The Projective Geometry Connection - RS & GW

Rudolf Steiner: ... When we do analytic geometry, we perform operations which we subsequently look for spatially; but in all our figuring we actually remain outside of a direct contemplation of geometrical forms. It is important to grasp this because when we consider projective geometry, we arrive at a very different picture of what we are doing. Here, as most of you know, we don't calculate, we really only deal with the intersection of lines and the projection of forms. In this manner we get away from merely calculating around the geometrical forms, and we enter " at least to some degree " the geometrical forms themselves. This becomes evident, for example, when you see how projective geometry goes about proving that a straight line does not have two, but only one point at infinity. If we set off in a straight line in front of us, we will come back from behind us (this is easily understood from a geometrical point of view), and we can show that we travel through exactly one point at infinity on this line. Similarly, a plane has only one line at infinity, and the whole of three-dimensional space has onlyone plane at infinity.
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Tags

  1. projective geometry
  2. thoth tarot

Comments


Mark de LA says
Chapter V Synopsis

Lecture V March 21, 1921

Modern sense-physiology and the twelve senses. The neurologist Meynert. Controversy in the Giordano Bruno Association concerning mental imaging. Theodor Ziehen's psychology. Analytic and synthetic (projective) geometry. Moriz Benedikt and mathematics. Inspirational cognition of the rhythmic system. The Yoga system. The nature of symbolism. The psychological origin of cultic action. The modern intellect. Earlier cultic activity and modern scientific experiment.



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Mark de LA says
Ming, a private dialect of Chinese, is used to condense explanations of the projective geometry to make the diagram and the explanation arrive at the same time on the same page.  It is also used in connection with the Tai Shu commentary on the Yi King.  The best dictionary of such can be found in Book Chameleon 2nd Edition from which this translator is made.


Mark de LA says
MR 2013-06-23 10:08:43 16592
The Tai Shu paper is much more advanced than what Steiner was talking about, but I have not yet found proof that parallel lines meet at infinity in the Tai Shu.  Am hitting the basic projective geometry Tai Shu near Tung Yun to find.



Mark de LA says
seth 2013-06-24 11:17:50 16592
interesting that here RS is oblivious to common geometric nowledge that says: "it  cannot be proven  whether parallel lines meet at infinity or not .... rather that must be something that is assumed".  perhaps RS was asserting that in physical space that would be the case ... i don't know ... your quote does not provide that answer. 
Well, since infinity is of the same flavor as nothing & the end of time you need to experience the the character of projective geometry to grasp such a meeting of lines.  I have scanned the appropriate parts at the beginning of this book:  Projective Geometry by Lawrence Edwards 1985.  Believe me it is a lot more cogent than the books GW developed his massive works with . Greg & I took projective geometry at UCLA & most of the geometry was left out in favor of abstract algebra development. ... Enjoy!  It also helps to grasp the 3 different kinds of consciousness that Rudolf Steiner is talking about, i.e. imagination, inspiration & intuition.

Seth says
interesting that here RS is oblivious to common geometric nowledge that says: "it  cannot be proven  whether parallel lines meet at infinity or not .... rather that must be something that is assumed".  perhaps RS was asserting that in physical space that would be the case ... i don't know ... your quote does not provide that answer. 

Seth says
& the Thoth Tarot Deck: http://newsletter.tarotstudies.org/2004/03/projective-synthetic-geometry/


Mark de LA says
Then there is this Scientific American article which asserts a controversy over infinity. It has a link to this article which asserts ZFC Axioms of choice regarding mathematical (or set theoretical) stuff.
Worth reading to keep things in the current mathematical academic context.
In my experience I took a course in projective geometry which was mostly set theory & abstract algebra which left out 99% of the geometry which is where the intuitive & creative imaginative stuff occurs.


Eiamyme says
What is interesting today is that the $3million Breakthrough Prize for mathematics included a research on algebraic geometry in it. GW often uses Peacock's Law as the duality of algebra and geometry. See P.gs
http://icybermind.net/media/hexscans/hexagram31-I/2774.jpg
http://icybermind.net/media/hexscans/hexagram7-BOO%20WHANG/2746.jpg
http://icybermind.net/media/hexscans/hexagram7-BOO%20WHANG/2750.jpg
http://icybermind.net/media/hexscans/hexagram8-PHI/2771.jpg

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