Efrique has two posts up that I'm certain are a tour de force of mathematics. I deduce they are not because I understand the math, but because I know that Efrique is a genius and his logic in other areas has never failed me.
I don't understand the math because of this:
Back when I was in school, I sailed through English and foundered on mathematics. My brain looks at numbers, screams, and flees. I blame the way math is taught.
I struggled with basic math for many years, until I hit a point in early middle school when things went "click." My sails filled with a good wind. I skimmed the waves of numbers. Each new concept slotted perfectly into place: we were plotting a good course, and there seemed nothing ahead but open ocean and the shores of Calculus sometime after a pleasant journey.
As soon as I reached 5 knots, my teachers, in their infinite wisdom, decided I could skip the rest of the basics and move right on to pre-algebra. For some children, this might have been a good move. They're the ones who "get it" intuitively. For me, it was a disaster. It was like telling a sailor that since he's so good at navigating by sight, he's ready to strike out across the open ocean.
And then, there was the Book.
I can't really describe my pre-algebra book. I remember very little of it. I just remember the look on my father's face when, disappointed by his daughter's inability to understand the simplest algebraic concepts, he sat down one night and lectured. Couldn't understand why I didn't understand, why I was failing, math is the easiest thing in the world, it's simple and obvious and -
-then he opened the book, looked at a problem, and stopped mid-rant.
And stared.
His forehead creased. A little thunderhead formed above his eyebrows. He turned red. He opened his mouth, closed it, looked at a few more problems, and looked at me in utter disgust as I quailed.
"No wonder you don't understand math," he snapped. "What is this shit?"
We then spent a delightful hour wherein he ripped the book a new one, while I watched his wrath in awe. He hated that book with a passion.
I never did recover momentum. The wind had been sucked from my sails, the hull staved in, and not even my father could right the ship. Part of that was because he worked 16-hour days and just didn't have the necessary time. Part of it was because we couldn't find any sane math books. And the rest was because I'd already taken a berth on another ship, and was starting to chart a literary course.
I would have focused all of my energy and attention on comprehending math, however, if I'd known that as an SF author, I'd someday need the bloody stuff for incidental details like planetary mass and gravitational force, orbits, and a billion other things that go into making a story universe work. I can't do even the simplest calculations.
One day, I keep telling myself, I'll take the time to rebuild the ship. I'll start with regular math and follow every iteration until I finally reach the promised land of calculus. Only, there's never time. And that impoverishes me. There's a whole world described in math that I'll never see and only vaguely comprehend.
When it comes for the math underlying my books, I'll just have to fake it.
Good thing I can cuss like a sailor, then, eh?
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The new math was a great idea, the problem wasn't the idea which was to teach math more like it really is as understood by mathematicians, the problem was the teachers themselves didn't understand the set theory stuff and the other ideas in it well enough to either teach it or to relate it to other concepts in math and science. Now we have students who do not even know what a set is or even that it is in fact fundamental to all of math and logic.
I had a horrible time in math, too. I never realized how lucky I was to be taught the traditional way. Still, I found it to be difficult.
I ended up majoring in chemistry anyway and suffering a lot. I was told that this was more intelligent than going into any field I was actually interested in (I was pre-med).
Now I hate chemistry; I hate medicine. I love all the fields that the scientists scoffed at. The most chemistry I ever used was the equations from high school chemistry so all that suffering was a complete waste of time. You probably saved yourself a lot of pain.
So there you go. You saved a lot of time. Still, I would admire it if you took math for its own sake. There is a certain beauty to it. It just takes a more intelligent person to "get it" I guess.
I have an English majoring friend who was horrible at math. Then he had a job tutoring math to high school children. He had to learn it on his own, and he loved it.
Hi Dana. Thanks for the linklove!
Could I get you to change the spelling of "Efrique" in your post?
I know it looks like "Enrique" which is probably what causes you to insert an "n" in when you type it, but the name doesn't have an "n". In the course of comment threads I don't care so much (it's a made-up name, what do I care how you spell it), but in a post on your blog (which gets more traffic than mine) I think it's probably better to put it right.
(If it helps, put on your best imitation of a Canadian and think "e-freak-eh?".)
I was 7 when my mother said "don't ask me any more questions about mathematics".
I was lucky enough to have reasonably good mathematics teachers after I left primary school (K-6), but to be honest a fair bit of what I learned was self-taught. Even more so at university level. Actually, I think it's true of most stuff I've learned - a formal class helps guide what I will learn about, but really, almost all the learning I do myself.
[Sometimes I wonder whether I actually manage to teach anyone anything. A few students have been kind enough to say I inspired them (which is nice), but I'm not sure I ever do much more than guide them through the material.]
Oh, and tours de force?
Hardly. Just merrily encouraging skepticism!
The underlying message is that sometimes a percentage or a graph doesn't necessarily say what it seems to say. Such mathematical arguments need to be read as critically as the text that draws on them.
@Efrique: Whoops! Humble apologies! Fixed. That's what I get for not paying close attention to spelling!
That was fast! Oh, and no need to apologise.
Talking about arithmetic in other bases (as Tom Lehrer was doing in his song), I showed my kids how they could count past 1000 on their fingers, by doing it in base 2.
Except, being evil atheist dad I actually counted all the way to 132 on my fingers in front of them.
Which they thought was absolutely hilarious, and couldn't wait to show their friends. And teachers.
(Why is it evil to show your kids what 132 is in base 2 on your fingers? I'll tell you later. And I'll probably tell a few other stories about me corrupting my kids...)
Counting in base 2 on your fingers.
Lesson 1. Hold up one or both hands, palm toward you. (If you're counting to someone else, start on your left hand, if you're counting to yourself, use your right.) Tuck all fingers (including thumbs) in, making a fist. That's 0.
a) Stick up your thumb. That's 1.
b) to get the next number at each stage, if your thumb is down, put it up (that adds 1). If it's up, put it down, and put up the next finger. If the next finger is already up, put it down and put up the next in its stead (and so on, until a finger goes up). So to get 2, thumb goes down, index finger comes up. Index finger is worth 2 whenever it's up, and it's the only thing up, so you've counted to 2.
c) So what's three? Well, your thumb is down, so it comes up; now your thumb and index finger are up, and that's 2+1 = 3.
d) What's four? well, thumb is up, so it should come down and the next finger goes up. Oops, it's already up, so it goes down as well; middle finger is worth 4 and comes up.
President Bush demonstrates his ability to count to 4 in base 2
Kitty shows she is Presidential material, because she, too, can count to 4.
Anyway, we proceed along like this. Each finger is worth double the previous finger, so your ring finger is worth 8, the little finger is worth 16, and then we move on to the next hand.
Here, an intelligent and erudite young lady demonstrates that she is familiar with counting in binary, by showing us how to indicate 132 (128 + 4).
Mathematics is sometimes useful, but not everyone appreciates subtle mathematical argument. Better save a demonstration of your mastery of base 2 (binary) arithmetic for people of great learning - your teachers, any religious ministers you find at school, that kind of thing.
...
I do try to encourage my offspring in their learning, and I like to demonstrate the fine joys that come with understanding the world around us, as the following charming anecdote may demonstrate.
My son has to do a project on the solar system, including a talk on a planet or moon. Needless to say, when my son mentioned this, given my keen interest in astronomy, I rattled off an impromptu example talk on the seventh planet to give him an idea of the kind of material that other nine-year-olds, and especially his teacher would likely enjoy; I encouraged him to address his remarks directly to the teacher:
"Uranus is very big - Uranus is about four times the size of the earth.
Uranus is very cold, and is filled with ice. Uranus is blue, which is not surprising.
The atmosphere around Uranus contains a lot of methane.
The gaseous atmosphere around Uranus experiences high wind speeds, upward of 250 km/h.
In 1977, astronomers discovered rings around Uranus.
... "
and so on, discussing the likely experiences of astronauts should they venture to try to get to Uranus, how Uranus was so big it was orbited by several moons and so on.
My son, of course, having a keen interest in astronomy himself, was delighted, and shed tears of joy at hearing my erudite exposition on the seventh planet. He was so moved that he was completely unable to speak for several minutes, but his childlike delight in the topic of astronomy was clear for all to hear.
He immediately resolved to talk on that very object - the seventh planet himself, a plan from which he would not be dissuaded, despite the great benefits of the other interesting objects in the solar system and has composed a lengthy and rivetting missive on the topic; indeed he has attacked the project with great enthusiasm.
I must congratulate his teacher for so engaging his enthusiasm with this topic on the solar system.
@Efrique: Would this counting to 132 be anything like the Number Eight! when fingerprinting a body?
(Sensitive persons with no sense of black humor, please vacate the room now.)
Right, my darlings? Right. So my friend, who works for the Phoenix PD, is visiting the morgue one day. A technician is fingerprinting a body. Each finger is numbered. (To play along at home: begin counting on your right thumb.) My friend isn't paying much attention until the tech says "Number eight!" in an "order up!" tone. My friend looks over, and finger Number Eight is waving in the air.
If you counted your fingers correctly, and you have the proper evil sense of humor, you should be cracking up about now.
@Starhawk: I think you're exactly right. If teachers can't understand a subject, there's very little chance the students who don't intuitively grasp it or have outside help will ever gain proficiency.
@Leroy: Thanks for the hope! LOL.
@Efrique, regarding counting in binary and speeches on Uranus: You are killing me, here! Do you know how hard it is to read that treatise whilst sitting at one's desk in a busy call center, trying not to scream with laughter? And I haven't even looked at the pics yet!
Brilliant!
Dana:
So you're a fan of astronomy too!
Yes, number 8 is the same basic idea. *That*'s counting in base 1 arithmetic, by the way. (So you've been doing mathematics in other bases than base 10 since you were a little kid and just didn't know it.)
And, yeah, some of those pictures would not be SFW (though I linked to google's tiny thumbnails not the originals, which helps).
Elegant and hilarious!
Funny that: just as I take a break from working on my newest Elitist Bastard essay, which will explore how we shortchange ourselves and our posterity with shitty-ass math education, what do I find but two of my blogofriends — Dana Hunter and Brian Switek — complaining about math classes. Too bad my essay is moving so slowly; it looks like it might be an important theme to visit. Well, I'll have it for next month's carnival — I may be elitist, but I never said I was fast, dammit.
Blake - I'd like to read that.
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