[Wittrs] popping in re mathematics foundations

  • From: kirby urner <kirby.urner@xxxxxxxxx>
  • To: wittrsamr@xxxxxxxxxxxxx
  • Date: Sat, 8 May 2010 18:56:54 -0700

Remarks on the Foundations of Mathematics (RFM)
is one of LW's lesser known works, coming after the
TLP and PI in notoriety.

I've poked my head in here a number of times to
relate foundational work in a particular set of geometric
language games (a domain) with RFM, because of
the illumination I get in both directions (LW helps
me understand, plus I find his work more understandable,
because of this bridge).

The domain in question evaluates triangles and
tetrahedra as models of 2nd and 3rd powering respectively,
in a way that's logically consistent i.e. appears not to
break any rules.[0]  This is precisely the kind of
gestalt-switching therapy we find applied in RFM
(in in the PI for that matter), so I'm finding this example
quite apropos.

Once you make this switch, to a unit volume tetrahedron,
you've got a lot of discoveries close at hand, many
still being disseminated.  In brief, you get a concentric
hierarchy of roughly spherical polyhedra with rational
whole number volumes, mixed with the expected
incommensurables.  The volumes are such as 1 for
the tetrahedron (as mentioned), 3 for the cube, 4 for
the octahedron, 6 for the rhombic dodecahedron,
and 20 of 2.5 for cuboctahedra of obvious edge
lengths.  A rhombic triacontahedron weighs in with
volume 5, also 7.5... and I could go on for more para-

What's interesting about this geometry is that it's
author dedicated his write-up to one H.S.M. Coxeter,
who was a student of Wittgenstein's, at least for
awhile, and committed his suites such that the
Blue and Brown Books might be written.  This was
a time when LW wanted a smallish set of listeners,
and so made up a game where they'd take notes
for those not selected to be in attendance.  Many
of us here are familiar with the bio and so know
some details about this chapter.

Coxeter wrote a book entitled 'Regular Polytopes'
among others and I've charted pages 71 and 119
as especially important.  In Wittgenstein, I keep
going to Part 2 of the PI and the duck/rabbit, as
I'm thinking gestalt switches are at the heart of
this philosophy, what he meant by "leaving every-
thing as it is" (i.e. what flips is ineffable, or has
the capability of so being).

Earlier in this archives, I go into much closer
detail regarding the specifics of the mathematics,
especially its logical foundations.  I was revisiting
a lot of that this morning in another archive, will
provide this link:


For those not familiar at all with this thread:
in some dimension we go back to Karl Menger,
a dimension theorist I stumbled upon.  Turns
out he was pretty famous in some circles and
his "geometry of lumps" essay continues to be
well received.  He provides another way of being
"non-Euclidean" (other than by jiggering with the
5th postulate), thereby challenging some of our
cherished notions of "dimensionality" and how
that concept must work.  He shows us a different
set of language games, alien yet grokkable.  He
calls it a "geometry of lumps".  Merge that with
the "4D" of a tetrahedrally based logic, and
you've got plenty of grist for a small army of
mathematicians and/or philosophers.[1]

I also recruit among computer scientists.  Most
recently I had the good fortune to lead a three
day workshop in Baltimore at the Johns Hopkins
campus, working for AURA and Holden Web.[2]

For some idea of what "tetrahedral mensuration"
might look like in Python, a computer language,
I'll close with a link to this logic (a demo /exercise
in one of the workshop segments):


I'm not sure there's much that's questionable here,
as no theses are being advanced.  However there might
be some need for clarification.  Standing by if so.


PS:  for those of you tracking brain <-> consciousness
literature, I recommend 'Tomorrow's Children' by
Dr. Susan Greenfield.  I was just at her lecture on
Thursday evening and found her mind/brain discourse
to be useful philosophy.  She's more in the "moving target"
school, i.e. consciousness may be qualitatively changing
thanks to technologies, though not necessarily for the
better (she's hoping to spark debate, brings a sense
of urgency to the equations, though also some humor).
Here's a write-up of her talk, with a picture of the book



[0]  http://www.rwgrayprojects.com/synergetics/s09/figs/f9001.html

[1]  http://coffeeshopsnet.blogspot.com/2009/03/res-extensa.html

[2]  http://worldgame.blogspot.com/2010/04/python-gig.html

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