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

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

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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.

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