[C] [Wittrs] Re: Modeling 2nd / 3rd powering etc. (tetrahedral mensuration)
- From: kirby urner <kirby.urner@xxxxxxxxx>
- To: wittrsamr@xxxxxxxxxxxxx
- Date: Wed, 10 Feb 2010 21:12:01 -0800
Going back to this thread:
http://groups.yahoo.com/group/WittrsAMR/message/1215
... I'm recommending this archive for readings into the
underlying philosophy, regarding how "non-traditional"
triangles and tetrahedra may serve as units of area
and volume respectively.
Remarks on the Foundations of Mathematics deals with
precisely these low level ethnographic or "form of life"
questions, regarding our most logical grammars, such
as Principia Mathematica. That's the level at which we
must deal with the relationship between right angles
and 1st / 2nd / 3rd etc. powering.
Moving from a more 90-degree to more 60-degree
aesthetic will be smoother if we preserve this philosophical
context, i.e. if we accomplish our "gear shifting" in terms of
"language games" (or "namespaces" as the case may
be), combined with new ways of looking.
The switch in question requires only a high school level
of computational ability, but the gestalt changes could
be more challenging, which is where Wittgenstein's
philosophy proves a help.
It's a two way switch we're talking about, i.e. going back
and forth, very like the duckrabbit in that way.
Links:
http://bfi.org/our_programs/bfi_community/synergetics/synergetics/nctm_embraces_synergetics
http://mathforum.org/kb/thread.jspa?threadID=2036171&tstart=0
http://coffeeshopsnet.blogspot.com/2009/12/duck-rabbit.html
Kirby Urner
4Dsolutions.net
PS: recall that H.S.M. Coxeter was Wittgenstein's student
for awhile. Coxeter went on to become the great geometer
of the 20th century. He partially overlapped with Bucky
Fuller and his philosophy (metaphysics) on numerous
occasions, an embedded example in this blog entry:
http://worldgame.blogspot.com/2010/02/small-steps.html
Other related posts:
- » [C] [Wittrs] Re: Modeling 2nd / 3rd powering etc. (tetrahedral mensuration) - kirby urner
