Projective Morphology 16:  Counterspace
Channel: Daniel Hafner
Date: 2021-06-18

First we show that Euclidean geometry is a specialization of projective morphology.  Then we show that there is a polar specialization:  an inside-out geometry, or outside-in.

Familiarity with most of the ideas presented hitherto is presupposed.

This presentation is part of a series:
     1 Polarity  https://youtu.be/1xcRJdxgKuU
     2 The Infinitely Distant  https://youtu.be/nlKTRYDBi1Q
     3 Metamorphosis  https://youtu.be/mW705pKwUvo
     4 Desargues's Triangle Theorem  https://youtu.be/S9uJbCtc1IM
     5 Harmonic Conjugates  https://youtu.be/9dSysBCjMtQ
     6 The Fundamental Harmonic Figure  https://youtu.be/xM__3Rv21BY
     7 Perspective and Projection  https://youtu.be/exly1JXIGSM
     Interlude  https://youtu.be/Us3Hj_CBhBU
     8 Curves of the Second Order  https://youtu.be/gMvsutuNTGg
     9 Proof of Steiner  https://youtu.be/g5CocUQwdbc
     10 Conic Sections  https://youtu.be/m-3Dt-NDMQ0
     11 The Theorems of Pascal and Brianchon  https://youtu.be/Y8mf3gP5tCg
     12 Pole and Polar  https://youtu.be/6DN5ahPHG_Y
     13 Inversion  https://youtu.be/YueFf2XFmXE
     14 Progression and Involution  https://youtu.be/gEJsKXVM0Bk
     15 The Imaginary  https://youtu.be/paKMtN0c6bw
     16 Counterspace  https://youtu.be/hY0ETd75IjM
     The Human Skeleton  https://youtu.be/JzLMQVCjg24

Other topics:  projective geometry, synthetic geometry, projective coordinates, evolution of consciousness, backward time, counter-Euclidean geometry, polar-Euclidean geometry, dual of Euclidean geometry, negative space, extensive space, intensive space, projective proof of the parallel postulate, Cartesian coordinate system, projective coordinate system, projective measurement, center of gravity, axis of levity, parallel translation, shear, mirroring, rotation, Felix Klein, Desargues, Euler line, Rudolf Steiner, Georg von Kaufmann, George Adams, Louis Locher-Ernst, Olive Whicher, Lawrence Edwards, Nick Thomas