Posts tagged with AAPL

This is how much people love to talk about and speculate on $AAPL.

The CBOE puts out a volatility index specifically on Apple stock. (Google has one too.)


It’s not universally agreed that mathematics is the worst subject everyone has to study in school, but I would say the agreement is close to universal. Why is it so boring?

Aesthetically, I prefer non-miraculous explanations that don’t invoke unique, incomparable properties of the thing considered. So for example I wouldn’t like the explanation that $AAPL is a $10^8 company because of “the magic of Apple”. I would prefer an explanation that involves definite choices they made that others didn’t—like that the Walkman was quite old when the iPod came out and they correctly assessed what the average consumer wanted and spent the right amount on an ad budget, and so on.

Even if it’s about company culture, there are probably some mundane, tangible, doable actions or corporate structures that cause culture—Greg Wilson pointed out, for example, that code is less tangled when multiple programmers are less separated in the organisational chart.


So here’s a theory of that aesthetic kind, about why mathematics is different from other subjects and ends up being taught worse.

  • The model of one teacher with a chalk and a blackboard, is more insufficient to explain mathematics than it’s insufficient in other subjects.
Here are some differences between mathematics and other subjects—not incomparable differences like “Well mathematics has group theory" or "Mathematics is for logical minds"—but comparable differences.
  1. One doesn’t become conversant in mathematics—like knowing the basic grammar and syntax—until after 3 years of upper-level courses. Typically linear algebra, analysis, modern algebra, measure theory, and a couple applied topics are required before one could be said to “speak the language”—not to be like Salman Rushdie with English, but to be like an 8th grader with English. So whereas an English teacher who went to university was working on honing skills and developing to a level of excellence, a maths teacher who went to university was becoming functionally literate.
  2. Visuals are necessary to teach mathematics. An ideal lecture in geometry would have heaps of images, videos, and interactive virtual worlds. Virtual worlds and videos take a long, long, long time to create compared to for example a lecture in history. History can be told in a story, whereas talking about for example hyperbolic geometry is not really showing hyperbolic geometry. Sure, a history lecture is nicer with some photos of faces or paintings of historical scenes—but I can get the point just by listening to the story. See my notes on a lecture by Bill Thurston to see how ineffective words are at describing the geometries he’s talking about.

So it takes longer to program a virtual world or a video than it does to write a story, and it takes longer to become functionally literate in mathematics than it does to become functionally literate in history.

Suddenly we’re not telling a story about mathematics being a special subject area with unique problems that can never be overcome. We’re not talking about heroes or villains or “Mathematics just is boring”. (Which is a ridiculous thing to say. That’s saying the way things currently are, is the only way things could ever be. “Mathematics by some intrinsic, unique, incomparable property is more boring than, say, history.” In reality, either can be taught in a boring way and yet both topics have interested people for thousands of years.) Now we’re telling a story about a subject in which it takes a lot of resources to produce a talk, compared to a subject in which it takes fewer resources to produce a talk.