious amount of memory work. It would be picking out a cell and checking what the valid possible numbers are, then going across the row, column, and cell to see if there were any obvious contradictions, or whether that forced something suspicious in a nearby cell. I don’t suppose that works well for hard puzzles, but for the silly little easy and almost-medium puzzles I attacked it was fine. Something would turn up soon.

        Liked by 1 person

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