*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- graphs. 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: http://groups.yahoo.com/group/synergeo/message/58683 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): http://www.4dsolutions.net/presentations/holdenweb/ch.py 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. Kirby 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 cover: http://worldgame.blogspot.com/2010/05/tomorrows-people.html ENDNOTES: [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 ========================================== Need Something? Check here: http://ludwig.squarespace.com/wittrslinks/

**Follow-Ups**:**[Wittrs] Re: popping in re mathematics foundations***From:*Rajasekhar Goteti

**[Wittrs] Re: [C] popping in re mathematics foundations***From:*Rajasekhar Goteti

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