Comic Strip Master Command wanted to give me a break as I ready for the All 2020 A-to-Z. I appreciate the gesture, especially given the real-world events of the past week. I get to spend this week mostly just listing appearances, even if they don’t inspire deeper thought.
Gordon Bess’s vintage Redeye for the 24th has one of his Cartoon Indians being lousy at counting. Talking about his failures at arithmetic, with how he doesn’t count six shots off well. There’s a modest number of things that people are, typically, able to perceive at once. Six can be done, although it’s easy for a momentary loss of focus to throw you off. This especially for things that have to be processed in sequence, rather than perceived all together.
Wulff and Morgenthaler’s WuMo for the 24th shows a parent struggling with mathematics, billed as part of “the terrible result of homeschooling your kids”. It’s a cameo appearance. It’d be the same if Mom were struggling with history or English. This is just quick for the comic strip reader to understand.
Andrés J. Colmenares’s Wawawiwa for the 25th sets several plants in a classroom. They’re doing arithmetic. This, too, could be any course; it just happens to be mathematics.
Sam Hurt’s Eyebeam for the 25th is built on cosmology. The subject is a blend of mathematics, observation, and metaphysics. The blackboard full of mathematical symbols gets used as shorthand for describing the whole field, not unfairly. The symbols as expressed don’t come together to mean anything. I don’t feel confident saying they don’t mean anything, though.
The last full week of the year had, again, comic strips that mostly mention mathematics without getting into detail. That’s all right. I have a bit of a cold so I’m happy not to have to compose thoughts about too many of them.
Percy Crosby’s Skippy for the 23rd has Skippy and Sookie doing the sort of story problem arithmetic of working out a total bill. The strip originally ran the 11th of August, 1932.
Cy Olson’s Office Hours for the 24th, which originally ran the 14th of October, 1971, comes the nearest to having enough to talk about here. The secretary describes having found five different answers in calculating the profits and so used the highest one. The joke is on incompetent secretaries, yes. But it is respectable, if trying to understand something very complicated, to use several different models for what one wants to know. These will likely have different values, although how different they are, and how changes in one model tracks changes in another, can be valuable. We’re accustomed to this, at least in the United States, by weather forecasts: any local weather report will describe expected storms by different models. These use different ideas about how much moisture moves into the air, how fast raindrops will form (a very difficult problem), how winds will shift, that sort of thing. It’s defensible to make similar different models for reporting the health of a business, particularly if company owns things with a price that can’t be precisely stated.
Marguerite Dabaie and Tom Hart’s Ali’s House for the 24th continues a story from the week before in which a character imagines something tossing us out of three-dimensional space. A seven-dimensional space is interesting mathematically. We can define a cross product between vectors in three-dimensional space and in seven-dimensional space. Most other spaces don’t allow something like a cross product to be coherently defined. Seven-dimensional space also allows for something called the “exotic sphere”, which I hadn’t heard of before either. It’s a structure that’s topologically a sphere, but that has a different kind of structure. This isn’t unique to seven-dimensional space. It’s not known whether four-dimensional space has exotic spheres, although many spaces higher than seven dimensions have them.
Part of my work reading lots of comic strips is to report the ones that mention mathematics, even if the mention is so casual there’s no building an essay around them. Here’s the minor mathematics mentions of last week.
Bob Scott’s Bear With Me for the 3rd has Molly and the Bear in her geometry class. Bear’s shown as surprised the kids are still learning Euclidean geometry, which is your typical joke about the character with a particularly deep knowledge of a narrow field.
Gary Brookins’s Pluggers for the 5th is the old joke about how one never uses algebra in real life. The strip is not dated as a repeat. But I’d be surprised if this joke hasn’t run in Pluggers before. I didn’t have a tag for Pluggers before, but there was a time I wasn’t tagging the names of comic strips.
While there were a good number of comic strips to mention mathematics this past week, there were only a few that seemed substantial to me. This works well enough. This probably is going to be the last time I keep the Reading the Comics post until after Sunday, at least until the Fall 2019 A To Z is finished.
Gordon Bess’s Redeye rerun for the 18th is a joke building on animals’ number sense. And, yeah, about dumb parents too. Horses doing arithmetic have a noteworthy history. But more in the field of understanding how animals learn, than in how they do arithmetic. In particular in how animals learn to respond to human cues, and how slight a cue has to be to be recognized and acted on. I imagine this reflects horses being unwieldy experimental animals. Birds — pigeons and ravens, particularly — make better test animals.
Art Sansom and Chip Sansom’s The Born Loser for the 18th gives a mental arithmetic problem. It’s a trick question, yes. But Brutus gives up too soon on what the problem is supposed to be. Now there’s no calculating, in your head, exactly how many seconds are in a year; that’s just too much work. But an estimate? That’s easy.
At least it’s easy if you remember one thing: a million seconds is about eleven and a half days. I find this easy to remember because it’s one of the ideas used all the time to express how big a million, a billion, and a trillion are. A million seconds are about eleven and a half days. A billion seconds are a little under 32 years. A trillion seconds are about 32,000 years, which is about how long it’s been since the oldest known domesticated dog skulls were fossilized. I’m sure that gives everyone a clear idea of how big a trillion is. The important thing, though, is that a million seconds is about eleven and a half days.
So. Think of the year. There are — as the punch line to Hattie’s riddle puts it — twelve 2nd’s in the year. So there are something like a million seconds spent each year on days that are the 2nd of the month. There about a million seconds spent each year on days that are the 1st of the month, too. There are about a million seconds spent each year on days that are the 3rd of the month. And so on. So, there’s something like 31 million seconds in the year.
You protest. There aren’t a million seconds in twelve days; there’s a million seconds in eleven and a half days. True. Also there aren’t 31 days in every month; there’s 31 days in seven months of the year. There’s 30 days in four months, and 28 or 29 in the remainder. That’s fine. This is mental arithmetic. I’m undercounting the number of seconds by supposing that a million seconds makes twelve days. I’m overcounting the number of seconds by supposing that there are twelve months of 31 days each. I’m willing to bet this undercount and this overcount roughly balance out. How close do I get?
There are 31,536,000 seconds in a common year. That is, a non-leap-year. So “31 million” is a bit low. But it’s not bad for working without a calculator.
Ryan North’s Dinosaur Comics for the 19th lays on us the Eubulides Paradox. It’s traced back to the fourth century BCE. Eubulides was a Greek philosopher, student of “Not That” Euclid of Megara. We know Eubulides for a set of paradoxes, including the Sorites paradox. As T-Rex’s friends point out, we’ve all heard this paradox. We’ve all gone on with our lives, knowing that the person who said it wanted us to say they were very clever. Fine.
But if we take this seriously we find … this keeps not being simple. We can avoid the problem by declaring self-referential statements exist outside of truth or falsity. This forces us to declare the sentence “this sentence is true” can’t be true. This seems goofy. We can avoid the problem by supposing there are things that are neither true nor false. That solves our problem here at the mere cost of ruining our ability to prove stuff by contradiction. There’s a lot of stuff we prove by contradiction. It’s hard to give that all up for this (Although, so far as I’m aware, anything that can be proved by contradiction can also be proven by a direct line of reasoning. The direct line may just be tedious.) We can solve this problem by saying that our words are fuzzy imprecise things. This is true enough, as see any time my love and I debate how many things are in “a couple of things”. But declaring that we just can’t express the problem well enough to answer it seems like running away from the question. We can resolve things by accepting there are limits to what can be proved by logic. Gödel’s Incompleteness Theorem shows that any interesting enough logic system has statements that are true but unprovable. A version of this paradox helps us get to this interesting conclusion.
So this is one of those things it should be easy to laugh off, but why it should be easy is hard.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st is about the other great logic problem of the 20th century. The Halting Problem here refers to Turing Machines. This is the algorithmic model for computing devices. It’s rather abstract, so the model won’t help you with your C++ homework, but nothing will. But it turns out we can represent a computer running a program as a string of cells. Each cell holds one of a couple possible values. The program is a series of steps. Each step starts at one cell. The program resets the value of that cell to something dictated by the algorithm. Then, the program moves focus to another cell, again as the algorithm dictates. Do enough of this and you get SimCity 2000. I don’t know all the steps in-between.
So. The Halting Program is this: take a program. Run it. What happens in the long run? Well, it does something or other, yes. But there’s three kinds of things it can do. It can run for a while and then finish, that is, ‘halt’. It can run for a while and then get into a repeating loop, after which it repeats things forever. It can run forever without repeating itself. (Yeah, I see the structural resemblance to terminating decimals, repeating decimals, and irrational numbers too, but I don’t know of any link there.) The Halting Problem asks, if all we know is the algorithm, can we know what happens? Can we say for sure the program will always end, regardless of what the data it works on are? Can we say for sure the program won’t end if we feed it the right data to start?
If the program is simple enough — and it has to be extremely simple — we can say. But, basically, if the program is complicated enough to be even the least bit interesting, it’s impossible to say. Even just running the program isn’t enough: how do you know the difference between a program that takes a trillion seconds to finish and one that never finishes?
For human needs, yes, a program that needs a trillion seconds might as well be one that never finishes. Which is not precisely the joke Weinersmith makes here, but is circling around similar territory.
So last week there were only a handful of comic strips which mentioned mathematics in any detail. That is, that brought up some point that I could go on about for a paragraph or so. There were more that had some marginal mathematics content. I gather them here for the interested.
Gordon Bess’s Redeye rerun for the 7th mentions mathematics as the homework that the chief is helping his son with. It could be any subject, but arithmetic is easy to fit into one panel of comic strip. And it’s also easy to establish that the work is on a low level. The comic originally ran the 18th of February, 1973.
John McPherson’s Close to Home for the 11th mentions percentages. The joke’s built on doing a meaningless calculation. And a bit of convention, in which the label has been reduced to the point people could mis-read it. You just know this guy would tell the “scanner didn’t pick it up, it must be free” joke if he thought of it that fast.
Paige Braddock’s Jane’s World for the 11th is part of a sequence from 2002 in which Jane concludes the problems in her life came from the introduction of algebra. Her niece is having fun with algebra, a thing I understand. Algebra can be a more playful, explorative kind of mathematics than you get with, like, long division. For some people it’s liberating. This one’s a new tag, so I’m sure to be surprised that I have ever mentioned Jane’s World sometime in the future.
Wiley Miller’s Non Sequitur for the 11th presents a Sphere of Serenity. Or, as Danae’s horse points out, a Cube of Serenity. There are ways that the difference between a sphere and a cube becomes nothing. If the cube and the sphere have infinitely great extent, for example, then there’s no observable difference between the shapes. Or if we use certain definitions of distance then the sphere — as in, the points all an equal distance from a center — can be indistinguishable from a cube. That’s not what the comic is going for.
People reading my Reading the Comics post Sunday maybe noticed something. I mean besides my correct, reasonable complaining about the Comics Kingdom redesign. That is that all the comics were from before the 30th of March. That is, none were from the week before the 7th of April. The last full week of March had a lot of comic strips. The first week of April didn’t. So things got bumped a little. Here’s the results. It wasn’t a busy week, not when I filter out the strips that don’t offer much to write about. So now I’m stuck for what to post Thursday.
The strip explains things well enough. The Library holds every book that will ever be written. In the original story there are some constraints. Particularly, all the books are 410 pages. If you wanted, say, a 600-page book, though, you could find one book with the first 410 pages and another book with the remaining 190 pages and then some filler. The catch, as explained in the story and in the comic strip, is finding them. And there is the problem of finding a ‘correct’ text. Every possible text of the correct length should be in there. So every possible book that might be titled Mark Twain vs Frankenstein, including ones that include neither Mark Twain nor Frankenstein, is there. Which is the one you want to read?
Henry Scarpelli and Craig Boldman’s Archie for the 4th features an equal-divisions problem. In principle, it’s easy to divide a pizza (or anything else) equally; that’s what we have fractions for. Making them practical is a bit harder. I do like Jughead’s quick work, though. It’s got the slight-of-hand you expect from stage magic.
Scott Hilburn’s The Argyle Sweater for the 4th takes place in an algebra class. I’m not sure what algebraic principle demonstrates, but it probably came from somewhere. It’s 4,829,210. The exponentials on the blackboard do cue the reader to the real joke, of the sign reading “kick10 me”. I question whether this is really an exponential kicking situation. It seems more like a simple multiplication to me. But it would be harder to make that joke read clearly.
Tony Cochran’s Agnes for the 5th is part of a sequence investigating how magnets work. Agnes and Trout find just … magnet parts inside. This is fair. It’s even mathematics.
Thermodynamics classes teach one of the great mathematical physics models. This is about what makes magnets. Magnets are made of … smaller magnets. This seems like question-begging. Ultimately you get down to individual molecules, each of which is very slightly magnetic. When small magnets are lined up in the right way, they can become a strong magnet. When they’re lined up in another way, they can be a weak magnet. Or no magnet at all.
How do they line up? It depends on things, including how the big magnet is made, and how it’s treated. A bit of energy can free molecules to line up, making a stronger magnet out of a weak one. Or it can break up the alignments, turning a strong magnet into a weak one. I’ve had physics instructors explain that you could, in principle, take an iron rod and magnetize it just by hitting it hard enough on the desk. And then demagnetize it by hitting it again. I have never seen one do this, though.
This is more than just a physics model. The mathematics of it is … well, it can be easy enough. A one-dimensional, nearest-neighbor model, lets us describe how materials might turn into magnets or break apart, depending on their temperature. Two- or three-dimensional models, or models that have each small magnet affected by distant neighbors, are harder.
I’d promised on Sunday the remainder of last week’s mathematically-themed comic strips. I got busy with house chores yesterday and failed to post on time. That’s why this is late. It’s only a couple of comics here, but it does include my list of strips that I didn’t think were on-topic enough. You might like them, or be able to use them, yourself, though.
Niklas Eriksson’s Carpe Diem for the 14th depicts a kid enthusiastic about the abilities of mathematics to uncover truths. Suppressed truths, in this case. Well, it’s not as if mathematics hasn’t been put to the service of conspiracy theories before. Mathematics holds a great promise of truth. Answers calculated correctly are, after all, universally true. They can also offer a hypnotizing precision, with all the digits past the decimal point that anyone could want. But one catch among many is whether your calculations are about anything relevant to what you want to know. Another is whether the calculations were done correctly. It’s easy to make a mistake. If one thinks one has found exciting results it’s hard to imagine even looking for one.
You can’t use shadow analysis to prove the Moon landings fake. But the analysis of shadows can be good mathematics. It can locate things in space and in time. This is a kind of “inverse problem”: given this observable result, what combinations of light and shadow and position would have caused that? And there is a related problem. Johannes Vermeer produced many paintings with awesome, photorealistic detail. One hypothesis for how he achieved this skill is that he used optical tools, including a camera obscura and appropriate curved mirrors. So, is it possible to use the objects shown in perspective in his paintings to project where the original objects had to be, and where the painter had to be, to see them? We can calculate this, at least. I am not well enough versed in art history to say whether we have compelling answers.
Art Sansom and Chip Sansom’s The Born Loser for the 16th is the rare Roman Numerals joke strip that isn’t anthropomorphizing the numerals. Or a play on how the numerals used are also letters. But yeah, there’s not much use for them that isn’t decorative. Hindu-Arabic numerals have great advantages in compactness, and multiplication and division, and handling fractions of a whole number. And handling big numbers. Roman numerals are probably about as good for adding or subtracting small numbers, but that’s not enough of what we do anymore.
And past that there were three comic strips that had some mathematics element. But they were slight ones, and I didn’t feel I could write about them at length. Might like them anyway. Gordon Bess’s Redeye for the 10th of February, and originally run the 24th of September, 1972, has the start of a word problem as example of Pokey’s homework. Mark Litzler’s Joe Vanilla for the 11th has a couple scientist-types standing in front of a board with some mathematics symbols. The symbols don’t quite parse, to me, but they look close to it. Like, the line about is close to what one would write for the Fourier transformation of the function named l. It would need to be more like and even then it wouldn’t be quite done. So I guess Litzler used some actual reference but only copied as much as worked for the composition. (Which is not a problem, of course. The mathematics has no role in this strip beyond its visual appeal, so only the part that looks good needs to be there.) The Fourier transform’s a commonly-used trick; among many things, it lets us replace differential equations (hard, but instructive, and everywhere) with polynomials (comfortable and familiar and well-understood). Finally among the not-quite-comment-worthy is Pascal Wyse and Joe Berger’s Berger And Wyse for the 12th, showing off a Venn Diagram for its joke.
Ah, yes, so, in the midst of feeling all proud that I’d gotten my Reading the Comics workflow improved, I went out to do my afternoon chores without posting the essay. I’m embarrassed. But it really only affects me looking at the WordPress Insights page. It publishes this neat little calendar-style grid that highlights the days when someone’s posted and this breaks up the columns. This can only unnerve me. I deserve it.
Tom Thaves’s Frank and Ernest for the 8th of February is about the struggle to understand zero. As often happens, the joke has a lot of truth to it. Zero bundles together several ideas, overlapping but not precisely equal. And part of that is the idea of “nothing”. Which is a subtly elusive concept: to talk about the properties of a thing that does not exist is hard. As adults it’s easy to not notice this anymore. Part’s likely because mastering a concept makes one forget what it took to understand. Part is likely because if you don’t have to ponder whether the “zero” that’s “one less than one” is the same as the “zero” that denotes “what separates the count of thousands from the count of tens in the numeral 2,038” you might not, and just assume you could explain the difference or similarity to someone who has no idea.
John Zakour and Scott Roberts’s Maria’s Day for the 8th has maria and another girl bonding over their hatred of mathematics. Well, at least they’re getting something out of it. The date in the strip leads me to realize this is probably a rerun. I’m not sure just when it’s from.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th proposes a prank based on mathematical use of the word “arbitrarily”. This is a word that appears a lot in analysis, and the strip makes me realize I’m not sure I can give a precise definition. An “arbitrarily large number”, for example, would be any number that’s large enough. But this also makes me realize I’m not sure precisely what joke Weinersmith is going for. I suppose that if someone were to select an arbitrarily large number they might pick 53, or a hundred, or million billion trillion. I suppose Weinersmith’s point is that in ordinary speech an arbitrarily made choice is one selection from all the possible alternatives. In mathematical speech an arbitrarily made choice reflects every possible choice. To speak of an arbitrarily large number is to say that whatever selection is made, we can go on to show this interesting stuff is true. We’d typically like to prove the most generically true thing possible. But picking a single example can be easier to prove. It can certainly be easier to visualize. 53 is probably easier to imagine than “every number 52 or larger”, for example.
Ted Shearer’s Quincy for the 16th of December, 1978 was rerun the 9th of February. It just shows Quincy at work on his mathematics homework, and considering dedicating it to his grandmother. Mathematics books have dedications, just as any other book does. I’m not aware of dedications of proofs or other shorter mathematics works, but there’s likely some. There’s often a note of thanks, usually given to people who’ve made the paper’s writers think harder about the subjects. But I don’t think there’s any reason a paper wouldn’t thank someone who provided “mere” emotional support. I just don’t have examples offhand.
Jef Mallet’s Frazz for the 9th looks like one of those creative-teaching exercises I sometimes see in Mathematics Education Twitter: the teacher gives answers and the students come up with story problems to match. That’s not a bad project. I’m not sure how to grade it, but I haven’t done anything that creative when I’ve taught. I’m sorry I haven’t got more to say about it since the idea seems fun.
Gordon Bess’s Redeye for the 30th of September, 1971 was rerun the 10th. It’s a bit of extremely long division and I don’t blame Pokey for giving up on that problem. Starting from 5,967,342 divided by 973 I’d say, well, that’s about six million divided by a thousand, so the answer should be near six thousand. I don’t think the last digits of 2 and 3 suggest anything about what the final digit should be, if this divides evenly. So the only guidance I have is that my answer ought to be around six thousand and then we have to go into actually working. It turns out that 973 doesn’t go into 5,967,342 a whole number of times, so I sympathize more with Pokey. The answer is a little more than 6,132.9311.
So one little secret of my Reading the Comics posts is I haven’t been writing them in a way that makes sense to me. To me, I should take each day’s sufficiently relevant comics, describe them in a paragraph or two, and then have a nice pile of text all ready for the posting Sunday and, if need be, later. I haven’t been doing that. I’ve let links pile up until Friday or Saturday, and then try to process them all, and if you’ve ever wondered why the first comic of the week gets 400 words about some subtlety while the last gets “this is a comic that exists”, there you go. This time around, let me try doing each day’s strips per day and see how that messes things up.
Jef Mallett’s Frazz for the 14th of January is another iteration of the “when will we ever use mathematics” complaint. The answer of “you’ll use it on the test” is unsatisfactory. But somehow, the answer of “you’ll use it to think deeply about something you had never considered before” also doesn’t satisfy. Anyway I’d like to see the idea that education is job-training abolished; I think it should be about making a person conversant with the history of human thought. That can’t be done perfectly, and we might ask whether factoring 32 is that important a piece, but it should certainly be striven for.
Ham’s Life on Earth for the 14th is a Gary Larsonesque riff on that great moment of calculus and physics history, Newton’s supposition that gravity has to follow a universally true law. I’m not sure this would have made my cut if I reviewed a week’s worth of strips at a time. Hm.
Mason Mastroianni’s B.C. for the 15th is a joke about story problem construction, and how the numbers in a story problem might be obvious nonsense. It’s also a cheap shot at animal hoarders, I suppose, but that falls outside my territory here.
Anthony Blades’s Bewley rerun for the 15th riffs on the natural number sense we all have. And we do have a number sense, remarkably. We might not be able to work out 9 times 6 instantly. But asked to pick from a list of possible values, we’re more likely to think that 58 is credible than that 78 or 38 are. It’s quite imprecise, but isn’t it amazing that it’s there at all?
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 16th is maybe marginal to include, too. It’s about the kinds of logic puzzles that mathematicians grow up reading and like to pass around. And the way you can fake out someone by presenting a problem with too obvious a solution. It’s not just professors who’ll be stymied by having the answer look too obvious, by the way. Everyone’s similarly vulnerable. To see anything, including an abstract thing like the answer to a puzzle, you need some idea of what you are looking at. If you don’t think the answer could be something that simple, you won’t see it there.
Elzie Segar’s Thimble Theatre for the 10th of August, 1931, was also reprinted the 17th. It’s an old gag, even back when it was first run. But I suppose there’s some numerical-conversion mathematics to wring out of it. Given the rate of exchange, a pezozee would seem to be 24 pazimees. I’m not sure we need so many units in-between the pazimee and the pezozee, but perhaps King Blozo’s land set its units in a time when fractions were less familiar to the public. The punch line depends on the pazimee being worth nothing and, taken literally, that has sad implications for the pezozee too. If you take the King as speaking roughly, though, sixteen times a small amount is … at least a less small amount. It wouldn’t take many doublings to go from an infinitesimally tiny sum to a respectable one.
And it turns out there were enough comic strips I need to split this into two segments. So I should schedule that to appear. It’s already written and everything.
If there was one major theme for this week it was my confidence that there must be another source of Jumble strips out there. I haven’t found it, but I admit not making it a priority either. The official Jumble site says I can play if I activate Flash, but I don’t have enough days in the year to keep up with Flash updates. And that doesn’t help me posting mathematics-relevant puzzles here anyway.
Mark Anderson’s Andertoons for January 29th satisfies my Andertoons need for this week. And it name-drops the one bit of geometry everyone remembers. To be dour and humorless about it, though, I don’t think one could likely apply the Pythagorean Theorem. Typically the horizontal axis and the vertical axis in a graph like this measure different things. Squaring the different kinds of quantities and adding them together wouldn’t mean anything intelligible. What would even be the square root of (say) a squared-dollars-plus-squared-weeks? This is something one learns from dimensional analysis, a corner of mathematics I’ve thought about writing about some. I admit this particular insight isn’t deep, but everything starts somewhere.
Norm Feuti’s Gil rerun for the 30th is a geometry name-drop, listing it as the sort of category Jeopardy! features. Gil shouldn’t quit so soon. The responses for the category are “What is the Pythagorean Theorem?”, “What is acute?”, “What is parallel?”, “What is 180 degrees?” (or, possibly, 360 or 90 degrees), and “What is a pentagon?”.
Terri Libenson’s Pajama Diaries for the 1st of February shows off the other major theme of this past week, which was busy enough that I have to again split the comics post into two pieces. That theme is people getting basic mathematics wrong. Mostly counting. (You’ll see.) I know there’s no controlling what people feel embarrassed about. But I think it’s unfair to conclude you “can no longer” do mathematics in your head because you’re not able to make change right away. It’s normal to be slow or unreliable about something you don’t do often. Inexperience and inability are not the same thing, and it’s unfair to people to conflate them.
Gordon Bess’s Redeye for the 21st of September, 1970, got rerun the 1st of February. And it’s another in the theme of people getting basic mathematics wrong. And even more basic mathematics this time. There’s more problems-with-counting comics coming when I finish the comics from the past week.
Dave Whamond’s Reality Check for the 1st hopes that you won’t notice the label on the door is painted backwards. Just saying. It’s an easy joke to make about algebra, also, that it should put letters in to perfectly good mathematics. Letters are used for good reasons, though. We’ve always wanted to work out the value of numbers we only know descriptions of. But it’s way too wordy to use the whole description of the number every time we might speak of it. Before we started using letters we could use placeholder names like “re”, meaning “thing” (as in “thing we want to calculate”). That works fine, although it crashes horribly when we want to track two or three things at once. It’s hard to find words that are decently noncommittal about their values but that we aren’t going to confuse with each other.
So the alphabet works great for this. An individual letter doesn’t suggest any particular number, as long as we pretend ‘O’ and ‘I’ and ‘l’ don’t look like they do. But we also haven’t got any problem telling ‘x’ from ‘y’ unless our handwriting is bad. They’re quick to write and to say aloud, and they don’t require learning to write any new symbols.
Later, yes, letters do start picking up connotations. And sometimes we need more letters than the Roman alphabet allows. So we import from the Greek alphabet the letters that look different from their Roman analogues. That’s a bit exotic. But at least in a Western-European-based culture they aren’t completely novel. Mathematicians aren’t really trying to make this hard because, after all, they’re the ones who have to deal with the hard parts.
Bu Fisher’s Mutt and Jeff rerun for the 2nd is another of the basic-mathematics-wrong jokes. But it does get there by throwing out a baffling set of story-problem-starter points. Particularly interesting to me is Jeff’s protest in the first panel that they couldn’t have been doing 60 miles an hour as they hadn’t been out an hour. It’s the sort of protest easy to use as introduction to the ideas of average speed and instantaneous speed and, from that, derivatives.
So for all I worried about the Gocomics.com redesign it’s not bad. The biggest change is it’s removed a side panel and given the space over to the comics. And while it does show comics you haven’t been reading, it only shows one per day. One week in it apparently sticks with the same comic unless you choose to dismiss that. So I’ve had it showing me The Comic Strip That Has A Finale Every Day as a strip I’m not “reading”. I’m delighted how thisbreaks the logic about what it means to “not read” an “ongoing comic strip”. (That strip was a Super-Fun-Pak Comix offering, as part of Ruben Bolling’s Tom the Dancing Bug. It was turned into a regular Gocomics.com feature by someone who got the joke.)
Comic Strip Master Command responded to the change by sending out a lot of comic strips. I’m going to have to divide this week’s entry into two pieces. There’s not deep things to say about most of these comics, but I’ll make do, surely.
Julie Larson’s Dinette Set rerun for the 8th is about one of the great uses of combinatorics. That use is working out how the number of possible things compares to the number of things there are. What’s always staggering is that the number of possible things grows so very very fast. Here one of Larson’s characters claims a science-type show made an assertion about the number of possible ideas a brain could hold. I don’t know if that’s inspired by some actual bit of pop science. I can imagine someone trying to estimate the number of possible states a brain might have.
And that has to be larger than the number of atoms in the universe. Consider: there’s something less than a googol of atoms in the universe. But a person can certainly have the idea of the number 1, or the idea of the number 2, or the idea of the number 3, or so on. I admit a certain sameness seems to exist between the ideas of the numbers 2,038,412,562,593,604 and 2,038,412,582,593,604. But there is a difference. We can out-number the atoms in the universe even before we consider ideas like rabbits or liberal democracy or jellybeans or board games. The universe never had a chance.
Or did it? Is it possible for a number to be too big for the human brain to ponder? If there are more digits in the number than there are atoms in the universe we can’t form any discrete representation of it, after all. … Except that we kind of can. For example, “the largest prime number less than one googolplex” is perfectly understandable. We can’t write it out in digits, I think. But you now have thought of that number, and while you may not know what its millionth decimal digit is, you also have no reason to care what that digit is. This is stepping into the troubled waters of algorithmic complexity.
Bob Weber Jr’s Slylock Fox and Comics for Kids for the 9th is built on soap bubbles. The link between the wand and the soap bubble vanishes quickly once the bubble breaks loose of the wand. But soap films that keep adhered to the wand or mesh can be quite strangely shaped. Soap films are a practical example of a kind of partial differential equations problem. Partial differential equations often appear when we want to talk about shapes and surfaces and materials that tug or deform the material near them. The shape of a soap bubble will be the one that minimizes the torsion stresses of the bubble’s surface. It’s a challenge to solve analytically. It’s still a good challenge to solve numerically. But you can do that most wonderful of things and solve a differential equation experimentally, if you must. It’s old-fashioned. The computer tools to do this have gotten so common it’s hard to justify going to the engineering lab and getting soapy water all over a mathematician’s fingers. But the option is there.
Gordon Bess’s Redeye rerun from the 28th of August, 1970, is one of a string of confused-student jokes. (The strip had a Generic Comedic Western Indian setting, putting it in the vein of Hagar the Horrible and other comic-anachronism comics.) But I wonder if there are kids baffled by numbers getting made several different ways. Experience with recipes and assembly instructions and the like might train someone to thinking there’s one correct way to make something. That could build a bad intuition about what additions can work.
Corey Pandolph’s Barkeater Lake rerun for the 9th just name-drops algebra. And that as a word that starts with the “alj” sound. So far as I’m aware there’s not a clear etymological link between Algeria and algebra, despite both being modified Arabic words. Algebra comes from “al-jabr”, about reuniting broken things. Algeria comes from Algiers, which Wikipedia says derives from `al-jaza’ir”, “the Islands [of the Mazghanna tribe]”.
Guy Gilchrist’s Nancy for the 9th is another mathematics-cameo strip. But it was also the first strip I ran across this week that mentioned mathematics and wasn’t a rerun. I’ll take it.
Donna A Lewis’s Reply All for the 9th has Lizzie accuse her boyfriend of cheating by using mathematics in Scrabble. He seems to just be counting tiles, though. I think Lizzie suspects something like Blackjack card-counting is going on. Since there are only so many of each letter available knowing just how many tiles remain could maybe offer some guidance how to play? But I don’t see how. In Blackjack a player gets to decide whether to take more cards or not. Counting cards can suggest whether it’s more likely or less likely that another card will make the player or dealer bust. Scrabble doesn’t offer that choice. One has to refill up to seven tiles until the tile bag hasn’t got enough left. Perhaps I’m overlooking something; I haven’t played much Scrabble since I was a kid.
Perhaps we can take the strip as portraying the folk belief that mathematicians get to know secret, barely-explainable advantages on ordinary folks. That itself reflects a folk belief that experts of any kind are endowed with vaguely cheating knowledge. I’ll admit being able to go up to a blackboard and write with confidence a bunch of integrals feels a bit like magic. This doesn’t help with Scrabble.
Gordon Bess’s Redeye continued the confused-student thread on the 29th of August, 1970. This one’s a much older joke about resisting word problems.
Ryan North’s Dinosaur Comics rerun for the 10th talks about multiverses. If we allow there to be infinitely many possible universes that would suggest infinitely many different Shakespeares writing enormously many variations of everything. It’s an interesting variant on the monkeys-at-typewriters problem. I noticed how T-Rex put Shakespeare at typewriters too. That’ll have many of the same practical problems as monkeys-at-typewriters do, though. There’ll be a lot of variations that are just a few words or a trivial scene different from what we have, for example. Or there’ll be variants that are completely uninteresting, or so different we can barely recognize them as relevant. And that’s if it’s actually possible for there to be an alternate universe with Shakespeare writing his plays differently. That seems like it should be possible, but we lack evidence that it is.