Channel 26 META-SCIENCE : GROWTH. FORM AND STRUCTURE Geometric Extensions of Consciousness excerpts from Ann e Griswold Tyng's article This was first printed in Zodiac 19 - a review of con- temporary architecture . The evolution of man's consciousness was built, atom by atom, into the configurations of matter and mind. Both for our understanding of its evolution and for its own ex- tensions of consciousness, the form of mind-matter finds clues in geometry . of the evolution of total spatial awareness-a repeating cycle in which man's perception and understanding have been stretched asymmetrically in different shapes of ten- sion between the individual and the collective, and be- tween consciousness and unconsciousness. Thus the more sion (a "return to the unconscious" when vitality is re- newed through a reunion with primitive natural sources) instead of being seen as part of a continuous process of expanding spatial awareness . from a balanced axial bilateral order to the movement of ed form of the spiral - a building up of form and energy which are integrated in a new cycle lateral symmetry, a new simplicity of order which includes and integrates the previous complexity, begins a new tational (space) to (time) to spiral (space-time) . ) As "generative molecular elements" inherent in man's own evolution, these principles may provide geometric . today when we know that the relationships of form ex- pressed in these five Platonic Solids are involved in the wa y in which 'fundamental' particles-protons and neu- trons-are built up into atoms of about a hundred dif- ferent elements (according to Pauling's Close-Packed- Spheron Theory and Fuller's proposals of atomic close- packing)' and are involved in the way in which different arrangements of these atoms form the building blocks of a million or so different forms of matter. both natural and . These five Platonic Solids-the only regular forms possible in three dimensional space, each with all of its faces the same and with the angles at which the faces meet each other the same-are involved, not only in the spatial or- ganization of forms at the level of nuclei of atoms and molecules, but also in cells, organs, plants, animals, the human embryo, the psychic structure of man, the works of man and in the astronomical forms of the universe which pre-existed man . Previously invisible ordering of the primordial atoms within us, revealed by the electron microscope, gives proof of internal geometry in natural forms . The four stages of symmetric form in this geometric pro- gression, as in the cyclic extensions of human conscious- spiral, with each stage seen as the motion of simpler forms of more complex shapes . . , concepts, Empedocles proposed as the building blocks of everything fire, air, earth and water . On mathemetical grounds Plato, in his Timaeus, determined the 'exact' forms of the smallest parts of these elements as the five shapes we now call the Platonic Solids dron, earth the cube, air the octahedron, water the icosa- hedron, and as the symbol of the cosmos, the dodecahe- dron Anne first architectural degree (M . Arch . worked for a the architect Louis associating im on the City in the Museum of Modern Art exhibit "Vision- ary . Based on a triangulated three dimensional sys- tem which had been used previously as structure separate space, as in Bucky Fuller's "octet truss", the which appears to have a life of its first honeycomb . Her independent forming principles, fo r which grant in '65, has been oriented primarily toward principles hierarchical ordering of form . editor of Zodiac, states, "It is geometry, with its oscillations be- tweensymmetry andasymmetry, to Anne Tyng, offers of or- becoming ." Louis Kahn, Bucky Fuller, Law Whyte the zoologist Adolf the work . J ung (Man and His Symbols of synthesis . In her articles, Urban Space Systems as Living Form in the .A . I .C. Journal 19), found has between the whole fam- ily of Platonic Solids not previously known by man . " ) and ,structure and human creativity . The polarity of a tetrahedron can be expressed in the po- suggest- . On e tetrahedron in two positions, which have a
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8/14/2019 ExcerptGeometric Extensions of Conciousness
A proportional i n c r ea s e i n t h e r ad i u s o f r ot a t io n o f t h e
h e l i c a lf o r m s , e x p r e s s i n g r o t a t i o n a l t e n s i o n s , r e s u l t s i n
spiralf o r m s , t h e f o u r t h s t a g e o f c o m p l e x i t y i n t h e c y c l e .
T h e o n l y r a t i o w h i c h s a t i s f i e s t h e c o n d i t i o n o f a l o g a r i t h -
m i c s p i r a l i n w h i c h w i d t h o f t u r n ' i n c r e a s e s a t a f i x e d r a t i o
t o l e n g t h i s a g a i n t h e r a t i o o f t h e D i v i n e P r o p o r t i o n. T h e
shifting order of these forms between polarity and rota-
t i o n i n c l u d e s t h e p r e v i o u s o r d e r w i t h i n t h e n e w o r d e r , s o
t h a t r o t a t i o n a l i n c l u d e s t h e p o l a r i t y o f b i l a t e r a l , h e l i c a l
w i t h i t s o w n p o l a r i t y i n c l u d e s r o t a t i o n p l u s p o l a r i t y , a n d
spiral w i t h i t s o w n d o m i n a n c e o f r o t a t i o n i n c l u d e s p o l a r i t y
p l u s r o t a t i o n p l u s p o l a r i t y , w i t h t h e n e w b i l a t e r a l p h a s e
i n c l u d i n g a l l t h e o r d e r i n g o f f o r m o f t h e p r e v i o u s c y c l e.
W h i l e i t c l e a r l y a p p e a r s t o b e a s p e c i a l a c h i e v e m e n t o f l i v -
i n g f o r m s , t h e r e p e a t i n g c y c l e o f b i l a t e r a l , r o t a t i o n a l , h e l i -
c a l a n d s p i r a l a p p a r e n t l y i s n o t v a l i d f o r n o n - l i v i n g o r ' i n -
o r g a n i c ' forms . The energies and configurations
p r o g r e s s i v e l y b u i l t u p i n t h e r h y t h m i c i n t e r p l a y o f r o t a t i o n
a n d p o l a r i t y r e s u l t i n t h e gradual i n t e n s i f i c a t i o n o f s t r u c -
t u r e a n d t h e f l e x i b l e v i t a l i t y w h i c h i s a s p e c i a l a c h i e v e -
m e n t o f ' h i g h e r ' l i v i n g f o r m s . ' I n o r g a n i c ' f o r m i s b a s e d o n
a g e n e r a l l y m o r e r i g i d b i l a t e ra lsymmetry, as in such atom-
i c s t r u c t u r e s a s g r a p h i t e , s a l t , p e r o n s k i t e , c o p p e r , d i a -
m o n d , c a r b o n d i o x i d e , a n d c r i s t a b a l i t e .
An example which does indicate evolution of formt h r o u g h a c o m p l e t e c y c l e i s t h e s t r u c t u r e of hemoglobin,w h i c h t o o k t h e 2 2 y e a r s w o r k o f P e r u t z a n d h i s a s s o c i a t e s
to uncover . This extraordinary configuration of 10,000atoms includes the b i l a t e ra l tetrahedral bonding of car-b o n a t o m s i n t h e g l y c i n e m o l e c u l e s , t h e
r o t a t io n a l c l u st e r-
ing in the heme molecules, the intricately helical alphaand beta chains which in turn are folded into irregulars p i r a l s , a n d f i n a l l y , e a c h o f t h e f o u r s p i r a l l i n g m y o g l o b i n - -
t y p e p a r t s n e s t l e d a n d i n t e r l o c k e d i n a s y m m e t r i c a l t e t r a -
hedral arrangement to form an overall bilateral symmetry .
T h i s b i l a t e r a l s y m m e t r y r e a f f i r m s a b a s i c s i m p l i c i t y o f o r -
g a n i z a t i o n o v e r t h e c o m p l e x i t y o f d i f f e r e n t i a t e d p a r t s t o
start a new cycle-a hierarchy of form . W i t h a l l t h e i n t e r-
n a l c o m p l e x i t y o f t h i s s t r u c t u r e , w e c a n b a r e l y c o n c e i v e o f
the fantastic number of hierarchies within hierarchieswhich include and give meaningful organization to the280 million such hemoglobin molecules contained in as i n g l e r e d b l o o d c e l l - w h i c h i n i t s e l f t a k e s t h e
r o t a t i o n a l
form of a disc . Not only does there appear to be ap r o g r e s s i n t h e l i f e f o r m s c o r r e s p o n d i n g t o t h e g e o m e t r i c
progression toward complexity and increase in scale, hutt h i s p r o g r e s s i o n c a n b e s e e n a s a r e p e a t i n g o n e w i t h e a c h
new cycle building hierarchy upon hierarchy which in-d i c a t e a t e a c h s t a g e o f d e v e l o p m e n t t h e
record of its earli-
e r e v o l u t i o n , t h e h i e r a r c h i e s o f f o r m a n d t h e h i e r a r c h i e s
of energy evolving from the i n t e r p l a y o f p o l a r i t y a n d r o t a -
t i o n .
F o r m t h u s f i n d s i t s o w n f o r m , e x t e n d i n g f e e l e r s , g i l l s a n d
t e n t a c l e s t o t h e w o r l d a r o u n d i t , i n i t s r o t a t i o n a l t e n s i o n -
ing, expanding its mag ic circle to new concepts of space
-from the first articulationoffinorfingertothespiritual
dimensions of human creativity .
Form finds new helical dimensions, elongating to dif-ferentiate intake and output, strengthening backbone be-t w e e n t u s k a n d t a i l , h e a d a n d a n a l p o l e s , a r t i c u l a t i n g t h e
t e n s i o n s b e t w e e n s p i r i t u a l i t y a n d s e x u a l i t y , s t r e t c h i n g t o
new concepts of time between awareness of darkest ori-g i n a n d h i g h e s t a s p i r a t i o n , b e t w e e n t h e d e p t h s o f t h e u n -
conscious mind and conscious thought .
Form stretches to elaborate both length and breadth ins p i ra l l i ng s h e l l s a n d b r a n c h e s , a n t e n n a e a n d a n t l e r s , d i v i d -
i n g a n d s u b d i v i d i n g i n t o t h e i n t r i c a t e f i l i g r e e o f b l o o d v e s -
s e l s a n d d e l i c a t e n e r v e e n d s , t e n s i o n i n g i n s p a c e a n d t i m e
t o w a r d a n i n f i n i t y o f m a t t e r .
In the fleeting moments of balance between the tensiono f r o t at i o n a nd p o l a ri t y , t h e te n s i o ns o f s p a c e
and time areresolved in bilaterall i v i n g f o r m , t h e t r a n s f o r m a t i o n o f t h e
e n d o f c o m p l e x i t y t o a n e w b e g i n n i n g o f s i m p l i c i t y - a
higher order-the discovery o f t h ec y c l e .
T h e l i f e c y c l e o f t h e b u t t e r f l y i s c l e a r l y d e f i n e d i n f o u r
phases : t h e r ot at io na l symmetry of its eggs, the helicals y m m e t r y i n i t s f o r m a s a c a t e r p i l l a r o r l a r v a , t h e s p i r a l
symmetry of the pupa of chrysalis form and its dramaticrebirth in a magnificent form of bilateral symmetry
. T h e
frog follows a cycle from ther o t a t i o n a l symmetry of the
z y g o t e , t o h e l i c a l embryonic bodystalk, to spiral form ofthe tapering tadpole to bilateral symmetry of the maturef r o g . The bilateral human being evolved from numberlessh i e r a r c h i e s o f c y c l e s o f f o r m , f r o m t h e p r i m o r d i a l o r d e r -
ing of atoms and molecules, goes through the cycle againi n t h e e a r l y s t a g e s o f e m b r y o n i c d e v e l o p m e n t f r o m t h e b i -
lateral, then rotational cleavages of the ovum, to theh e l i c a l
b o d y s t al k o f 1 8 o r 1 9 d a y s , t o t h e s pi ra l embryo ofa b o u t 4 w e e k s t o t h e m i n i a t u r e c o m p l e x i t y i n t e g r a t e d i n t o
u l t i m a t e b i l a t e ra l form as a 10 week 2 inch embryo of po-tential human being .
8/14/2019 ExcerptGeometric Extensions of Conciousness
T h e p s y c h i c s y n t h e s i s o f ' r e b i r t h ' i s f a r r e m o v e d f r o m t h e
structure of hemoglobin, but in each case the simplified
relationship of complex internal structure creates a newunity, and, in the process of psychic individuation, an e w i n v o l u t i o n o f s t r u c t u r e c r e a t e s f r o m a l l t h e c o m p l e x -
i t y o f a c o l l e c t i v e a n d p r i m i t i v e o r i g i n a n u n i q u e l y i n d i v i d -
u a l f o r m . S o a re l a t i o n s h i p t o t h e p ri n c i p l e s o fs p a c e , t i m e ,
c a u s a l i t ya n d s y n c h r o n i c i t y i s v a l i d f o r t h e p s y c h i c c y c l e ,
space expressing the tension of individual man with col-lective consciousness of external environment, time thetension between conscious thought and unconsciousmemory, causality the interrelated and combined ten-sions of both space and time, between the individuatingconscious psyche and the vast reaches of primordialmemory in the collective unconscious, and synchronicity
t h e b a l a n c i n g o f t e n s i o n s , t h e s y n t h e s i s o f s p a c e a n d t i m e
in concepts such as immortality. Jung wrote " . .. Thef e e l i n g o f i m m o r t a l i t y , i t s e e m s t o m e , h a s i t s o r i g i n i n a
p e c u l i a r f e e l i n g o f e x t e n s i o n i n s p a c e a n d t i m e . " '
G e n e r a l l y i n c y c l e s o f h u m a n c r e a t i v i t y t h e p e r i o d s o f r o -
t a t i o n a l t e n s i o n r e l a t e t o p e r i o d s o f e x t e r n a l o r d e r i n g o f
the psyche, periods of expansion, of materialism andp r a c t i c a l i t y , o f o p e n n e s s , s p a c e , o f c o n c e r n w i t h l i f e , l i g h t ,
s u n , o f p h y s i c a l c o m f o r t a n d p l e a s u r e , o f r a t i o n a l i s m , o f
b e l i e f i n t h e e s s e n t i a l g o o d n e s s a n d c r e a t i v i t y o f m a n; t h e
p h a s e s o f h e l i c a l t e n s i o n r e l a t e t o p e r i o d s o f i n t e r n a l o r -
d e r i n g o f t h e p s y c h e , o f s u b j e c t i v i t y a n d i n s t i n c t , o f c o n -
t a i n m e n t a n d v e r t i c a l i t y ( p o l a r i t y ) , o f c o n c e r n w i t h o r i -
gins, with past and future and the element of t i m e , withd e a t h a n d t h e p r i n c i p l e o f e v i l , o f d a r k n e s s , o f e m p h a s i s
o n i r r a t i o n a l i t y , e m o t i o n a n d i n n e r s p i r i t ; the phases ofspiral
tension relate to periods of increased tension and
containment of opposites, of complexity, of bizarre ande x o t i c s t y l e s , o f f a s c i n a t i o n w i t h t h e o c c u l t , o f e x a g g e r a t e d
motion and energising of form, forms with complexcurves, pointed arches, ovals, winding processionals andlabyrinths, tapering towers and spires, forms dema-t e r i a l i z e d b y l i g h t , f o r m s w i t h w e i g h t l e s s n e s s , w i t h p r o -
g r e s s i v e l y d i m i n i s h i n g h o r i z o n t a l a n d v e r t i c a l d i m e n s i o n s ,
of the combined t e n s i o n s of space and time ; and thep h a s e s o f b i l a t e r a l s y n t h e s i s of t e n s i o n s r e l a t e t o p e r i o d s
o f s e r e n i t y a n d b a l a n c e , o f u n i t y , o f c u b i c f o r m s w i t h e m -
phasis on horizontality and planar surfaces, forms withr e c t i l i n e a r i t y , s i m p l i c i t y , a x i a l i t y a n d s o l i d i t y , f o r m s e x -
p r e s s i n g t h e i n t e g r a t i o n o f t e n s i o n s i n e q u i l i b r i u m , f o r m s
embodying the p r in c ip l e o f a b st r ac t io n free of space and
time .
F r o m c o u n t l e s s l e v e l s o f s u c h h i e r a r c h i e s t h e b r a i n o f m a n
was formed, the evolution of human consciousness andthe psychic potentials of 'individuation' and rebirth,
m a n ' s s e a r c h f o r t h e s e c r e t o f c r e a t i o n , f o r c o n c e p t s o f i m -
m o r t a l i t y f r e e o f t i m e , s p a c e , c a u s a l i t y - f o r s y n c h r o n i c i t y
f o r t h e i m m o r t a l ' s t a t i c ' s y n t h e s i s o f m o r t a l ' k i n e t i c ' c o n -
c e p t s .
1 .Buckminister Fuller lectured on and illustrated relationships o f
c l o s e -p a c k e d s p h ere s a s p ro po s a l s o f a t omi c c o nfi g ura ti o ns i n 1 9 4 9 .
p r i n t e das " I t e m 0 " p r e p a r e d b y N o rt h C a ro l i n a S t a t e S c h o o l o f
D e s ig n s tu d en ts i n 1 95 5 . L i n u s P a u l i n g 's C l o se - P a c k e d - S p h e r o n
Th e o ry o f t h e N u cl e u s a p p e are d i n S c i en c e O ct o b er1 9 6 5 .
2 . P . 1 4 2 , C . G . J u n g ,T h e A r c h e t y p e s a n d t h e C o l l e c t i v e U n c o n - s
c i o u s ,
3 . S e e C . G . J u n g , " S y n c h ro n i c i t y - A n A c a s u a l C o l l e c t i o n P ri n -
c i p l e , " i nTh e In t e rp re t a t i o n o f N a t u re a n d t h e P s y c h e , with W .
