Present Epoch

Stone monuments with no secular use continued to be built within the historical period and many of them appear to share the megalithic metrology and geometrical ideas then developed further into religious buildings. This section explores a few examples what came to be called sacred geometry based upon different cultural and sacred driving forces; including Greek, Arabic and Gothic religious spaces.

Bryan E Penprase has written an unusual summary of the role of Astronomy in shaping civilisations' view of the world, and it has a section (p205) on Celestial Cities from Ancient Civilizations and Their Alignments in The Power of Stars, Springer 2011. Whilst in line with scientific conservatism he presents an interesting range of monuments ancient and more recent which appear to conform to some sense of cosmic orientation, including the Kaaba in Mecca, the central pole of Islam as aligned to Solstice winter sunset and summer sunrise. In his diagramming of this using NASA's World Wind software, he presents Clive Ruggles 2005 [1] finding that these solstitial facings of opposite faces of the stylised cubic building also then leave the southernmost face pointing to Canopus rising on the horizon. He tells us " This same alignment was incorporated into other structures in the Islamic world - early mosques in Iraq facing the featured prayer walls that face the winter solstice, while many mosques in Egypt were built with prayer walls facing the direction of the summer solstice sunrise.", presumably then as alignments of that latitude and no longer at right angles to Canopus, which bright yellow star (the heavy one - El Ponderosa) was considered the pole of the world in its southerly manifestation and a source of understanding for some Sufi mystics.

alignmentsOfKaaba Penprase

The prophet Mohammad declared himself the last prophet of Allah, a name resembling the El Shaddai (trans. Lord God, KJV) of Abraham in the Bible. Mohammad galvanised the Arabs and nearby nations with an original religion, branching off from the start of the Patriarchs found in the Bible's first book, Genesis. His story follows Ishmael, the first son of Abraham, from whom the Arabs believe themselves descended.

 

Kaaba Abraham Mohammed

Figure 0 "Reconstruction of the Ka'bah as it must have been (left) when Abraham built it"  and
(right) "as it must have been rebuilt in Muhammad's lifetime" 
[Esin. 24. & 46.]
[Shaikh Tahir al-Kurdi of Mecca, after al-Sab'ai, A. Tarikh Makkah. 1952.]

As Europe emerged from the Romanesque, undocumented Norman and Benedictine influences manifested a "Gothic" style of cathedral building, conflating church building with exotic cosmological ideas involving sacred geometry and astro-harmonic symbolism. The prime exemplar of Gothic is perhaps the Cathedral of Chartres, now shrouded in many mysteries including who could have built such a masterpiece. John James [1] reports that records concerning its construction were lost in the century following its completion.

Chartres Towers 240

Figure 1 The Western Towers of Chartres Cathedral

The ratio between the twin towers is the same as that between the 12 month to 13 month lunar years, the latter being the same astronomical period John James proposed as intended for the whole length of church (then in Std Geo Royal feet.)

Figure 1 The Cathedral at Night by Robert Breuer, CCSA, Wikipedia Commons

Koelner Dom bei Nacht 1 RB 1It seems worthwhile to look at the geometry and metrology of this cathedral, to the extent that I can. It has the greatest ratio of height to width, over three times as high. As usual the building plan is in the shape of a cross (figure 2), with a thin upper roof describing a Roman cross in the proportions of 5 across and 8 down. The ratio has meaning as two early Fibonacci numbers, hence approximating the Golden Mean (phi). Eight also generates an octagon - an arena of completedness whilst Five generates the pentagon and is a humanly divine number - four limbs and a head of the "human fiver", a geometry filled with the phi ratio. Astronomically, the practical solar year of 365 days divides into five 73 day units, which unit then divides into the synod of Venus, 584 days equalling 8 x 73 days.

Cologne Roof

Figure 2 The crucifix of the roof seen from the air.

A link was made by medieval symbolists between the Virgin Mary and Venus, not least through the astrological connotation of Virgo (the Virgin constellation) diametrically opposite to Pisces (the Fish), the latter embematic of Jesus as Pantocrator and master of an Age of Pisces, into which the spring equinox had entered (dispelling Pan as Aries). I have previously noted how the mother-and child-motif could symbolise the inner solar system of Venus and the Moon, the two being strongly present in the star and crescent and brightest reflective objects of our skies. The moon dies for three days only to be resurrected and so on, whilst Venus, due to orbital resonance, has a highly structured set of Fibonacci relationships to those living on earth. 

The analysis in Figure 2 is using pure ratios (or relative proportions) to see the building as a whole. Exact measures are not important as one can see that the ratios, in providing a simpler view, directly reveal an intentionality to the building's design. I would also like to invoke another view of the building; as it having precedents in ancient Greek temple design, occupying a rectangular plot normal for land use, explored in previous articles Megalithic Origins of Greek Temples and Fields, Racetracks and Temples in Ancient Greece. That is that the Gothic cathedral is not far different to the traditions of the Greek temple prior to Rome and the Romanesque which preceeded the Gothic style.