Tag: 584

Double squares: Venus and the Golden Mean

The humble square, with side length equal to one unit, is like the number one. It’s area is one square unit and, when we add another identical square to one side, the double square appears. Above right the Egyptian Djed column is shown within a double square. The Djed is the rotating earth which the gods and demons have a tug of war over. This is also a key story in the Indian tradition, called The Churning of the Oceans, where the churning creates both the food of the gods (soma) and every wonderful thing that emerges upon the Earth. In this, the double square symbolized the northern and southern hemispheres of the Earth. The anthropomorphic form Djed shown above has elbows indicative of the Double square.

Figure 1 The churning of the ocean (Samudra Manthan in Sanskrit)

The Djed appears to be the general principle of rotation of, and apparent motion around, the earth.

The god Isis is (as a planet) Venus and is shown (fig.2) offering up the sun disk: another Djed is below, with her Ankh symbol of Life atop the Djed, now having female arms . This sun most probably points to the practical year as 365 days which is 5/8 of the Venus synod of 584 days. (This ratio of 1.6 is the sixth note of the octave 1 to 2.)

In figure 2, two female attendants provide the duality which one might take to be her two famous manifestations of (firstly) the brightest Evening Star, as the sun goes down, and then (after that) the brightest Morning Star before the sun rises. Above there is duality again with three baboons either side of the sun, perhaps representing the six visible planets: Moon, Venus and Mercury: Jupiter, Saturn, Mars and their “tug of war”.

Figure 2 The creation of Horus-Ra from out of an ankh with female arms atop a djed. from Budge 1899, also fig. 7.8 of Richard Heath, The Harmonic Origins of the World.

The numbers 5 and 8 are Fibonacci approximations {1 2 3 5 8 13 21 34 …} to the golden mean, a transcendent number {1.618034…} which rational numbers can only approximate. Venus and the Earth have clearly settled into orbits around the sun resonant with Fibonacci ratios since the Venus orbital period (224.701 days) is 8/13 of the solar year. And it is this fact that eventuates in what we see on Earth, namely the manifestations of Venus every 8/5 of a practical year. of 365 days.

Figure 3 The double square, its in-circle and out-circle manifesting golden rectangles around itself.

In this post, I developed a result sent to me, that a square drawn within the upper hemisphere of a circle must define a golden mean rectangle either side from its height of 1 and the remaining radius of 0.618034… and so it can be seen that the divine principle of the Golden Mean emanates from the double square, either side of each square, when the double square is embraced by a circle drawn from its center. Obviously, on Earth and between orbits (of Venus and Earth), the Golden Mean (also called Phi) has to be approximated by whole number ratios but the principle is present within the geometry and its out-circle. Schwaller de Lubicz thought the dynastic Egyptians held the Golden Mean to be “the fundamental scisson” (literally “scissor cut”) in the range one to two and, its reciprocal can be seen to share the portion over 1 (figure 3).

One can see that geometry and the early numbers would have been seen as two aspects of what we call space and time, in which “things” are separate from each other in Existence but somehow conjoined within Eternity. What we call order is in fact an achievement of harmony made possible by the arranging and fitting of parts to form a coherent whole. It is this insight which gave meaning to their study of geometry and numbers from the prehistoric onwards, into the recorded history of early civilizations. The meaning for Life on Earth became encoded within ancient and prehistoric symbols, whose geometrical and numerical language of expression went to the heart of phenomena.

The Stonehenge Trilithons (Part 2): Day-Inch Counting

In the previous article, it was shown that the form of the trilithons, of five taller double sarsens approximating to a five-pointed star, matches the astronomical phenomena of the successive morning and evening stars, as Venus approaches Earth from the east and then recedes to the west as the morning pass. On approach, the planet rises in the evening sky and then dives into the evening sun and if one traces this motion it have the appearance of a horn. Venus shoots past the sun and reappears in the morning sky as the sun rises, creating another traced horn shape, symmetrical to the evening.

Figure 1

In support of the form of the trilithons resembling five successive double horns of Venus over 8 years, the width of the inner faces can also be interpreted as to their length being one megalithic rod, that is 2.5 megalithic yards. The distance between each pillar is ¼ of a megalithic rod so that, each inner face is divided by 4 of these units which units are 5/8ths of a megalithic yard, the ratio of the practical year of 365 days relative to the Venus synod of 584 days (365 / 584 = 5/8), the common factor between the two periods being 73 days.

The combined inner width of each pair of supports would therefore symbolize 8 x 73 days, or 584 days. Five of these pairs would then be 5 x 584 days, which equals 2920 days, this time period also being 8 x 365 days or eight practical years.

The inner surfaces lie on an ellipse which can be framed by a 5 by 8 rectangle whose sides are exactly the diameters required to form a day-counting circle for 365 day-inches (116.136 inches) and 584 day-inches (185.818 inches). The 365 day-inch circle (shown red and dashed in figure 4) has its centre in the center of the ellipse and so would have touched the two trilithons at A and B, at a tangent to their faces.

Figure 2 The Venus count of 584 day-inches (shown blue and dashed) was concentric to both the bluestone and sarsen circles, sitting inside of the bluestone circle.

The high degree of correlation between,

  1. the five-fold form of the Venus synod and the five couplets of trilithons,
  2. the summed inner widths of the trilithons as being 5 x 8 = 40 units of 73 days = 2920 days.
  3. the out-rectangle of the inner ellipse being 8 by 5 and
  4. the rectangle’s sides being the diameters of two circles of 584 inches and 365 inches, suitable for day-inch counting,

……. points to the 5-fold horseshoe of trilithons as a “temple” to the unique astronomical behavior of Venus in its synodic relationship to the solar year of 365 whole days.

No other compelling explanation exists, though many interpretions have been proposed such as

The Stonehenge trilithons as synods of Venus

Figure 1 The five Trilithons of Stonehenge 3, highlighted in yellow within the Sarsen ring to express the five evening and morning star couplets which occur in eight practical years of 365 days. Plan from Megalithic Remains in Britain and Brittany, Oxford U.P. Central portion is fig.3, upside down to match the horseshoe of trilithons..

Inside the Sarsen ring of Stonehenge, there once stood a group of five trilithons, each made up of two uprights and a lintel stone, repeating the unique style of building found in the Sarsen ring. However the Trilithons were higher than the sarsens, punctuating an elliptical cup shape towards the midsummer sunrise, the axis of Stonehenge and its solstice-marking “heel” stone.

The Horns of Venus

The symbolism therefore involved (a) the Sun, (b) the number five of the trilithons while (c) expressed something involving close pairs. The dominant astronomical significance of the number 5 comes through the brightest planetary phenomenon of all, in which the planet Venus approaches the Earth, as Venus approaches from the east, preceding the Sun in the evening sky. It is often therefore called the Evening Star. Venus then shoots past the sun and reappears in the morning sky, again growing in brightness as the Morning Star.

Figure 2 The Horns of Venus when the evening and morning “stars” are visualised over an extended present moment of the Venus synodic period of 1.6 (⅝) practical years of 365 days. Fig. 2.2 of my Matrix of Creation, Inner Traditions, 2004 . (Drawn by Robin Heath.)

The original astronomers of the megalithic only saw the planetary system from the Earth and not (conceptually) from the Sun, as we do today. That is, they were naturally geocentric whilst the present worldview is heliocentric.

The astronomers could study cosmic time periods without arithmetic, through counting days, using a constant unit length to mark each single day adding up to a fixed length of days. Through such counting they would see 365 whole days between the solstices and (more reliably) between the equinoxes (when the Sun moves most rapidly on the horizon). It was also quite obvious that the horns of Venus were bracketing the Sun, just as the elliptical cup of the trilithons they erected at Stonehenge bracketed the solstitial sun, a sun which travels every day from east to west.

Five-ness in the Zodiac

If the earth was their viewpoint then the Zodiac of the sun’s path over the year could, like the Sarsen Circle, be seen as a circle of 365 days, and when the time between evening or morning stars was counted, the result was 584 days between the horn-like and brilliant manifestations of Venus. 584 days is 219 days more than 365 days. The sun has therefore moved 3/5th of a year forward and hence it became noticeable, as stated above, that 1/5th of the practical year is 73 days, the practical year 5 units of 73 days long whilst the Venus synod is 8 units of 73 days long. The Venus synod therefore has exactly 1.6 (8/5) practical years between its phenomena.

Figure 3 The Horns of evening (E) and morning (M) stars shown upon the circle of the Zodiac, each successive pair 3/5ths advanced within the solar year. [from Joachim Schultz, Movement and Rhythms of the Stars, Floris, 1986, fig 88]

The form of Venus upon the Zodiac therefore describes a 5-fold pentacle star. This would later make the number 5 and all of its properties, sacred by association to the planet Venus who became the leading goddess of the Ancient Near East. The Golden Proportion or Mean (1.618034…), often seen in Classical and Neoclassical architecture, has the number 5 as its root. Also, many living bodies share forms derived from the number 5, or of the Fibonacci approximations to the Golden Mean.

The Fibonacci series (of 1, 1, 2, 3 ,5 ,8 ,13 ,21, …) has successive numbers that sum to give the next number, and each new ratio, between successive numbers in the series, yields an ever-better approximation to the Golden Mean: (2, 1.5, 1.6, 1.6, 1.617, …).

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