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  • Joseph Nebus 6:00 pm on Sunday, 1 January, 2017 Permalink | Reply
    Tags: Albert Einstein, , Bad Machinery, Buni, Daily Drawing, , Madeline L'Engle, , , , Speechless, Wrong Hands   

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

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

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

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

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

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

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

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

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

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

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

  • Joseph Nebus 6:00 pm on Tuesday, 13 December, 2016 Permalink | Reply
    Tags: Albert Einstein, , , 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, 4 December, 2016 Permalink | Reply
    Tags: Albert Einstein, , , egg salad, Eureka, , ,   

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

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

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

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

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

    Scientisty type: 'Yessirree, there we have it: I've just proved we're completely alone in a cold, dying universe'. This provokes an angry stare from the other scientisty type, who's wearing an 'I Believe' grey-aliens T-shirt.

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

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

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

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

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

    Jughead and Archie reflect how it seems like a waste to learn mathematics when they have calculators, or spelling when they have spell-checkers. Archie suggests getting a snack and his dad says he's *got* a garbage disposal.

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

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

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

  • Joseph Nebus 6:00 pm on Sunday, 27 November, 2016 Permalink | Reply
    Tags: Albert Einstein, Betty Boop, blackboard, , communication,   

    Reading the Comics, November 23, 2016: Featuring A Betty Boop Cartoon Edition 

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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


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

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



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

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

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

        Liked by 1 person

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

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


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

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

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

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

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


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

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


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

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

            Liked by 1 person

  • Joseph Nebus 6:00 pm on Sunday, 6 November, 2016 Permalink | Reply
    Tags: Albert Einstein, , 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: Albert Einstein, , 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 Sunday, 2 October, 2016 Permalink | Reply
    Tags: Albert Einstein, , ,   

    Reading the Comics, October 1, 2016: Jumble Is Back Edition 

    Comic Strip Master Command sent another normal-style week for mathematics references. There’s not much that lets me get really chatty or gossippy about mathematics lore. That’s all right. The important thing is: we’ve got Jumble back.

    Greg Cravens’s The Buckets for the 25th features a bit of parental nonsense-telling. The rather annoying noise inside a car’s cabin when there’s one window open is the sort of thing fluid mechanics ought to be able to study. I see references claiming this noise to be a Helmholz Resonance. This is a kind of oscillation in the air that comes from wind blowing across the lone hole in a solid object. Wikipedia says it’s even the same phenomenon producing an ocean-roar in a seashell held up to the ear. It’s named for Hermann von Helmholtz, who described it while studying sound and vortices. Helmholz is also renowned for making a clear statement of the conservation of energy — an idea many were working towards, mind — and in thermodynamics and electromagnetism and for that matter how the eye works. Also how fast nerves transmit signals. All that said, I’m not sure that all the unpleasant sound heard and pressure felt from a single opened car window is Helmholz Resonance. Real stuff is complicated and the full story is always more complicated than that. I wouldn’t go farther than saying that Helmholz Resonance is one thing to look at.

    Michael Cavna’s Warped for the 25th uses two mathematics-cliché equations as “amazingly successful formulas”. One can quibble with whether Einstein should be counted under mathematics. Pythagoras, at least for the famous theorem named for him, nobody would argue. John Grisham, I don’t know, the joke seems dated to me but we are talking about the comics.

    Tony Carrillos’ F Minus for the 28th uses arithmetic as as something no reasonable person can claim is incorrect. I haven’t read the comments, but I am slightly curious whether someone says something snarky about Common Core mathematics — or even the New Math for crying out loud — before or after someone finds a base other than ten that makes the symbols correct.

    Cory Thomas’s college-set soap-opera strip Watch Your Head for the 28th name-drops Introduction to Functional Analysis. It won’t surprise you it’s a class nobody would take on impulse. It’s an upper-level undergraduate or a grad-student course, something only mathematics majors would find interesting. But it is very interesting. It’s the reward students have for making it through Real Analysis, the spirit-crushing course about why calculus works. Functional Analysis is about what we can do with functions. We can make them work like numbers. We can define addition and multiplication, we can measure their size, we can create sequences of them. We can treat functions almost as if they were numbers. And while we’re working on things more abstract and more exotic than the ordinary numbers Real Analysis depends on, somehow, Functional Analysis is easier than Real Analysis. It’s a wonder.

    Mark Anderson’s Andertoons for the 29th features a student getting worried about the order of arithmetic operations. I appreciate how kids get worried about the feelings of things like that. Although, truly, subtraction doesn’t go “last”; addition and subtraction have the same priority. They share the bottom of the pile, though. Multiplication and division similarly share a priority, above addition-and-subtraction. Many guides to the order of operations say to do addition-and-subtraction in order left to right, but that’s not so. Setting a left-to-right order is okay for deciding where to start. But you could do a string of additions or subtractions in any order and get the same answer, unless the expression is inconsistent.

    Four people sitting at a table divided up as a pie chart. The one sitting behind the overwhelming majority of the chunk says, 'C'mon guys ... I feel like I'm doing all the work here.'

    Daniel Beyer’s Long Story Short for the 30th of September, 2016. I think Randolph Itch, 2am did this joke too but then had everyone retire to the bar chart.

    Daniel Beyer’s Long Story Short for the 30th is a pie chart joke. There’s not a lot of mathematics to it, but I’m amused.

    Justin Boyd’s Invisible Bread for the 30th has maybe my favorite dumb joke of the week. It’s just a kite that’s proven its knowledge of mathematics. I’m a little surprised the kite didn’t call out a funnier number, by which I mean 37, but perhaps … no, that doesn’t work, actually. Of course the kite would be comfortable with higher mathematics.

    LIPOS O-O-O; PURTE OO---; VONPER -OO---; YETMSS --O-OO. Her students were beginning to understand addition and subtraction OOOO OO OOOO.

    David L Hoyt and Jeff Knurek’s Jumble for the 1st of October, 2016. I don’t know that there even is a permanent link for this that would be any good.

    And as promised, David L Hoyt and Jeff Knurek’s Jumble for the 1st of October mentions mathematics. That’s enough for me to include here.

  • Joseph Nebus 6:00 pm on Sunday, 25 September, 2016 Permalink | Reply
    Tags: Albert Einstein, , , ,   

    Reading the Comics, September 24, 2016: Infinities Happen Edition 

    I admit it’s a weak theme. But two of the comics this week give me reason to talk about infinitely large things and how the fact of being infinitely large affects the probability of something happening. That’s enough for a mid-September week of comics.

    Kieran Meehan’s Pros and Cons for the 18th of September is a lottery problem. There’s a fun bit of mathematical philosophy behind it. Supposing that a lottery runs long enough without changing its rules, and that it does draw its numbers randomly, it does seem to follow that any valid set of numbers will come up eventually. At least, the probability is 1 that the pre-selected set of numbers will come up if the lottery runs long enough. But that doesn’t mean it’s assured. There’s not any law, physical or logical, compelling every set of numbers to come up. But that is exactly akin to tossing a coin fairly infinity many times and having it come up tails every single time. There’s no reason that can’t happen, but it can’t happen.

    'It's true, Dr Peel. I'm a bit of a psychic.' 'Would you share the winning lottery numbers with me?' '1, 10, 17, 39, 43, and 47'. 'Those are the winning lottery numbers?' 'Yes!' 'For this Tuesday?' 'Ah! That's where it gets a bit fuzzy.'

    Kieran Meehan’s Pros and Cons for the 18th of September, 2016. I can’t say whether any of these are supposed to be the PowerBall number. (The comic strip’s title is a revision of its original, which more precisely described its gimmick but was harder to remember: A Lawyer, A Doctor, and a Cop.)

    Leigh Rubin’s Rubes for the 19th name-drops chaos theory. It’s wordplay, as of course it is, since the mathematical chaos isn’t the confusion-and-panicky-disorder of the colloquial term. Mathematical chaos is about the bizarre idea that a system can follow exactly perfectly known rules, and yet still be impossible to predict. Henri Poincaré brought this disturbing possibility to mathematicians’ attention in the 1890s, in studying the question of whether the solar system is stable. But it lay mostly fallow until the 1960s when computers made it easy to work this out numerically and really see chaos unfold. The mathematician type in the drawing evokes Einstein without being too close to him, to my eye.

    Allison Barrows’s PreTeena rerun of the 20th shows some motivated calculations. It’s always fun to see people getting excited over what a little multiplication can do. Multiplying a little change by a lot of chances is one of the ways to understanding integral calculus, and there’s much that’s thrilling in that. But cutting four hours a night of sleep is not a little thing and I wouldn’t advise it for anyone.

    Jason Poland’s Robbie and Bobby for the 20th riffs on Jorge Luis Borges’s Library of Babel. It’s a great image, the idea of the library containing every book possible. And it’s good mathematics also; it’s a good way to probe one’s understanding of infinity and of probability. Probably logic, also. After all, grant that the index to the Library of Babel is a book, and therefore in the library somehow. How do you know you’ve found the index that hasn’t got any errors in it?

    Ernie Bushmiller’s Nancy Classics for the 21st originally ran the 21st of September, 1949. It’s another example of arithmetic as a proof of intelligence. Routine example, although it’s crafted with the usual Bushmiller precision. Even the close-up, peering-into-your-soul image if Professor Stroodle in the second panel serves the joke; without it the stress on his wrinkled brow would be diffused. I can’t fault anyone not caring for the joke; it’s not much of one. But wow is the comic strip optimized to deliver it.

    Thom Bluemel’s Birdbrains for the 23rd is also a mathematics-as-proof-of-intelligence strip, although this one name-drops calculus. It’s also a strip that probably would have played better had it come out before Blackfish got people asking unhappy questions about Sea World and other aquariums keeping large, deep-ocean animals. I would’ve thought Comic Strip Master Command to have sent an advisory out on the topic.

    Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 23rd is, among other things, a guide for explaining the difference between speed and velocity. Speed’s a simple number, a scalar in the parlance. Velocity is (most often) a two- or three-dimensional vector, a speed in some particular direction. This has implications for understanding how things move, such as pedestrians.

  • Joseph Nebus 3:00 pm on Monday, 23 May, 2016 Permalink | Reply
    Tags: Albert Einstein, , , , , , pyramids   

    Reading the Comics, May 17, 2016: Again, No Pictures Edition 

    Last week’s Reading The Comics was a bunch of Gocomics.com strips. And I don’t feel the need to post the images for those, since they’re reasonably stable links. Today’s is also a bunch of Gocomics.com strips. I know how every how-to-bring-in-readers post ever says you should include images. Maybe I will commission someone to do some icons. It couldn’t hurt.

    Someone looking close at the title, with responsible eye protection, might notice it’s dated the 17th, a day this is not. There haven’t been many mathematically-themed comic strips since the 17th is all. And I’m thinking to try out, at least for a while, making the day on which a Reading the Comics post is issued regular. Maybe Monday. This might mean there are some long and some short posts, but being a bit more scheduled might help my writing.

    Mark Anderson’s Andertoons for the 14th is the charting joke for this essay. Also the Mark Anderson joke for this essay. I was all ready to start explaining ways that the entropy of something can decrease. The easiest way is by expending energy, which we can see as just increasing entropy somewhere else in the universe. The one requiring the most patience is simply waiting: entropy almost always increases, or at least doesn’t decrease. But “almost always” isn’t the same as “always”. But I have to pass. I suspect Anderson drew the chart going down because of the sense of entropy being a winding-down of useful stuff. Or because of down having connotations of failure, and the increase of entropy suggesting the failing of the universe. And we can also read this as a further joke: things are falling apart so badly that even entropy isn’t working like it ought. Anderson might not have meant for a joke that sophisticated, but if he wants to say he did I won’t argue it.

    Scott Adams’s Dilbert Classics for the 14th reprinted the comic of the 20th of March, 1993. I admit I do this sort of compulsive “change-simplifying” paying myself. It’s easy to do if you have committed to memory pairs of numbers separated by five: 0 and 5, 1 and 6, 2 and 7, and so on. So if I get a bill for (say) $4.18, I would look for whether I have three cents in change. If I have, have I got 23 cents? That would give me back a nickel. 43 cents would give me back a quarter in change. And a quarter is great because I can use that for pinball.

    Sometimes the person at the cash register doesn’t want a ridiculous bunch of change. I don’t blame them. It’s easy to suppose that someone who’s given you $5.03 for a $4.18 charge misunderstood what the bill was. Some folks will take this as a chance to complain mightily about how kids don’t learn even the basics of mathematics anymore and the world is doomed because the young will follow their job training and let machines that are vastly better at arithmetic than they are do arithmetic. This is probably what Adams was thinking, since, well, look at the clerk’s thought balloon in the final panel.

    But consider this: why would Dilbert have handed over $7.14? Or, specifically, how could he give $7.14 to the clerk but not have been able to give $2.14, which would make things easier on everybody? There’s no combination of bills — in United States or, so far as I’m aware, any major world currency — in which you can give seven dollars but not two dollars. He had to be handing over five dollars he was getting right back. The clerk would be right to suspect this. It looks like the start of a change scam, begun by giving a confusing amount of money.

    Had Adams written it so that the charge was $6.89, and Dilbert “helpfully” gave $12.14, then Dilbert wouldn’t be needlessly confusing things.

    Dave Whamond’s Reality Check for the 15th is that pirate-based find-x joke that feels like it should be going around Facebook, even though I don’t think it has been. I can’t say the combination of jokes quite makes logical sense, but I’m amused. It might be from the Reality Check squirrel in the corner.

    Nate Fakes’s Break of Day for the 16th is the anthropomorphized shapes joke for this essay. It’s not the only shapes joke, though.

    Doug Bratton’s Pop Culture Shock Therapy for the 16th is the Einstein joke for this essay.

    Rick Detorie’s One Big Happy rerun for the 17th is another shapes joke. Ruthie has strong ideas about what distinguishes a pyramid from a triangle. In this context I can’t say she’s wrong to assert what a pyramid is.

  • Joseph Nebus 3:00 pm on Tuesday, 26 April, 2016 Permalink | Reply
    Tags: Albert Einstein, , , , , , weekdays   

    Reading the Comics, April 24, 2016: Mental Mathematics and Calendars Edition 

    Warning! I do some showing off in this installment of the Reading the Comics series. Please forgive me. I was feeling a little giddy.

    Scott Hilburn’s The Argyle Sweater I had just mentioned to a friend never seems to show up in these columns anymore. And Hilburn would so reliably do strips about anthropomorphized numerals. He returns on the 20th, after a hiatus of some length I haven’t actually checked here, with a name-drop of Einstein instead. I grinned, although a good part of what amused me was the look of the guy in the lower right of the panel. Funny pictures carry a comic strip far. Formulating the theory of relativity is a tricky request. The special theory … well, to do it properly takes some sophisticated work. But it doesn’t take much beyond the Pythagorean Theorem to realize that “how long” a thing is, or a time span is, is different for different observers. That’s the most important insight, I would say, and that is easily available. General relativity, which looks at accelerations and gravity, that’s another thing. I’d be interested in a popular treatment that explained enough mathematics people could make usable estimates but that could still make sense to a lay audience. Probably it’s not possible to do this. Too bad.

    Mark Tatulli’s Heart of the City just uses arithmetic because it’s a nice compact problem to give a student. It did strike me that 117 times 45 is something one could amaze people with by doing in one’s head, though. Here’s why. 117 times 100 would be easy. Multiplying by hundreds always is. 117 times 50 would be not almost as easy: that’s multiplying by 100 and dividing by two. 117 times 45 … well, that’s 117 times 50 minus 117 times 5. And if you know 117 times 50, then you know 117 times 5: it’s one-tenth that. And one-tenth of a thing is easy to find.

    Therefore: 117 times 100 is 11,700. Divide that by two and that’s kind of an ugly-looking number, isn’t it? But all’s not lost. Let me use another bit of falsework: 11,700 is 12,000 minus 300. Half that is 6,000 minus 150. Therefore, half of 11,700 is 5,850. So 117 times 50 is 5,850. One-tenth of that is 585. Therefore, 117 times 45 is 5,850 minus 585. And that will be … 5,275. Ta-da!

    Well, no, it isn’t. It’s 5,265. I messed up the carrying. I still think that’s doing well for multiplying ugly numbers like that without writing it down. It just won’t impress people who want the actual you know correct answer.

    Mark Anderson’s Andertoons wouldn’t let me down by vanishing for a while. The 21st is not explicitly a strip about extrapolating graphs. I’ll take it as such, though. Once again the art amuses me. I like the crash-up of charted bars. Yes, I saw the Schrödinger’s Cat thing two days later.

    Jef Mallett’s Frazz for the 23rd I drag into a mathematics blog because of the long historical links between calendars and mathematics. But Caulfield does talk about something that’s baffled everyone. There’s seven days to the week. There’s seven classically known heavenly bodies in the solar system, besides the Earth. Naming a day for each seems obvious now that we’ve committed to it. But why aren’t the bodies honored in order?

    Geocentrism seems like, at first, a plausible reason. The ancients wouldn’t order the sky Sun-Mercury-Venus-Moon-Mars-Jupiter-Saturn. But that doesn’t help. Geocentric models of the solar system (always, so far as I’m aware) put the Moon closest, then Mercury, then Venus, the Sun, Mars, Jupiter, and Saturn.

    The answer that, at least, gets repeated in histories of the calendar (for example, here, David Ewing Duncan’s The Calendar: The 5000-Year Struggle To Align The Clock And The Heavens — And What Happened To The Missing Ten Days, which was the first book I had on hand) amounts to a modular arithmetic thing. The Babylonians, if Duncan is right, named a planet-god for each hour of the day. (We treat the Moon and Sun as planets for this discussion.) The planet-gods took their hourly turn in order. If the first hour of the day is Saturn’s to rule, the next is Jupiter’s, then Mars’s, the Sun’s, Venus’s, Mercury’s, and the Moon’s. Then back to Saturn and the system keeps going like that.

    So if the first hour of the day is Saturn’s, then who has the first hour of the next day? … the Sun does. If the Sun has the first hour of the day, then who has the first hour of the day after that? … the Moon. And from here you know the pattern. At least you do if you understand that English derives most of its day names from the Norse gods, matched as best they can with those of the Roman State Religion. So, Tiw matches with Mars; Woden with Mercury; Thor with Jupiter; Freya with Venus. The apparently scrambled order of days, relative to the positions of the planets, amounts to what you get if you keep adding 24 to a number by modulo 7 arithmetic.

    That is, at least, the generally agreed-upon explanation. I am not aware of what actual researchers of Babylonian culture believe. Duncan, I must admit, takes a hit in his credibility by saying on the page after this that “recently chronobiologists have discovered that the seven-day cycle … may also have biological precedents”. I’m sorry but I just don’t believe him, or whoever he got that from.

    Kevin Fagan’s Drabble for the 24th amuses me by illustrating the common phenomenon. We have all taken out the calculator (or computer) to do some calculation that really doesn’t need it. I understand and am sympathetic. It’s so obviously useful to let the calculator work out 117 times 45 and get it right instantly. It’s easy to forget sometimes it’s faster to not bother with the calculator. We are all of us a little ridiculous.

  • Joseph Nebus 3:00 pm on Tuesday, 8 December, 2015 Permalink | Reply
    Tags: Albert Einstein, reciprocals, ,   

    Reading the Comics, December 5, 2015: Awkward Break Edition 

    I confess I’m dissatisfied with this batch of Reading the Comics posts. I like having something like six to eight comics for one of these roundups. But there was this small flood of mathematically-themed comics on the 6th of December. I could either make do with a slightly short edition, or have an overstuffed edition. I suppose it’s possible to split one day’s comics across two Reading the Comics posts, but that’s crazy talk. So, a short edition today.

    Jef Mallett’s Frazz for the 4th of December was part of a series in which Caulfield resists learning about reciprocals. The 4th offers a fair example of the story. At heart the joke is just the student-resisting-class, or student-resisting-story-problems. It certainly reflects a lack of motivation to learn what they are.

    We use reciprocals most often to write division problems as multiplication. “a ÷ b” is the same as “a times the reciprocal of b”. But where do we get the reciprocal of b from? … Well, we can say it’s the multiplicative inverse of b. That is, it’s whatever number you have to multiply ‘b’ by in order to get ‘1’. But we’re almost surely going to find that taking 1 and dividing it by b. So we’ve swapped out one division problem for a slightly different one. This doesn’t seem to be getting us anywhere.

    But we have gotten a new idea. If we can define the multiplication of things, we might be able to get division for almost free. Could we divide one matrix by another? We can certainly multiply a matrix by the inverse of another. (There are complications at work here. We’ll save them for another time.) A lot of sets allow us to define things that make sense as addition and multiplication. And if we can define a complicated operation in terms of addition and multiplication … If we follow this path, we get to do things like define the cosine of a matrix. Then we just have to figure out why we’d want have a cosine of a matrix.

    There’s a simpler practical use of reciprocals. This relates to numerical mathematics, computer work. Computer chips do addition (and subtraction) really fast. They do multiplication a little slower. They do division a lot slower. Division is harder than multiplication, as anyone who’s done both knows. However, dividing by (say) 4 is the same thing as multiplying by 0.25. So if you know you need to divide by a number a lot, then it might make for a faster program to change division into multiplication by a reciprocal. You have to work out the reciprocal, but if you only have to do that once instead of many times over, this might make for faster code. Reciprocals are one of the tools we can use to change a mathematical process into something faster.

    (In practice, you should never do this. You have a compiler that does this, and you should let it do its work. But it’s enlightening to know these are the sorts of things your compiler is looking for when it turns your code into something the computer does. And looking for ways to do the same work in less time is a noble side of mathematics.)

    Charles Schulz’s Peanuts for the 4th of December (originally from 1968, on the same day) sees Peppermint Patty’s education crash against a word problem. It’s another problem in motivating a student to do a word problem. I admit when I was a kid I’d have been enchanted by this puzzle. But I was a weird one.

    Dave Coverly’s Speed Bump for the 4th of December is a mathematics-symbols joke as applied to toast. I think you could probably actually sell those. At least the greater-than and the less-than signs. The approximately-equal-to signs would be hard to use. And people would think they were for bacon anyway.

    Ruben Bolling’s Super-Fun-Pak Comix for the 4th of December showcases Young Albert Einstein. That counts as mathematical content, doesn’t it? The strip does make me wonder if they’re still selling music CDs and other stuff for infant or even prenatal development. I’m skeptical that they ever did any good, but it isn’t a field I’ve studied.

    Bill Whitehead’s Free Range for the 5th of December uses a blackboard full of mathematical and semi-mathematical symbols to denote “stuff too complicated to understand”. The symbols don’t parse as anything. It is authentic to mathematical work to sometimes skip writing all the details of a thing and write in instead a few words describing it. Or to put in an abbreviation for the thing. That often gets circled or boxed or in some way marked off. That keeps us from later on mistaking, say, “MUB” as the product of M and U and B, whatever that would mean. Then we just have to remember we meant “minimum upper bound” by that.

  • Joseph Nebus 3:00 pm on Monday, 21 September, 2015 Permalink | Reply
    Tags: Albert Einstein, Brownian motion, , symmetries,   

    Reading the Comics, September 16, 2015: Celebrity Appearance Edition 

    I couldn’t go on calling this Back To School Editions. A couple of the comic strips the past week have given me reason to mention people famous in mathematics or physics circles, and one who’s even famous in the real world too. That’ll do for a title.

    Jeff Corriveau’s Deflocked for the 15th of September tells what I want to call an old joke about geese formations. The thing is that I’m not sure it is an old joke. At least I can’t think of it being done much. It seems like it should have been.

    The formations that geese, or other birds, form has been a neat corner of mathematics. The question they inspire is “how do birds know what to do?” How can they form complicated groupings and, more, change their flight patterns at a moment’s notice? (Geese flying in V shapes don’t need to do that, but other flocking birds will.) One surprising answer is that if each bird is just trying to follow a couple of simple rules, then if you have enough birds, the group will do amazingly complex things. This is good for people who want to say how complex things come about. It suggests you don’t need very much to have robust and flexible systems. It’s also bad for people who want to say how complex things come about. It suggests that many things that would be interesting can’t be studied in simpler models. Use a smaller number of birds or fewer rules or such and the interesting behavior doesn’t appear.

    The geese are flying in V, I, and X patterns. The guess is that they're Roman geese.

    Jeff Corriveau’s Deflocked for the 15th of September, 2015.

    Scott Adams’s Dilbert Classics from the 15th and 16th of September (originally run the 22nd and 23rd of July, 1992) are about mathematical forecasts of the future. This is a hard field. It’s one people have been dreaming of doing for a long while. J Willard Gibbs, the renowned 19th century physicist who put the mathematics of thermodynamics in essentially its modern form, pondered whether a thermodynamics of history could be made. But attempts at making such predictions top out at demographic or rough economic forecasts, and for obvious reason.

    The next day Dilbert’s garbageman, the smartest person in the world, asserts the problem is chaos theory, that “any complex iterative model is no better than a wild guess”. I wouldn’t put it that way, although I’m not sure what would convey the idea within the space available. One problem with predicting complicated systems, even if they are deterministic, is that there is a difference between what we can measure a system to be and what the system actually is. And for some systems that slight error will be magnified quickly to the point that a prediction based on our measurement is useless. (Fortunately this seems to affect only interesting systems, so we can still do things like study physics in high school usefully.)

    Maria Scrivan’s Half Full for the 16th of September makes the Common Core joke. A generation ago this was a New Math joke. It’s got me curious about the history of attempts to reform mathematics teaching, and how poorly they get received. Surely someone’s written a popular or at least semipopular book about the process? I need some friends in the anthropology or sociology departments to tell, I suppose.

    In Mark Tatulli’s Heart of the City for the 16th of September, Heart is already feeling lost in mathematics. She’s in enough trouble she doesn’t recognize mathematics terms. That is an old joke, too, although I think the best version of it was done in a Bloom County with no mathematical content. (Milo Bloom met his idol Betty Crocker and learned that she was a marketing icon who knew nothing of cooking. She didn’t even recognize “shish kebob” as a cooking term.)

    Mell Lazarus’s Momma for the 16th of September sneers at the idea of predicting where specks of dust will land. But the motion of dust particles is interesting. What can be said about the way dust moves when the dust is being battered by air molecules that are moving as good as randomly? This becomes a problem in statistical mechanics, and one that depends on many things, including just how fast air particles move and how big molecules are. Now for the celebrity part of this story.

    Albert Einstein published four papers in his “Annus mirabilis” year of 1905. One of them was the Special Theory of Relativity, and another the mass-energy equivalence. Those, and the General Theory of Relativity, are surely why he became and still is a familiar name to people. One of his others was on the photoelectric effect. It’s a cornerstone of quantum mechanics. If Einstein had done nothing in relativity he’d still be renowned among physicists for that. The last paper, though, that was on Brownian motion, the movement of particles buffeted by random forces like this. And if he’d done nothing in relativity or quantum mechanics, he’d still probably be known in statistical mechanics circles for this work. Among other things this work gave the first good estimates for the size of atoms and molecules, and gave easily observable, macroscopic-scale evidence that molecules must exist. That took some work, though.

    Dave Whamond’s Reality Check for the 16th of September shows off the Metropolitan Museum of Symmetry. This is probably meant to be an art museum. Symmetries are studied in mathematics too, though. Many symmetries, the ways you can swap shapes around, form interesting groups or rings. And in mathematical physics, symmetries give us useful information about the behavior of systems. That’s enough for me to claim this comic is mathematically linked.

  • Joseph Nebus 9:45 pm on Friday, 14 November, 2014 Permalink | Reply
    Tags: Albert Einstein, , , , , , , , ,   

    Reading The Comics, November 14, 2014: Rectangular States Edition 

    I have no idea why Comic Strip Master Command decided this week should see everybody do some mathematics-themed comic strips, but, so they did, and here’s my collection of the, I estimate, six hundred comic strips that touched on something recently. Good luck reading it all.

    Samsons Dark Side of the Horse (November 10) is another entry on the theme of not answering the word problem.

    Scott Adams’s Dilbert Classics (November 10) started a sequence in which Dilbert gets told the big boss was a geometry major, so, what can he say about rectangles? Further rumors indicate he’s more a geography fan, shifting Dilbert’s topic to the “many” rectangular states of the United States. Of course, there’s only two literally rectangular states, but — and Mark Stein’s How The States Got Their Shapes contains a lot of good explanations of this — many of the states are approximately rectangular. After all, when many of the state boundaries were laid out, the federal government had only vague if any idea what the landscapes looked like in detail, and there weren’t many existing indigenous boundaries the white governments cared about. So setting a proposed territory’s bounds to be within particular lines of latitude and longitude, with some modification for rivers or shorelines or mountain ranges known to exist, is easy, and can be done with rather little of the ambiguity or contradictory nonsense that plagued the eastern states (where, say, a colony’s boundary might be defined as where a river intersects a line of latitude that in fact it never touches). And while perfect rectangularity may be achieved only by Colorado and Wyoming, quite a few states — the Dakotas, Washington, Oregon, Missisippi, Alabama, Iowa — are rectangular enough.

    Mikael Wulff and Anders Morgenthaler’s WuMo (November 10) shows that their interest in pi isn’t just a casual thing. They think about what those neglected and non-famous numbers get up to.

    Sherman does poorly with mathematic problems that look more like short stories. And don't have pictures.

    Jim Toomey’s Sherman’s Lagoon for the 11th of November, 2014. He’s got a point about pictures helping with this kind of problem.

    Jim Toomey’s Sherman’s Lagoon starts a “struggling with mathematics homework” story on the 11th, with Sherman himself stumped by a problem that “looks more like a short story” than a math problem. By the 14th Megan points out that it’s a problem that really doesn’t make sense when applied to sharks. Such is the natural hazard in writing a perfectly good word problem without considering the audience.

    Homework: Megan points out that a problem about walking in the rain with umbrellas doesn't make much sense for sharks or other underwater creatures.

    Jim Toomey’s Sherman’s Lagoon for the 14th of November, 2014.

    Mike Peters’s Mother Goose and Grimm (November 12) takes one of its (frequent) breaks from the title characters for a panel-strip-style gag about Roman numerals.

    A Roman medic calls for an IV; the nurse asks if he means this numeral 4.

    Mike Peters’s Mother Goose and Grimm for the 12th of November, 2014.

    Darrin Bell’s Candorville (November 12) starts talking about Zeno’s paradox — not the first time this month that a comic strip’s gotten to the apparent problem of covering any distance when distance is infinitely divisible. On November 13th it’s extended to covering stretches of time, which has exactly the same problem. Now it’s worth reminding people, because a stunning number of them don’t seem to understand this, that Zeno was not suggesting that there’s no such thing as motion (or that he couldn’t imagine an infinite convergent sequence; it’s easy to think of a geometric construction that would satisfy any ancient geometer); he was pointing out that there’s things that don’t make perfect sense about it. Either distance (and time) are infinitely divisible into indistinguishable units, or they are not; and either way has implications that seem contrary to the way motion works. Perhaps they can be rationalized; perhaps they can’t; but when you can find a question that’s easy to pose and hard to answer, you’re probably looking at something really worth thinking hard about.

    Bill Amend’s FoxTrot Classics (November 12, a rerun) puns on the various meanings of “irrational”. A fun little fact you might want to try proving sometime, though I wouldn’t fault you if you only tried it out for a couple specific numbers and decided the general case too much to do: any whole number — like 2, 3, 4, or so on — has a square root that’s either another whole number, or else has a square root that’s irrational. There’s not a case where, say, the square root is exactly 45.144 or something like that, though it might be close.

    Susan tries to figure out either what year she was in Grade Ten or what her age was back then. She admits she was never any good at math, although the real trouble might be she hasn't got a clear idea what she wants to calculate.

    Sandra Bell-Lundy’s Between Friends for the 13th of November, 2014.

    Sandra Bell-Lundy’sBetween Friends (November 13) shows one of those cases where mental arithmetic really is useful, as Susan tries to work out — actually, staring at it, I’m not precisely sure what she is trying to work out. Her and her coffee partner’s ages in Grade Ten, probably, or else just when Grade Ten was. That’s most likely her real problem: if you don’t know what you’re looking for it’s very difficult to find it. Don’t start calculating before you know what you’re trying to work out.

    If I wanted to work out what year was 35 years ago I’d probably just use a hack: 35 years before 2014 is one year before “35 years before 2015”, which is a much easier problem to do. 35 years before 2015 is also 20 years before 2000, which is 1980, so subtract one and you get 1979. (Alternatively, I might remember it was 35 years ago that the Buggles’ “Video Killed The Radio Star” first appeared, which I admit is not a method that would work for everyone, or for all years.) If I wanted to work out my (and my partner’s) age in Grade Ten … well, I’d use a slightly different hack: I remember very well that I was ten years old in Grade Five (seriously, the fact that twice my grade was my age overwhelmed my thinking on my tenth birthday, which is probably why I had to stay in mathematics), so, add five to that and I’d be 15 in Grade Ten.

    Bill Whitehead’s Free Range (November 13) brings up one of the most-quoted equations in the world in order to show off how kids will insult each other, which is fair enough.

    Rick Detorie’s One Big Happy (November 13), this one a rerun from a couple years ago because that’s how his strip works on Gocomics, goes to one of its regular bits of the kid Ruthie teaching anyone she can get in range, and while there’s a bit more to arithmetic than just adding two numbers to get a bigger number, she is showing off an understanding of a useful sanity check: if you add together two (positive) numbers, you have to get a result that’s bigger than either of the ones you started with. As for the 14th, and counting higher, well, there’s not much she could do about that.

    Steve McGarry’s Badlands (November 14) talks about the kind of problem people wish to have: how to win a lottery where nobody else picks the same numbers, so that the prize goes undivided? The answer, of course, is to have a set of numbers that nobody else picked, but is there any way to guarantee that? And this gets into the curious psychology of random numbers: there is absolutely no reason that 1-2-3-4-5-6, or for that matter 7-8-9-10-11-12, would not come up just as often as, say, 11-37-39-51-52-55, but the latter set looks more random. But we see some strings of numbers as obviously a pattern, while others we don’t see, and we tend to confuse “we don’t know the pattern” with “there is no pattern”. I have heard the lore that actually a disproportionate number of people pick such obvious patterns like 1-2-3-4-5-6, or numbers that form neat pictures on a lottery card, no doubt cackling at how much more clever they are than the average person, and guaranteeing that if such a string ever does come out there’ll a large number of very surprised lottery winners. All silliness, really; the thing to do, obviously, is buy two tickets with the exact same set of numbers, so that if you do win, you get twice the share of anyone else, unless they’ve figured out the same trick.

  • Joseph Nebus 2:59 am on Monday, 30 December, 2013 Permalink | Reply
    Tags: Albert Einstein, , , , ,   

    Reading the Comics, December 29, 2013 

    I haven’t quite got seven comics mentioning mathematics themes this time around, but, it’s so busy the end of the year that maybe it’s better publishing what I have and not worrying about an arbitrary quota like mine.

    Wuff and Morgenthaler’s WuMo (December 16) uses a spray of a bit of mathematics to stand in for “something just too complicated to understand”, and even uses a caricature of Albert Einstein to represent the person who’s just too smart to be understood. I’m a touch disappointed that, as best I can tell, the equations sprayed out don’t mean anything; I’ve enjoyed WuMo — a new comic to North American audiences — so far and kind of expected they would get an irrelevant detail like that plausibly right.

    I’m also interested that sixty years after his death the portrait of Einstein still hasn’t been topped as an image for The Really, Really Smart Guy. Possibly nobody since him has managed to combine being both incredibly important — even if it weren’t for relativity, Einstein would be an important figure in science for his work in quantum mechanics, and if he didn’t have relativity or quantum mechanics, he’d still be important for statistical mechanics — and iconic-looking, which I guess really means he let his hair grow wild. I wonder if Stephen Hawking will be able to hold some of that similar pop cultural presence.

    (More …)

    • ivasallay 7:59 am on Monday, 30 December, 2013 Permalink | Reply

      Thank you for posting these! Some of these comic strips are brand new to me. I can see that I have really been missing out. I had no problem seeing Hillary Price’s Rhymes with Orange comic even though I’m not a subscriber. It took me a few second to get the joke: 28 is 4 in dog years. However, since 14 is also 2 in dog years, this dog isn’t consistent with his number system.


    • elkement 7:58 pm on Tuesday, 31 December, 2013 Permalink | Reply

      Thanks for your efforts in providing these reports regularly!!
      Happy New Year, Joseph!


      • Joseph Nebus 5:58 pm on Friday, 3 January, 2014 Permalink | Reply

        Aw, thank you. And thank you for writing so often, also. Happy new year, I hope.


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