CronoDAS comments on The scourge of perverse-mindedness - Less Wrong

95 Post author: simplicio 21 March 2010 07:08AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Article Navigation

Comments (249)
Tags: science philosophy

Comments (249)

You are viewing a single comment's thread. Show more comments above.

Comment author: CronoDAS 21 March 2010 07:06:27PM *  5 points [-]

In mathematics, "obvious" is one of those words. It tends to mean "something I don't know how to justify."

Comment author: PeteSchult 22 March 2010 03:03:08AM 3 points [-]

A joke along these lines has the math professor claiming that the proof of some statement is trivial. They pause for a moment, think, then leave the classroom. Half an hour later, they come back and say, "Yes, it was trivial."

Comment author: RobinZ 22 March 2010 03:07:46AM 4 points [-]

I heard about a professor (I think physics) who was always telling his students that various propositions were "simple", despite the fact that the students always struggled to show them. Eventually, the students went to the TA (the one I heard the story from), who told the professor.

So, the next class the professor said, "I have heard that the students do not want me to say 'simple'. I will no longer do so. Now, this proposition is straightforward..."

Comment author: SoullessAutomaton 23 March 2010 03:04:51AM *  10 points [-]

At the Princeton graduate school, the physics department and the math department shared a common lounge, and every day at four o'clock we would have tea. It was a way of relaxing in the afternoon, in addition to imitating an English college. People would sit around playing Go, or discussing theorems. In those days topology was the big thing.

I still remember a guy sitting on the couch, thinking very hard, and another guy standing in front of him, saying, "And therefore such-and-such is true."

"Why is that?" the guy on the couch asks.

"It's trivial! It's trivial!" the standing guy says, and he rapidly reels off a series of logical steps: "First you assume thus-and-so, then we have Kerchoff's this-and-that; then there's Waffenstoffer's Theorem, and we substitute this and construct that. Now you put the vector which goes around here and then thus-and-so..." The guy on the couch is struggling to understand all this stuff, which goes on at high speed for about fifteen minutes!

Finally the standing guy comes out the other end, and the guy on the couch says, "Yeah, yeah. It's trivial."

We physicists were laughing, trying to figure them out. We decided that "trivial" means "proved." So we joked with the mathematicians: "We have a new theorem -- that mathematicians can prove only trivial theorems, because every theorem that's proved is trivial."

The mathematicians didn't like that theorem, and I teased them about it. I said there are never any surprises -- that the mathematicians only prove things that are obvious.

-- Surely you're joking, Mr. Feynman!

Comment author: nhamann 21 March 2010 07:20:54PM 3 points [-]

Most of the time I've run into the word "obviously" is in the middle of a proof in some textbook, and my understanding of the word in that context is that it means "the justification of this claim is trivial to see, and spelling it out would be too tedious/would disrupt the flow of the proof."

Comment author: SoullessAutomaton 21 March 2010 09:19:55PM 8 points [-]

I thought the mathematical terms went something like this:

  • Trivial: Any statement that has been proven
  • Obviously correct: A trivial statement whose proof is too lengthy to include in context
  • Obviously incorrect: A trivial statement whose proof relies on an axiom the writer dislikes
  • Left as an exercise for the reader: A trivial statement whose proof is both lengthy and very difficult
  • Interesting: Unproven, despite many attempts
Comment author: CronoDAS 21 March 2010 07:35:19PM *  3 points [-]

Well, that's what it's supposed to mean. One of my professors (who often waxed sarcastic during lectures) described it as a very dangerous word...

Comment author: kpreid 21 March 2010 08:03:02PM 2 points [-]

Do you really assert that it is more often used incorrectly (that the fact is not actually obvious)?

Comment author: wnoise 23 March 2010 01:22:53AM 8 points [-]

I assert that it ("obviously" in math) is most often used correctly, but that people spend more time experiencing it used incorrectly -- because they spend more time thinking about it when it is not obvious.

Comment author: CronoDAS 21 March 2010 08:11:33PM 3 points [-]

No, I guess not.

Comment author: CronoDAS 22 March 2010 12:14:54AM *  1 point [-]

A list of common proof techniques. ;)

Powered by Reddit Powered by Reddit