Let’s Get Lost 2

 

In my labors to become less bad at math I encountered the word subitize. I had not known this was a word, but apparently there are five-year-olds who do.

I’ve been trying to learn combinatorics (another word I’d not known existed). That binomial coefficient, man: exclamation points, n choose k … Pete choose headache!

 

 

I’ve read a few books on math now and am distressed that my childhood experience replicates in middle age: math is easy at first, quickly gets very difficult, and not long thereafter loses me completely.

E.g. I’m reading Mathematician’s Delight (on the strength of its title and groovy cover). The author was a British professor of mathematics, and he has a kindly, assured tone that makes it seem like he’s invited me over for a fireside chat.

It starts off well:

Professor: Owing to the accidental fact that we possess ten fingers, the multiplication tables depend on this number 10. If we had eight or ten fingers, the patterns would be different.

Pete: [sips port, chuckles amiably] Quite right!

But in a few pages he’s talking about a fire-watching rota:

Professor: How long will it be before Alf and Bill are again on duty together? Alf and Charlie? Bill and Charlie?

Pete: [drains glass] Uh, can I have a pencil and paper? And what’s a fire-watching rota?

And then Alf and Charlie start wrapping ropes around posts to lower an injured comrade:

Professor: Now what will happen if we wind 0.301 of a turn on one post, and then 0.477 on the next?

Pete: [asks for coat]

 

See also: Let’s Get Lost 1

Base Fiddle

 

Occasionally you learn something astonishing. The other day I was in the midst of Mathematics for the Nonmathemetician* and read this:

There are people who campaign for the adoption of base twelve, because it offers special advantages.

I mean, this is America. There’s a lot you can say about the place, but it does not lack for heterogeneity of the mind. Yet I have never heard – or even heard of – anyone saying “You know what? We need to get rid of our base ten numerical system and replace it with base twelve.”

 

Image result for dozenalism

 

Turns out I’ve led a sheltered life.

Dozenalists aren’t cranks or crotchety anti-metric grouches. We just find the dozenal system easier, more efficient, and otherwise better than the decimal. This is a reasonable opinion well founded in the facts.

Don Goodman, The Dozenal Society of America

 

 

*I could use more books like this, e.g. Conversation for the Nonconversationalist, Patience for the Nonpatient, etc.

 

The Bricklayer

 

So you think you’re bad at math?

It’s not you, it’s…

Uh, anyway. In the Light of What We Know is one of the better novels I’ve read in the past few years, all the more so because it’s a first novel.

Image result for in the light of what we know

 

I was so taken with this one passage that I copied it and promptly forgot about it until last week:

One bad maths teacher, he explained, can wreak havoc. A bad history teacher, when you’re twelve years old, say, might mean you don’t acquire a very good grasp of the First World War or the Potsdam Conference. It leaves a hole in your education. The next year, you manage. The early deficiency doesn’t hinder you very much when you later study the Russian Revolution, not in those years when you’re not studying any of these things in great depth anyway. But mathematics is different. If you fail to digest the material prescribed for that year, then everything that follows, in every subsequent year, is next to impossible to take in. Right from the beginning, mathematics education is accretive, a pyramid, each layer of brickwork building up carefully on the last. You can’t understand trigonometry if you haven’t grasped the idea of similar triangles. You can’t grasp calculus if you haven’t understood areas and velocities. And you can’t understand anything at all if your basic algebra is poor. It’s why mathematics professors have such a hard time explaining their work to the public. The great majority of students are vulnerable to one bad teacher. It isn’t enough for a child’s mathematics teachers as a whole to be generally just as bad and just as good as his history teachers. In fact, even if mathematics teachers were generally, which is to say as a group, better than history teachers, the presence of one bad maths teacher early on hampers him mathematically if it doesn’t doom the child to mathematical ignorance.

When I first read the above, I taught English; now I mostly teach math.

Rereading it offers what David St. Hubbins calls “too much… perspective.”

 

Image result for spinal tap 11

 

Clear Cut

 

It is not so easy to run again when you have been ejected from office by a clear majority of voters (he lost to Mr. Hollande by more than three percentage points).

It’s statements like the above that make me think I don’t understand democracy, or math.

I mean, yes, I can calculate that fifty-one is greater than forty-eight without creating two piles of pebbles. But to my mind you should be able to assemble ten people and demonstrate a clear majority without having to fetch a saw.

Image result for saw

 

Although, to be fair, in American presidential elections “landslide” is often used for what might be better described a “clear majority.” (I’m talking popular vote, not the Electoral College, which I still don’t understand.)

I am, of course, with Sir Winston on democracy, but I can see this guy’s point too:

In the hazy heat Tata Ndu paused to take off his hat, turn it carefully in his hands, then replace it on the high dome of his forehead. No one breathed. “White men tell us: Vote, bantu! They tell us: You do not all have to agree, ce n’est pas nécessaire! If two men vote yes and one says no, the matter is finished. À bu, even a child can see how that will end. It takes three stones in the fire to hold up the pot. Take one away, leave the other two, and what? The pot will spill into the fire.”

– The Poisonwood Bible, Barbara Kingsolver

Things That Make You Go Hmmm

 

Leibniz remarked about his enemy Newton: “Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.” The same could be said of Bach. Compared with the entire body of music before his time, his own was the finer half.

 

Gottfried_Wilhelm_von_Leibniz

My first thought on reading the above was “Whoa!” Because I definitely had not thought about music that way before. Or math either.

The second was “Uh, who’s Leibniz?” Turns out he was “a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.” Ah yes.

And their enmity apparently had to do with Calculus.

Image result for professor calculus

 

Now then. The above quote is from The Stream of Music by Richard Anthony Leonard, published in 1945 (when, presumably, music streaming meant something else).

Some more fun facts about Bach:

Continue reading “Things That Make You Go Hmmm”

Fastball

Chounumerals

Let us record my characteristic prescience [solipsism? – Ed.] by noting that my latest piece, on the rigors of re-learning math, is accompanied by two articles on math education:

I don’t recall being bad at math until high school. It reminds me a bit of how, when I started Little League at age seven or eight, I was pretty good, and remained so (at least in the rosy mists of memory) until about age twelve. All of a sudden, pitches seemed very difficult to hit, if not murderous. So I stopped playing, and gradually lost interest in baseball.

I’ll pause while you dry your eyes.

Baseball_(crop)

Anyway, high school math was like that for me. And if you factor into the equation (get it?!) the possibility that I approached my secondary education with something less than ardent devotion, well… I became one of those people who says (with fair accuracy in my case) he’s bad at math.

I do remember being surprised when a high school history teacher mentioned, in an aside during a lesson on the Enlightenment, that mathematicians were attracted to the subject by its beauty. It seemed, then anyway, such a dissonant statement, like declaring the beauty of plumbing.

Factoring polynomials won’t supplant my crossword, nor will the Fields Medal folks be calling (I’m forty-two, dammit), but I do wish I’d seen math’s beauty earlier.