Explanation of the Weekday Order

Sevenfold Star
Menorah
Star of David
Binary Tree
Octahedron
Geometry
Numerical Curiosity
Concluding Remarks

What is attempted here is an explanation why the weekdays are ordered the way they are. This explanation is based on geometry and the polarities and may be part of the knowledge coded into the weekday order.


Sevenfold Star

The Sevenfold Star seems to be the best mnemonic key to the weekday order. It is shown below that there are other keys.

My thanks go to Kevin Tobin, who told me about the "Star of Gaia" in April 1999. Without Kevin's final hint, this page would probably never have been finished.

The Star of Gaia not only incorporates the Sevenfold Star but also the zodiac. The zodiacal calendar is the often unnoticed "parallel calendar" to the Gregorian time system.

Construction Principle

Draw a sevenfold star. Follow the lines of the star and assign a weekday-planet to each point in the order of the weekdays. With the Sun at the top, a meaningful arrangement emerges (image below).

Follow the circle from Saturn in a counterclockwise direction. You will find that the "astrological planets" are ordered by their sidereal (sic!) revolution periods.
The approximate periods are: Saturn (10760 days), Jupiter (4333 days), Mars (687 days), Sun (i.e. Earth; 365 days), Venus (225 days), Mercury (88 days), Moon (27 days).

System

It may be helpful to have a look at the connotation table first. There are four levels:
  1. The Sun at the top represents unity of opposites, full splendour.
  2. The gender and yin-yang polarity Venus-Mars.
  3. The mental and conceptual polarity Mercury-Jupiter. Words, numbers, math, systems of thought.
    Mercury: observation, cunning, research, serving, impartial, uncommitted, intuition, words, math.
    Jupiter: decision, intention, ruling, clarity of vision, lawmaking, rational.
  4. The time polarity Moon-Saturn.
    Moon: cyclical time, periodicities, birth, changing flow, sinusoidal, eternal recurrence, unending.
    Saturn: linear time, uniform flow, death, limitation.

It is interesting that time is at the base of the system.

The left side of the star represents the passive, more female side. The right side stands for the male, active aspects.

The purple thread follows the chakra order. Start at the root chakra (Saturn). Next in the line up the human body are gonads (Moon), solar plexus (Mars), heart (Venus), throat (Mercury), brow (Jupiter). The thread ends at the top of the head (Sun).

Note that horizontal opposites are always directly connected by the thread, pairing male and female aspects: fm-mf-fm-u, unity at the end. The other three connections are oblique and show all three possibilities: directly adjacent (Venus - Mercury), one planet between (Jupiter - Sun), two planets between (Moon - Mars).

Augmentations

The center is occupied by a yin-yang symbol (t'ai ch'i) with the yang side on the right, rising, and the yin side on the left, descending. The circular symbol is embedded in a rosé- or lotos-colored heptagon, that stands for the primal intent, Love.

The colors have been assigned according to the connotation table: Saturn: dark violet, Moon: silver, Mars: fiery red, Venus: verdant green, Mercury: turquoise, Jupiter: royal blue, Sun: golden.

Note that in many imperial flags the "ruling colors" of Jupiter and Mars (blue and red) appear, e.g. in the Union Jack, the Tricolore, the American flag. I don't know about Roman flags, but I guess they had blue and red in them.

The grey circle of time around the Sevenfold Star emphasizes the self-similarity of the diagram: the sun symbol at the top resembles the circle of time and its center.

The circle of time is fuzzy for more than one reason:

Sevenfold Star

There is another possible sevenfold star with less acute points. I preferred the above order, because in the alternative order

Similar arguments apply to the simple weekday heptagon.


Menorah

The Menorah is the Jewish seven-branched candelabrum, symbolizing the seven days of creation. Some things represented in the Sevenfold Star appear again, with a different emphasis.

The weekday order is seen from left to right. The start is at the center (Sunday).

Predominantly male planets have a downward-pointing triangle above them ("broad shoulders"). Predominantly female planets have an upward-pointing triangle above them ("wide hips"). On Sunday, male and female conjoin to form the Star of David ("As above, so below"). Male and female planets alternate in the weekday order (ufmfmfm), more regular than in the chakra order.

The polarities of time, concept/mental, and gender are shown by the half-circle of the menorah. The two branches of each half-circle are always male-female pairs.

The chakra order is realized the following way: start at Saturn, circle to Moon, outward to Mars, circle to Venus. A jump to the other side occurs (7 = 4 + 3, like a musical halftone in a heptatonic scale), to Mercury. Circle to Jupiter, end in the center at the Sun.

Note also the mental/conceptual polarity is outermost. Time is innermost.

Menorah


Star of David

Note that the Star of David has seven fields: six equilateral triangles and one hexagon. Moon, Venus, and Mercury form the female triangle with Mercury at the top. The male triangle carries the polar opposites.

The solar hexagon in the center is equal in size to the six triangles which can be thought of as six opened petals of a flower. If this flower closes, all opposites are united.

The weekday order is shown by the aleph-like figure around the sun. Aleph is the first letter of the hebraic alphabet and a mathematical infinity symbol.

This diagram can be seen as a projection of the octahedron (see below). Six octahedron edges are not shown in the Star of David diagram. They run from point to point of the star and form an outer hexagon.

Star of David

Here is a geometric figure similar to the Star of David: Draw a circle with a compass. With the same radius, draw a circle with its center on the border of the first circle. The overlap area is called vesica pisces, also called mandorla, which is sometimes seen as vertical halo around saints in medieval paintings. Draw two new circles with their centers on the crossing points of the first two circles. Continue, until you have seven circles, one central circle and six around it. Note the similarities to the Star of David.

The Star of David is also called hexagram.


Binary Tree

We have already seen in the above paragraphs that Sunday occupies the center of the week structure. Moreover, the remaining six days split into two groups of three: Mon-Tue-Wed and Thu-Fri-Sat (see also below in the trigram connotations).

It is possible to construct a binary tree, similar to the Menorah above, where unity (Sun) splits into the time polarity first and each time into gender and mental/conceptual branches:

                          Sun
                           |
                    /---------------\
                    |               |
                  Moon            Saturn
                   |                 |
              /--------\         /-------\
              |        |         |       |
              |      Venus     Mars      |
           Mercury                    Jupiter

This binary tree may be seen as a pyramid with four stones as basis (Venus and Mars in the back), two stones in the middle layer, and one top stone.


Octahedron

Set each polarity pair as opposites on the ends of the three main octahedron axes and put the Sun at the center.

Presently, I favor
Mercury (lapis philosophorum) at the zenith and Jupiter at the nadir.
Saturn at the front of the time axis and Moon at the back. This is the perspectivically longer horizontal axis in the image below.
Venus a the left of the gender axis and Mars at the right.

The eight triangular planes each combine three endpoints of the three polarity axes time, gender, and conceptual/mental.

Weekday and chakra order can be visualized along the edges and the three primal axes (space).

Following the weekday order, we remain on the upper left triangle of the octahedron (Moon, Mars, Mercury). Then we change from zenith to nadir and traverse the opposite plane (Jupiter, Venus, Saturn). Like in the Menora, a distinct 1 + 2 * 3 structure emerges.
Coincidentally, 1, 2, and 3 are the only ciphers that occur in the
likeness-sequence.

Following the chakra order the passing through the center is emphasized. In the weekday order, we have only two passings, here we have 3 (or 3 +1/2, if you want): Saturn, through center to Moon, along edge to Mars, through center to Venus, along edge to Mercury, through center to Jupiter, and back to center (Sun).

Octahedron

Here is how to see the similarity between the Star of David and the octahedron: Mentally rotate the octahedron, so that the center of the female triangle (Moon-Venus-Mercury) is in your line-of-sight with the center. Then the front and back triangles form the Star of David (see above).

The eight equilateral triangles (faces) of the octahedron can be matched to the eight trigrams (ba gua) of Chinese geomancy (feng shui). The Yin-Yang polarities are:

Mercury-Jupiter: Heaven (upper line).
Venus-Mars: Man (middle line).
Moon-Saturn: Earth (bottom line).

The eight octahedron faces then represent

                chinese feng shui:
trigram planet  element name     direction  number 
                         
-- --   Mercury
-----   Mars    water   Water    North      1
-- --   Moon            (voyage)  

-- --   Mercury
-- --   Venus   earth   Earth    Southwest  2
-- --   Moon            (relations)
 
-- --   Mercury
-- --   Venus   wood    Thunder  East       3
-----   Saturn          (elders)

-----   Jupiter
-----   Mars    wood    Wind     Southeast  4
-- --   Moon            (blessings)


The t'ai ch'i (yin-yang) is in the center   5


-----   Jupiter
-----   Mars    metal   Heaven              6
-----   Saturn          (helpful friends)

-- --   Mercury
-----   Mars    metal   Lake                7
-----   Saturn          (children, creativity)

-----   Jupiter
-- --   Venus   earth   Mountain            8
-- --   Moon            (contemplation)

-----   Jupiter
-- --   Venus    fire   Fire                9
-----   Saturn          (enlightenment)



the magical square this system is based on:


       SE              S            SW

             Wind     Fire    Earth
                   ---------  
                  |4   9   2|
                  |         |
       E  Thunder |3   5   7| Lake  W
                  |         |
                  |8   1   6|
                   ---------  
         Mountain    Water    Heaven

       NE              N            NW


                     

Sunday is in the center of the octahedron, hence represents all aspects. Since each other weekday occupies a point of the octahedron, each "normal" weekday is formed by four faces and hence four directions associated with it:

weekday    trigrams                           
                                              
Monday     Water Earth  Wind    Mountain
Tuesday    Water Heaven Wind    Lake 
Wednesday  Water Earth  Thunder Lake
Thursday   Fire  Heaven Wind    Mountain 
Friday     Fire  Earth  Thunder Mountain 
Saturday   Fire  Heaven Thunder Lake
Sunday     all eight

Traditionally the eight trigrams are ordered in opposite pairs: Water-Fire, Earth-Heaven, Wind-Thunder, and Mountain-Lake.

The first three weekdays are Water, the last three Fire. In the second column Earth and Heaven alternate regularly. The pairs Wind-Thunder and Mountain-Lake appear in such an order to emphasize the "turning" of the week between Wednesday and Thursday. A nice ordering was to be expected from the structure of the trigrams.

I hope this correspondence of trigrams and weekdays is of value to anyone - it seems to follow naturally from the octahedral structure.

The octahedron, a figure in space, shows forth the order of time. I like to think of this geometrical body as a luminous double pyramid. It can also be thought of as a "star" with six spokes along the main axes - or eight spokes through the planes. Counting these spokes, we have six plus eight = twice seven.


Geometry

All the above "explanations" are essentially based on geometry.

The Menorah gives the one-dimensional weekday order, with an indication of a second dimension by the three half-circles.
The binary tree may be seen as a pyramid.
The Sevenfold Star or the Star of David bring the two-dimensional explanation, with an indication of a third dimension. In the case of the Sevenfold Star by the fuzzy circle of time, the Star of David may be recognized as a projection of the octahedron (see above).
The octahedron is a fully three-dimensional space object.

The order of the weekdays is most easily remembered by the Sevenfold Star. But the fundamental structure seems to be catched best by the octahedron representation. It is similar to the cube, but faces and corners are exchanged. Both are Platonic polyhedra and both have twelve edges (possibly matching the twelve zodiac signs).

I'd like to add some ideas on the higher-dimensional geometry of time. Imagine three time dimensions:

  1. Linear, calendrical clock time.
  2. Cyclical time, perpendicular to the first, associated with "eternal recurrence" (déja vu, Ecclesiastes 3:15, and the possibility of prophecy)
  3. Perpendicular to the first two, the way of "going on higher" or "jumping out of the system".

If the same things happen again, we have a curvature in time. And we need at least two dimensions for that. The geometrical model could be a circle (everybody lives the same life again and again, birth and death identical) or a spiral (not quite the same life again, but revolving around the same central theme).

In the helical model, each revolution around the central axis is also a movement in the third dimension ("progress"). And if someone has learned the nature of the helical axis well enough, a switch to the next helix may occur.

A good article on higher time dimensions is "Eternal Recurrence and the Laws of Manu", being chapter XI in P.D.Ouspenky, A New Model of the Universe, Third Edition, p.464ff, Routledge & Kegan Paul, London and Henley, Reprint 1978, ISBN 0-7100-7925-7

So, if we have three space and three time dimensions, what is the seventh dimension? Maybe this knowledge is not useful or possible for us to have now. It could be, like Sunday, the Unity of All, the end of spacetime.


Numerical Curiosity

The interlaced order of the chakras compared to the order of the weekdays (2, 3, 5, 6, 4, 1, 7) may show forth some mathematical properties. Square (1 / 0.5641723) and you get pi to 4 1/2 significant digits. I think this is coincidence - who searches, will find - but I have computed the probabilities for this occurrence anyhow:

84 permutations of 5040 approximate pi within 1 %
84 is equivalent to 1.7 % of all possibilities.

36 permutations of 5040 approximate pi within 0.3 %
36 is equivalent to 0.71 % of all possibilities.

18 permutations of 5040 approximate pi within 0.1 %
18 is equivalent to 0.36 % of all possibilities.

12 permutations of 5040 approximate pi within 0.03 %
12 is equivalent to 0.24 % of all possibilities.

4 permutations of 5040 approximate pi within 0.01 %
4 is equivalent to 0.079365079365079 % of all possibilities.

The four best solutions:

permutation  "pi"     relative error
5641723    3.141785   0.0061 % <-- 2nd best (chakra order)
5641732    3.141775   0.0058 % <-- best solution
5642137    3.141324   0.0085 %
5642173    3.141284   0.0098 %
So the probability to get one of the two best solutions is only
2 / 5040 = 0.0003968
A rare event, so the chakra order doesn't seem to be chance. If you'd do a different random try each day, you'd probably need two years or more until you hit one of the two good solutions. On the other hand, if this is real, shouldn't the chakra order be the best solution?

Another argument against this speculation: The algorithm, although rather simple, is deliberately chosen to get near pi. Because the output numbers lie closely together, some number is bound to approximate pi quite good.


Concluding Remarks

Someone has said "you can fit an infinite number of formulae to a finite number of data points". This surely also applies to the geometrical explanations above. Because for any given territory, there are a lot of maps. But some look nicer than others. The quest of science goes on ...

I hope at least one of the "maps" given above is helpful to you.


... the manifest Universe is born of sacred geometry. ...
The best way to escape the darkness of the past
is to dream and work to manifest
the light of the future.


Kevin Tobin, Mother Time, chapter 1, (1999)


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