Re: plausibility argument (sefara) for twin primes conjecture

From: KRamsay (kramsay_at_aol.com)
Date: 07/11/04 

Date: 11 Jul 2004 02:48:00 GMT

In article <080720042328515015%suh@math.ucdavis.nospam.edu>, Chan-Ho Suh
<suh@math.ucdavis.nospam.edu> writes:
|I don't like this example because it's one of those examples where what
|people are thinking and saying are two different things. When a layman
|hears or says "continuous curve" s/he has a particular idea of
|something, usually a very tame kind of curve for which the intuition is
|correct in asserting it "cannot fill a region of space". This is more
|of an example of miscommunication rather than a case of intuition
|leading one astray.

People seem to have the same intuition, though, even after having
been given a rigorous definition.

The fact that it's possible to have an informal notion like this without
a definition in mind is one reason for pursuing informal arguments
like the original poster mentioned. It's also a reason why it's useful
to go beyond them, because one can study curves in an informal
way for a long time before you realize there's any such thing as
what we call a space-filling curve (whether it's the kind of thing you
had in mind by a "curve" or not). Having to say what additional
properties you mean to assume of your "nice smooth" curves adds
to the clarity of the exposition of their properties.

Keith Ramsay

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