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 Gothic, Arabic and Greek temples.
- Category: Post Megalithic
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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  reports that records concerning its construction were lost in the century following its completion.
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 2 John James interpretation of the overall design was
an embodiment of 12 and 13 month lunar years.
1. The Master Masons of Chartres. James, John. Routledge and Kegan Paul: London 1982.
"The most important astronomicial calculations undertaken in the middle ages were to compute accurately the dates for Easter. Though dependant on the moon, the dates still had to keep in step with the cycle of the solar year. This hey did through a simple formula, where for two years running they fixed Easter from the short year of thirteen [twelve]lunations, followed by one long or embolismic year of 384 days which, with suitable adjustments, brings the Easter cycle back into phase with the sun." 111.
Two times 12 (=24) plus 13 equals 37 lunar months, three of those 111 months and six such periods equal 235 months, the duration taken for the 19 year (Metonic) anniversary of sun, moon and stars. In the Julian calendar of that date, an extra month every three lunar years could keep Easter later than the Spring Equinox. Meanwhile, 37 lunar months equals three Saturnian years of 364 days thus synchronising Easter with the seven day week, since the rubric for Easter established by the synod of Whitby was "the first Sunday after the first full moon after the equinox." (see also our articles)
Another possible view, taken here, is that the heights of these towers, were in root geographical roman feet of 0.971003 ft since 344 ft (as quoted) is 354.367 x 0.971003=344.09142 ft. 
2.This view became possible due to Ernst Levy's appendix to Simson, Otto von. The Gothic Cathedral. Bollingen: Tennessee 1956. called On the Proportions of the South Tower of Chartres Cathedral. This was removed from later editions)
In a previous article, Chartres: Relation of Western Towers to Gothic Floor Plan, Keith Crichlow's ideas were explored: that the two towers were (a) symbolic of the sun and the moon (as per their popular naming) in their heights but that (b) these heights also figured a horizontal lengths in that the Rose Window equated to the Labyrinth and the aisle lengths might correspond to the linear development of the cathedral's floor space, from a common line at the base of the towers. Two key questions emerged:
- Do the Tower lengths correspond to features along the floor plan?
- And why would such a concept have been employed at Chartres?
Firstly one can see (figure 3 below) a correspondence between the façade and the floor plan: The single lunar month difference between 12-month and 13-month lunar years corresponds to the radius of the Rond. Though Critchlow thought the two towers were 365 and 354 feet high (the sun and moon towers in both name and measure) the ratio in their heights of ~1.08 is not the ratio between the solar and lunar years but (as stated) is 12:13, the ratio between the 12 (normal) and 13 month (embolismic) lunar years.
Figure 3 Identifying the 1.08 ratio in the floor plan
and locating the labyrinth as mirroring the Rose Window
Do the Tower lengths correspond to features along the floor plan?
If the metrology within the cathedral had a starting point on entry to the Nave one can reach the start of the Apse as delimiting one lunar year using a new measure, a cubit of 1.77 feet*** . One hundred of those cubits equals 354 half cubits whilst the diagonal across the Nave and Choir is then 360 half cubits eight times 45, the harmonic root of Adam (see figure 4 below).
[***Root version of the cubit of Al Mamun. NEAL. 2000. 92.]
Figure 4 Metrological Interpretation of Chartres Floor Plan,
organised according to astronomical time
The first pillar of the Ambulatory defines the 13 month year and before that lies the solar year (as red diagonal of a purple four-square rectangle) on an arc so as to touch the central ceiling boss, which boss then marks the solar year of 365.2422 days as central to the Apse/Rond (the sun central to the solar year and solar system.)
The embolismic year defines side length of a 24 by 7 rectangle (in blue) to the first pillars of the Rond, a proportion of chromatic semitone 25/24 to the lunar and a 25 unit diagonal of 400 days (see below). The width of this rectangle is 112 half cubits (16 times seven), the same as the number of cusps around the outside of the Labyrinth.
And why would such a concept have been employed at Chartres?
The answer lies in the diabolical functional approach to calculating Easter and why the Synod of Whitby should have fought the Celtic church so hard to have such a labyrinthine definition for Easter. I highlight the word functional because the method of calculation is just that and carries no understanding of the phenomena behind the two lunar years which the twin towers of Chartres represent also relating to the Easter of the western church.
Every solar year there are 12 and 7/19th lunar months and this means that after nineteen years there are 12 x 19 = 228 + 7 = 235 lunar months, the Metonic count. These seven extra months are being distributed so as to become 12 + 12 + 13 = 37 lunar months so that six of these are 222 lunar months. Add one month and one obtains the Saros eclipse period of 223 lunar months. Add thirteen months and one obtains the 235 lunar months of the Metonic. The Metonic has seven embolismic years of 13 months because of the 7/19th of a lunar month per year. Since the Embolismic is a normal lunar year plus one, then seven lunar years can be taken off the 12 x 19 leaving only twelve, used for the mixed counting scheme with seven longer years.
Whilst towers, aisles and their metrology can be symbolic, we saw in the earliest Greek temple (the Heraion of Samos) that its columns (thought merely symbolic or supportive) had an astronomical counting function. The twelve columns up to the rond seem to offer a counting function but instead it is the bosses of the gothic arches above each stall of the aisles that appears to have a celestial counting function as equalling a single lunar eclipse. There are twelve bosses/stalls in each side aisle and in the central nave/crossing/ choir able each to count twelve lunar months. If the central twelve are linked to the single boss of the Rund, then the central hall plus Rund add up to the Embolismic year of thirteen lunar months and, with the side aisles, a total of 37 lunar months can be counted, as shown in figure 5.
Figure 5 Chartres Cathedral as Device
for Counting Astronomical Time
Since a count of the Saros and Metonic requires a common basis of six such counts of 37 lunar months then the six columns of the Rund appear to give a mechanism for knowing where the count has reached. Having made six counts of 12 + 12 + 13 = 37 x 6 = 222 then counting the Rund gives the Saros of 223 lunar months whilst then counting the central twelve gives the Metonic period of 223 + 12 = 235 lunar months or nineteen years.
One can say that the arrangement above resembles an abacus in form and also that the notion of placing the lunar months in the highest point of each ribbed ceilings boss has considerable symbolic merit that might even point to how the boss functions to keep the ceiling from falling; like an ethereal equivalent of a column, the boss is connected to the sky.
Figure 6 The Bosses of Chartres Cathedral Choir and Rund
CCAS by Marianne Casamance
- Category: Post Megalithic
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The Kaaba appears to express a geometrical progression of adjacent odd numbers starting with one and three. This differs from the super-particular ratios findable within the right triangles of astronomical time periods in the Megalithic, ratio pairs separated by only one rather than two. However, the multiple-square rectangles, used by the megalithic as approximations to celestial ratios, made use of the three-square rectangle. One of the earliest of these rectangles, this rectangle approximates two pairs of ratios: The eclipse year (346.62 days) to the solar year (365.2422 days) and the solar year to the thirteen lunar month year (384 days)
Figure 1 The three-square approximations in a triple series of astronomical periods. Note that the diagonals relative to the base are the result of having three squares in a rectangle then one high and three along - and two different. Two such rectangles geometrically sum (their angles) to give that of the (First Pythagorean) 3-4-5 triangle, 36.8 degrees.
If one adopts a square of 36 inches side length and projects outwards from the triple-square, one generates succeeding "odd couples" 3:5, 5:7, 7:9 and then 9:11 inside the walls and then 11:13 as the normalised plan for the Kaaba.
Figure 2 The geometrical progression of odd sided rectangles leading to the Kaaba wall plan.
This suggests that the design was to include the building within an implicit progression of odd-sided rectangles for reasons connected to the monuments orientation to astronomical time (lunar maximum standstill) and the facility of the triple-square "origin point" for the geometrical progression and of the triple time periods relating to the lunar nodes, in figure 1.
When the unit side length for this architectural grid is the plain yard of three (English) feet and 36 inches, then
- The inner perimeter is 9 x 2 + 11 x 2 = 40 yards, 120 feet and 1440 inches, 1,440 being the number of Adam.
- The outer perimeter is then 11x 2 + 13 x 2 = 48 yards, 144 feet, or 1,728 inches, 1728 being 12 cubed (one possible meaning for the Kaaba name) associated then with Arks and Ages in the ancient traditions.
The 11 by 13 rectangle is therefore the perfect scheme for expressing Adam, (whose temple the Kaaba was said to originally be) in relation to the head number (sans zeros) of Krita Yuga number 1,728,000.
Figure 3 Numerically symbolic perimeters of the Kaaba walls
Since the Kaaba was aligned to the 18.618 years (6800 days) of the nodal period, then in those 6800 days, there are 19.618 eclipse years (of 346.62 days). And this is exactly the ratio generated at the centre of the rectangular progression of figure 2 where the three-square rectangle has a diagonal that stands in the ratio of 19.618 to 18.618. If the three-long base of the rectangle is 18.618 years then the diagonal is 19.618 eclipse years long because such right triangles (half the rectangle) represent the inverse relationship of periodic frequency (within the same period) as well as the (same) ratio between periods.
Figure 4 The ratio between eclipse and solar years will be inversely reflected in the number of each contained in the 18.618 nodal period of the Moon's orbit.
This reveals that the eclipse and solar year lengths express a rationic difference normalised to a unit of time equal to 18.618 days. There are 18.618 of these in the eclipse year and 19.618 of these in the solar year, but what is this 18.618 day period? It is the time taken for the moon's node to move one DAY in angle on the ecliptic, and this is the average angle traversed by the sun on the ecliptic in one solar day. It is therefore true that the movement of the lunar nodes are synchronised to the sun's motion per day according to the number 18.618. The nodes are slower and retrograde in their angular motion and so the nodes take 18.618 solar years to completely traverse the ecliptic.
For the Kaaba, it is profoundly significant that the two numbers (1440 and 1728) naturally emerge from the three-square geometry which encapsulated the meaning of the monument's orientation; only when 36 units (inches) is taken as the unit length, and both sides of the rectangle are repeatedly lengthened by two units. Most ancient temples employed grid designs and most ancient mythology seems to have found a use for 1440 and 1728 in some of their greatest stories, but the Kaaba links, in an original and probably unique way, mythological numbers to astronomical facts in the numerical geometry of its design and its orientation of the Moon's Maximum Standstill.
- Category: Post Megalithic
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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.
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.]
Mohammad's religion of Islam ("salvation") started in Mecca where he received visions of angels and spontaneously recited suras (verses) which became the Quran and associated texts. An unknown history of Abraham and Ishmael emerged, intimate with Mecca, long a spiritual centre for the Arabs. Mecca's principle monument, the Kaaba or "cube", has taken a number of forms. Adam located it as a dolmen created by God when Adam was formed; Ishmael built the next design for his father, "open to the sky", using surface stones from nearby mountains; and Mohammad's dispensation adds ancient stories about cubic arks and located these as a renewed Kaaba, the prime centre, or Pole of redemption for the world.
The Kaaba as Ark
Within both myth and the historical period, the Kaaba has been restored or rebuilt many times. Mohammed himself was involved in one restoration effort after flood damage, and that version was probably not much different from the present form; which is not cubic. I believe the original Kaaba was referenced to a cubic relationship in time, which was then adapted into the harmonic number most favoured for arks, the cube of twelve or 1,728. These two references to a cube are anciently megalithic and (more recently) harmonically symbolic. Mohammed and his fellow rebuilders of the Kaaba appear to have demonstrated a contact with the harmonism of YHWH and hence with the Abrahamic tradition found in the Bible.
Figure 1 The symbolic use of numbers for Adam and Ark
in the interior and exterior perimeter of the present Kaaba, in inches.
The Prophet's Kaaba, if it involved 1440 inches as its interior circumference, placed Adam* at the heart of the monument whilst the outer perimeter appears to be 1728 inches in length**, referencing the Kaaba as an Ark. Such a simple integration is achievable in a rectilinear building by having a wall depth of 36 inches. The notion of using perimeters in a focal monument (as a simulacrum of the centre of the world***) is then enacted by perambulations of the faithful and the calling to prayer facing Mecca from around the world. Islam is a distinctly oral religion with its own sounds and of course the recitation of the Quran and other originally oral works, after Mohammed.
* this basis for Adam's name code was discovered by Ernest G. McClain (1975.) whose work I use extensively in my next book on planetary harmony, published later this year.
** the author has here used the plan, with thanks, provided by Bjank through Wikipedia
*** in Lords of Time, p178-180, the author demonstrated how the wall of Jerusalem's Temple Mount was a scale model of the Earth's Meridian referencing precession of the Equinoxes according to an ancient model of the celestial earth, in the sky.
The Kaaba as Pole
The older signification of the Kaaba as cube can be seen in its (continuing) orientation to the maximum northerly ("standstill") moonrise to the east, every 18.6 years. The monument was (always) located with Mount Hira in the east (frequented by Mohammed during key visions and recitations) whose northern limit is a valley enabling visibility of the maximum moonrise in the northeast. A further circumstance for Mohammed's time was that Canopus rose to the south-east, at right angles to the maximum moonrise. At that moment, the semi-circular Hatim would have pointed towards the axis of the moon's orbit within the circumpolar stars.
Figure 2 The alignment of Canopus to the axis of the lunar orbit in Mohammed's time
Canopus, a giant golden star, second brightest star in the sky, is emblematic of the Golden Age within the precessional cycle of 25,920 years since it is the bright southern pole of that Age, whilst the Babylonian ark of 1,728,000* is (numerically) the Hindu Krita Yuga or duration of the golden age in "years". As such, Canopus was shining into Mohammad's Kali Yuga Age and the star Canopus figures in the illuminist literature of Islamic Sufi orders, especially Persian, as Kutb (Pole), the teacher of the Age. These orientations of the Moon evidently go back to the Arab monument which, by Mohammed's time, had 360 stone monuments to worship, and we know the harmonic root of Adam, according to his Hebrew letter-numbers, is A.D.M. = 1 + 4 + 40 = 45, when summed, which times two cubed or 8 equals 360, a number rooted in Adam's 45.
* The thousands are not arbitary: being the cube of 10 x 10 x 10 but also the decimal base of 1440 = 360 x 4.
The Kaaba as Great Time
The original monument was described (see figure 3) as trapezoidal, involving four lengths of 20, 22, 32 and 37 ells, and from this one can make a trapezoidal shape which does not simply use these lengths as sides. One finds that the draconic period of 18.618 years, in which the moon's nodes travel around the ecliptic, can numerically appear when a base length of 32 ells and hypotenuse of 37 ells, are used to form a right triangle.
Figure 3 An interpretation of Ishmael's Kaaba as Code for the 32:37 right triangle
whose third side is closely 18.618, the years in the moon's nodal period.
(compare to first figure above of Abraham's Kaaba)
At this point one needs to know that the cube of 18.618 years is one quarter of 25,814 years, so that the 18.618 side of the triangle is the side length of a cube of time related to one quarter of a Great Year (to the extent that precession of the equinoxes could be established then or now.) The revision of the Kaaba in Mohammad's time appears to have placed the cube of Twelve in the outer perimeter of the monuments wall and then subtly located Adam's 1440* by having walls of suitable thickness.
* 4 x 360 = 1,440 and Adam's name using position notation of 1.4.40 (again after Ernest McClain 1975. 126-7: "now 8 is a cube number in both decimal and sexagesimal systems, and the cube plays a sacred role in many religions, including that of Mecca and Delphi.")
It remains to be seen whether the uniqueness of Islam as an Abrahamic religion comes from a fresh perspective on the Great Year connecting Abram, Adam and the Moon. It is certainly true that the rotation of the Earth, the length of its orbit and the motion of the moon's nodes are normalised with respect to each other, and that the tilt of the earth's axis would have been changed by the primordial collision with the moon, and thus the creation of the Moon is the reason for the separation of earth and heaven, then subject to precession.
Esin, Emel. MECCA the Blessed MADINAH the Radiant. London: Paul Elek, 1963.
McClain, Ernest G. (see http://ernestmcclain.net/ for pdf)
The Myth of Invariance. New York : Nicolas Hays, 1976.
Meditations on the Quran. New York: Nicolas Hays, 1981
- Category: Post Megalithic
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As Greece began to develop the notion of a Polis (or people), temple design went from using small dedicated buildings to creating, in the first Heraion, on Samos, the first Hecatompedos or hundred footer, whose walled room's only entrance faced east. Its axis was 14 degrees south of east, an angle familiar as that of the diagonal of a four-square rectangle, whose diagonal stands in relation to the four-square base as being the solar year relative to the lunar year. At the western end we believe there stood a statue of Hera, wife of Zeus, after whom the monument is named. Herwit's excellent The Art and Culture of Early Greece 1100-480 B.C. shows the monument's early evolution with a plan indicating the most likely metrology for the monument was of 100 common Egyptian feet of 48/49 feet (0.9788) which gives 36 megalithic yards of 2.72 feet along the axis. The diagonal is then 37.1 megalithic yards long so that these two lengths show exactly the sort of count found at the Le Manio Quadrilateral in southern Brittany. This is summarised in the diagram below:
Figure 1 The Interpretation of the Cella of the Peristyle Heraion
The early monument had no columns and in mid-8th century, the outer "wooden columns were added on stone bases around the long room"; Herwit believes this was probably the earliest tentative use of the portico idea but that its lack of utility (being neither structurally necessary nor functionally significant) indicates that it was found aethetically helpful: "It elaborated, dignified and identified the goddess's house, and from now on the peristyle would clearly and immediately distinguish divine architecture from human" (Herwit p76). From it the notion of the Cella or inner chamber developed, seen in Athena's Parthenon.
Figure 2 The possible use of the peristyle to count long astronomical periods*
However, in looking at the composition of the pillars (added to the central ones already required to suspend the roof) it is possible to use them to count two significant astronomical numbers: 68, the moon's nodal period divided by 100 days and 38, the number of eclipse seasons in the Saros eclipse period. If Hera was associated with the moon then her nodal period would pass 68 columns, each gap representing 100 days and Hera might represent the lunar maximum (or minimum) standstill. If only the north, west and south pillar were counted as eclipse seasons, then these outer columns would represent the Saros of 19 eclipse years of 346.62 days and the monument would at least symbolise the moon's marriage to Jupiter, but could have been used (with other means of counting days and lunar months) to provide a high-end counting function, not merely aethetic in character but able to synchronise the ritual calendar with the planetary time periods. For a general background see Wikipedia
Since the Heraion is the first peristyle temple we know of, it must represent why sacred rooms were elongated to form the characteristic Cella for the god, a hundred-footer, surrounded soon after by wooden columns to form the peristyle necessitating an expansion of the platform, initially with stone footings. The first Heraion cella, if identical with the one presented by Walters, would have been a five square as below.
Figure 3 Restoring the four-square nature of the earlier Heraion.*
However the orientation of the site as based upon east along the diagonal of the later Heraion suggests that the initial cella was not so long and would have conformed to the four-square diagonal so that the squares involved would be 4/5 of the later Heraion's stylobate (platform). Reducing the four-square rectangle by 4/5 indeed restores this feature in the earlier cella, which was probably therefore 4/5 the length of the later stylobate.
In that case the four-square design is primary and, it would appear, the stylobate evolved to provide an outer image of the god within which, if gods are astronomical and related to time periods, was the externalisation of the counting of astronomical periods, possibly only as symbolic but also, quite possibly used to count time for the rituals of that god.
We know that in the Dark period of Greece, after the late Bronze Age Collapse, the new tribes (whose names describe the musical modal scales) entered mainland Greece and the Aegean Islands from northern Europe, where these geometrical forms of knowledge seem to have originated in the megalithic form of the late Stone Age. Samos is an island associated with the Ionians from which the Homeric tradition largely came and so the forms of knowledge seen in the Heraion could be Ionian. The only real difference between the later Heraion and the Le Manio Quadrilateral, as regards the portrayal of the interval ratio between the solar and lunar year, is the movement from counting days to counting lunar months, and the units of counting, from inches to megalithic yards. In Le Manio, thirty six stones traverse an accurate 1063 day-inches whilst in the Heraion, these symbolic stones have become thirty six megalithic yards. (These "yards" are actually steps of 2.5 feet and their foot is therefore 2.72 feet divided by 2.5, or 1.1088 feet, technically a standard canonical Saxon foot or the root Saxon foot of 1.1 feet times the standard canonical micro-variation 126/125 [see John Neal All Done With Mirrors 2000]: look for it here).
A megalithic yard has forty digits of 0.816 inches so that 4/5th of a yard is thirty two digits and so; a double foot would have been used to define the earlier cella, with the same thirty six units along its walls, now double feet rather than steps. Such are the powers of astronomy, geometry, and metrology when facing a past culture whose roots could not be guessed at without understanding their possible number sciences. The cella seems to have evolved from the chambered tombs of the megalithic, aligned in various ways to horizon events marking celestial time, and the peristyle has then merged the role of the cairn or mound surrounding the chambered tomb and the stone circle whose circumference was sometimes used to count time longer time periods.
*[adapted from fig 33 of The Art and Culture of Ancient Greece by Jeffrey Herwit; CORNELL: 1985 (being fig 32 and 39 of H Walter's Das Heraion von Samos (Munich, 1976)]
- Category: Post Megalithic
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Bryan E Penprase has written an unusual summary of the role of Astronomy in shaping civilisations' view of the world, and has 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  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.
Unfortunately, the author of the diagram seems to have ignored the fact that the (red line) alignment passes through the two "guard" alignments formed by the 18.6 year cycle of the moons nodes, that is, of the retrograde precession of the lunar orbit around the ecliptic plane (of the sun's path) at an angle of 5 degrees. At the angles shown by the guards, the moon can rise further away from east and set further away from west, and so it is then not the solstice sunrise which lines up with the Kaaba but the northernmost moonrise at lunar maximum. The same is symmetrically true regarding solstice sunset, that in fact it is the southernmost moonset at lunar maximum which is indicated in the diagram. This is illustrated below for the situation much further north, in Brittany around 4000BC.
In megalithic terms (and the Kaaba was based on a preexisting megalithic structure) it is the maximum standstill of the moon (at the latitude of the Kaaba) which is at right angles to the star Canopus, but when? Did Penprase use the diagram of solar and lunar extremes of the founding of Islam or of today or some other date? Did he realise that the guard alignments of the solsticial extremes belong to lunar maximum and mininum standstill? The reference to Ruggles below shows Penprase built the diagram.
1. Ruggles, C L N, Ancient Astronomy: and Encyclopedia of Cosmologies and Myth, Santa Barbara, CA, ABC-CLIO
page 202: "...the base of the Kaaba itself—the cube-shaped stone structure at the center of the Great Mosque in Mecca that forms the sacred center of the Muslim world— had been known as far back as the seventh century to have its longer axis oriented upon the rising of the star Canopus and its minor axis aligned (roughly) in line with midsummer sunrise and midwinter sunset. Historically, the assumed qibla is most evident in the orientation of mosques and in the layouts of some cities. In some cases, historical accounts attest to how the sacred direction was actually determined. Thus, we know that the earliest mosques in Iraq were built with their prayer walls facing midwinter sunset in order to face the northeastern wall of the Kaaba, while Egyptian ones were built with their prayer walls facing midwinter sunrise in an attempt to be parallel with the Kaaba’s northwestern wall. However, in many cases we can only speculate about the methods used to determine the qibla. Since the errors were sometimes considerable, anyone trying to reconstruct the motivation behind mosque orientations in the absence of anything but the orientations themselves would have a hard time fathoming that the intention was always to orient them toward Mecca."
There is some historical information of the Kaaba being associated as early as 300BC: "In her book, Islam: A Short History, Karen Armstrong asserts that the Kaaba was at some point dedicated to Hubal, a Nabatean deity, and contained 360 idols that probably represented the days of the year.", but a right angle to Canopus would not apply to that epoch (using CyberSky) and it is also clear that at that latitude, the solstice is going to be around 64 degrees of azimuth (measured from true North, clockwise). Therefore, why not see if Canopus relates to the moon's maximum standstill around the time of Mohammed? Anthony Aveni has prepared a table of sun, moon and star alignments for 1500BC to 1500AD and I have used his figures for 500AD to text whether this is likely the case, as extracted below.
The azimuth for Canopus (the rudder of Argo Navis) is 148 degrees and 21 minutes which, minus 90 degrees is within half a degree of the northernmost lunar maximum moonrise at 58 degrees and 54 minutes. However, Canopus is a bright star which would suffer atmospheric effects, casting doubt on a 0 degree horizon observation being what was being observed. This means that, within the context of Penrase's diagrammatic observations, the lunar maximum was effectively at right angles to the star Canopus on the horizon at the time of Mohammed's involvement with the Kaaba. If the walls of the "cube" monument were built (in proportions 3:4:5) at that time, then the walls aligning to the lunar maximum and Canopus could then be the Muslim tradition thereafter. This is not too surprising because the Islamic calendar is primarily lunar, as seen in the shifting location of ritual months and days within the solar year. I will be confirming the alignments some time soon, with the help of my brother's QuickAz program.
Significance of the Nodal Periods of 18.6 years (6800 days)
In my own Sacred Number and the Lords of Time and on this website, the lunar nodal period can be seen to have had great importance for the prehistoric astronomers and builders of chambered tombs. It was also noted in Mysteries of the Hopewell by Romain that some Native American funerary structures appear to have been aligned to lunar maximum events. An 18.6 year cycle was time on such a scale that only a few cycles, perhaps just one or two, could occupy an individual's lifetime. Monuments have shown, through metrology, that counting within the nodal period from a lunar maximum standstill could predict the minimum standstill after 3400 days and the maximum again after another 3400 days and 3400 (= 17 x 2 x 100) is an easily factored number, an important consideration in pre-arithmetic times. 3400 was 34 lengths of 100 day units of length. Counting added to alignment allows a cycle of time to turn into an organised calendar including midpoints, quarter times and so on.
To study megalithic structures requires the ability to propose alignments as important intentional features. Star alignments, popular in New World astroarchaeology but not encouraged in the Old World, move with precession of the equinoxes whilst sun and moon move as the axial tilt of the earth also changes with time. It is a matter of solving problems using various tools and information that today must be somewhat technical whilst in prehistory, more could be relied upon as directly observed phenomena and this sums up how humanity has changed, from being phenomenon-based observers to problem-solving using mathematics and computation.
For "anyone trying to reconstruct the motivation behind mosque orientations in the absence of anything but the orientations themselves", it may be more important to see Canopus' connection to the lunar maximum in the 7th Century as having been seen emblematic of the creation of a major new religion on earth.
There is a new topic in the new forum where this can be discussed
- Category: Post Megalithic
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Here we continue (from a previous article) to study the Kaaba, spiritual centre of Islam, from the point of view of megalithic science. We will restrict ourselves to considering the astronomy which word means relating to the stars (sidereal), and appears to hark back to a past world where the movements of stars were considered by naked-eye astronomers to hold some religious meaning, religion in turn meaning to "reconnect" to a spiritual world.
It was suggested in a book by Bryan Penprase that the Kaaba, and Mecca, had been located geographically so as to have a north eastern sightline to the moonrise on the horizon at Maximum Standstill, and that Canopus rose to the south east, then at right angles to that sightline* at the time of the prophet Mohammad after 600 CE.
* (but not the summer solstice as suggested)
In the present Kaaba, probably similar in form to that Mohammad himself helped rebuild, the longest dimension is towards Canopus, the shorter sides being SW-NE. The significance of the SW alignment is far from empty since (a) the semi circular area called the Hatim is an outdoor annex to that SW wall and (b) the alignment would have pointed to the axis of the lunar orbit at Maximum Standstill, at the moment of moonrise. Thus Canopus formed the southern pole of the lunar axis at that moment, whilst Canopus is traditionally symbolic as having been near the southern Pole of the earth, at the time of the so-called Golden Age, when the spring Equinox stood within the zodiacal sign of Leo the lion.
The Hatim would be a perfect representation of the circumpolar region of the golden age. In 600CE our present pole star (Polaris) marked the Pole but only at midnight, being higher in the sky as the Polaris slowly approached its present position beside the actual North Pole, to become a rare unmoving marker of it, and a true pole star. The culmination of Polaris in 600CE therefore gave the nomadic traveller a bearing to true north at night. CyberSky allows us to see the northern sky at Mecca in 600 CE:
Polaris can be seen above the north celestial pole at the latitude of Mecca.
- Category: Post Megalithic
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Here we continue (from a previous article) to study the Kaaba, spiritual centre of Islam, from the point of view of megalithic science and sacred geometry. We will restrict ourselves to considering the astronomy. The word considering (derived from sidereal), harks back to a past world view in which the movements of stars were considered by naked-eye astronomers to hold religious meaning, religion meaning to "re-connect" to a spiritual world and consider "an inspection of the stars" for their meaning.
An Unexpected Geometry
The part of Abraham's story beyond that recorded in the Bible involves Ishmael and his mother Hagar, after they were sent away. Abraham visits and has Ishmael build a second Kaaba where an original had once stood, created by God when he created Adam. The description of this second Kaaba is four side lengths (see figure below) given in a unit of measure called the ell [see Esin, Emil. Mecca the Blessed, Madinah the Radiant. London:Elek Books, 1963. 15-22.]. The below graphic integrates this story of a dimensional monument with the northerly maximum moonrise at maximum standstill.
The curved side is hence radius 14 ells since 22/11 x 7 = 14, a piece of sacred geometrical lore.The arc is slightly more than 22 but is modelled then by 22/7 as PI. (This curve is aligned to moonset in the south west at maximum standstill rather than, as the Hatim, aligned towards the northern pole of the lunar orbit at its northerly rising and southerly setting, at maximum standstill.)
A Metrology for the Ell
If two 13-month-years of day-inch counting equals 18.618 ells then 767.79 day-inches divided by 18.618 = 41.239 inches = 3.4366 feet = 24/7 feet x 176/175 441/440 - the standard royal yard used at the Royal Tombs at Thebes*. Please note correction.
* quoted Neal, John. All Done With Mirrors. London: Secret Academy, 2001. referencing Clark and Engelback. Ancient Egyptian construction and architecture. New York: Dover Publications, 1990. original: Oxford University Press, 1930..The ratio 440 to 441 is that found between the polar radius of the Earth and its mean (or spherical) radius. There is good evidence that the mean radius was considered representative of the sacred earth and used within sacred architecture to signify a belonging to that earth. Perhaps more interesting is that two 13 month years divide by the nodal ratio 18.618 to give a standard royal yard.
The Ell could have been a standard royal yard, perhaps from southern Egypt, and 18.618 ell in equalling 26 lunar months could relate to YHWH's Hebrew gematria of 10.5.6.5 summing to 26. And whilst the ell might also have the simultaneous meaning of standing for 1 year of the moon's nodal period, the lengths quoted for the sides of the Kaaba sum in a way pointing to the primary eclipse cycle now called the Saros, to which we first turn.
Counting the Saros eclipse period
Adding 20 + 22 + 32 + 37 produces 111 (= 3 x 37) and as we know from previous articles () the Saros period counted in lunar months is 223 lunar months = 111 + 111 + 1 months long. And in Gavrinis, stone L9 appears to use the symbol like a carrot as a counter of the 37 lunar months in three solar (or possibly 364-day Saturnian) years. three times 37 is 111 so that a common factor might be found between Gavrinis' stone L9, the Phaistos disk and the mythical Kaaba. Certainly, this idea of counting 223 using 111 and its factor 37 seems to show that keeping track of counting the Saros was easily achievable by counting the lunar months already primary to the Semitic calendar. There seems no objection to it having been employed prior other timekeeping methods yet delivering a sophisticated result: reliable Eclipse Prediction.
Symbolising the Nodal period
The orbit of the moon crosses the sun's path (called the ecliptic) twice every orbit at two nodes. When the sun is at one of the nodes, an eclipse of the moon is likely and or the sun possible. But the moon's nodes move backwards (retrograde) with respect to planetary motion (east to west), so that eclipse nodes travel backwards in the year. It takes the sun an eclipse year (346.62 days) to cross the same node again and half that to reach the other node, but the nodes reach the same point in the stars after 18.618 solar years, this because the nodes move 1/18.618 DAYS of solar motion every day.
Resolving a number like 18.618 days or years is difficult when one has no fractions. However nature is kind in giving almost exactly 6800 days to that period so that one could count that number in various ways at megalithic monuments such as Thornborough Henge, the Stonehenge Aubrey Circle and Le Menec's Western Cromlech in Carnac. But here, if 18.618 stands for years in the nodal period then this proto-Kaaba triangle of long sides 32:37 resolves the number quite well (18.574) as a symbol for the nodal period that the Kaaba noted in its alignments, especially to the north eastern moon rise maximum standstill.
There is then a quirk well known to my brother and myself regarding the Precession of the Equinoxes: that 18.618 can be seen as one side of a cube whereupon the volume of the cube (then in year-ells) would equal 6453 solar years and this is a precessional season, that is one quarter of the precessional period is taken to be 25814 years. Given that precession as a period cannot be quantified except based upon what it appears to be today and predictions of solar system forces of many millennia, then this is a very adequate quarter, within 30-50 years of most modern estimates.
Given that each Abrahamic religion was granted its own perspective upon the God Abraham first saw, the mysticism of Islam in particular might have been influenced by a renewed historical context, this time embracing a long and hoary process of human spiritualisation known to pre-literate, oral cultures who remembered themselves through recitation. Islam appears to have inherited from the Kaaba aspects of its original intended meanings whilst becoming Islam's spiritual axis.
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