tgivens
12-21-2007, 07:02 AM
I have been a student of Astrology and the I Ching since about 1994 and I've been investigating how these two systems of thought are semantically and symbolically related. I began researching these two divination systems after extensively studying Richard McKeon and a very fascinating book titled “On Knowing – The Natural Sciences,” a book that was, in effect, a compilation of lecture notes from students who attended his courses at University of Chicago (404 - Document Not Found) and the above book contains a fascinating tetrahedral schema of philosophic and scientific terminology that I am certain will become the semantic "Rosetta Stone" for all scholarly Astrology and I Ching practitioners. Having said all that, I’m going to simply lay out all the ideas.
Richard McKeon managed to introduce a system of thinking about philosophic language that was, in fact, a system of Astrology disguised as a tetrahedral representation of Natural Philosophy and Science. His schema of philosophic semantics depicts a set of vectors or transformations between four key concepts called “Cognates,” which are the variables operative in cognition. The four cognates are:
Knowledge (Mode of Thought = Assimilation), Transcendental
Known (Mode of Thought = Resolution), Functional
Knowable (Mode of Thought = Construction), Reductive
Knower (Mode of Thought = Discriminatin), Perspectival
These ideas are easily mapped to the four elements of Fire, Earth, Air and Water:
Knowledge (Transcendental) = Air
Known (Functional) = Water
Knowable (Reductive) = Earth
Knower (Perspectival) = Fire
Twelve transforms, tensors, or vectors can be drawn between any two variables. The vectors begin with an idea that can be considered primary or (causal) and the vector ends with an idea that characterizes the effect produced by the initial cause. These vector definitions describe a kind of semantic “alchemy,” a kind of cognitive “transmutation” of conceptual elements involved in knowing. The following list of vectors will show Richard McKeon’s philosophic terminology and the corresponding astrological signs they represent:
1) Knower --> Knowable = Actional Principle (Intentional, Thinking) = Aries
2) Knowable --> Knowledge = Entitative Interpretation (Practical, Feeling) = Taurus
3) Knowledge --> Knower = Dialectical Method (Systemization, Perceiving) = Gemini
4) Known --> Knowledge = Reflexive Principle (Subjective, Judgement) = Cancer
5) Knower --> Known = Existential Interpretation (Productive, Sensing) = Leo
6) Knowable --> Known = Logistic Method (Proof, Intuition) = Virgo
7) Knowledge --> Known = Comprehensive Principle (Rational, Judgement) = Libra
8) Known --> Knower = Essential Interpretation (Instrumental, Sensing) = Scorpio
9) Knower --> Knowledge = Operational Method (Discovery, Perceiving) = Sagittarius
10) Knowable --> Knower = Simple Principle (Objective, Thinking) = Capricorn
11) Knowledge --> Knowable = Ontological Interpretation (Theoretic, Feeling) = Aquarius
12) Known --> Knowable = Problematic Method (Inquiry, Intuition) = Pisces
You could, of course, represent each cognate in the form of a vector if it was necessary:
Knower --> Knower = Knower
Knowable --> Knowable = Knower
Knowledge --> Knowledge = Knowledge
Known --> Known = Known
The traditional Astrological “modes” (Cardinal, Fixed, Mutable) correspond with what McKeon calls “Moments of Thought”:
Principles (Thoughts) = Cardinal
Methods (Processes) = Mutable
Interpretations (Manifestations) = Fixed
Here is how Richard McKeon specifically described the Moments of Thought:
Principles (n-terms, a Set)
Methods (3-Terms, Syllogism)
Interpretations (2-Terms, Propositions)
The four cognates can be assigned numerical values that correlate with their sequence in the Astrological cycle:
Knower = Fire = 1
Knowable = Earth = 2
Knowledge = Air = 3
Known = Water = 4/0
Each sequentially numbered Astrological signs can be rewritten as a numeric transform:
1) Aries = 1-->2
2) Taurus = 2-->3
3) Gemini = 3-->1
4) Cancer = 0-->3
5) Leo = 1-->0
6) Virgo = 2-->0
7) Libra = 3-->0
8) Scorpio = 0-->1
9) Sagittarius = 1-->3
10) Capricorn = 2-->1
11) Aquarius = 3-->2
12) Pisces = 0-->2
A very curious pattern emerges when you analyze the numeric values of all the right-most vector variables when all the vectors are arranged in the circular Astrological sequence. I will show the numeric sequence value (identifier) for each sign first so as to provide a reference:
| 11 | 12 | 01 |
___|____|____|____| ____
| | | |
10 | | | | 02
___| ___| ___| ___| ___
| | | |
09 | | | | 03
___| ___| ___| ___| ___
| | | |
08 | | | | 04
___| ___| ___| ___| ___
| | | |
| 07 | 06 | 05 |
Now here are the ending values for each sequentially numbered vector shown above:
| 2 | 2 | 2 |
___|____|____|____| ____
| | | |
1 | | | | 3
___| ___| ___| ___| ___
| | | |
3 | | | | 1
___| ___| ___| ___| ___
| | | |
1 | | | | 3
___| ___| ___| ___| ___
| | | |
| 0 | 0 | 0 |
Let’s now consider the Tic-Tac-Toe grid to be comprised of nine “orthogonal” or “tetrahedral” values. Each cell of the grid adds up to a number that is the sum of the four directional values found on the periphery of the grid. The result is the following:
| 2 | 2 | 2 |
___|____|____|____| ____
| | | |
1 | 6 | 6 | 6 | 3
___| ___| ___| ___| ___
| | | |
3 | 6 | 6 | 6 | 1
___| ___| ___| ___| ___
| | | |
1 | 6 | 6 | 6 | 3
___| ___| ___| ___| ___
| | | |
| 0 | 0 | 0 |
A very curious set of numbers appear. They reminds me of a particular set of passages from the Book of Revelations:
“This calls for wisdom. If anyone has insight, let him calculate the number of the beast, for it is man’s number. His number is 666 (Revelations 13:18, NIV)
There is also the classic reference to the Beast resembling three specific animals and a vague animal with regenerative abilities, which I interpret as representing the tetrahedral qualities of Man (the beast), characterized by the Fixed signs of the Zodiac.
The beast I saw resembled a leopard, but had feet like those of a bear and a mouth like that of a lion. The dragon gave the beast his power and his throne and great authority. One of the heads of the beast seemed to have had a fatal wound, but the fatal wound had been healed. The whole world was astonished and followed the beast. (Revelations 13:2-3, NIV)
Leopard (Aquarius?, Air?)
Bear (Taurus?, Earth?)
Lion (Leo, Fire)
A fatal wound that had been healed (Scorpio, Water)
What if the age old divination system we call Astrology has always had an occult representation that was tetrahedral and triangular in nature?
Constructing a visual representation of the tetrahedral representation of the Zodiac signs is fairly easy to do.
Here’s an interesting twist; Reverse all of the vector orientations along each of the six edges...and you end up with a new set of four points. What do you suppose the meaning of these “new” points might be?
Well, I suspect that the I Ching and the Astrological tetragrammaton have the following symbols in common:
Fire (Astrological) = Fire (I Ching)
Earth (Astrological) = Earth (I Ching)
Air (Astrological) = Heaven (I Ching)
Water (Astrological) = Water (I Ching)
This implies that the “inverse” vertexes of the “inversioned” tetragrammaton could correlate with the other four I Ching symbols:
Thunder
Wood/Wind
Mountain
Lake
But I really don’t want to guess what the conventional meanings of the I Ching trigrams are...I want to be able to COMPUTE them. So, in order to derive the CONVENTIONAL meanings for the I Ching Trigrams using Astrological definitions, the following technique is required; you must assign specific Bigram symbols to specific vertexes comprising the Astrological tetrahedron. I will be using a Bottom (1)-To-Top(2) methodology for depicting the Bigrams (vectors).
2 -----
1 ----- Knowledge (Trancendental) ( ----- ==> ----- )
2 -- --
1 -- -- Knowable (Reductive) ( -- -- ==> -- -- )
2 -----
1 -- -- Known (Functional) ( -- -- ==> ----- )
2 -- --
1 ----- Knower (Perspectival) ( ----- ==> -- -- )
Now, in order to create an I-Ching like representation of an astrological sign, say Aires, you have to stack two Bigrams vertically, starting at the bottom and ending at the top.
Let's use the "Knowing" Tetrahedron and the four "elements" in this example of constructing an "Aires" Quadragram and then compressing it down to a Trigram:
4 -- --
3 -- -- Knowable (Reductive)
^
|
| Aires (Knower --> Knowable)
|
2 -- --
1 ----- Knower (Perspectival)
In order to create the trigram that corresponds to this Quadragram, consider only the bottom three lines as relevant, which leaves:
-- --
-- --
----- (Thunder)
The I Ching's concept of "Thunder" is a pretty accurate descriptor of the Aries energetic disposition.
There is, however, another Quadragram capable of producing the Thunder Trigram resultant:
4 -----
3 -- -- Known (Functional)
^
|
| Leo (Knower --> Known)
|
2 -- --
1 ----- Knower (Perspectival)
This implies that Thunder may be related to both Aires and Leo. Perhaps Aires is analogous to the sound, voice, or Word that thunders within the actively thinking mind and perhaps Leo is the energy of the lightning flash?
Let's take the idea of Capricorn and see how it manifests the using the Tetrahedral logic:
4 -- --
3 ----- Knower (Perspectival, "Fire")
^
|
| Capricorn (Knowable --> Knower)
|
2 -- --
1 -- -- Knowable (Reductive, "Earth")
The Capricorn Quadragram reduces down to the following Trigram
3 -----
2 -- --
1 -- -- Mountain
Again, the Mountain Trigram can be derived by a second combination of Bi-grams:
4 -----
3 ----- Knowledge (Transcendental, "Air")
^
|
| Taurus (Knowable --> Knowledge)
|
2 -- --
1 -- -- Knowable (Reductive, "Earth")
So it seems that Mountain is an I-Ching idea related to Capricorn and Taurus.
You can repeat this procedure for all of the Trigrams. It should be remembered that this generalized approach to discerning the Astrological correlates to the Trigram meanings IS NOT the same set of meanings used to arrive at a Hexagram judgment. I am pretty confident that the judgments are derived from the “obverse” and “reverse” Astrological tetrahedrons.
Well, this is just the tip of the iceberg. Once you have the obverse and inverse tetrahedrons, a CUBE can be constructed where each of the twelve edges of the cube explicitly map to each of the Zodiac signs. To be more accurate, each edge connects the beginning points (primary ideas) of two vectors pertaining to any one Zodiac sign.
The ternary Hsuan Ching monograms and bigrams are, I believe, a different and more sophisticated method of representing the Astrological signs AND the six psychological functions that generalize the pairs of Astrological vectors that reside on each edge of the Tetrahedron: Thinking (T), Feeling (F), Perceiving (P), Judging (J), Sensing (S), Intuiting (N).
Here’s a potential way to represent each edge of the Tetrahedron in general and each vector in particular:
+T = Aires
+/-T = Thinking
-T = Capricorn
+F = Aquarius
+/-F = Feeling
-F = Taurus
I am prone to want to experiment with the triple-valued nature of ternary monogram symbols in the following way:
+ = ( ----- )
+/- = ( - - - )
- = ( -- -- )
Thus the above Thinking and Feeling vectors and edges can be formatted in the following way:
T( ----- ) = Aires (Intentional)
T( - - - ) = Thinking
T( -- -- ) = Capricorn (Deterministic)
F( ----- ) = Aquarius (Theoretic)
F( - - - ) = Feeling
F( -- -- ) = Taurus (Practical)
I am also inclined to correlate the ternary symbols to the “number of terms” each of the Astrological “Modes” (Moments of Thought according to Richard McKeon) pertain to:
Interpretations (2-Terms, Propositions) = ( -- -- ), Manifestation
Methods (3-Terms, Syllogism) = ( - - - ), Process
Principles (n-Terms, Set) = ( ----- ), Thought
There is not only a way to use ternary monograms to denote the components of tetrahedron edges, but there is a way to represent all six tetrahedron edges using ternary bigrams:
- - -
----- , ----- ==> - - - , Judging (J)
-----
- - - , - - - ==> ----- , Perceiving (P)
-- --
----- , ----- ==> -- -- , Thinking (T)
-----
-- -- , -- -- ==> ----- , Feeling (F)
- - -
-- -- , -- -- ==> - - - , Sensing (S)
-- --
- - - , - - - ==> -- -- , Intuiting (N)
There’s certainly lots of room for experimentation. I hope this provides food for thought and I welcome any and all comments you may have.
Tim Givens
Richard McKeon managed to introduce a system of thinking about philosophic language that was, in fact, a system of Astrology disguised as a tetrahedral representation of Natural Philosophy and Science. His schema of philosophic semantics depicts a set of vectors or transformations between four key concepts called “Cognates,” which are the variables operative in cognition. The four cognates are:
Knowledge (Mode of Thought = Assimilation), Transcendental
Known (Mode of Thought = Resolution), Functional
Knowable (Mode of Thought = Construction), Reductive
Knower (Mode of Thought = Discriminatin), Perspectival
These ideas are easily mapped to the four elements of Fire, Earth, Air and Water:
Knowledge (Transcendental) = Air
Known (Functional) = Water
Knowable (Reductive) = Earth
Knower (Perspectival) = Fire
Twelve transforms, tensors, or vectors can be drawn between any two variables. The vectors begin with an idea that can be considered primary or (causal) and the vector ends with an idea that characterizes the effect produced by the initial cause. These vector definitions describe a kind of semantic “alchemy,” a kind of cognitive “transmutation” of conceptual elements involved in knowing. The following list of vectors will show Richard McKeon’s philosophic terminology and the corresponding astrological signs they represent:
1) Knower --> Knowable = Actional Principle (Intentional, Thinking) = Aries
2) Knowable --> Knowledge = Entitative Interpretation (Practical, Feeling) = Taurus
3) Knowledge --> Knower = Dialectical Method (Systemization, Perceiving) = Gemini
4) Known --> Knowledge = Reflexive Principle (Subjective, Judgement) = Cancer
5) Knower --> Known = Existential Interpretation (Productive, Sensing) = Leo
6) Knowable --> Known = Logistic Method (Proof, Intuition) = Virgo
7) Knowledge --> Known = Comprehensive Principle (Rational, Judgement) = Libra
8) Known --> Knower = Essential Interpretation (Instrumental, Sensing) = Scorpio
9) Knower --> Knowledge = Operational Method (Discovery, Perceiving) = Sagittarius
10) Knowable --> Knower = Simple Principle (Objective, Thinking) = Capricorn
11) Knowledge --> Knowable = Ontological Interpretation (Theoretic, Feeling) = Aquarius
12) Known --> Knowable = Problematic Method (Inquiry, Intuition) = Pisces
You could, of course, represent each cognate in the form of a vector if it was necessary:
Knower --> Knower = Knower
Knowable --> Knowable = Knower
Knowledge --> Knowledge = Knowledge
Known --> Known = Known
The traditional Astrological “modes” (Cardinal, Fixed, Mutable) correspond with what McKeon calls “Moments of Thought”:
Principles (Thoughts) = Cardinal
Methods (Processes) = Mutable
Interpretations (Manifestations) = Fixed
Here is how Richard McKeon specifically described the Moments of Thought:
Principles (n-terms, a Set)
Methods (3-Terms, Syllogism)
Interpretations (2-Terms, Propositions)
The four cognates can be assigned numerical values that correlate with their sequence in the Astrological cycle:
Knower = Fire = 1
Knowable = Earth = 2
Knowledge = Air = 3
Known = Water = 4/0
Each sequentially numbered Astrological signs can be rewritten as a numeric transform:
1) Aries = 1-->2
2) Taurus = 2-->3
3) Gemini = 3-->1
4) Cancer = 0-->3
5) Leo = 1-->0
6) Virgo = 2-->0
7) Libra = 3-->0
8) Scorpio = 0-->1
9) Sagittarius = 1-->3
10) Capricorn = 2-->1
11) Aquarius = 3-->2
12) Pisces = 0-->2
A very curious pattern emerges when you analyze the numeric values of all the right-most vector variables when all the vectors are arranged in the circular Astrological sequence. I will show the numeric sequence value (identifier) for each sign first so as to provide a reference:
| 11 | 12 | 01 |
___|____|____|____| ____
| | | |
10 | | | | 02
___| ___| ___| ___| ___
| | | |
09 | | | | 03
___| ___| ___| ___| ___
| | | |
08 | | | | 04
___| ___| ___| ___| ___
| | | |
| 07 | 06 | 05 |
Now here are the ending values for each sequentially numbered vector shown above:
| 2 | 2 | 2 |
___|____|____|____| ____
| | | |
1 | | | | 3
___| ___| ___| ___| ___
| | | |
3 | | | | 1
___| ___| ___| ___| ___
| | | |
1 | | | | 3
___| ___| ___| ___| ___
| | | |
| 0 | 0 | 0 |
Let’s now consider the Tic-Tac-Toe grid to be comprised of nine “orthogonal” or “tetrahedral” values. Each cell of the grid adds up to a number that is the sum of the four directional values found on the periphery of the grid. The result is the following:
| 2 | 2 | 2 |
___|____|____|____| ____
| | | |
1 | 6 | 6 | 6 | 3
___| ___| ___| ___| ___
| | | |
3 | 6 | 6 | 6 | 1
___| ___| ___| ___| ___
| | | |
1 | 6 | 6 | 6 | 3
___| ___| ___| ___| ___
| | | |
| 0 | 0 | 0 |
A very curious set of numbers appear. They reminds me of a particular set of passages from the Book of Revelations:
“This calls for wisdom. If anyone has insight, let him calculate the number of the beast, for it is man’s number. His number is 666 (Revelations 13:18, NIV)
There is also the classic reference to the Beast resembling three specific animals and a vague animal with regenerative abilities, which I interpret as representing the tetrahedral qualities of Man (the beast), characterized by the Fixed signs of the Zodiac.
The beast I saw resembled a leopard, but had feet like those of a bear and a mouth like that of a lion. The dragon gave the beast his power and his throne and great authority. One of the heads of the beast seemed to have had a fatal wound, but the fatal wound had been healed. The whole world was astonished and followed the beast. (Revelations 13:2-3, NIV)
Leopard (Aquarius?, Air?)
Bear (Taurus?, Earth?)
Lion (Leo, Fire)
A fatal wound that had been healed (Scorpio, Water)
What if the age old divination system we call Astrology has always had an occult representation that was tetrahedral and triangular in nature?
Constructing a visual representation of the tetrahedral representation of the Zodiac signs is fairly easy to do.
Here’s an interesting twist; Reverse all of the vector orientations along each of the six edges...and you end up with a new set of four points. What do you suppose the meaning of these “new” points might be?
Well, I suspect that the I Ching and the Astrological tetragrammaton have the following symbols in common:
Fire (Astrological) = Fire (I Ching)
Earth (Astrological) = Earth (I Ching)
Air (Astrological) = Heaven (I Ching)
Water (Astrological) = Water (I Ching)
This implies that the “inverse” vertexes of the “inversioned” tetragrammaton could correlate with the other four I Ching symbols:
Thunder
Wood/Wind
Mountain
Lake
But I really don’t want to guess what the conventional meanings of the I Ching trigrams are...I want to be able to COMPUTE them. So, in order to derive the CONVENTIONAL meanings for the I Ching Trigrams using Astrological definitions, the following technique is required; you must assign specific Bigram symbols to specific vertexes comprising the Astrological tetrahedron. I will be using a Bottom (1)-To-Top(2) methodology for depicting the Bigrams (vectors).
2 -----
1 ----- Knowledge (Trancendental) ( ----- ==> ----- )
2 -- --
1 -- -- Knowable (Reductive) ( -- -- ==> -- -- )
2 -----
1 -- -- Known (Functional) ( -- -- ==> ----- )
2 -- --
1 ----- Knower (Perspectival) ( ----- ==> -- -- )
Now, in order to create an I-Ching like representation of an astrological sign, say Aires, you have to stack two Bigrams vertically, starting at the bottom and ending at the top.
Let's use the "Knowing" Tetrahedron and the four "elements" in this example of constructing an "Aires" Quadragram and then compressing it down to a Trigram:
4 -- --
3 -- -- Knowable (Reductive)
^
|
| Aires (Knower --> Knowable)
|
2 -- --
1 ----- Knower (Perspectival)
In order to create the trigram that corresponds to this Quadragram, consider only the bottom three lines as relevant, which leaves:
-- --
-- --
----- (Thunder)
The I Ching's concept of "Thunder" is a pretty accurate descriptor of the Aries energetic disposition.
There is, however, another Quadragram capable of producing the Thunder Trigram resultant:
4 -----
3 -- -- Known (Functional)
^
|
| Leo (Knower --> Known)
|
2 -- --
1 ----- Knower (Perspectival)
This implies that Thunder may be related to both Aires and Leo. Perhaps Aires is analogous to the sound, voice, or Word that thunders within the actively thinking mind and perhaps Leo is the energy of the lightning flash?
Let's take the idea of Capricorn and see how it manifests the using the Tetrahedral logic:
4 -- --
3 ----- Knower (Perspectival, "Fire")
^
|
| Capricorn (Knowable --> Knower)
|
2 -- --
1 -- -- Knowable (Reductive, "Earth")
The Capricorn Quadragram reduces down to the following Trigram
3 -----
2 -- --
1 -- -- Mountain
Again, the Mountain Trigram can be derived by a second combination of Bi-grams:
4 -----
3 ----- Knowledge (Transcendental, "Air")
^
|
| Taurus (Knowable --> Knowledge)
|
2 -- --
1 -- -- Knowable (Reductive, "Earth")
So it seems that Mountain is an I-Ching idea related to Capricorn and Taurus.
You can repeat this procedure for all of the Trigrams. It should be remembered that this generalized approach to discerning the Astrological correlates to the Trigram meanings IS NOT the same set of meanings used to arrive at a Hexagram judgment. I am pretty confident that the judgments are derived from the “obverse” and “reverse” Astrological tetrahedrons.
Well, this is just the tip of the iceberg. Once you have the obverse and inverse tetrahedrons, a CUBE can be constructed where each of the twelve edges of the cube explicitly map to each of the Zodiac signs. To be more accurate, each edge connects the beginning points (primary ideas) of two vectors pertaining to any one Zodiac sign.
The ternary Hsuan Ching monograms and bigrams are, I believe, a different and more sophisticated method of representing the Astrological signs AND the six psychological functions that generalize the pairs of Astrological vectors that reside on each edge of the Tetrahedron: Thinking (T), Feeling (F), Perceiving (P), Judging (J), Sensing (S), Intuiting (N).
Here’s a potential way to represent each edge of the Tetrahedron in general and each vector in particular:
+T = Aires
+/-T = Thinking
-T = Capricorn
+F = Aquarius
+/-F = Feeling
-F = Taurus
I am prone to want to experiment with the triple-valued nature of ternary monogram symbols in the following way:
+ = ( ----- )
+/- = ( - - - )
- = ( -- -- )
Thus the above Thinking and Feeling vectors and edges can be formatted in the following way:
T( ----- ) = Aires (Intentional)
T( - - - ) = Thinking
T( -- -- ) = Capricorn (Deterministic)
F( ----- ) = Aquarius (Theoretic)
F( - - - ) = Feeling
F( -- -- ) = Taurus (Practical)
I am also inclined to correlate the ternary symbols to the “number of terms” each of the Astrological “Modes” (Moments of Thought according to Richard McKeon) pertain to:
Interpretations (2-Terms, Propositions) = ( -- -- ), Manifestation
Methods (3-Terms, Syllogism) = ( - - - ), Process
Principles (n-Terms, Set) = ( ----- ), Thought
There is not only a way to use ternary monograms to denote the components of tetrahedron edges, but there is a way to represent all six tetrahedron edges using ternary bigrams:
- - -
----- , ----- ==> - - - , Judging (J)
-----
- - - , - - - ==> ----- , Perceiving (P)
-- --
----- , ----- ==> -- -- , Thinking (T)
-----
-- -- , -- -- ==> ----- , Feeling (F)
- - -
-- -- , -- -- ==> - - - , Sensing (S)
-- --
- - - , - - - ==> -- -- , Intuiting (N)
There’s certainly lots of room for experimentation. I hope this provides food for thought and I welcome any and all comments you may have.
Tim Givens