Below: “Jupiter’s Zodiac”, an oil painting by Tom Gilmore.
In pie-chart form, the colors of the color-cube are shown by Sign.

The Deduction of the Color-Cube

by Tom Gilmore
Copyright 2017
All graphics by Tom Gilmore
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Part I -- Astrological Houses

A Long-Lost Secret Revealed

The deduction of the color-cube shown below is detailed starting in Part II.  The color-cube is the lost source of the esoteric meanings of the astrological Houses. 

The edges are labeled with Signs, and the faces with Planets.  Each Sign is an edge that connects 2 faces in unique pairs.  For example, refer to the cube above to see that Leo, the front-right edge, pairs the Sun and Mercury. The chart below lists the Signs in astronomical sequence, showing the Planet pairs for each Sign.  You can verify the list by examining the color-cube above.

 1 Aries           Mars    Sun                 
 2 Taurus         Moon   Venus             
 3 Gemini        Mars    Mercury         
 4 Cancer         Moon   Sun                 
 5 Leo             Sun      Mercury         
 6 Virgo           Mars    Venus             
 7 Libra           Venus  Mercury         
 8 Scorpio        Mars    Moon              
 9 Sagittarius   Saturn  Sun     
10 Capricorn   Saturn  Venus             
11 Aquarius    Saturn  Mercury         
12 Pisces         Saturn  Moon              

Concatenating the planetary Key-Words listed below, the planetary pairs reveal the lost source of the traditional Hermetic interpretation of the Houses. 

"Planet"           Key-Words                  Key-Words
 
Mars                Active              Initial to Intermediate
Sun                                          Self     
Mercury          Structure         Mentality
Venus              Relations         Social Position           
Moon                                       Regulator
Saturn              Transition       Mature

House        Pairs                      Concatenation                         Hermetic Tradition
 
 
1         Mars    Sun                  Active Self                              Body & Personality
 2         Moon   Venus              Regulator of Social Position  Possessions & Obligations
 3         Mars    Mercury          Initial Mentality                     Lower Mind & Education
 4         Moon   Sun                  Regulator of Self                    Homelife & Mother
 5         Sun      Mercury          Self Mentality                         Emotionality & Creativity
 6         Mars    Venus              Intermediate Social Position  Employment & Health
 7         Venus  Mercury          Structured Relationships        Marriage & Partners
 8         Mars    Moon               Intermediate Regulator          Transition & Inheritance
 9         Saturn  Sun                 Mature Self                             Friends and Hopes
                                                                                    Higher Mind & Interests (traditional)
10        Saturn  Venus              Mature Social Position           Positions & Honors
11        Saturn  Mercury          Mature Mentality                    Higher Mind & Interests
                                                                                    Friends and Hopes (traditional)
12        Saturn  Moon               Transitional Regulator           Karmic Debt & Spirituality

It is obvious that the 9th and 11th House interpretations have been switched, because Saturn & Mercury (House 11) is "Mature Mentality", which logically would be "Higher Mind and Interests".  These switched interpretations are shown in gray, underneath the corrected interpretations shown in Orange.

There are a number of single switches made to the Hermetic Tradition by the Occultists hiding the knowledge from the Inquisition, and the switches lend themselves to obvious correction, as with the 9th and 11th Houses.  For example 2 of the letter category designations relevant to deciphering the Kabalistic “Tree of Life Choices” were switched. 

It is clear that the Houses are generally progressing through life.  Mars represents the advent and progression of life (and Mars is distributed through the first 8 Houses), and Saturn represents the transition to death (and Saturn is clumped together in the last 4 Houses).

Sidereal Time

Sidereal periods of rotations and revolutions of astral bodies are measured by a return to facing a given star, while solar periods measure by a return to facing the Sun.  Due to the revolution of the Earth around the Sun in the same direction as the Earth's rotation, starting from facing the Sun a full sidereal rotation of the Earth does not return to facing the Sun.  The Earth must rotate an additional distance to complete a full solar day, since it has moved around the Sun during that time in its orbit.  The average solar day is longer than the sidereal day by 3.9425 minutes.

Sidereal Astrology uses the actual star constellations, while Tropical Astrology is based on the seasons.  Today, in Tropical Astrology, on the spring equinox the Ascendant is by definition at the cusp of Aries, but the actual constellation rising is Aquarius, due to the precession of Earth’s axis (refer to article on Sun, Earth, Moon).  To work with Sidereal Astrology the Tropical Zodiac must be shifted back by 2 Signs, such that the spring equinox is Aquarius, followed by Pisces and then Aries. 

The Natal Horoscope

The Natal Ascendant is the Sign rising at the horizon at the moment of birth (first breath).  A Natal Horoscope first locates the Signs of the Planets by degrees, and places them in a pie-chart of the Zodiac (seen at left below).  To locate the planets an Ephemeris is used, which logs the daily planetary positions for noon at Greenwich, England (zero degrees longitude).  The time of birth is adjusted to Greenwich-time by adding (if west of Greenwich) or subtracting (if east) 4 minutes for each degree of the longitude of birth (irregular time zones and daylight savings complicate this).  The time of birth, adjusted to Greenwich-time, is used to proportion the planetary locations between the bracketed noon position logs in the Ephemeris.

Note: Greenwich Mean Time (GMT) is the average time at which the Sun passes the zero longitude (Greenwich Meridian), but due to the varying velocity of Earth’s elliptical orbit the solar day varies in duration by time of year.  The elliptical orbit and the tilt of the axis combines to vary the discrepancy between the Greenwich Mean Time (an average) and when the Sun actually crosses the Greenwich Meridian (ahead by up to 16 ½ minutes, and behind by as much as 14 minutes), with the result that the calculated ascendant using GMT is often inaccurate.

After the Planets are located, the cusps of the Signs of the Houses are positioned on the pie-chart, automatically placing the Planets in the Houses.  The Ascendant is the Sign (by degree) that is rising on the horizon at the moment of birth.  The Houses are numbered, and begin with the Ascendant (as seen at right below). 

To position the cusps of the Houses a “Table of Houses” is used.  A single table suffices, set for the cusp of Aries, because subtracting the sidereal time (found in the daily Ephemeris) adjusts any day of the year to the spring equinox (cusp of Aries).  However, the table has entries for every degree of latitude, because a circle seen at an angle is oval, and the greater the angle (called the declination) the more squished the oval, so the Table of Houses delineates cusps for the Houses for each degree of latitude.  The House segments are wider at the top of the oval and narrower at the sides of the oval.

Esoteric Astrology (interpretation of the Natal Horoscope) is based on a generalized psychological system of human characteristics.  It is primarily a platform for psychological counseling (possibly a Bohemian product of traveling Gypsies).  The system of astrology defines characteristics common to all people, so interpretations are only selecting a personalized subset from a totality of aspects that all apply to everyone.  Thus it is essentially irrelevant if the horoscope is accurate, uses stars or seasons, or corrects the switched Houses of 9 and 11.

There is no established scientific connection between personal psychological characteristics and either the stars or the seasons.

Beyond the static esoteric interpretations of the Natal Horoscope, progressive esoteric astrology compares the natal planetary configuration with the current planetary configuration.  It is possible that the angular relationships between Sun, Earth and Moon (and perhaps the other planets as well) affect the configuration of molecules of air, and stamp the body with that configuration at first breath.  This concept could validate progressive astrology as comparing current air molecule configurations (being breathed) to the stamp of the first breath.

Part II – Astro-Logic

Factors of 12

The science of astronomy and the art of esoteric astrology are irrelevant to Astro-Logic, which only uses the names of the constellations (called Signs) and the names of the Planets as labels of components of the logic.  (Planet means roving permanent astral bodies, which includes the Sun and Moon).

The astro-logic associated with the Signs has to do with the factoring of 12 into (4x3) and (6x2).

The article on the Fixed Cross discusses the traditional (12=4x3) permutation of “elements” and “polarities”.  The elements are Fire, Earth, Air, and Water, and the polarities are positive, negative, and neutral (Cardinal, Fixed, and Mutable).  The permutation is shown in the chart below.

 

Deducing the Color-Cube

The mathematical symmetry of (12=4x3) and (12=6x2) set me looking for the (6x2).  I noticed that (12=6x2) matched with the geometry of a cube’s 12 edges, in that each edge joins a pair of the six faces.  Since the 12 edges could only be the 12 Signs, I decided that the faces would be associated to 6 of the 7 traditional Planets.

I noticed a relevant pattern in the astrological tradition of associations between Signs and Planets known as exaltation.   Of the various lists of exaltations that I encountered, there were 8 associations that were common to most of them, and the first 5 were the same in all the lists (shown in teal below).  

Sign             element  exalted Planet 

Aries (1)         Fire     Mars
Taurus (2)      Earth  Venus
Gemini (3)      Air      Mercury
Cancer (4)      Water Moon
Leo (5)            Fire     Sun

Scorpio (8)      Water  Mars
Capricorn(10) Earth   Saturn
Aquarius(11)   Air       Saturn

There is a traditional association of element/planet/color of
Earth to Venus (yellow),
Air to Mercury (green),
Water to Moon (blue), and
Fire to both Mars and the Sun (red).

The correspondence between element and planet is evident in the exaltation of Signs 1 through 5.

It is the color that is significant, so I show the traditional colors of the Planets in their labels:
Sun, Venus. Mercury, and Moon.

These associations led me to assign the 4 element/planet associations (to all 12 Signs) as the first planet of the planet-pair of each edge of the cube.  This is shown on the list below under the heading “element Planet”.  The 2 Planets (Mars and Saturn) in the exalted list above, that are not already represented by element/planet associations, are shown in brown on the list below, under the heading “extra”.

Sign        element Planet         extra

Aries               Sun
                  Mars
Taurus            Venus 
Gemini            Mercury
Cancer            Moon
Leo                  Sun
Virgo              Venus             
Libra              Mercury        
Scorpio           Moon              Mars
Sagittarius     Sun
Capricorn      Venus              Saturn
Aquarius        Mercury         Saturn
Pisces              Moon 

The 4 Signs with second exalted Planets (in brown above) are distributed in the 4 elements, with Sun (Aries) and Moon (Scorpio) associated with Mars, and Mercury (Aquarius) and Venus (Capricorn) associated with Saturn. 

This list was sufficient to dictate both the planet/colors of the cube-faces, and the Signs associated to the cube-edges.

Each cube-face is a single color, so the distribution of the 12 Signs to 4 elements (12=4x3) required 3 Signs of each color on 4 of the 6 faces.

Also, due to the “extra” list, the Mars and Saturn faces had to have common edges with at least 2 of the 4 element-faces.  The only way this could occur is if the 4 element-faces were all centered on a common plane.

In orienting the color-cube in space, I arranged the 4 element-faces as the vertical faces of the cube, as shown below. 

I placed the active Mars on top and the passive Saturn on the bottom, which seemed intuitively appropriate.

The 4 Signs involved with the “extra” list (in brown above) dictated that the 3 Signs on each of the element-faces had to be arranged as shown below.  This is highlighted with triangular colored lines connecting the 3 Signs.

Notice the coherent symmetry of the colored triangles, confirming the logic in the astro-logical deduction.  The solved color-cube above dictates the missing second planetary pairs (shown in black below). 

Aries               Sun                  Mars
Taurus            Venus             
Moon
Gemini            Mercury        
Mars
Cancer            Moon             
Sun
Leo                  Sun                 
Mercury
Virgo              Venus             
Mercury
Libra              Mercury        
Venus
Scorpio           Moon              Mars
Sagittarius     Sun                 
Saturn
Capricorn      Venus              Saturn
Aquarius        Mercury         Saturn
Pisces              Moon             
Saturn

Part III – Ramifications of the Color-Cube

Journeys of Gilgamesh, and Electron Spin

The deduction of the colors of Mars (orange) and Saturn (purple) is detailed in Part IV (these colors are used in the following astro-logic).

In the myth of the “(Mortal) Journeys of Gilgamesh”, there are 22 chapters that end with the disappearance of Gilgamesh into the western desert (his death), but there are actually 2 more chapters that delve into his “afterlife” (his eternal journey).  It was the full 24 chapters that led to the discovery of electron spin.  Each chapter (steps of the journey) has either direct or oblique references both a Planet and a Sign.  I found that many of the direct references corresponded with the edges (and their paired planets), and having deduced the color-cube the oblique references were revealed to also match.

In the Gilgamesh myth the Signs of the Zodiac are called "double-hours".  This is because there are 12 Signs on the ecliptic and 24 hours, so each Sign spans 2 hours.  This relates to the 24 steps (chapters) of the eternal journey.  In a cube, the 12 edges each connect a unique pair of 2 faces, such that in the journey each edge is approached on one face and is departed from on another face, involving 2 faces to each of the 12 edges (2x12=24).

These Sign/Planet correspondences are listed by chapter number below.

Leo                  1  Sun  à        2  Mercury
Gemini           
3  Mercury     4  Mars
Aries               5  Mars           6  Sun
Cancer            7  Sun              8  Moon
Scorpio          
9  Moon          10 Mars
Virgo               11 Mars          12 Venus
Libra              13
Venus         14 Mercury
Aquarius       
15 Mercury    16 Saturn
Capricorn        17 Saturn       18 Venus
Taurus             19 Venus         20 Moon
Pisces              21 Moon         22 Saturn
Sagittarius     23 Saturn       24 Sun
à Leo             Sun      à

Due to the jumbled order of the Signs in the myth, it would have been extremely difficult to deduce the color-cube from the astrological clues of the journeys of Gilgamesh.  However, plotting the Journey on the color-cube revealed a continuous connection, a looping eternal journey (as illustrated below).  You can verify the cube journey to the list above.

The myth starts with the Sun in Leo (marked with an S on the journey diagram above).  Although the culturally modified Greek version of the myth (where Gilgamesh is Hercules) has only 12 “labors” (having lost the planetary coordination), they begin with “strangling” the Nemean Lion (Leo).  The strangling was also a misinterpretation.  As depicted below, Gilgamesh merely headlocks the lion (see the article Headlocks of the Fixed Cross).

 Assyrian beard removed from this photo of Assyrian statue of Gilgamesh

In his right hand Gilgamesh headlocks the tree serpent.

The myth refers to the “eternal journey of the serpent”, which generally describes the undulating flow of the closed loop of paths.  I had already developed the Geocubic Model, based on spheres compressed inside cubes, and I noticed that by projecting the journey path to the inside of the cube and onto a contained sphere, a smooth looping “serpent” path was produced.  Seeing this, I recognized that I had found the form of the never-ending electron spin as illustrated below.

In addition I had found the origin of the tradition of the serpent representing knowledge.

In Egypt this eternal concept was reduced to a serpent eating its tail, encircling the solar disc Ra.  See the Egypt article.

The Polarity-Color-Cube and Time

In the Geocubic Model, the cubic matrix of impenetrable force planes is flashing in and out of existence, and this flashing is the cause of the flow of time (which can only be measured by motion).

The Polarity-Cube

The Cube shown below reveals a polarity pattern involving the 12 edges and 6 faces of the cube.  The cube diagram labels the 12 edges with a permutation of 4 colors assigned to the vertical faces of the cube (Yellow, Blue, Red, Green) combined with 3 polarity conditions (+ - 0), positive, negative, and neutral (Cardinal, Fixed, and Mutable). 

A triangle connects the 3 polarities on each vertical face of the cube, and these triangles all face in the same rotational direction (clockwise).  No two triangles have the same configuration of polarity assignments.  The 6 square faces, each having 4 edges, combine 4 edge polarities, revealing that all 3 pairs of opposite faces have the same combined polarity (labeled by large polarity symbols at the face centers).

The Polarity-Cube is symbolic of the mechanism of time.  The attraction of opposite polarities (+,-) creates a current in the direction the triangles point (clockwise).  The symbolic “rotation” of the colored faces creates a current of alternating polarity, from + to – to + to – and on.  This represents energizing (+) and de-energizing (-) the force planes of the matrix, or a flashing on and off, from existing (+) to not-existing (-) and back to existing (+) endlessly (subject to eventual termination).  Endlessness in time is called eternity, and in mathematics is called infinity.  Eternity and infinity are imaginary words.  If infinity were real, then infinity plus one would prove infinity was finite.  The same is true of eternity plus a day.

Yellow and Red are +
Green and Blue are

 

Notice that the + faces are the "warm" colors of yellow and red, and the – faces are the "cold" colors of green and blue.

Part IV – Quarks and the Color-Cube

The Deduction of the Color-Number-Cube

From the pairs of planets joined by the 12 edges of the color-cube, and numerical/astrological clues on Tarot cards, I was able to deduce a numerical association with the colors of the faces.

To reiterate, the Planet pairs of the Signs relevant to the deduction are:
Aries is Mars and the Sun
Taurus
is Venus and the Moon.
Leo is, Mercury and the Sun
Aquarius is Saturn and Mercury
Pisces, is Saturn and the Moon

5 astrological/numerical clues found on Tarot cards, enumerated below, were adequate to the deduction.

Card 4 has the horns of a bull pictured, making Taurus(4)
            so the, sum of Venus and the Moon is 4.

Card 15 of the Tarot has a ram pictured, and this is the symbol of Aries(15),
            so the sum of Mars and the Sun is 15.

Card 11 has a male lion pictured, making Leo(11)
            so the sum of Mercury and the Sun is 11.

Card 14 has a figure pouring water between 2 jugs (the water-bearer of Aquarius(14)),
            so the sum of Saturn and Mercury is 14.

Card 13 has fishes pictured on it.  Fishes are the symbol of Pisces(13)
            so the sum of Saturn and the Moon is 13.

From the numerical value Tarot-clues of these 5 Signs, and using additive pigment colors, the following deductions are made.

Taurus = 4       =Moon + Venus         since Blue + Yellow = Green, confirming Mercury is green, Mercury=4 =Taurus

Aries =15        =Mars + Sun
Leo = 11          =Mercury + Sun         The Sun is common to Aries(15) and Leo(11), and (15-11=4), so
                                                            Mercury(4) + 4 = Mars(8)

Aquarius = 14 =Mercury + Saturn     Mercury is common to Leo(11) and Aquarius(14), and (14-11=3), so
                                                            Sun + 3 = Saturn      

Aries(15) = Mars(8) + Sun. so Sun=7

Saturn = Sun(7) + 3, so Saturn=10

Pisces(13) = Moon + Saturn(10), so Moon=3

Taurus(4) = Moon(3) + Venus, so Venus=1

For the colors of Mars(8) and Saturn(10), since 8 and 10 must combine using only 1, 3, 4 and 7, it follows that 8 must equal 7+1, and 10 must equal 7+3.

Mars(8)=7+1 =Red + Yellow, so Mars is Orange
Saturn(10)=7+3 =Red + Blue, so Saturn is Purple

The deduced Color-Cube is shown above, and the deduced numerical values of the Signs and Planets are:

Venus(1) - Moon(3) - Mercury(4) - Sun(7) - Mars(8) - Saturn(10)

Aries(15)         Sun(7) + Mars(8)
Taurus(4)        Venus(1) + Moon(3)
Gemini(12)     Mercury(4) + Mars(8)
Cancer(10)      Moon(3) + Sun(7)
Leo(11)           Sun(7) + Mercury(4)
Virgo(9)          Venus(1) + Mars(8)
Libra(5)           Mercury(4) + Venus(1)
Scorpio(11)     Moon(3) + Mars(8)
Sagittarius(17)   Sun(7) + Saturn(10
Capricorn(11)   Venus(1) + Saturn(10)
Aquarius(14)   Mercury(4) + Saturn(10)
Pisces(13)       Moon(3) + Saturn(10)

A Symbolic Clue

Another clue (not used) is that the symbol for Mercury combines the symbols for Venus and the Moon.

The Quark Connection

I noticed that the additive pigment colors corresponded with the addition of the associated numbers (as follows).

Green is Blue plus Yellow (4=3+1)
Orange is Red plus Yellow (8=7+1)
Purple is Red plus Blue (10=7+3)

Description: C:\Geocubic\quark2.jpg

I also noticed that 3 face-pairs sum to 11 (7+4, 8+2, and 10+1).
These pairs are joined in the cube expansion shown above.

It turned out that these color and number associations to the faces of the 3 paired-faces of the color-cube are symbolic of the Quark components of atomic particles.

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