[FOM] Removing Deep Pathology 1

Molino, Gianmarco MOLINO at hartford.edu
Wed Aug 19 13:32:10 EDT 2015

On Aug 18, 2015, at 9:33 PM, Hendrik Boom <hendrik at topoi.pooq.com<mailto:hendrik at topoi.pooq.com>> wrote:

On Tue, Aug 18, 2015 at 02:47:34PM -0400, Hendrik Boom wrote:

4)  The partition of 3-space by (infinitely long) non-parallel lines.
4a)  "      "     "     "     "  non-parallel circles.

If it's the one I vaguely remember, no.  But it's truly beautiful.

It was the Hopf fibration I was thinking of.  Which i beautiful, but
just what does nonparallel mean for circles?

-- hendrik
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I found http://mathforum.org/kb/thread.jspa?forumID=13&threadID=28874&messageID=89334#89334, an old post from September ’97 that I think might be relevant (especially if the W.Taylor who posted the list here and the W.Taylor who posted in mathforum are the same.)  The post is a proof by Brian Scott of the existence of a partition of R^3 into circles that are parallel in the sense that no two circles are co-planar and no two circles intersect.

While this is certainly related to the idea Hopf fibration, I don’t believe they are necessarily equivalent; can someone correct me if I’m wrong on this?

I am interested, however, in the question of pathology as it relates to the mathforum posting; specifically, the question was raised in another thread (http://mathforum.org/kb/message.jspa?messageID=93509) as to how acceptable the use of AC was in Brian Scott’s proof, specifically in regards to “Brouwer’s notion of a choice sequence,” with which I am not very familiar. Is this an argument over intuitionism?

Thank you for any comments, corrections, and other information,

Gianmarco Molino
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