Sunday, October 24, 2010

Laughing at what you don't understand

Entertainment at tea time

The anti-intellectual culture of the day must be quite a treat for the subomegaloids who watch Fox News and frequent Tea Party gatherings. One of the country's major political powers is now a wholly-owned subsidiary of the know-nothing right wing, indicating a kind of high-water mark for bumptious ignorance and anti-science. Still, it remains something of a disappointment when the waves slop over onto New York magazine. You'd think that a publication naming itself after the cosmopolitan Big Apple would keep a stiff upper lip and refuse to frolic among the scum-sucking bottom-dwellers.

Well, you'd be wrong.

This past week New York magazine decided to go for some easy yuks by mocking some math classes. It was a piece of cake. A group of five people—yes, it took five people to do this—pored over the course offerings at several American liberal arts colleges, found some math courses they didn't understand, and merrily made fun of them.

What a treat for New York's readers. (The ignorant ones, at least.)

Let's join the fun, shall we?

October 19, 2010

Every year, liberal-arts majors anxiously scour their college's course listings looking for classes that will fulfill their math requirement but aren't so, you know, math-y. Here's what they're signed up for this year.

10. Topology: The Nature of Shape and Space: “In geometry we ask: How big is it? How long is it? But in topology we ask: Is it connected? Is it compact? Does it have holes?” [Sarah Lawrence]
Topology is not a trivial topic. By what metric do the writers gauge this to be a “ridiculous-sounding” course? They're off to an embarrassing start (assuming they're capable of embarrassment).
9. The Mathematics of Chance: “Most topics are introduced in a case-study fashion, usually by reading an article in a current periodical such as the New York Times.” [Bard]
And already it gets worse. Probability and statistics pervade our technological culture but are often misunderstood. If people had better number sense, they would be fooled less often by nostrum-peddlers and dishonest politicians. Scanning a periodical is an excellent way to find numerical arguments (e.g., polling data, unemployment figures, medical claims) that should be subjected to some critical thinking.
8. Mathematics in Many Cultures: “Mathematical ideas are found in many cultures, among both literate and non-literate peoples. This course examines both mathematics and the role it plays in the cultures. Examples chosen from the mathematical ideas of present-day peoples of Africa, Asia, Oceania and the Americas, as well as historic Egypt, Mesopotamia, Greece, Islam and China.” [Pomona]
Mathematics is a human endeavor that spans cultures and exhibits the variety of our thinking. The course title is straightforward and the description apt, yet the New York contributors deemed this another “ridiculous-sounding” math class.
7. The Magic of Numbers: “This course will explore the beauty and mystery of mathematics through a study of the patterns and properties of the natural numbers 1, 2, [and] 3." [Harvard]
I clicked through to the course link on this one. Sure enough, the writers had “improved” the course description by omitting the ellipsis after the numerals. (The natural numbers go on forever. And what does Harvard say about this “ridiculous” course? Here's the rest of the description: “We discuss various special classes of numbers, such as prime numbers, factorials, and binomial coefficients, and the many ways they arise in mathematics. We will discuss questions in probability (such as: the likelihood that two people in a class of 25 have the same birthday). We also study modular arithmetic and secret codes based on it.”

Yeah. Sounds stupid, doesn't it?
6. Models of Life: “In particular, we will ask such questions as: How do you model the growth of a population of animals? How can you model the growth of a tree? How do sunflowers and seashells grow?” [Kenyon]
This terse description is sufficient to identify exponential growth as one of the topics (for population, naturally) and Fibonacci sequences for sunflower growth (and other cases, too), and probably the over-hyped but still nontrivial golden ratio.

So inane. The New York contributors must have dislocated their jaws from yawning (when they weren't sniggering, of course).
5. Mathematical Origamist’s Toolkit: “Topics include modular origami and how this models the creation of polyhedra and coloring of graphs, comparison of origami-axiomatic constructions to straight-edge and compass constructions, the combinatorics of possible crease patterns, the mathematics of origami design (circle packing, optimization), matrix models for paperfolding, spherical geometry, Descartes’ Theorem, and Gaussian curvature.” [Hampshire]
I can think of only one possible reason for the inclusion of this course: The writers (and I use the term loosely) thought that “origamist” was just too funny for words. This course is full of clever and subtle stuff that a good instructor could have a lot of fun with—and I don't mean the kind of mocking fun that New York magazine is trying to have at its expense.
4. Mathematics and Narrative: “Many literary works (Arcadia, Proof, and Uncle Petros and the Goldbach Conjecture) use mathematics as an integral part of their narrative. Movie and television narratives such as Good Will Hunting and Numb3rs are also mathematically based. Nonfiction works about mathematics and mathematical biographies like Chaos, Fermat's Enigma, and A Beautiful Mind provide further examples of the connection between mathematics and narrative.” [Vassar]
Sir Tom Stoppard? David Auburn? Apostolos Doxiadis? Heck, no one has ever heard of these writers. Right? At least, the New York writers appear to have failed to see the value of exploring the mathematical underpinnings of major recent literary works. Why, they didn't even appreciate Good Will Hunting, which was a movie they could watch in slack-jawed amusement while munching popcorn (while ogling Matt Damon). I doubt, however, that they would appreciate the accuracy of the mathematical boardwork that appeared in the movie. (I did!)
3. Borges and Mathematics: “Jorge Luis Borges was one of the most important writers of the 20th century. Many of his short stories and essays were concerned with philosophical, metaphysical, and mathematical questions. The thesis motivating this course is that if we know the mathematics that Borges referred to, then we will read him differently, and we will read him better.” [Bennington]
The inclusion of this course is beyond outrageous. The New York magazine ni kulturni don't recognize the significance of mathematics in the work of Borges, who famously imagined “The Library of Babel” and thereby created a fascinating combinatorial icon that has persisted in literature and mathematics.
2. Mathematics and Science as Art in Contemporary Theatre: “Playwrights such as Tom Stoppard, Rinne Groff, Michael Frayn, and others have effectively explored mathematical and scientific themes for artistic purposes. Through readings and exercises, and by conducting labs and staging scenes, this class will gain some first-hand insight into the complementary ways in which science and art aim to seek out their respective truths.” [Middlebury]
Aha! A theme! (And three in a row.) These people don't like any explorations of the connections between lit and math. And they were also getting desperate to pad their list out to ten.
1. Meaning, Math, And Motion: “Quoting a charming articulation by Kinsman (a mathematician-turned-oceanographer, in the preface to Wind Waves): 'To the beginner, science is a conversation that has been in progress for a very long time.' Our collective work is to catch up on the conversation.” [Evergreen]
At this point, my patience is exhausted and I'm unwilling to give the benefit of any doubt to the writers. This one might be just a little light-weight and silly, but I've come to regard their disdain as a mark of distinction. Go ahead and take the class, students of Evergreen College. It's probably better than its rather vapid description.

The list of “ridiculous-sounding” courses ends with a bit of snark:
This is why Asia is winning, by the way.
I have a better suggestion, but the New York contributors won't like it (even though they consider mockery an art form).


Improbable Joe said...

Thanks... I was almost not pissed off enough today, and you had to go and ruin it. I knew from the inclusion of topology that the people behind the list are too proudly ignorant to be able to understand how stupid they look.

Zeno said...

Always glad to be of service, Joe.

Anonymous said...

I just wanted to point out that listing #5 at Hampshire College is actually a course for some of the brightest high school math students in the country. And the lecturer is excellent.

Zeno said...

Thanks for pointing that out, Anonymous. It's good to hear from someone who knows. And I am not in the least surprised.

Anonymous said...

Well, at least my favorite field (topology) is the least ridiculous-sounding of the most ridiculous-sounding math classes.

What about calculus? That must be pretty ridiculous--just sitting around calculating things, right? 1+1=2, 2+2=4, …

Dr24Hours said...

Wow. I would enjoy taking at least 8 of those courses. And the other two, I probably should take, but wouldn't enjoy.

Eamon Knight said...

Topology? Hell, anyone who can't tell that a course about "Chance" is important is too much of an idiot to take seriously. The authors probably play lotteries, picking the numbers by some "system" or other.

coherentsheaf said...

To be fair, most of those courses are not the type of serious math courses that a mathematics student would take (except topology, which is--or can be--very very serious). I have no problem with liberal-arts students taking those sorts of courses and getting out of complex analysis (just as I don't want to have to take an overly intense humanities course, and having humanities majors learn something about probability is not, you know, bad), but I do not think these compare favorably in mathematical intensity: they're the sort of interesting thing you could give to a high-schooler to catch her curiosity. But if that curiosity were to continue, she would have to take a more rigorous course (with, say, proofs).

Zeno said...

Not arguing your point, coherentsheaf. They are, after all, supposed to be courses aimed at providing some math experience for liberal arts students, not rigorous nor proof-based. That does not, however, make them worthy of ridicule or the kind of myopic mockery provided by New York magazine. That's all I'm saying, and in so doing I believe I am being eminently fair to the five writers.

coherentsheaf said...

Yes, this is true: such courses for humanities majors are hardly the reason for the problems in math education. (In any case, I've never heard of a *high school* offering one--and the problems in education are, AFAIK, generally considered to be at the school level.)

Brassy said...

To give a slight indication of my bias, I will first say that I am not a math major; I earned a bachelor's in molecular/cellular biology.

It seems that the New York authors are working on the assumption that if it isn't straightforward, dull (to them) calculations, then it isn't math. My initial impression is that these authors strongly dislike math and don't think it applies to them. These course descriptions sound like they are courses designed to bring some mathematical concepts to the "non-math people" and illustrate how they are present in real and fascinating ways. Getting people who are not math majors to love math can be difficult, and it's important. Many adults that I know are, frankly, afraid of math. When math is presented in an idea-focused way, and related to something else they are interested in, many people have an easier time appreciating math and grasping it's relevance to their day-to-day life.

Of course, if you already hate math and have already decided that it isn't interesting and is in no way relevant to courses and topics outside of math, then you'll have a harder time seeing why these "non-math" courses are valuable offerings.

PS: The Mathematics of Chance sounds like a course I wish I could force many adults I have known to take.

Zeno said...

Thanks, Brassy. I appreciate your perspective on this. (And I agree about the Chance course.)

Blake Stacey said...

The topology class is actually an advanced elective which lists calculus as a prerequisite. It's not "doughnuts and coffee cups for non-majors". Maybe it's less intense and rigorous than 18.901 at MIT, but the New York magazine's presentation is still remarkably deceptive.

Shoddy journalism.

Blake Stacey said...

The thesis motivating this course is that if we know the mathematics that Borges referred to, then we will read him differently, and we will read him better.

Knowing stuff can make art more enjoyable? I'm shocked, shocked!

Blake Stacey said...

Sure enough, the writers had "improved" the course description by omitting the ellipsis after the numerals.

That caught my eye, too. It's not a mistake which anyone who knew even a smidgeon of number theory — we're talking "read the first paragraph of the Wikipedia article on natural numbers" here — would make. Whoever wrote that had to be either dishonest or incompetent.

Kathie said...

Zeno, you overlooked the Washington Post's contribution this weekend to the anti-math mob.

"How much math do we really need?" by G.V. Ramanathan (described as a professor emeritus of mathematics, statistics and computer science at the University of Illinois at Chicago):

The meat of his argument: "Unlike literature, history, politics and music, math has little relevance to everyday life. That courses such as 'Quantitative Reasoning' improve critical thinking is an unsubstantiated myth. All the mathematics one needs in real life can be learned in early years without much fuss. Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation."


Zeno said...

Not at all, Kathie. I saw Ramanathan's piece and have been wondering when I'll have the time to do a post on it. Perhaps later this week.

Tualha said...

#1 goes beyond sniggering into blatant dishonesty and quote-mining, which the author or authors of this part seem to have attempted to hide by giving a bad link. The offered link takes you to a page that requires an Evergreen login, and the URL appears to contain nothing specific to the course in question. Here's a link to the course:

The quote takes two frivolous-sounding sections from the rather long course description and ignores all of the more serious material. I'm actually kind of surprised they didn't include the entire quote; it all sounds somewhat frivolous out of context.

Though the only prereq is intermediate algebra, it doesn't sound like a lightweight course to me. It sounds like a course intended for serious students, though not necessarily ones in math or the sciences, who want to do serious interdisciplinary work and exercise their brains. To some depth, it covers precalc and beginning calculus, at least part of the usual first two semesters of physics, and topics in linguistics.

I'm not sure how much New York is to blame for all of this, though. Clicking on the authors' names, I see these articles are described as "posts." It's unclear how much editorial control, if any, New York imposes on these.

P.S. Regarding Prof. Ramanathan's comments: e-meritus indeed!

Tualha said...

Gah. There's always one missed error. Here's a link to the course:

My apologies to those who copied-and-pasted before they saw this.

Zeno said...

Thanks for the link, Tualha. I have taken the liberty of incorporating it in that last item so that readers of this post get referred to the correct description. I hadn't bothered with the links in general, but this seems like a worthwhile corrective.

Blake Stacey said...

Ramanathan's piece made me chuckle. He advises asking "the next 10 people you meet" how much mathematics one requires "in everyday life". It's funny, because I'm a scientist: if I reach out and touch someone, odds are they'll be a programmer, an engineer or a physicist-by-training like me. Those are just the social circles I move in — my co-workers, my housemates, my friends from university. My companions skew toward heavy mathematics users, so they won't be representative of the nation as a whole. See, there's this thing called "sampling bias", which you'd learn about if you took a statistics class. . . .

You can see attempts at embarrassing the public in popular books written by mathematicians bemoaning the innumeracy of common folk and how it is supposed to be costing billions

And Ramanathan has evidence that it isn't? His argument seems to be, "Because nobody knows mathematics, nobody needs to know mathematics."

Then you have the weird notion that if the elite is doing fine, we don't have to worry about everybody else. Johnny can't do arithmetic? Don't worry: lots of Americans have won the Nobel Prize!

I don't often curl up with an algebra book, in either the junior-high or the "modern" sense of the word. I do, however, use the audio from the Feynman Lectures on Physics as relaxation tapes.

Anonymous said...

I was a student at Evergreen a number of years ago, and can tell you that despite the sometimes hippy-dippy atmosphere, the professors are excellent and I never took a "lightweight" course. They specialize in interdisciplinary courses and do it very well.

Tualha said...

I wasn't aware that editing your own blog post involved taking any liberties :)

I suppose you're referring to using the results of another's research without proper citation. Oh dear. Don't have a cow, it's a frickin' blog, not American Mathematical Monthly :)

Joseph said...

I missed any connection to the Tea-Party protests in the original article.

In the unlikely event there is a political connection, if you claim that Science backs your political opinion loudly enough, you should not be surprised when people actually believe it.

Tualha said...

I seem to recall some of PZ Myers' students got some nasty comments and backtraced them; found out name, address, employer, etc. Didn't do anything with it but PZ was pretty impressed. Think you could find out who posts this spam and expose him? (I'm certain it's a "him".)

I have no idea how one does that - start with the IP address, I suppose?

Zeno said...

We know exactly who it is, Tualha. His threats are being collected and delivered to law enforcement officials. Some bloggers are also investigating the possibility of legal action against him. All of us think he's addled and off his meds. (It's always sadly amusing when a supposedly devoutly religious person uses profanity, death threats, and "vain repetition" to advance his cause. By his own standards, he gets to burn in hell.)

The general practice here (and most other places) is to ignore his incoherent rants.

Kathie said...

Zeno wrote: "All of us think he's addled and off his meds."

Wasn't it Einstein's definition of insanity as something to the effect of doing the same thing over and over, while expecting a different result?

Charlie Brown had a better chance of making a field goal with Lucy holding the football than a troll does of having his droppings unscooped from a blog's comment page.

Anonymous said...

As a student currently in the program that made the #1 spot, I can tell you that the coursework is NOTHING to laugh at.

Also, I am definitely showing this to the professors. They'll know that they've been doing well if they're getting the anti-intellectuals in a tizzy. (However, that course description really COULD have used some work...)