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From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>)
Newsgroups: net.math
Subject: Re: Re: Strange Shapes
Message-ID: <6067@brl-tgr.ARPA>
Date: Sun, 25-Nov-84 22:22:51 EST
Article-I.D.: brl-tgr.6067
Posted: Sun Nov 25 22:22:51 1984
Date-Received: Wed, 28-Nov-84 03:02:57 EST
References: <3489@ecsvax.UUCP> <121@talcott.UUCP>
Organization: Ballistic Research Lab
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> Painting an object means putting a coat of paint *of uniform thickness* on
> the object.  All objects with finite volume and infinite surface area have
> arbitrarily small cracks and crevices where a coat of paint "does not fit".
> 
> As someone aptly pointed out, an example of such an object is a snowflake.
> Try putting a coat of paint on a snowflake.

"On" an object in practice means "within cohesive distance" of the object.
There are always tiny cracks in practice but they are covered by paint.
This means that it is easy to paint a snowflake; just immerse it.

And there you have the difference between a physicist and a mathematician.

This is not as facetious as it sounds.  If you admit conventional concepts
of infinity, set theory, and the like, then you support such paradoxes as
the Banach-Tarski dismantling of a sphere into a few congruent parts that
can be reassembled into a smaller sphere, and so forth.  There is more to
reality than that, since in practice no real sphere can be so rearranged.