Something I Did Read: Literature’s Greatest Opening Lines, As Written By Mathematicians

I imagine anyone likely to read my little notes here is already familiar with Ben Orlin’s great blog, but there’s always someone who missed the cool stuff earlier. And it’s going around Mathematics Twitter again so people are still learning. So here. Math With Bad Drawings — exactly what it says on the tin — had this amusing bit, Literature’s Greatest Opening Lines, as Written By Mathematicians.

My lone regret is the best one, Anna Karenina, is really only funny if you got into advanced mathematics classes. There’s several follow-ups in the comments. I’m tempted to try writing a couple myself. Do enjoy.

Reading the Comics, August 26, 2017: Dragon Edition

It’s another week where everything I have to talk about comes from So, no pictures. The Comics Kingdom and the strips are harder for non-subscribers to read so I feel better including those pictures. There’s not an overarching theme that I can fit to this week’s strips either, so I’m going to name it for the one that was most visually interesting to me.

Charlie Pondrebarac’s CowTown for the 22nd I just knew was a rerun. It turned up the 26th of August, 2015. Back then I described it as also “every graduate students’ thesis defense anxiety dream”. Now I wonder if I have the possessive apostrophe in the right place there. On reflection, if I have “every” there, then “graduate student” has to be singular. If I dropped the “every” then I could talk about “graduate students” in the plural and be sensible. I guess that’s all for a different blog to answer.

Mike Thompson’s Grand Avenue for the 22nd threatened to get me all cranky again, as Grandmom decided the kids needed to do arithmetic worksheets over the summer. The strip earned bad attention from me a few years ago when a week, maybe more, of the strip was focused on making sure the kids drudged their way through times tables. I grant it’s a true attitude that some people figure what kids need is to do a lot of arithmetic problems so they get better at arithmetic problems. But it’s hard enough to convince someone that arithmetic problems are worth doing, and to make them chores isn’t helping.

John Zakour and Scott Roberts’s Maria’s Day for the 22nd name-drops fractions as a worse challenge than dragon-slaying. I’m including it here for the cool partial picture of the fire-breathing dragon. Also I take a skeptical view of the value of slaying the dragons anyway. Have they given enough time for sanctions to work?

Maria’s Day pops back in the 24th. Needs more dragon-slaying.

Eric the Circle for the 24th, this one by Dennill, gets in here by throwing some casual talk about arcs around. That and π. The given formula looks like nonsense to me. \frac{pi}{180}\cdot 94 - sin 94\deg has parts that make sense. The first part will tell you what radian measure corresponds to 94 degrees, and that’s fine. Mathematicians will tend to look for radian measures rather than degrees for serious work. The sine of 94 degrees they might want to know. Subtracting the two? I don’t see the point. I dare to say this might be a bunch of silliness.

Cathy Law’s Claw for the 25th writes off another Powerball lottery loss as being bad at math and how it’s like algebra. Seeing algebra in lottery tickets is a kind of badness at mathematics, yes. It’s probability, after all. Merely playing can be defended mathematically, though, at least for the extremely large jackpots such as the Powerball had last week. If the payout is around 750 million dollars (as it was) and the chance of winning is about one in 250 million (close enough to true), then the expectation value of playing a ticket is about three dollars. If the ticket costs less than three dollars (and it does; I forget if it’s one or two dollars, but it’s certainly not three), then, on average you could expect to come out slightly ahead. Therefore it makes sense to play.

Except that, of course, it doesn’t make sense to play. On average you’ll lose the cost of the ticket. The on-average long-run you need to expect to come out ahead is millions of tickets deep. The chance of any ticket winning is about one in 250 million. You need to play a couple hundred million times to get a good enough chance of the jackpot for it to really be worth it. Therefore it makes no sense to play.

Mathematical logic therefore fails us: we can justify both playing and not playing. We must study lottery tickets as a different thing. They are (for the purposes of this) entertainment, something for a bit of disposable income. Are they worth the dollar or two per ticket? Did you have other plans for the money that would be more enjoyable? That’s not my ruling to make.

Samson’s Dark Side Of The Horse for the 25th just hurts my feelings. Why the harsh word, Samson? Anyway, it’s playing on the typographic similarity between 0 and O, and how we bunch digits together.

Grouping together three decimal digits as a block is as old, in the Western tradition, as decimal digits are. Leonardo of Pisa, in Liber Abbaci, groups the thousands and millions and thousands of millions and such together. By 1228 he had the idea to note this grouping with an arc above the set of digits, like a tie between notes on a sheet of music. This got cut down, part of the struggle in notation to write as little as possible. Johannes de Sacrobosco in 1256 proposed just putting a dot every third digit. In 1636 Thomas Blundeville put a | mark after every third digit. (I take all this, as ever, from Florian Cajori’s A History Of Mathematical Notations, because it’s got like everything in it.) We eventually settled on separating these stanzas of digits with a , or . mark. But that it should be three digits goes as far back as it could.

15,000 And A Half

I’d failed to mention the day it happened but I reached my 15,000th page view, just a couple days past the end of April. (If I haven’t added wrong, it was somebody who read something on the 5th of May.) So I like that my middling popularity is continuing, and, as I said in the review of April’s statistics, the blog-writing has felt particularly rich for me of late, for reasons I don’t consciously know. Meanwhile I’m already about a sixth of the way to 16,000, again, a gratifying touch. It’s horribly easy for a personality like mine to get worried about readership statistics; the flip side is when I’m not worried it feels so contented.

To cover the other half of my title, my dear love mentioned tripping over something in the tangent-plane article: “imagine the sphere sliced into a big and a small half by a plane. Imagine moving the plane in the direction of the smaller slice; this produces a smaller slice yet.” And how can there be a big and a small half?

Well, because I was sloppy in writing, is all. I should’ve said something like “a big and a small piece”. I failed to spend enough time editing and rereading before publishing. All I can say is this made me notice that apparently one can speak of two unequal halves of something without noticing that one is defying the literal meaning of the word. Maybe the ability to do so reflects an idea that a division of something might be equal in one way and unequal in others and the word “half” has to allow either sense. Maybe it just reflects that English is a supremely flexible language in that any word can mean pretty much anything, at any time, without any warning. Or I was just being sloppy.

Cutting Commentary

It might be that one functional definition of a friend is “someone who can say stuff that would be insulting, but you mostly don’t mind”. I had been chatting with a friend who wasn’t aware of my little blogging effort here, and gave the front page URL. My friend claimed to get a headache “from just a casual perusal!”

I know what’s intended: an acknowledgement that the writing I’ve been doing has been at least math-flavored, and that’s got almost universal acclaim as something really hard that stresses the mind to think about, and delivered in the form of a joke. It’s an overused joke, to my tastes, but an overused joke can serve several positive purposes. It can be one of the landmarks that one is in an emotionally comfortable place, or mark that the people sharing it share this in common, or that whatever is being joked about has connections to other times the joke’s been used.

Still, the joke is a bit of a complicated insult too: it insults both the writer, for not being understandable, and the reader, for not understanding. But I know that it’s not meant to insult, and I’m hardly in a position to turn away compliments when I can find them.

All this muttering I mean, largely, to warn that I am working out whether I’m good enough to write a couple pieces towards a question that really is somewhat head-spinning in a way that someone who isn’t a math or physics major would have a hope of following. I might not be; as I do research I realize I’m hitting questions I can’t fully satisfy myself about. If I can, I may go forward and you’ll see what perusal headaches really look like.