The Legacy of Antonin Scalia

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Teaching Mathematics Differently?

http://www.theatlantic.com/education/archive/2013/11/the-stereotypes-about-math-that-hold-americans-back/281303/

... article seems to support the idea that traditional and formalistic approaches to mathematics were themselves an unnecessary dressing. If true, an interesting idea: one that has resonance with the notion that meaning is more important than analysis and that "getting it" is something different from calculating. Reminds me of how Wittgenstein thought that the commutative law for multiplication could simply be taught with a picture of dots. Hence (a x b) = ( b x a) could be shown thusly:

On Facts and Intelligence

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Thoughts on "Scholarship"

I absolutely detest writing for journals because it is as if you have to sound like you are writing for a magazine. You cannot be frank. You cannot simply be demonstrative, as one might be in, say, mathematics. You have to “compose” the idea. You have to do, intellectually, something similar to what television shows do to make the presentation interesting. In short, what you have to do is make your thoughts into a good piece of journalism –- showing why the problem is interesting, what others have said, what you say and why it is helpful. Honestly, a better program would simply be to have the person’s thought following his frank remarks as to why they are offered. All of the rest of it is just fluff, pomp and dress – and it is so meaninglessly tedious in the labor it requests. Some of it, also, is showing off. “I read this and that."

Where Insight Comes From

[The following are notes written in Wittgensteinian format during a lunch break at APSA on August 30, 2007]

1. Here's the problem: If you wait and catch it, it has certain way about it.  It is fresh and interesting. You understand it. It could happen at anytime. It is like something sort of deposits it in the brain.

2. But if you have to labor to find it -- if you have to "go to work," so to speak -- it becomes arduous and something else. It becomes technical. It becomes, in a way, "argumentative" [... not the right word: "proof-like," addressing all contingencies and objections].  You can find yourself feeling like you are laboring so tediously on an "outpost" of some kind.  It is like, instead of going into coal mines, you go into "mental mines." It is like finishing or polishing or welding or something.

2.1.  It is no longer a process (cognitively) like "art," but rather becomes a sort of menial or technical labor.

2.2.  The product also changes. Go try to state something as a proof. Go try and address all of the bloody senses of talking at once.

3. Once the train of thought ends and you try to revisit it, it becomes so artificial, boring and lifeless. Where did it go? Can it only be seen in a momentary impression? How do you then communicate it to others?

4. ... you had better not be interrupted.  [note: lunch came -- Ed.].