Tag: St Peter's

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.

The solar day is clearly the same duration every day and two lunar months clearly repeat twice after 59 days. But our modern life is the extended straight line of day numbers belonging to unequal months of the sun so that the loops that recur are lost in the framework of man-made time. The stone age “lesson from nature” was, that events in the sky largely run according to a definite schedule along cyclic paths, most of these being along the path of the sun, along which the sun, moon, and planets follow their own cyclicities, seen from the earth. This reliable cyclicity shaped our notion of an unchanging realm of Eternity, different to Life upon the Earth as our ever-developing present moments within Existence. In this way, knowledge from the sky came to be considered sacred, and interconnected through numbers when counted as days and months, especially through counting the often identically sized discs of the Sun and Moon and their respective years.

While astronomy started as a stone age hobby it later became a tribal science quite unlike our own astrophysics. Only latterly could farmers support city specialists that would assimilate this prehistoric science, by forming religious sciences and cosmologies in the East, of Egypt, Babylonia, India, China and so on. But millennia later, the 16th century altogether discarded this geocentric view-from-the-Earth and adopted a new heliocentric view of a solar system:  this enabled the planetary orbits of the sun to be clearly seen as mathematical ellipses by Kepler, a system soon seen to be held together by Newton’s newly intuited force called gravity, of the central sun’s large mass.

If counting the moon had synchronised both female fertility and male hunting then this shaped the format we call the hunter-gatherer, who foraged for food before there was farming. Their women formed a naturally less-mobile core for the tribe and its children, the men hunting over extensive ranges. All adults were used to working together for the greater good and, since they were in-common descended from the women, so a matrilineal society was an effective format for problems requiring larger groups.

Stone age art of the goddess seems to have been very varied and geometrical (see Language of the Goddess by Marija Gimbutas). In Sacred Geometry in Ancient Goddess Cultures, myexperience in analysing megalithic sites had caused me to question whether the megalithic monuments were the work of Neolithic or New Stone Age farming revolution moving west from the Middle East where it started. Because the farming revolution was only slowly advancing through central Europe towards the Atlantic coast (see figure 2) it was pretty much avoiding the Mediterranean. For a start, the megalithic revolution was largely taking place within the islands and hinterlands of the Mediterranean and Atlantic Coast of Europe, between 5000BC and 2500BC. It was therefore much more likely to have have been carried out by the late middle stone age (Mesolithic) people, before the farming way-of-life arrived. And the indigenous culture of old Europe was mesolithic, well established and centred around women, foraging, and matrilineage (using your mother’s name) rather than the neolithic norm, led by men, farming and patrilineage (using your father’s name).

Figure 2 The journey of the Neolithic from the Middle East (see colored circles), via central Europe, was in stark contrast to the dating (dark circles) of megalithic sites on the Mediterranean and Atlantic coasts: And the neolithic were patriarchal farmers using the seasonal year while the late middle stone age were matriarchal foragers, truly interested in the sacred time world of the celestial objects, and hence building and using the megalithic observatories. [Globe by Google Earth, data from Barry Cunliffe and Bettina Schulz Paulsson]. Figure 1.1 in Sacred Geometry in Ancient Goddess Cultures.

The Clash of the Titans

Being indigenous, the matrilineal tribes were far more likely and able to innovate the megalithic astronomy which effectively inherited from the long tradition of day counting seen on the stone age tallies like the Blanchard plaque. But this continuity of interest in the sky conflicts with the today’s model of history and our foundation myth for modern science, as grandchild of ancient Near Eastern civilizations and exact sciences, fuelled by farming on fertile soils using irrigation.

Through comparing day counts, sky time could be given geometrical forms such as the circle, square and rectangle/triangle, these rightfully considered sacred by the coherent megalithic culture on Europe’s shores. The civilization was numerate, intelligent, but not stone age in the vernacular sense, of having no ability to reason. Having an extended family of adults and no urgent need to seasonally grow crops, conserve seeds or tend their animals, nature already provided food through foraging There was a natural collaborative workforce and this perhaps explains the dearth of neolithic settlement noted alongside the earliest megalithic monuments.

Having overcome this misnomer that megaliths were automatically neolithic, a further work is required to see why our own science cannot understand the sky phenomena in the way the stone age must have. We do not today study the synodic periods of the planets because they are seen as a merely incidental composite of the planetary orbits and our solar year. But, and quite unexpectedly, the view from the Earth is supremely important since the structure of time on earth is a phenomenon reflecting the form and structure of the numerical world. This would suggest that the earth was, in some way, influenced by the abstract world of numbers to have formed  this type of time environment. This might also suggest that the evolution of Life was an intended outcome for the third planet.

Having discarded the earth-centred model of the universe and having rid ourselves of the religions and gods proposed to explain this phenomenon, modern humans are free to live in an accidental universe where one is just alive  on an existential line-of-time with no end except for death, and without any appreciation of the deeper structural recurrences, implicate within the sky. Instead there is a hotch potch Roman calendar whose roots were literally man-made.

Figure 3 Fibonacci Golden Mean. 1.618 is found in the Fibonacci approximation of 8/5 = 1.6 of the practical year of 365 days to the Venus Synod 584 days. Venus was seen as the youthful goddess, Earth as the mother of all that lives and the Moon as the wise older goddess, these together forming the ancient Triple Goddess. [photo by C. Messier for Wikipedia] see section Statues representing Knowledge in Sacred Geometry in Ancient Goddess Cultures, pages 106 to 111.

The Greek myths referred to women, but in ways designed to put matrilineage norms in a bad light. The patriarchal farmers of Jupiter-Zeus had defeated the religion of the Goddess, whose representatives had snakes (perhaps the dreadlocks of the Medusa or knowledge of the snake shaped ecliptic, see figure 3) or had kept men sexually enslaved on an island (as in the Odyssey) or sacrificed a sacred king after “a year …” (of 364 days) “… and a day” (making 365 in all). Our 7-day week derived from this Saturnian year of 364 days (52 weeks), named because the synod of Saturn is exactly 378 days (54 weeks) while the synod of Jupiter is 57 weeks. In this one is seeing through a series of invisible filters, that the ancient Greeks were against the tribal age that had preceded farming and cities, when women rather than men were most important to that way-of-life. And the western Enlightenment adopted the heliocentric planets as a binary removing the foundations of a vast past cultural corpus of religious and pre-scientific thought that had quite reasonably shown something special about the world that modern science would never choose to see. If we can fathom megalithic astronomy, its uniquely powerful discoveries will reveal what the religious texts were about: that the environment of the earth is no accident within in the universe, but that it is that of a planet for the evolution of Life.

Megalithic discoveries had been transmitted, only subconsciously, into the cultural subconscious of the later civilizations, and it was and is still informing and infecting our arts and the classical form of numeracy called mathematics. This diffusion had benefited from the clash of the Titans, namely between the matriarchal and patriarchal ways-of-life in the Eastern Mediterranean and Levant. It would be recorded in the intellectual life of the Greeks and Hebrews, thus informing Islamic then Christian world view, as a code of numbers and stories often agreeing with those of the East.

Continuity in Sacred Building

If you know how to look, one finds the units of measure and geometries of the megalithic repeated in later sacred buildings, built under disparate religions as if the design of sacred buildings had some sort of megalithic origin. The Chinese, Indian, Buddhist, Minoan, Classical Greek, Romanesque, Islamic, South Asian, Amerindian, Gothic, Sufi, and Renaissance buildings draw upon common geometric and metrological blueprints relating, for example, to the relative size of the Earth and  Moon, and the sophisticated celestial time cycles such as the eclipse phenomena, as if to celebrate the cosmic environment even though many religions had conceptualized the heavens as if not found in the sky.

For this reason, my books can explore buildings of the historical period in the same way as megalithic buildings, to demonstrate this continuity of an invisible language, as if there were people with megalithic knowledge behind the construction of buildings without the outer religion officially acknowledging this fact. And in some strange way, I and others are recapitulating ancient works as to their meaning, by employing skills belonging to the past. For example,

  • In Cappadocia, Turkey, stone cut churches inexplicably contain high levels of meaning in their dimensions and definition of circular apse and rectangular naos occupied by hermit monks.
  • Angkor Wat is shown to be a massive statement of astronomical cyclicities alongside an outer meaning of Vedic mythological carving and Indian temple design.
  • St Peter’s Basilica was a renaissance rebuilding involving many great architects, including Michaelangelo who displayed sacred geometrical skill in translating a Greek square-cross basilica design into a Latin cross cathedral design, through the golden mean relationship of a square to such a rectangle (see figure 4). St Peter’s tomb is then in the centre of a model of the Earth and Moon.

Figure 4: St Peter’s Basilica: Sacred buildings followed geometrical and numerical rules that reflect both the cycles of the sky and the geometrical methods and numerical results of the megalithic. [plan courtesy The New York Metropolitan Museum]

Chapter 11 demonstrates that the equal perimeter model of the earth and moon had been related to the now-abandoned geocentric model. The Earth is at the centre (of course) and a system of growing square areas, for each planet’s synod, grows to embrace the whole figure to show it was the archetypal form taken as the norm for Buddhist Mandalas. And mandalas have recently been used by Jungian therapists and others to enable interaction with the subconscious mind. This suggests that our very being, as micro-cosmos, is part of the Earth and its planetary Sky environment of time. Celestial time appears to be a carrier wave for reality and not just a straight line.

Figure 4 The geometry of Equal Perimeter circle and square, with moon circles, showing the influence of the time world of the earth and moon, as the true basis for far-eastern designs called mandalas.
[photo: Cesar Ojeda 17th century Tibetan -Five Deity Mandala from Sacred Number: Language of the Angels. Fig 7.20]

References

Cunliffe, Barry. Europe Between the Oceans: 9000 BC to AD 1000. Yale 2008.

Gimbutas,Marija. The Language of the Goddess. Thames & Hudson 1989.

Heath, Richard.

______Sacred Geometry in Ancient Goddess Cultures. Inner Traditions 2024.

______Sacred Geometry: Language of the Angels. Inner Traditions 2021.

______Tragic Loss of the Geocentric Arts and Sciences: When Poetry was the Language of Cosmology, NewDawnMagazine.com #185***

Marshack, Alexander. The Roots of Civilization: The Cognitive Beginnings of Man’s first Art, Symbol and Notation. Weidenfeld and Nicolson 1972.

Paulsson, Bettina Schulz. Time and Stone. The Emergence and Development of Megaliths and Megalithic Societies in Europe. Archaeopress 2017.

Angkor Wat and St Peter’s Basilica

Unexpectedly, three more chapter were written to conclude Sacred Geometry in Ancient Goddess Cultures, on Cambodian temple Angkor Wat and Rome’s St Peter’s Basilica.

Here is a taster of the later chapters.

figure: the punctuation of towers and western outlook. Possibly a funerial building for the king, it could be used as a living observatory and complex counting platform for studying the time periods of the sun, the moon, and even the planetary synods.

Chapter 9 is on the design of Angkor Wat and chapter 10 is on St Peter’s basilica in Rome (see below). Some early articles on these can be accessed on this site, most easily through the search function, tag cloud and tags on this post..

As you can see, my books partly emerge through work presented on this website. This has been an important way of working. And whilst I am providing some ways of working that could be duplicated by others, at its heart, my purpose is to show that the celestial environment of our living planet appears to have been perfectly organized according to a numerical scheme.

My results do not rely on modern techniques yet I have had to avail myself of modern techniques and gadgets to work out what the ancient techniques arrived at over hundreds if not thousands of years.

My basic proposal is that ancient astronomers learned of the pattern of time in the sky by counting days and months between events on the horizon or amongst the fixed stars. Triangles enabled the planetary motions to be compared as ratios between synodic periods.

Continue reading “Angkor Wat and St Peter’s Basilica”

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.

The natural geometry of the Golden Mean is the Pentacle, traced out by planet Venus upon the Zodiac as evening and morning star. (from Sacred Number and the Origins of Civilization)

In the renaissance, the Classical tradition of Ancient Greece and Rome was reborn as neoclassicism, a famous proponent being Palladio, and further neo-classicism arose in the 19th Century and continues in the United States. From this, the previous article on St Peter’s saw its original square become rectangular in a golden way. The whole basis for this is due to the nature of squares and circles, that is: golden rectangles are easily formed geometrically through squares and circles.

The extension of St Peter’s from a square, by adding a golden rectangle, can be seen to also apply within the original square. Furthermore, there is a medium-sized square within the golden rectangle plus a small golden rectangle (see below).

The overall golden rectangle of St Paul’s of a square and golden rectangle below. Using the square within the golden rectangle, the original square above can have four such overlapping squares, to create a cruciform pattern, the upper part of which was used to lay out the Umayyad Mosque.

The medium square can be tiled four times within the large square to overlap the other medium squares, as shown above. This creates a small central square while the four regions that overlap are smaller golden rectangles. The lower golden rectangle is also repeated four times with overlapping, twice horizontally and twice vertically. It is seen that squares and golden rectangles can recede within a square, into smaller sizes, or expand around a square. It is as if all levels of scale hold a kind of fractal, based upon the golden mean.

The top six elements of the square can be seen to match the site plan of the Great (Umayyad) Mosque of Damascus, built 900 years before St Peter’s Basilica, on the site of an Orthodox Cathedral and, before that, a Roman temple to Jupiter. In other words, any golden rectangle design can contain resonances of somewhat different golden mean designs, that may express a different meaning or context; in this case the Mosque gives the notion of two squares overlapping to generate an intervening region of blending and the rectangle of overlap will then be phi squared in height (shown yellow below) relative to the width being unity – the central square’s side length.

The geometry of the Umayyad Mosque

My thanks to Dan Palmateer, for his emails and diagramming whilst on this theme of golden rectangles. One of his own pictures (below) shows the central square of the main square, by tiling the main square with the small golden rectangle.

The central square within the greater square is revealed in St Peter’s as a square within a circular area, noting that this plan (held by The Met Museum) was made after the building had been completed.

There was obviously a vernacular of golden rectangular building in Islam which was carried forth in Renaissance Europe. The potential for golden rectangular building can be all-embracing, as it is a property of space itself, due to numbers.

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

HAPPY NEW YEAR

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.

The question is whether the extension from a square was related the previous square design. The original square seems quite reworked but similar still to the original square. The four gates were transformed into three ambulatories defining four circles left, above, right and centre, see below.

Equal Perimeter models at the center of St Peter’s Basilica

Equal Perimeter Models

The central circle can be considered as 11 units in diameter so that its out-square is then 44 units. The circle of equal perimeter to the square will then be 14 units in diameter and the difference of 3 defines a circle diameter 3 units. The 11-circle represents the Earth while the 3-circle represents the Moon, to very high precision – hence making this model a representative of the Mysteries inherited from deep antiquity; at least the megalithic age and/or early dynastic Egypt, when the earth’s size can be seen in Stonehenge and Great Pyramid. This inner EP model, is diagonal so that the pillars represent four moons.

An outer Equal Perimeter model is in the cardinal directions (this alternation also found in the Cosmati pavement at Westminster Abbey, and inner models are related to the microcosm of the human being relative to the slightly larger model of Moons). The two sizes of Moon define the circles at the center, around St Peter’s monument. The mandala-like character of the Equal Perimeter model give here the impressions of a flower’s petals and leaves.

Golden Rectangles

You may remember a recent post about double squares and golden rectangles, where a half-circle that fits a Square has root 5 diagonal radius which, arced down, generates a golden triangle. It is therefore possible to fit the square part of the original design and draw the circle that fits the half-diagonal of the square as shown below.

The golden extension of the Basilica’s Square Plan

By eye, the square’s side is one {1} and the new side length below is 1/φ and the two together are 1 + 1/φ = φ (D’B’ below) which is the magic of the Golden Mean. This insight can be quantified to grasp this design as a useful generality:

Quantifying how the golden mean rectangles are generating phi (φ)

Establishing the lengths from the unit square and point O, the center of the right hand side. OA’ is then √5/2. When this is arced, the square is placed inside a half circle A’C, BC is √5/2 + 1/2 = 1/φ.

The rectangle sides ACD’B’ are the golden mean relative to the width A’B = 1, the unit square’s side, but that unit side length A’B is the golden mean relative to the side of the golden rectangle BC. In addition the length B’D’ is the golden mean squared relative to BC, the side of the golden rectangle.

Commentary

It seems that the equal perimeter models within the square design of Bramante were adjusted. The golden mean was used to extend the Basilica (originally an Orthodox square building named after St Basil) into a golden rectangle. This could be done by adding the equivalent lesser golden rectangle, relative to the unit square through the properties of the out half-circle from O.

The series of golden rectangles can travel out in four directions, each coming naturally from a single unitary square. The likely threefold symbolic message, added by the extension seems to be the primacy of the unitary square, of St Peter (on whom the Church was to be founded) and of the Pope (as a living symbol of St Peter).

St Peter’s Basilica: Starcut & Equal Perimeter

In Malcolm Stewart’s book on Sacred Geometry, his starcut diagram was applied to Raphael’s painting The School of Athens to create radiants to the people standing around the Athenium Lyceum. “If the starcut was the central geometrical determinant for Raphael’s formal depiction of classical philosophy” it was a “known authoritative device” or framework for geometrical understanding. Stewart found a potential antecedent for such a technique Donato Brahmante’s plan for St Peter’s (see above) which was square like a starcut diagram.

left: Stewarts book cover right: The simplest version of the starcut square where the sides are divided by two and the outer square is four squares of nine, which is 62 = 36 squares and there an octagon within the crossing lines. If there were 72 squares, then the octagon’s vertices would all be on crossings.

A starcut diagram works as a linear interpolator of lines drawn between its sides which are then divided by a number of points that radiate out to other points. The inner lines in this one are eight in number, three per side. Malcolm Stewart shows (see below) the number of coincidences between the plan and a starcut, as if the design was partly arrived at by establishing this pattern. The cardinal cross between its four entrances could have be arrived at, as could the corner octagons with their entrance and side circles lying on starcut radiants. And the central square has corners defining the central space and pillars for supporting the dome.

There seems to be other signs of starcutting such as Honnecourt’s Man, that masons were using such frameworks to build all manner of buildings, sculptures and designs. To investigate further, I made a diagram of my own, over Bramante’s plan and used the method of modular analysis, based on the fact that the central cross of walk ways is one fifth of the square’s side length so that 5 by 5 squares (in red) will define that feature. But there also seems to be a 3 by 3 grid of squares at work (shown in blue) to define the central space in the standard style of the Basilica from the Orthodox (Eastern Church) tradition, this then accounting for most of Stewart’s dotted lines.

Reconstructing most of Malcolm Stewart’s fig. 8.18 using grids of five and three, and applying modular analysis to the Basilica, to quantify it in relative units 1/120th of its side length.

The plan has no scale from which metrology can be deduced, but the smallest number able to hold these two grids together is 60. But to resolve the width of the corner octagons (as 15) I have used a side length of 120. The squares of 24 divided by the octagon width is 24/15 = 8/5 = 1.6. On can see that the starcut diagram was probably part of modular analysis, a technique popular in modern studies of cathedrals which, of necessity, can’t have been designed except as a meaningful whole. But this design would go through many hands including  Michelangelo, Carlo Maderno and Gian Lorenzo Bernini to become a transcept cathedral design (see below).

Later Plan for St. Peter’s 16th–17th century. Anonymous. Metropolitan Museum.

My own book on sacred geometry found a different framework was often present in such capital buildings, a model called Equal Perimeter which is a model of pi as 22/7 but is also the basis for a cosmological model of the Earth and the Moon, as 3/11ths of the Earth in size. This model is principally a circle the same perimeter size as a given circle’s circumference, the square being symbolic of the earth in its side length, as a scaled down mean diameter for the Earth. The basilica square limits could then the Earth and the circle of equal perimeter and size of the Moon, as shown overlaid below. Just as the presence of starcut or modular frameworks were linked to a medieval tradition, perhaps parts of that tradition were conscious of this long lost knowledge of the size of the Earth and Moon.

The Equal Perimeter model seems quite clear within the Basilica as originally conceived by Bramante.

It would seem that the equal perimeter design was in use in medieval times because the Cosmati pavement of Westminster Abbey holds it very clearly, and it was the Pope who sent Cosmati guildsmen for its construction. If the basilica was completed on 18 November 1626, the Westminster pavement was completed by 1268 for king Henry III. Its mosaic is depicted in Hans Holbein’s The Ambassadors. The interpretation I gave to it is in my Sacred Geometry book was first published here.

In summary, sacred geometry became a repository for esoteric information and techniques useful for laying out the capital buildings and other religious artifacts in which the exoteric aspects of religion are performed. Rituals often have a deeper meaning, only accessible when one seeks to understand rather than merely know them. It may be that this was a necessary compromise between the outer and inner meaning of life in those times.

Cosmati Great Pavement at Westminster Abbey as a model of the Earth and Moon.
[Copyright: Dean and Chapter of Westminster]