Reading the Comics, December 5, 2016: Cameo Appearances Edition


Comic Strip Master Command sent a bunch of strips my way this past week. They’ll get out to your way over this week. The first bunch are all on Gocomics.com, so I don’t feel quite fair including the strips themselves. This set also happens to be a bunch in which mathematics gets a passing mention, or is just used because they need some subject and mathematics is easy to draw into a joke. That’s all right.

Jef Mallet’s Frazz for the 4th uses blackboard arithmetic and the iconic minor error of arithmetic. It’s also strikingly well-composed; look at the art from a little farther away. Forgetting to carry the one is maybe a perfect minor error for this sort of thing. Everyone does it, experienced mathematicians included. It’s very gradable. When someone’s learning arithmetic making this mistake is considered evidence that someone doesn’t know how to add. When someone’s learned it, making the mistake isn’t considered evidence the person doesn’t know how to add. A lot of mistakes work that way, somehow.

Rick Stromoski’s Soup to Nutz for the 4th name-drops Fundamentals of Algebra as a devilish, ban-worthy book. Everyone feels that way. Mathematics majors get that way around two months in to their Introduction To Not That Kind Of Algebra course too. I doubt Stromoski has any particular algebra book in mind, but it doesn’t matter. The convention in mathematics books is to make titles that are ruthlessly descriptive, with not a touch of poetry to them. Among the mathematics books I have on my nearest shelf are Resnikoff and Wells’s Mathematics in Civilization; Koks’ Explorations in Mathematical Physics: The Concepts Behind An Elegant Language; Enderton’s A Mathematical Introduction To Logic; Courant, Robbins, and Stewart’s What Is Mathematics?; Murasagi’s Knot Theory And Its Applications; Nishimori’s Statistical Physics of Spin Glasses and Information Processing; Brush’s The Kind Of Motion We Call Heat, and so on. Only the Brush title has the slightest poetry to it, and it’s a history (of thermodynamics and statistical mechanics). The Courant/Robbins/Stewart has a title you could imagine on a bookstore shelf, but it’s also in part a popularization.

It’s the convention, and it’s all right in its domain. If you are deep in the library stacks and don’t know what a books is about, the spine will tell you what the subject is. You might not know what level or depth the book is in, but you’ll know what the book is. The down side is if you remember having liked a book but not who wrote it you’re lost. Methods of Functional Analysis? Techniques in Modern Functional Analysis? … You could probably make a bingo game out of mathematics titles.

Johnny Hart’s Back to B.C. for the 5th, a rerun from 1959, plays on the dawn of mathematics and the first thoughts of parallel lines. If parallel lines stir feelings in people they’re complicated feelings. One’s either awed at the resolute and reliable nature of the lines’ interaction, or is heartbroken that the things will never come together (or, I suppose, break apart). I can feel both sides of it.

Dave Blazek’s Loose Parts for the 5th features the arithmetic blackboard as inspiration for a prank. It’s the sort of thing harder to do with someone’s notes for an English essay. But, to spoil the fun, I have to say in my experience something fiddled with in the middle of a board wouldn’t even register. In much the way people will read over typos, their minds seeing what should be there instead of what is, a minor mathematical error will often not be seen. The mathematician will carry on with what she thought should be there. Especially if the error is a few lines back of the latest work. Not always, though, and when it doesn’t it’s a heck of a problem. (And here I am thinking of the week, the week, I once spent stymied by a problem because I was differentiating the function ex wrong. The hilarious thing here is it is impossible to find something easier to differentiate than ex. After you differentiate it correctly you get ex. An advanced squirrel could do it right, and here I was in grad school doing it wrong.)

Nate Creekmore’s Maintaining for the 5th has mathematics appear as the sort of homework one does. And a word problem that uses coins for whatever work it does. Coins should be good bases for word problems. They’re familiar enough and people do think about them, and if all else fails someone could in principle get enough dimes and quarters and just work it out by hand.

Sam Hepburn’s Questionable Quotebook for the 5th uses a blackboard full of mathematics to signify a monkey’s extreme intelligence. There’s a little bit of calculus in there, an appearance of “\frac{df}{dx} ” and a mention of the limit. These are things you get right up front of a calculus course. They’ll turn up in all sorts of problems you try to do.

Charles Schulz’s Peanuts for the 5th is not really about mathematics. Peppermint Patty just mentions it on the way to explaining the depths of her not-understanding stuff. But it’s always been one of my favorite declarations of not knowing what’s going on so I do want to share it. The strip originally ran the 8th of December, 1969.

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Reading the Comics, June 3, 2016: Word Problems Without Pictures Edition


I haven’t got Sunday’s comics under review yet. But the past seven days were slow ones for mathematically-themed comics. Maybe Comic Strip Master Command is under the impression that it’s the (United States) summer break already. It’s not, although Funky Winkerbean did a goofy sequence graduating its non-player-character students. And Zits has been doing a summer reading storyline that only makes sense if Jeremy Duncan is well into summer. Maybe Comic Strip Master Command thinks it’s a month later than it actually is?

Tony Cochrane’s Agnes for the 29th of May looks at first like a bit of nonsense wordplay. But whether a book with the subject “All About Books” would discuss itself, and how it would discuss itself, is a logic problem. And not just a logic problem. Start from pondering how the book All About Books would describe the content of itself. You can go from that to an argument that it’s impossible to compress every possible message. Imagine an All About Books which contained shorthand descriptions of every book. And the descriptions have enough detail to exactly reconstruct each original book. But then what would the book list for the description of All About Books?

And self-referential things can lead to logic paradoxes swiftly. You’d have some fine ones if Agnes were to describe a book All About Not-Described Books. Is the book described in itself? The question again sounds silly. But thinking seriously about it leads us to the decidability problem. Any interesting-enough logical system will always have statements that are meaningful and true that no one can prove.

Furthermore, the suggestion of an “All About `All About Books’ Book” suggests to me power sets. That’s the set of all the ways you can collect the elements of a set. Power sets are always bigger than the original set. They lead to the staggering idea that there are many sizes of infinitely large sets, a never-ending stack of bigness.

Robb Armstrong’s Jump Start for the 31st of May is part of a sequence about getting a tutor for a struggling kid. That it’s mathematics is incidental to the storyline, must be said. (It’s an interesting storyline, partly about the Jojo’s father, a police officer, coming to trust Ray, an ex-convict. Jump Start tells many interesting and often deeply weird storylines. And it never loses its camouflage of being an ordinary family comic strip.) It uses the familiar gimmick of motivating a word problem by making it about something tangible.

Ken Cursoe’s Tiny Sepuku for the 2nd of June uses the motif of non-Euclidean geometry as some supernatural magic. It’s a small reference, you might miss it. I suppose it is true that a high-dimensional analogue to conic sections would focus things from many dimensions. If those dimensions match time and space, maybe it would focus something from all humanity into the brain. I would try studying instead, though.

Russell Myers’s Broom Hilda for the 3rd is a resisting-the-word-problems joke. It’s funny to figure on missing big if you have to be wrong at all. But something you learn in numerical mathematics, particularly, is that it’s all right to start from a guess. Often you can take a wrong answer and improve it. If you can’t get the exact right answer, you can usually get a better answer. And often you can get as good as you need. So in practice, sorry to say, I can’t recommend going for the ridiculous answer. You can do better.

How October Treated My Mathematics Blog


So, that wasn’t as bad as September. Last month I began my review of readership with the sad news I’d lost about a fifth of my readers from August. I haven’t got them all back yet. But the number of page views did rise to 733 in October. It’s just a bit over September’s 708, but that’s an improvement. That’s a good trend. But I do notice there was a little readership rise between July and August, and then the bottom dropped out. And 733 is still fewer than the number of readers my humor blog got from just people trying to figure out what the heck is wrong with the comic strip Apartment 3-G. (Nothing is happening in Apartment 3-G and the rumor is the strip’s been cancelled.)

The number of unique visitors rose, from 381 to 405. That’s only the eighth-highest result of the past twelve months. But it is only a little below the twelve-month average. (If you’d like to know: the 12-month mean number of visitors was 419.55, and standard deviation 39.715, so there you go. The median was 415.)

The number of likes rose again, from September’s absolutely unpopular 188 to a tolerable 244. That’s a little below the twelve-month mean (266.91) and twelve-month median (259), although given the standard deviation is 107.71 that’s hardly anything off the average.

The number of comments rose to 47, which looks good compared to September’s 25, but is nothing compared to the glory days of August and its 95 and the like. That’s farther below the twelve-month mean of 68.9 and median of 64 (standard deviation of 30), but, eh. I’ll take signs of hope. I maybe need to publicize more of my better material, more often.

Countries sending me readers have been the United States with 387 page views, the United Kingdom with 55, the Canada with 48, the Austria with 33, and the Philippines with 25. India only offered fourteen page views; Singapore, nine. The European Union got listed with five.

Single-reader countries for October were Belgium, Czech Republic, Georgia, Lebanon, Lithuania, Nigeria, Norway, Pakistan, Paraguay, Qatar, Saudi Arabia, Switzerland, Taiwan, Thailand, Turkey, and Uruguay. Repeats from September on that list are Saudia Arabia and Uruguay. None of the countries are on a three-month streak.

Among the most popular posts the past month were, of course, Reading the Comics surveys. To avoid flooding the list of what’s popular I’ll just list the category for Comic Strips instead.

  1. Reading the Comics, an ongoing series.
  2. How Many Trapezoids I Can Draw which hasn’t made the top-five or top-ten in a couple months. Curious.
  3. The Set Tour, Part 6: One Big One Plus Some Rubble and I’m glad to see this series getting a little bit of love. I’m having more fun with this than I’ve had with anything since the Summer A To Z.
  4. Phase Equilibria and the usefulness of μ, a reblogged post that’s part of my attempt to get people to pay attention to statistical mechanics.
  5. The Kind Of Book That Makes Me Want To Refocus On Logic, talking about a book I liked. I should probably talk about books I like more.

The search terms were mostly the usual bunch: origin is the gateway to your entire gaming universe and otto soglow little king and how fast is earth spinning. Delighting me, although I haven’t got anything to answer it exactly, was +how to start a pinball league. I’ve picked up a couple things about how they work, but that’s kind of outside the mathematics field proper.

The Kind Of Book That Makes Me Want To Refocus On Logic


For my birthday my love gave me John Stillwell’s Roads to Infinity: The Mathematics of Truth and Proof. It was a wonderful read. More, it’s the sort of read that gets me excited about a subject.

The subject in this case is mathematical logic, and specifically the sections of it which describe infinitely large sets, and the provability of theorems. That these are entwined subjects may seem superficially odd. Stillwell explains well how the insights developed in talking about infinitely large sets develops the tools to study whether logical systems are complete and decidable.

At least it explains it well to me. I know I’m not a typical reader. I’m not certain if I would have understood the book as well as I did if I hadn’t had a senior-level course in mathematical logic. And that was a long time ago, but it was also the only mathematics course which described approaches to killing the Hydra. Stillwell’s book talks about it too and I admit I appreciate the refresher. (Yeah, this is not a literal magical all-but-immortal multi-headed beast mathematicians deal with. It’s also not the little sea creature. What mathematicians mean by a ‘hydra’ is a branching graph which looks kind of like a grape vine, and by ‘slaying’ it we mean removing branches according to particular rules that make it not obvious that we’ll ever get to finish.)

I appreciate also — maybe as much as I liked the logic — the historical context. The development of how mathematicians understand infinity and decidability is the sort of human tale that people don’t realize even exists. One of my favorite sections mentioned a sequence in which great minds, Gödel among them, took turns not understanding the reasoning behind some new important and now-generally-accepted breakthroughs.

So I’m left feeling I want to recommend the book, although I’m not sure who to. It’s obviously a book that scouts out mathematical logic in ways that make sense if you aren’t a logician. But it uses — as it must — the notation and conventions and common concepts of mathematical logic. My love, a philosopher by trade, would probably have no trouble understanding any particular argument, and would probably pick up symbols as they’re introduced. But there’d have to be a lot of double-checking notes about definitions. And the easy familiarity with non-commutative multiplication is a mathematics-major thing, and to a lesser extent a physics-major thing. Someone without that background would fairly worry something weird was going on other than the weirdness that was going on.

Anyway, the book spoke to a particular kind of mathematics I’d loved and never had the chance to do much with. If this is a field you feel some love for, and have some training in, then it may be right for you.

Reading the Comics, April 27, 2014: The Poetry of Calculus Edition


I think there are enough comic strips for another installment of this series, so, here you go. There are a couple comics once again using mathematics, and calculus particularly, just to signify that there’s something requiring a lot of brainpower going on, which is flattering to people who learned calculus well enough, at the risk of conveying a sense that normal people can’t hope to become literate in mathematics. I don’t buy that. Anyway, there were comics that went in other directions, which is why there’s more talk about Dutch military engineering than you might have expected for today’s entry.

Mark Anderson’s Andertoons (April 22) uses the traditional blackboard full of calculus to indicate a genius. The exact formulas on the board don’t suggest anything particular to me, although they do seem to parse. I wouldn’t be surprised if they turned out to be taken from a textbook, possibly in fluid mechanics, that I just happen not to have noticed.

Piers Baker’s Ollie and Quentin (April 23, rerun) has Ollie and Quentin flipping a coin repeatedly until Quentin (the lugworm) sees his choice come up. Of course, if it is a fair coin, a call of heads or tails will come up eventually, at least if we carefully define what we mean by “eventually”, and for that matter, Quentin’s choice will surely come up if he tries long enough.

Continue reading “Reading the Comics, April 27, 2014: The Poetry of Calculus Edition”

Reading the Comics, April 5, 2013


Before getting to the next round of comic strips that mention mathematics stuff, I’d like to do a bit of self-promotion. Freshly published is the book Oh, Sandy: An Anthology Of Humor For A Serious Purpose, edited by Lynn Beighley, Peter Barlow, Andrea Donio, and A J Fader. This is a collection of humorous bits, written out of a sense of needing to do something useful after the Superstorm. I have an essay in there, based on the strange feelings I had of being remote (and quite safe) while seeing my home state — and particularly the piers at Seaside Heights, New Jersey — being battered by a storm. The book is available also through CreateSpace.

Jenny Campbell’s Flo and Friends (March 23) mentions π, and what’s really a fairly indistinct question for a tutor to ask the student. “Explain pi” is more open-ended than I think could be useful to answer: you could write books trying to describe what it’s used for, never mind the history of studying it. After all, it’s the only transcendental number with enough pop cultural cachet to appear routinely in newspaper comic strips; what constitutes an explanation of it? Alas, the strip just goes for the easiest pi pun to be made.

Scott Hilburn’s The Argyle Sweater (March 25) returns to the gimmick of anthropomorphized numerals. It’s a cute enough joke; it’s also apparently a different pair of 1 and 2 from earlier in the month. I do wonder what, in this panel’s continuity, subtraction might mean. Still, Hilburn is obviously never far from thinking of anthropomorphized numbers, as he came back to the setting on April 3, with another 2 putting in an appearance.

Continue reading “Reading the Comics, April 5, 2013”

Gibbs’ Elementary Principles in Statistical Mechanics


I had another discovery from the collection of books at archive.org, now that I thought to look for it: Josiah Willard Gibbs’s Elementary Principles in Statistical Mechanics, originally published in 1902 and reprinted 1960 by Dover, which gives you a taste of Gibbs’s writings by its extended title, Developed With Especial Reference To The Rational Foundation of Thermodynamics. Gibbs was an astounding figure even in a field that seems to draw out astounding figures, and he’s a good candidate for the title of “greatest scientist to come from the United States”.

He lived in walking distance of Yale (where his father and then he taught) nearly his whole life, working nearly isolated but with an astounding talent for organizing the many complex and confused ideas in the study of thermodynamics into a neat, logical science. Some great scientists have the knack for finding important work to do; some great scientists have the knack for finding ways to express work so the masses can understand it. Gibbs … well, perhaps it’s a bit much to say the masses understand it, but the language of modern thermodynamics and of quantum mechanics is very much the language he spoke a century-plus ago.

My understanding is he published almost all his work in the journal Transactions of the Connecticut Philosophical Society, in a show of hometown pride which probably left the editors baffled but, I suppose, happy to print something this fellow was very sure about.

To give some idea why they might have found him baffling, though, consider the first paragraph of Chapter 1, which is accurate and certainly economical:

We shall use Hamilton’s form of the equations of motion for a system of n degrees of freedom, writing q_1, \cdots q_n for the (generalized) coördinates, \dot{q}_1, \cdots \dot{q}_n for the (generalized) velocities, and

F_1 q_1 + F_2 q_2 + \cdots + F_n q_n [1]

for the moment of the forces. We shall call the quantities F_1, \cdots F_n the (generalized) forces, and the quantities p_1 \cdots p_n , defined by the equations

p_1 = \frac{d\epsilon_p}{d\dot{q}_1}, p_2 = \frac{d\epsilon_p}{d\dot{q}_2}, etc., [2]

where \epsilon_p denotes the kinetic energy of the system, the (generalized) momenta. The kinetic energy is here regarded as a function of the velocities and coördinates. We shall usually regard it as a function of the momenta and coördinates, and on this account we denote it by \epsilon_p . This will not prevent us from occasionally using formulas like [2], where it is sufficiently evident the kinetic energy is regarded as function of the \dot{q}‘s and q‘s. But in expressions like d\epsilon_p/dq_1 , where the denominator does not determine the question, the kinetic energy is always to be treated in the differentiation as function of the p’s and q’s.

(There’s also a footnote I skipped because I don’t know an elegant way to include it in WordPress.) Your friend the physics major did not understand that on first read any more than you did, although she probably got it after going back and reading it a touch more slowly. And his writing is just like that: 240 pages and I’m not sure I could say any of them could be appreciably tightened.


Also, I note I finally reached 9,000 page views! Thank you; I couldn’t have done it without at least twenty of you, since I’m pretty sure I’ve obsessively clicked on my own pages at minimum 8,979 times.