Goddess of Time in the Sky

Explores the relationship between ancient astronomical practices and megalithic cultures, highlighting how early societies understood time through celestial cycles. It contrasts matrilineal hunter-gatherer societies with later patriarchal agricultural ones, suggesting that megalithic structures reflect deep, sacred knowledge of the cosmos and have influenced subsequent architectural designs across civilizations.

Above: (center) The form of the Minoan “horns of consecration”, on the island of Crete, followed (outside) the form of the manifestations of Venus in her synodic period.

Time appears to march on at what seems a constant rate. In this way time has two opposite directions, the somewhat known past and the largely unknown future. However, events in the sky repeat and so they can be predicted as seasons within a year or lunar phases within a month. Even before modern calendars, stone age humans counted the days in a month to understand recurrence of the menstrual period and know when moonlight would be strong again at night.

Figure 1 (above) L’Abri Blanchard Tally Bone 30,000 BP with (below) Alexander Marshack’s interpretation, showing marks as days shaped to express the moon’s phase, over 59 whole days or two lunar months.

Two months happen to equal 59 whole days: a lunar month is 29.53 days long, just over twenty-nine and a half, which is half of 59. In the artifact shown on the top of figure 1, each day was carved upon a flat bone, each mark appearing varied in shape and depth to show the moon’s changed phase on a given day. The flat bone enabled a cyclic shape to be used, of 59 marks, which “ate its own tail”: showing there were always the same number of days in two “moons”. This sameness emerges from dividing the recurring time of the solar day into the time of the month’s phases over two months, to give the recurring whole number of 59, then forever useful as a knowledge object.

Continue reading “Goddess of Time in the Sky”

Umayyad Mosque: Golden Rectangles from Squares

photo above of Umayyad Mosque, Damascus by Bernard Gagnon for Wikipedia CC BY-SA 3.0.

In previous articles on double squares and then St Peter’s Basilica, it became clear that squares and double squares have been embodied, within sacred buildings and art, because circles can then spawn golden rectangles from them. A golden rectangle has one dimension related to its other dimension as the golden mean {1.618034…}. Firstly, the original square plus golden rectangle is a larger golden rectangle but, secondly, the new golden rectangle (beside the square) shares its side length as one unit {1} but its other side is then the reciprocal of the golden mean (0.618034).

The golden mean is the only irrational number whose reciprocal, and square share its fractional part {0.618034 1.618034 2.618034}: there can be only one real number for which this is true. But it is in its geometrical expression, living structure and aesthetics (as in classical architecture) that lead its uniqueness to be seen as a divine ratio. Therefore, it seems, ancient human civilizations sought this golden form of harmony within the form of the Temple, especially in Dynastic Egypt and Classical Greece. The planet Venus must have reinforced this significance since its synod {584 days} is 8/5 of the solar year {365 days} and its manifestation such as evening and morning stars, move around the zodiac tracing out a pentacle or five-pointed star, the natural geometry of the golden mean.

Continue reading “Umayyad Mosque: Golden Rectangles from Squares”

St Peter’s Basilica: A Golden Rectangle Extension to a Square

above: The Basilica plan at some stage gained a front extension using a golden rectangle. below: Later Plan for St. Peter’s 16th–17th century. Anonymous. Metropolitan Museum.

Continue reading “St Peter’s Basilica: A Golden Rectangle Extension to a Square”

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.

Continue reading “Double squares: Venus and the Golden Mean”

Double Square and the Golden Rectangle

above: Dan Palmateer wrote of this, “it just hit me that the conjunction of the circle to the golden rectangle existed.”

Here we will continue in the mode of a lesson in Geometry where what is grasped intuitively has to have reason for it to be true. It occurred to me that the square in the top hemisphere is the twin of a square in the lower hemisphere, hence this has a relationship to the double square rectangle. So one can (1) Make a Double Square and then (2) Find the center and (3) a radius can then draw the out-circle of a double square (see diagram below).

Continue reading “Double Square and the Golden Rectangle”

Powers of the Golden Mean

Sheikh Lotfollah Mosque  is one of the masterpieces of Iranian architecture that was built during the Safavid Empire, standing on the eastern side of Naqsh-i Jahan Square, Esfahan, Iran. Construction of the mosque started in 1603 and was finished in 1619.
for Wikipedia by Phillip Maiwald

The Golden Mean (1.618034) or Phi (Greek letter) is renowned for the behavior of it’s reciprocal and square which are 0.618034 and 2.618034 respectively; that is, the fractional part stays the same. Phi is a unique singularity in number. While irrational, shown here to only 6 figures, it is its infinite fractional part which is responsible for Phi’s special properties.

The Fibonacci series: Found in sacred buildings (above), it is also present in the way living forms develop. Many other series of initial number pairs tend towards generating better and better approximations to Phi. This was most famously the Fibonacci series of 0 1 1 2 3 5 8 13 21 34 55 89 … (each right hand result is the simple sum of the two preceding numbers (0+0 = 1, 1+1=2, etc.

Continue reading “Powers of the Golden Mean”