[Wittrs] Re: Modeling 2nd / 3rd powering etc. (tetrahedral mensuration)
- From: Justintruth <truth.justin@xxxxxxxxx>
- To: wittrsamr@xxxxxxxxxxxxx
- Date: Thu, 18 Feb 2010 15:18:23 -0800 (PST)
I for one would have been very glad to have had the fact that it is a
convention that area is measured in numbers of squares exposed and
made made far more explicit as I think the fact that it was not caused
me many problems when trying to understand general relativity.
In studying the subject I came accross covariant and contravarient
vectors and the metric tensor, of course immediately, and their
defininiton in terms of transformations was not intuitive. My exposure
to these subjects was only in the context of non eclidian geometry - a
deficiency that is usual I think as most people approach the subject
in order to understand general relativity.
Only when I realized that the concepts that motivated covarient and
contravarient vectors existed in planar geometry in a sense did I
realize that my lack of understanding was a deficiency that had
nothing to do with curved spaces. Unmixing the two was a great step
that need not have takes so long. I further realized that the
pythagorean theorum works for right triangles only because the unit of
area is squares and that it will work for non-right triangles if
instead of square area a parralellegram is used. The relationship
between the numeric and geometric views had a degree of freedom that
was missing from the very begining - even if in the end it is a scale
change -The problem occured probably when I studied Euclidian geometry
in high school and the fact that it wasn't exposed tripped me up much
latter.
So for a long time my penetration of the material of general
relativity was prevented by a deficiency in my thinking about the
notion of area and this deficiency was precisely the fact that I did
not realize that there was a fairly arbitray choice made to use the
square to measure area instead of a rhombus or even more generally a
parallelegram. This choice leads to different geometric
representations of co and contra variant vectors for the same
algebraic formulas.
To me the real issue is not whether triangle or parallelegram is used
as the right triangle corresponds to the square area case. The issue
is the angle subtended by the two triangles. I know that Fuller was
interested in triangles because of their structural properties a
square being dependent on the triangles in its corners in a sense and
a much weaker, or completely weak in the limit, structure but for pure
geometry the issue is the rhombus vs the square - or the rectangle vs
the parallelegram I think.
On another note, I will pass on some hearsay to you. I was told that
Fuller spent a night at a house that had a copy of some of Teihard de
Chardin's books. They claim was that Fuller was found in the basement
crying after he had stayed up all night reading. He was moved to tears
because he realized that Teihard de Chardin was dead and that he had
missed his chance to speak to him. Its definately unconfirmed rumor
but if you are interested perhaps it could be traced to first persons.
Sometimes our intellectual climate pushes the idea that an idea can be
mine to such a point that we are hiding our ideas and selves from each
other so that our ideas are not "stolen". I think Linus Pauling and
Watson and Crick had that happen to them and, unfortunately, I think
Bucky never recovered from the Dymaxion experience, never trusted
enough and consequently his interactions with some key people never
occured and the challenges that should have been leveled at his work
early never occurred. He ended up being therefore more of a quirky
side show albeit one of stunning success. How much better it would
have been had the environment been more honest.
That having been said I do not think that Synergetics was a coherent
metaphysics. I poured over it a long time ago and it seemed too
dependent on geometric metaphor. It seems to be afflicted by a
confusion of physics with metaphysics which is at the core of a kind
of secular fundamentalism. I prefer to separate them clearly in order
not to fall prey to fundamentalism.
On Feb 11, 12:12 am, kirby urner <kirby.ur...@xxxxxxxxx> wrote:
> 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/nct...http://mathforum.org/kb/thread.jspa?threadID=2036171&tstart=0http://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
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