In 1972 John Michell inferred an enormous ten-sided form nearly sixty three miles across, in which important historical and neolithic sites had been intended as ten vertices around an ancient centre, signified by a Whiteleafed Oak.

Michell had previously [1991] developed the idea of the enchantment of the land as an actual practice; land areas were enchanted by using a geometrical pattern integrated with myths and ritual calendars, enacted within that framework. This was long before, around 930, such a pattern was being established of thing-places in Iceland. The idea of thing places is still find-able in English names such as Goring, the centre northeast of Stonehenge, where the summer solstice sun arose.

“Perpetual choirs were a Celtic institution, from pagan into early Christian times. In Iola Morganwg’s Triads of Britain, translated from Welsh, it is stated that ‘in each of these three choirs there were 24,000 saints; that is,

there were a hundred for every hour of the day and the night in rotation, perpetuating the praise and service of God without rest or intermission.’ ”– The Measure of Albion“Three of the choirs were located at Stonehenge, at Glastonbury, and near Llantwit Major in Wales. Others appear to have been at Goring-on- Thames and at Croft Hill in Leicestershire, a traditional site of ritual, legal, and popular assemblies.”

The Dimensions of Paradise

Michell inferred a decagon because, from Stonehenge, the angle between the westerly bearing to Glastonbury and that to Goring-on-Thames was 144 degrees, the internal angle of the vertices of a regular decagon. Being regular, this decagon of perpetual choirs is inscribed within a circle that can be viewed as a scale model of the mean earth in which 80 feet on the circle’s circumference is equivalent to a geographical mile of 5068.8 feet on the surface of the mean earth, then having been reduced by 63.36, the scaling involved (5068.8 equaling 80 times 63.36). Michell also found that the sides of the decagon, between the choir sites, were also a metrological model of the mean earth radius and I noticed that, in this case, it is the inter-site distance (the ten sides) which are 63.36 of the mean earth radius. There is therefore some common factor, of 63.36, operating to make the sides and outer circle of the decagon relate to the mean earth. We must remember Michell’s assertion here; that the mean earth was ancient man’s conception of the spiritual world, and also note that 63.36 is one fiftieth of 3168, the number he found associated with the boundaries of ancient sacred spaces.

The decagon symbolically replaces the circular norm of the mean earth whilst presenting 10 smaller models of the mean earth between adjacent sides, each a thing-place. This is therefore an advanced geometric modelling of the mean earth containing unfamiliar features. It models the mean earth in two ways, each of different scale. Whilst using the metrological model of the mean earth, it seems to have broken with the ancient metrology in that Michell found a unit of 2.0412 feet (100,000 between choirs sites) and this unit does not belong to ancient metrology, as it is not based solely upon the primes 2, 3, 5, 7 and 11. This metrological anomoly is due to the usage of geometrical properties of the regular decagon, and whilst Michell was aware of those properties it is necessary to understand this decagon as a *new type of numeracy *arising out of geometrical methods, visible in designs as early as Archaic Greece and possibly even earlier, in Egypt.

The decagon has ten identical segments and the radii are the Golden Mean relative to outer side lengths as unity. This enables the mean earth radius to “be” the golden mean (Greek PHI) whilst introducing PHI as a different invariant to the Greek PI found in circular structures, an invariant for which many integer approximations exist including those found in the Fibonacci series (0-1-1-2-3-5-8-13-21-34- etc). Understanding the decagon, Michell used the approximation 160/99 = 1.6162 to model phi and we note that 160 is twice the factor of 80 found modelling the Greek mile above and that 99 contains 11 as a factor, a factor also of 3168 and hence 63.36, the scaling factors found between radius and side length. Whilst more could be said, a general truth has perhaps emerged:

Any regular decagon, of any scale relative to the mean earth will relate to the mean earth in both radius and side length. Is this true?

- The side length of 204120 feet divides into the circle’s radius as 160 / 99 =1.6162 /7
- The radius divides the mean earth’s as 63.36 whilst the sides divide it as 102.4 and 102.4/63.36 = 1.6162 .

This means that the ratio of the different sides are a model of the scale chosen for the decagon relative to the mean earth. It follows that the invariant nature of the decagon is only ideally suited to be a double model of the mean earth at this exact size: since 63.36 gives the 316.8 factor required for the decagon to have a 3168 perimeter.

The decagon of perpetual choirs demonstrates the mean earth can be
usefully seen as a decagon, whose nature can be transmitted to earth using the
decagon’s unique invariance, at a scale of 63.36. In this ability, it is the triangular segment
which has the visually direct (but analytically confusing) ability to
reciprocally reflect the sides of the decagon back to the circle’s radius, then
modelling the mean earth radius. So what are the characteristics of the triangular segment?

Firstly, 512 / 316.8 equals 160 / 99 and is merely inflated numerically
by 16 top and bottom. Secondly, by this means the Decagon is transferring the
attention away from the circle and onto the chord of the circle and the sum of
the decagon’s sides sum to 3168, Michell’s idealised spiritual circumference.
This was usually modelled in the metrological circumference of sacred circles
but was transferred to the decagon’s side lengths as ten chord lengths.
Importantly, *this allowed segments to be
alignments between sites.*

When Michell identified the side length (204120 ft) as 1/102.4 of the mean earth radius (20,901,888 ft), he was seeing a numerical transmission of the 512 length, where 512/5 = 102.4. The same transformation of the side length is 316.8/5 = 63.36, the mystery factor alluded to earlier.

The true unit for the decagon then emerges, as that required to make the
perimeter of the whole decagon 3168 units. There must be 316.8 in each side so
204120/316.8 = 644.3182 feet or 675 units of 21/22 ft – *a unit then belonging to metrology *as 175/176 of the Roman foot (a
root reciprocal Roman foot in John Neal’s classification). This new unit makes
the radius of the perpetual choirs a canonical 345600 feet of 21/22 feet which,
divided by 675, equals 512 such lengths so as to give the side length of 316.8
of those lengths (of 644.318 feet.) The units were after all ideal and
metrological but, because the key geometrical transformation was re-entrant and
reversible, the familiar relationship of radius, circumference and scaling
found in circular models of the mean earth was broken. Instead we find a
dynamic symmetry (meaning “analogy”) similar to that found in archaic
Greek designs. *note: This interpretation
has been superceded in the next posting by adopting the proper furlong of the
5000 foot mile, 625 feet long.*

Therefore, when asking when such a landform might have been organised, one is attracted towards the late Bronze Age, when Stonehenge existed and the doctrine of perpetual choirs and enchantment may well have been developed by proto-Celtic cultures, then an advancing religious concept connected to megalithic geomancy. This form allowed Stonehenge and the solstice sun to have been used as an anchor for other sites, the alignment to the summer solstice sunrise giving the bearing to Goring, then -144 degrees of azimuth relative to Glastonbury, from where a further +36 degrees of azimuth would find Llantwit Major.

John
Michell wrote about the perpetual choirs in *Twelve-Tribe Nations *but then found them to be ten-fold. He packaged
up his own work in progress in *The
Measure of Albion *and later wrote a less numerical view of it in the second edition of *Dimensions of Paradise *(see above figure from that).

The analysis above adds validity to John Michell’s proposal, not least because one can see how the decagon can achieve a very elegant modelling of the mean earth upon the earth. We have learnt something from it, which may be “the proof of the pudding” as to whether numerical interpretations are likely to have been intended. We can also now question whether the pattern was actually completed and how it could have been achieved in practice, whilst noting that the sun’s solstice angle is increasing away from east-west, over the pattern’s two degrees of latitude north of Stonehenge.

The circle around the outside of the decagon is 207360 feet long and to make this 216,000, like the radius of Einar Palsson’s Icelandic image only requires that length to be modelled in root Roman feet of 24/25 = 0.96 feet!
This means the arc over each decagon side (or chord) is 216,000

Roman feet whilst the chord is 63/64
less than that which translates (as above) into 316.8 units of 644.318
feet each equalling 675 units of 24/25 x 175/176 – the reciprocal Roman foot.

A further point to reflect upon is that the three choirs referred to in
Iola Morganwg’s*** *Triads of Britain*,
each of 24,000, add up to 72,000 which is half of the 144,000 singers in the
Choir referred to in *The Revelation of St
John, *a number with special properties for ancient tuning theory – an
apparent anachronism unless such harmonic knowledge prefigured the Christian
era yet was transmitted into it.

*** The modern judgment of Iolo Morganwg is as an “Influential antiquarian, collector and literary forger whose bardic name was Iolo Morganwg (1747-1826).” Evidence for the choirs does not appear forged but there are issues about how given place names correspond with modern places. As to when these literary references were made; the modern standard text by Rachel Bromwich found “these triads were codified in writ as a whole more or less in the 13th century, in our surviving versions. All of them are not of the same origin and from the same period. But Bromwich clearly states that these triads are the result of a long tradition that was oral for several centuries before starting to be written down at some time in the 12th century, maybe and probably a little bit earlier.”

- Mean Earth Radius: 20901888 feet (ancient model)
- Radius of decagon: 329,890.9091 feet (345600 RRR feet, 512 units)
- Side length of decagon: 204,120 feet (316.8 units)
- Proposed foot: 21/22 feet (root reciprocal Roman foot = RRR)
- Proposed unit: 675 such feet (644.318 feet)
- Circumference of out circle 2,073,600 feet
- Perimeter of decagon 2,041,200 feet (3168 units)

*City of Revelation: On the Proportions and Symbolic Numbers of the Cosmic Temple*. Garnstone Press:London 1972. ISBN 978-0-85511-040-6-
*Twelve-Tribe Nations and the Science of Enchanting the Landscape*(reprinted 2008.) 68-70. *The Measure of Albion: The Lost Science of Prehistoric Britain*

(/index.php/monuments/landforms/126-circle-of-perpetual-choirs). 112-115.*The Dimensions of Paradise: Sacred Geometry, Ancient Science, and the Heavenly Order on Earth.*(reprinted 2006 as*Lost Science of Measuring the Earth*) 101-104.

Perhaps as early as 4000 BC, there was a tradition of making chalk drums. Three highly decorated examples were found in a grave dated between 2600 and 2000 BC in Folkton, northern England and one undecorated chalk drum in southern England at Lavant in an upland downs known for a henge and many other neolithic features discovered in a recent community LIDAR project. The Lavant LIDAR project and the chalk drum found there are the first two articles in PAST, the Newsletter of The Prehistoric Society. (number 83. Summer 2016.) It gives the height and radius of both the Folkton drums 15, 16 and 17 and the Lavant drum, presenting these as a graph as below.

Local chalk is a relatively easily carved
yet substantial material and a cylindrical drum can be rolled and, being given
a definite diameter, causes the circumference to travel a known distance on the
earth. Folkton 17 has a 4 inch diameter which gives an 88/7 inch circumference
(using PI = 22/7) which equals 22/21 feet of twelve inches. In *Sacred Number and the Lords of Time*, 167-171, I point out that the
microvariations to be found between measures of the same module (in historical
metrology), [identified first by John Michell in *Ancient Metrology* and then
John Neal in *All Done With Mirrors*] include **176/175**. This
ratio is the product of two early versions of PI since **176/175 = 8/25 times 22/7**. leading to the fact that 1/3 foot
diameter (= 4″) will give a circumference of 22/21 feet. (see panel). The
module is 25/24 feet, varied by 176/175 to give 176/175. Since the accurate PI
of 22/7 is present in the ratio 176/175, then a circumference of 22/21 feet
times 7/22 gives a diameter of **22/21 feet times 7/22 equalling a 1/3 foot** diameter or the 4 inch diameter of Folkton 17.

There are three levels of interpretation:

- Firstly,
**the four inch radius appears to imply that inches were the native units of measure**and the five inch radius of Folkton 16 appears to support this. It is uncontested (though not peer reviewed) that Le Manio Quadrilateral used inches to count days to resolve the megalithic yard, as the day-inch difference when counting three lunar and three solar years. - Secondly, if the later megalith builders had evolved a network of fractional measures based upon the English foot as unit, 1/1, then new measures were made from that foot by
**laying out right triangles in feet**, with a different number of whole units in the two longest sides, numbers we would call the numerator and the denominator of a fraction. In the case of 22 feet for hypotenuse and 21 for base, the 21 divisions of the base can be made to rise at right angles to define 21 divisions on the hypotenuse, each 22/21 feet long. The chalk drum would perform 21 revolutions in travelling the 22 feet of such a hypotenuse. The diameter has to be 1/3 of a foot so that 1/3 times 22/7 equals 22/21 feet. - Thirdly, if one wishes to make a circumference of 22 feet or 21 rotations of this chalk drum, then the diameter must be 21 times 1/3 feet or seven feet.
**22/21 is in fact the Thoth ratio found between the 1/6 arc on the circumference relative to the straight distance between the ends of the arc.**Egyptian Thoth presents this in his iconography, because PI was a sacred invariant to geometers and this brings us to decorated drums being found in a high status burial, if the family involved were the geometers who laid out megalithic monuments and pathways. The undecorated drum found at Lavant shows signs of usage as if it had been rolled many times.

The largest of the three drums, Folkton 15, appears to have a circumference of 18 inches and, if so, the drum transfers the idea of rationality to the circumference so that the diameter is an irrational number of inches, 7 and 9/11th inches. Such a drum would be able to lay out cubits of 3/2 = 1.5 feet in a line, enabling yards to work extensively. One also notices that the designs on the tops of drums has a possible role in dividing the rotation of the drum like a rotary ruler or in the angular sense.

Stop Press: Since this article was written, the archaeologists have indeed proposed that chalk drums were employed to easily lay out lengths at Stonehenge. Please see the Times article.

I was fortunate to recover this article from the Wayback Machine after much searching since it was destroyed when the RAID backup failed.

]]>Gurdjieff first presented his ideas to groups in pre-revolutionary Russia. Amongst his carefully chosen students it was the habit to reconstruct talks and diagrams as much as possible, an endeavour that gave us a textbook of Gurdjieff’s ideas called *In Search of the Miraculous (P.D. Ouspensky, 1950). *This early form of the teaching was radically revised and extended by Gurdjieff, now as an author, during the 1920s, producing *All and Everything *whose part one was *Beelzebub’sTales to his Grandson (G.I. Gurdjieff, 1950)*. Prior to drawing this diagram just after February 1917, Gurdjieff had been presenting ideas about transformation of energies, human and cosmic, using the musical theory surrounding the octave of eight notes. The Diagram of Everything Living was “still another system of classification… in an altogether different ratio of octaves… [that] leads us beyond the limits of what we call ‘living beings’ both higher [and lower] than living beings. It deals not with individuals but with classes in a very wide sense.”

The diagram has eleven units connected in macro steps three units high and three units deep, and each unit is itself a class, a terminology which J.G. Bennett evidently expanded into his theory of twelve essence classes where each class was an ipseity or “thing in itself”, modelled by Bennett using a five-term **systematics **called the** pentad **(see appendix 2 *The Great Laws *to *Gurdjieff: Making a New World*, by Bennett,1973). Differences between eleven units and twelve can be irrelevent when, as with the octave where seven intervals link eight notes, eleven intervals can lie between twelve boundaries.

The lower nine square units each have three circles filled with a number whose factors are 2^n times 3 and these numbers define levels of Hydrogen corresponding with (left) the being itself, (bottom) what it needs to eat and (top) what is nourished by it and larger numbers are lesser beings. One can immediately correlate the right hand elements as forming the outer significance or context of the being. One can see in man that 24 must be doubled twice to reach his food of 96, and the intermediate hydogen is that of the beings below him, the vertebrates. Similarly, what he nourishes is doubly halved as 6, and 12 is the level of the next higher being. Thus the inner range of potentiality of the essence class Man is between the animal (48) and the angelic (12) so that the pentad is clearly prefigured in this Diagram and Bennett’s system of twelve essence classes. Bennett’s *The Great Laws *should be read alongside, noting that Ouspensky, present when the Diagram was first drawn, was for many years Bennett’s teacher. The group receiving the Diagram thought perhaps angels and archangels were planets and stars and Gurdjieff said of it “This diagram will not be very comprehensible to you at first. But gradually you will learn to make it out. Only for a long time you will have to take it separately from all the rest.”

The upper two diagrams of the highest steps will be correlated with cosmic information. Most distinctive is the topmost Absolute and it is of an equilateral triangle drawn within a circle and a circle drawn within that. geometrically this is an invariant relationship between two circles of radial doubling, that is the inner circle is half the diameter of the outer circle’s diameter, reminding us of the Diagram’s doubling theme. John Martineau made a detailed survey of such invariant ratios found within sacred geometrical constructions, published as *A Book of Coincidence*. (Wooden Books , 1998.). He also looked at the nearest, mean and furthest orbital distances of planets from the sun and found the equilateral geometry between Saturn and Uranus’ mean orbits (ratio 2.01121) and in a more complex form, Saturn and Neptune, the outermost planet.

This geometry is that of the ABSOLUTE given in the Diagram whilst the ETERNAL UNCHANGING geometry could have been that given by Martineau, as Being the relationship between Jupiter and Saturn.No geometrical connection between the circles was given and quite possibly, the square that linked them was not noticed and remembered by the students. This geometry is figure 4.

In some unfamiliar way, numbers are associated with the form of how the Creation works and of course geometry is one of the number sciences, in which numbers define invariant structures only possible when there is an existential reality involving space, things within space and distances in between them.Proportion is born to a world of forces which could tear it apart and yet the world of number is invariant, one could say transcendent (ABSOLUTE) whilst also being unmoving (FIRM).

Between these two is something like the Diagram of Everything Living in which transcendent power of numbers and invariant form are blended, as we see in the nature of diagrams. The diagram is part of the human essence class, a combination of number, form and aesthetics designed to represent. It moves towards the higher nature of humanity and delves into cosmic archetypes. The role of diagrams is largely degenerate as also the role of numbers in modern societies, where both are ten-a-penny and merely record or express. In the Diagram of Everything Living therefore everything finds its own level according to its manifestations whilst the Diagram looks on.

Beelzebub’s Tales relied
on a form of words
rather than of this Diagram,
as Gurdjieff went back to his father’s
roots as a teller
of tales in an oral tradition spanning
five millennia. Bennett
opens his Appendix
II (to *Making a New World*) on *The Great
Laws*:

“Our customary way of thinking and talking about the world is in terms of objects and events, both of which are abstractions. Gurdjieff saw the world as the universal process of transformation of energies, regulated by two fundamental laws and various ‘second-grade’ laws arising from their interaction. The two basic realities are

relationsandtransformations. The first are governed by the Law of Threefoldness variously calledTriamoniaandTriamazikamnoand the second by the Law of Sevenfoldness calledEftalogodiksisorHeptaparaparshinokh. The interaction of these two laws is represented by the Enneagram symbol and by the Diagram of All Living referred to in Chapter 11. It is also noteworthy that Gurdjieff refers in the Purgatory Chapter to a scale of energies of different ‘degrees of vivifyingness’, which is divided into twelve steps or stages.” [emboldening is added forterms]

Bennett remarks that Gurdjieff seems to follow Plato’s Pythagoreanism (in *Timaeus*) by using only products of two and three, omitting use of prime numbers five, seven and eleven. Five would be necessary to embody the Just intonation of ancient near eastern music and seven and eleven are further crucial to the Model of the Earth and other operations in which pi can be assumed to be 22/7.

” [Gurdjieff] departs however from the Platonic tradition in his description of Reciprocal Maintenance (viz. the Pentad of figure 2 and

harnelmiatznel) which has no place in Greek cosmology and did not enter European thinking until Gurdjieff came to the West. … nevertheless we can find traces in the Rosicrucian literature of the sixteenth and seventeenth centuries … when the Khwajagan (lit. Masters of Wisdom) had finished their work in Central Asia and were handing on their knowledge to various Sufi brotherhoods … and probably also to European societies with the same fundamental aim.”

In *Robert Fludd: Hermetic philosopher and surveyor of two worlds*, Joscelyn Godwin wrote

“[Robert Fludd] lived at the very end of the [Renaissance] era in which it was possible for one mind to encompass the whole of learning … and he betrays something approaching despair in his endless plans for a magnum opus…. in place of [the modern view] of an infinite material cosmos expanding in all directions, he could envisage a few well-defined regions and then terminated in the utter simplex of God.” In this view, Fludd was not transmitting Rosicrucian ideas which may have come from a common origin to those of Gurdjieff.

Bennett continues “the Rosicrucian symbol of the pentad which appears in Dr Fludd’s

Systema Universicorresponds exactly to the ‘Diagram of All Living’ and hence to the structure of theTrogoautoegocrat(or principle of Reciprocal Maintenance). The same work contains the doctrine of the quintessence and transformation. Every cosmic manifestation has its higher and lower natures, the interaction of which produces the quintessence. This is also Gurdjieff’s teaching expressed in the statement(Beelzebub’s Tales. p. 763) “The Higher blends with the Lower to actualise the Middle”. The pentad symbol is:”

*Figure 6 J G Bennett’s compressed version of a Pentad for the essence class Man. from Making a New World: AppendixII.*

Bennett writes: “By placing the five terms at different levels in the diagram, we indicate the five nodal points. Reading from left to right, we show three kinds of relationships:

- What it is in itself; the quintessence.
- The essence classes from which and to which it evolves.
- How it enters into the
*Trogoautoegocratic*process.” [*Making a New World*,*281-282*]

The form of this idea is invariant whilst its manifestations including diagrams can be various and, in *Gurdjieff: Making a New World *and *The Masters of Wisdom*, Bennett presents his own search for its origins in the neolithic revolution of Persia identified with the original prophet Zoroaster. Bennett thought the principle of Reciprocal Maintenance was articulated as the first cities came to be dependent upon agriculture. Bennett has a final word, related to our subject: the Diagram of Everything Living:

“The Cosmic Individuality is directly associated with the Creation and Maintenance of the World. In Gurdjieff’s symbol this is called the Eternal Unchanging: in

Beelzebub’s Talesit is theTrogoautoegocrat, which in some passages Gurdjieff personifies as the Holy Spirit. This is the eleventh and penultimate stage in the creation and redemption of the world. One can sense Gurdjieff’s difficulty in conveying the picture of a cosmic process that is also a state of being. TheTrogoautoegocratis not part of the Creation, but a manifestation of the Divine Will whereby time and eternity are reconciled.” (Making a New World, 213)

Bearing this in mind, it is interesting to put flesh on the bones of the pentad by looking at the nature of the **ancient middle eastern cities**, with emphasis on the city states begun by the Sumerians in Mesopotamia. Cities had a God and a king (archangels) whilst their existence depended upon the *surpluses *created by **ploughing the soil **(invertebrates) and **farming with animals **(vertibrates), these two enabling more than *subsistence*. Cities and the farming needed for surpluses naturally creates property *ownership and trade*, especially as a *social hierarchy *develops of **leaders and specialists **(angels). The leaders and specialists came to depend upon information in order to preserve knowhow and recorded ownership and trade, whilst *heroic myths *and historic legends reenforce legitimacy and establish values.The land and the city became fused in a *sacredization of the landscape *connecting earth to the heavens and gods. Farming methods meant that in some fashion the solar calendar needed to run alongside the prehistoric lunar calendar. War (between cities) became conflated with Sacrifices to the city gods.

The discipline of the five-term pentad gives insights as to what the essence class of the city is. Cities must be a development of the human essence-class since they facilitate some of the potentials (the inner range) of the human essence-class, through creating proxies for the angels and archangels of the Diagram we are considering. This would also apply to Greek cities, and the Mexican cities of the Olmec and Maya. By creating proxies for the higher essence classes,useful specialists come into existence such as tradesmen, soldiers, traders, supervisors, and scribes. But the fact that these”upper classes” develop makes them dead-ringers for *representing *the higher worlds, as is seen when religious ideas and religious specialisms arise within them. Their work concerns the heroic myths, sacrifices and sacredization of the calendar and landscape – all of which emanate from the god-king. Bennett called this period in the ancient world the Hemitheandric epoch (3200 to 800 BC), where special humans, heroes and priest-kings, were believed to have superhuman attributes and powers enabling them to act as intermediary between the gods and ordinary people (*Dramatic Universe. *volume 4. *307-10,324, 438*.). And so on….

**I went to Thornborough some years back **and later found English Heritage Research Report 174: *Cult, Religion, and Pilgrimage: Archaeological investigations at theNeolithic and Bronze Age Monument Complex of Thornborough, North Yorkshire*,ed: Jan Harding, (Council for British Archaeology: York) 2013, ISBN978-1-902771-97-7.

As usual with three slightly off-line objects, the parallel to Orion’s belt has been made, and this has become an acceptable interpretation (unusually in this case) by archaeological interpreters. One can see from the title of report 174, *Cult, Religion, and Pilgrimage, *religio-anthropological parallels are preferred by archaeology as a social explanation for the unique geography of riverine Yorkshire, east of the Pennines. However, astronomical alignments and the metrology within sites are dutifully ignored as a source of meaning relevent though to the widespread practice of horizon astronomy and counting using lengths of identical length (such as inches or digits).

The report provides three interesting alignment angles, each carefully derived from other studies, from the bipolar entrances of each of the three henges; which alignments are here found astronomically significant and relevant to the design and dimensions of Thornborough Henges,when seen as an astronomical timepiece.

Figure 2 illustrates what these alignments could mean from the standpoint of horizon astronomy, namely that

- the northern henge is aligned to an approaching maximum standstill moon-set to the north
- The central henge is aligned to the standstill moon-set as full disc
- The southern henge is aligned to the standstill moon-set as a last flash.

**My Thanks to Robin Heath for his *QuickAz* data, for which see assumptions below

The alignment of the Henge to the lunar maximum standstill points to the purpose of the monument as being related to megalithic astronomy that may then have had an emerging religious significance (which can usually only be guessed at.) I gave examples in *Sacred Number and the Lords of Time *of two circular monuments where the diameter is rationally based upon the number of days between lunar maxima, 6800 days, by having a diameter of 3400 inches (Aubrey circle) or 3400 megalithic inches (Le Menec western cromlech). Any measured line can be traversed twice to form a continuous count, then exemplifying the form of duality visible in the nodal cycle of 18.618 years, each end in this case being the maximum or the minimum lunar standstills, 3400 days apart. Thornborough expresses just such a duality between the northern and southern henges, with the central Henge equidistant from both.

It should also be realised, with any lunar maximum monument, that Alexander Thom’s long alignments to the lunar maximum would have been essential for measuring the 6800 day length of the nodal cycle of the moon’s extremes. After this *measurement phase*, a long count could be reproduced by seeing that 6800 was simply 17 times four multiplied by 10 times two (a rectangular number of 68 times 100), and this number could become extremely useful as a countable length during the 18.6 year nodal cycle. By being accurately aligned to the lunar maximum moon-set, a linear counting of 3400 (to the minimum) and back would allow the progress of the nodes to be tracked through the stars of the sun’s path, these probably organised in someway similar to today, in our Zodiac.

It therefore becomes of interest to study the metrology between and within these henges, in which a simple 4th millennium metrology of inch, foot and megalithic yard can then be used to detect for astronomically relevant lengths within the monument.

The three henges are of similar design, each being of an avenue running through concentric circular banks. The inner ring appears to have a mean diameter equal to the lunar year in day-feet, which can also be 12 lunar years in day-inches. This measurement was made off the Report by placing a circle in the visually “best” position and then converting its scanned diameter, according to the scale provided, into meters and then feet.The diameter read in this way was 108 meters, which length equals, in feet, the number of days in the lunar year: 354.367. But read in day-inches, this length as a count would be twelve times this and hence 144 lunar months long.

Twelve lunar years is 144 lunar months, and it was then discovered that the distance between the entrances to northern and southern henges was 12 lunar years in length when measured in day-feet. This 12 lunar years (in day-feet) is then twelve times the diameter of the inner split ring of the central Henge (in day-inches), implying that 144 lunar months was,for some reason, an important period for the builders in their astronomical understanding, available inside the central Henge as a countable length, but then in inches rather than in the cursus where it had been realised twelve times as large, in feet.

One is drawn back to identifying some means of counting the 6800 day period between the lunar maximum, to which the monument is aligned. A solution hinges on the ratio to be seen between 144 lunar months, equalling the 4252 day-feet length of the cursus, and the 6800 day period, which ratio is exactly 8/5 or 1.6. This ratio is the same as that between the lengths of the Venus synod and the solar year (365 whole days). Therefore, if one counted the cursus length in units just 5/8th of a foot, the cursus would be 6800 such units long but, better still, if the day unit chosen was 10/8 of afoot, that is 5/4 feet, then there would be 3400 days to be counted one way and 3400 days to be counted in coming back to the end one started at.

One then feels drawn to have the northern Henge represent the lunar maximum, to which the whole triple Henge is aligned, thus having the southern Henge represent the lunar minimum. This would make the central Henge, being equidistant, representative of the point at which the lunar extremes from east- west on the horizon equal those of the sun at its winter and summer solstice. At this midpoint in the nodal cycle, the sunset and northerly moonset would (at different moments) shine diagonally across the aisle of the central henge at an angle of 45 degrees to north and west. Hence perhaps, the henge alignment to the full disk and width of its entrance follow a pattern familiar to the corridor of Gavrinis, where the moon enters straight down the corridor whilst the sun’s extreme (then rising in the winter solstice), can only cut diagonally to end stone C3 (see figure 5.6 of *SacredNumber and the Lords of Time*), at the end of a passage and chamber only 14 metres long.

- full disc azimuth = 324.5849
- last flash azimuth = 326.413

Epoch | 3800BC |

lunar declination | 29.228 |

Latitude | 54.20972 |

Horizon | 0 deg to NNW |

Earth Curvature | 0.72 |

Parallax | 0.95 |

Refraction | 0.55 |

It has been remarked that the form of the **northern** alignments of Edeven were similar
to those starting at Le Menec’s egg-shaped stone circle 4.25 miles away, at a
bearing 45 degrees southeast. Whilst huge gaps have been caused in those of
Edeven by agriculture, the iconic Le Menec alignments seem to have fared better
than the alignments of Kermario, Kerlescan and Petit Menec which follow it
east, these being known as the Carnac Alignments above the town of that name.

One similarity between alignments is the idea of starting and terminating them with ancillary structures such as cromlechs (stone kerb monuments), such as the Le Menec egg and, despite road incursion, a3-4-5 structure similar to Crucuno, aligned to the midsummer sunset by a length 235 feet long. This is the number of lunar months in the 19 year Metonic period and is factored 5 times 47. Another similarity may be seen in Cambray’s 1805 drawing of these Kerzerho alignments, at the head of ten stone rows marching east (figure 1).

In these northern alignments, the bearing of the 18-19-6 triangle has the same angle to the south-east as the Carnac alignments have to north-east because both recorded the same relationship between the solar and eclipse years, whilst having a different focus on eclipses and the moon’s nodal period, respectively.

As previously stated, the northern project was studying the Metonic period as consisting of five of the 47-month long Octon eclipse period of four eclipse years, and in 5 of these 235 lunar months equal the 19 solar years of the Metonic.

In contrast, the Carnac alignments over 4 miles south-east were initially studying the movement of the deviation of the moon from the ecliptic, by continuously observing the horizon events of the moon.Normally, only the maximum and minimum standstill of the moon can be deduced as alignments of interest for megalithic astronomers and, at Carnac, these alignments were easy, being very closely the alignment of the diagonals of single and double square respectively. But it is the triple square whose diagonal’s length, relative to its base, gives the length of the solar year relative to the eclipse year. This interplay between lunar alignments and Carnac’s natural counting geometry can be seen in figure 2.

All of the indications are that the northern alignments preceded the southern (Carnac) alignments in that; having established the best eclipse period of all (the Saros), the next objective would be to study the 18.618 years over which the range of moon-rises and moon-sets (to east and west) have available angular range over an 18.618 year cycle, the minimum being the least angle (26.565 degrees) from east or west and the maximum over the greatest angle (~45 degrees) from east or west (- a right angle).

Another interesting comparison between Kerzerho and Le Menec is to place Thom’s survey of the Le Menec over the Google Earth image so as to make a direct visual comparison of unsuspected similarities.

The staggering of Erdeven’s northern-most rows is very similar to those at Le Menec, noting that only Le Menec’s first rows follows Thom’s abstract line to the cromlecs informing Pythagorean triangle’s (3-4-5) hypotenuse. Thom found for the angle of a 1-2-root 5 hypotenuse relative to north as appears the case at Erdeven also. The white line, marked by its 18.4 degree angle from east, to Er Groh would point directly east if Figure 3 was tilted instead for Le Menec, showing that these two alignments are like symmetrical twins. The 36.8 degree line to midsummer sunset would then become the egg’s shorter axis pointing to the midsummer sunrise.

This sort of comparison draws attention to the eastern hypotenuse of where the egg would be, it the back garden of the house. One stone apparently exists on that hypotentuse (and starting line of alignment) in the position that would terminate row 10 of Le Menec, but at Kerzerho also would terminate arrow, as per figure 4.

This demonstrates that more than passing comparison of the northern and southern alignments may reveal mysterious similarities pointing to new ideas as to the purposes of the two monuments.

]]>*Decoding European Palaeolithic Art: Extremely Ancient knowledge of Precession of the Equinoxes*

This work concerns our understanding of the astronomical knowledge of ancient people. This knowledge, it seems, enabled them to record dates, using animal symbols to represent star constellations, in terms of precession of the equinoxes. Conventionally, Hipparchus of Ancient Greece is credited with discovering this astronomical phenomenon. We show here that this level of astronomical sophistication was known already within the last ice- age, and very likely by the time Homo sapiens entered western Europe around 40,000 years ago.

They go on to say “The evidence used to verify our hypothesis is accumulated from many of the most famous Palaeolithic cave art sites across Europe, representing dates up to 38,000 BC including;• Hohlenstein-Stadel cave, southern Germany circa 38,000 BC• Chauvet, northern Spain circa 33,000 BC• Lascaux, southern France circa 15,000 BC• Altamira, northern Spain circa 15,000 BC. Moreover, this system of representing dates is fully consistent with our interpretation of Neolithic sites in Anatolia, namely;• Göbekli Tepe, southern Turkey circa 10,000 BC• Çatalhöyük, southern Turkey circa 7,000 BC”

The question of ancient origins and precession was brought up well by de Santillana and von Deschend in *Hamlet’s Mill* (1969) and in Tilak’s *The Orion* (1893,) based largely upon mythic texts. A number of authors have previously found for star maps in stone age art, but this work appears to have crossed some scientific Rubicon and may find itself in Rome. There is a direct descendent of Hamlet’s Mill in *The Spiritual Science of the Stars *by Peter Stewart (who wrote it after decades of follow-up to that book).

My own book on *Precessional Time and the Evolution of Consciousness* “harmonized the revelations of those great originals G.I. Gurdjieff, Alexander Thom and Ernest McClain, and the authors of Hamlet’s Mill – the kind of synthesis one has long hoped for.” Josylyn Godwin, author of *Atlantis and the Cycles of Time: Prophesies, Traditions and Occult Revelations – *documenting the impact of the notion of ancient knowledge deep within precessional time.

A book loosed upon the English-speaking world by Swami Sri Yukteswar, *The Holy Science*, gave precession a spiritual significance. Whilst his time period and mechanics of precession might have been questionable scientifically. His idea was that the earth comes under the sway of a grand center every 24,000 years in which the mental virtue of humanity grows into a golden age in which the structure of reality can be directly intuited rather than known theoretically or not known at all.

In the context of the new paper from Sweatman and Coombes, this might account for high knowledge existing in the hands of stone age painters without access to a technical culture such as the megalithic or our own.

Alternatively, an Atlantean culture could have existed from a technical culture then coming from a region of precession close to ours. This idea then naturally proposes a cyclicity of human civilizations and cultures in which high knowledge is partially preserved, leading to the perceived anachronism’s seen then as occult or merely made-up through biased interpretations.

The new paper therefore, if it shows objective evidence of “Extremely Ancient knowledge of Precession of the Equinoxes”, will perhaps deepen our intellectual history and validate some of the efforts made outside of official science. For example, recording dates through presenting precessional configuration of the stars is a well developed theme of mythic texts from India to South America: it can happen by simply showing the angle of say the Great Bear in rock art. After all, Precession is a naturalistic equivalent of a Maya/Olmec Long Count.

]]>The picture below is a composite of three things

- The Chartres eleven level labyrinth discussed in chapter seven.
- The iconography of Thoth as Pi within the circle (from
*Temple of Man*). - The hexagonal number 19 as circles

The 22 units of the 21 unit sector of Thoth’s fathom correspond to 19 “cogs” of the circumference of the Chartre labyrinth.

It is fabulous that the cogs are used to define, by their centres, the perimeter as the unit called *ped manualis *by the builders*, *according to John James (the foremost investigator of that cathedral’s construction order – see his website).

Whilst the *ped manualis* is a Royal Foot, 8/7, in Neal’s *Standard Geographical *variation (times 126/125 and times 176/175), it is also close to 22/19 feet (different by 8 thousandths of an inch and 99.94% accurate). Thus whilst 19 cogs equal 22 units, the cogs are 22/19 which times 19 is 22 feet – plus 19 is a hexagonal number and there is the motif of six petals in the centre.

The entire circumference is, like the iconography of Thoth, 6 x 22 = 132 feet long. Using Pi at 22/7, the 22s cancel and the result is a diameter of 6 x 7 or 42 English feet. Like the Scottish brochs, the units directly interpret the ideal value of Pi itself as 22/7, employing as it does the prime numbers 11/7 that also define "Ancient Model of the World".

]]>*Published in Nexus Magazine in 2004*

When understanding the origins of human knowledge, we tend not to look into the everyday aspects of life such as the calendar, our numbering systems and how these could have developed. However, these components of everyday life hold surprising clues to the past.

An example is the seven day week which we all slavishly follow today. It has been said that seven makes a good number of days for a week and this convenience argument often given for the existence of weeks.

Having a week allows one to know what *day of the week* it is for the purposes of markets and religious observances. It is an informal method of counting based on names rather than numbers. Beyond this however, a useful week length should fit well with the organisation of the year (i.e. the Sun), or the month (i.e. the Moon) or other significant celestial or seasonal cycle. But the seven day week *does not fit in* with the Sun and the Moon.

Whilst some historical cultures ran a 360 day year, within which a 10 day, 6 day, 12 day or even 8 day week would fit, seven does not divide into 360. Neither does it divide into 365, the number of whole days in a solar year.

Seven would divide into a year of 364 days as the familiar 52 weeks in a year, only exactly instead of one day out. This is why our own 365 day year leads to days of the week moving forward one day every most clear when birthdays and Christmas are on different weekdays. The seven day week’s “fit” to a 364 day year leads to some familiar numerical logic, for there can then be 13 months of 28 days, each month then having four seven day weeks. In such a calendar, the days of the week within the year are kept synchronised by having a special extra day. More important, with a 364 day year there is then some justification for having a seven day week.

We know that this calendar of 364 days must have been practiced within living memory for the expression “King for a year and a day” hails from the time when society was centred around women rather than men. It is quite clear that matriarchy and not patriarchy once ruled domestic and tribal politics. This natural fact of life, emerging out of the stone age, ran into the Neolithic: As humankind developed a more settled agrarian economy the “gatherers”, within the hunter gatherer partnership, were the home builders and the creators of new humans.

There is a connection between the seven day week and this age of different sexual politics shown by the archaic use of a “Saturnian” calendar in Crete.

In the modern age there are always attempts to say that four weeks of seven days is a lunar month, but the month is twenty nine and a half days long according to the Moon’s phases and not twenty eight. The lunar orbit of the Earth (a hidden aspect) is twenty seven and one third of a day long and it is unlikely the ancients “rounded up” that invisible time period. In other words, there is *no fit between the lunar month and the week*,and yet this wrong idea is quite widespread. The origins of the seven day week are not with the Moon’s periodicity.

Another accepted premise for the week is that the Babylonians and possibly the Sumerians before them used it. These cultures of the fertile crescent hosted one of the earliest city state cultures and they were keen astronomers, but surely that just means that they would likely have an astronomical reason for having a seven day week. In those days, astrology was indistinguishable from astronomy and the five visible planets were added to the Sun and Moon to obtain seven, leading to the “astrological” week with planetary day names.

Two accepted historical channels for receiving a seven day week from the Babylonians are:

**The Greeks brought back the seven day week from the conquests of Alexander the Great and gave it to the Romans.**The Romans moved from a ten day to a seven day week with their assimilation of Christianity, which itself was partly a Greek system of thought.**The Jews adopted the week from the Babylonians after their captivity.**Theirs was a different version however since planetary deities could not represent the days (Saturday = Saturn’s day) as with most of the other cultures that have this week. The number seven was especially sacred in the Jewish tradition. For instance the Babylonian epic of a seven day creation starts the Bible as one of the earliest stories of the original Pentateuch and the sacred measures (in cubits, etc) often expressed the number seven. Seven in the Jewish week was sacred but not planetary like that of the Greeks.

In the undocumented times we call prehistory, traditions like the week could have been the “diffusion” of something innovated in a single place like Sumaria. On the other hand such ideas can also come from a common experience such as the astronomical observation of time periods. When the latter is the case, arguments for diffusion only look good until we find the same tradition, but out of the required timing for diffusion to have taken place. It looks as though the seven day week did not need to have come from the East; it was already in the Mediterranean in bronze age Crete.

To find an astronomical cause appears initially difficult because, as stated above, the periods of Sun and the Moon, the year and the month, do not divide by seven days and neither does Venus, the most visible planet.

And why should any astronomical length of time, such as the day on Earth, fit any other astronomical periods anyway? The whole premise of modern science is that the planetary system merely “settled down” into a set of planets and that, within certain limits, there can be no detailed order relating the rotation and orbit of the Earth with the periodicity, seen from Earth, of another planet. However this is exactly what is found, and there are such exact relationships between celestial periods seen from Earth: This is the subject of my book *Matrix of Creation, Sacred Geometry in the Realm of the Planets* (Inner Traditions, Vermont, 2003). What follows is new and complementary material to *Matrix of Creation *{only partially found in my second book on *Sacred Number and the Origins of Civilization* in 2007}.

Traditionally it is the planet Saturn that is associated with the number seven, and of course the Jewish Sabbath is Saturn’s day or Saturday. Also interesting is the fact that the Jewish calendar is lunar throughout, as is the Islamic, and so the arrangements of seven days into a four week month of twenty eight days seems perfect, so much so that the Nazarenes are reputed to have had four such weeks, ending in a sabbath at the end of each major phase of the Moon: New, Half waxing, Full and Half waning, so as to make seven work with a month longer than twenty eight.

In *Matrix of Creation *I point out that in 29 Practical Years of 365 days there are 28 synodic periods of Saturn,where a synodic period is the time taken for Saturn to again be opposed the Sun seen from Earth, like a full moon but seen as a loop of Saturn every year in the sky. So 28 is found within the behaviour of Saturn but not yet in a way that yields a 7 day week. However, larger numerical coincidences are, as we shall see, based upon the numerical interrelationships found between smaller periods of time.

The evolution of sky observation into a calendar and our week is perhaps as simple as counting itself.

Alexander Marshak in *The Roots of Civilisation *illustrates many examples of stone age markings, often on bones, that appear to be keeping a tally of the Moon’s phases. The counts typically run over two lunar months, probably because the month is itself 29 and one half days long: a double count gives a whole number of 59 days and is quite accurate. Since the processes of the sky are essentially circular, returning to the same condition to rejoin the beginning of the cycle then the natural tendency, when the medium will allow it, is to draw the cycle as a circle of marks.

Such counting is a *measurement* from which a number emerges associated naturally with the celestial cycle in question. It marks the achievement of knowledge but not necessarily the ability to *use it*. To synchronize life to a celestial cycle, beyond observation in the sky, requires that the new knowledge be translated into a *model *on Earth.

Now we know that from Megalithic times and into the bronze age, many large models of calendric knowledge were being built throughout Europe. Many of these were directly observational, such as stone circles and their alignments with solsticial sunrise, sunset, and lunar maximum. These seem to form a continuity with the bone count measurements, yet they also form an *operational* calendar. Something new then became possible, a calendrically based building that could contain observances connecting to the gods of celestial time phenomena.

The creation of numerical rings would then allow a further possibility: that a numerical ring could simulate celestial phenomena and, to a degree, become detached from the sky as an abstract system more akin to a clock. If and when a series of celestial cycles were found to be interrelated, these would have allowed the creation of an orrery or planetarium which outputs the condition of a number of different celestial phenomena through the relatively simple *activity* of counting smaller time periods.

Our clocks today have evolved from such roots by employing gear wheels as numerical rings and the activity of counting is automated in the form of a spring-driven escapement, that produces a regular advancement of the gears according to the numerosity of these cogs, rotating in circles. Thus, a clock or an orrery is based upon the relative counting of cogs cut into wheels but is essentially no different to what can be achieved by the manual movement of markers in rings of holes moved in time with a regular celestial cycle, with the day being the simplest choice.

If the ancients wanted to create an orrery, their best option was to use a ring of holes and indeed this has been suggested as one of the uses for the circles of post holes, most notably the Aubrey Circle of 56-holes around Stonehenge. Fred Hoyle showed how the Aubrey Circle could be driven as an orrery to accurately track the Sun, Moon and eclipse nodes around the ecliptic stars, using a procedure further refined by Robin Heath.

In fact a bronze device using gears has been found from no later than 80 BCE, near Crete. It is a planetarium designed to simulate multiple celestial periods, called the“Antikythera Clock”, and it used advanced mathematical knowledge of “continuing fractions” (reported in June 1959 Scientific American, p.60-7, see first page below.) It remains an anomaly that undermines the consensus view that clock mechanisms were a product of our industrial revolution.

The main point here is that the use of numbers to model the movements of celestial objects, relative to each other,should not be seen as unlikely back in the bronze age or even within the later Neolithic period, that encompasses the Megalithic. There are objects displaying the capacity and desire of those peoples to do just this. A counting device only requires the identification of a time period that divides well into one or more larger time periods, as a whole number of counts. It will be shown that the day and week are just perfect for this purpose – a fact since forgotten inits applications but retained as our seven day week associated with Saturn, The King of Time.

When visiting Crete, the southernmost Island of Greece and home to the Minoan Culture between 2500 and 1450 BC, it is obligatory to visit the Heraklion Museum filled with Minoan artefacts. In the final room relating to Knossos, the famous Minoan complex, one comes across item 2646, a “perforated utensil” of a sort that might be interpreted as an incense burner/diffuser from the period.

As seen below, it is made of spun pottery, painted with a seven-fold wave pattern and covered in circles of holes. When counted, the number of holes count *1:15:22:38:62, *and the holes seems to have been punched into the clay in a slightly ragged way. I will spare the reader a longer discussion of this disk’s construction, available elsewhere here, and get to the point that concerns us here, the origin of the week of seven days.

The central motif is “seven-rayed” which seems to point towards Saturn. Looking first at the 15 hole ring, I discovered that the ratio of the lunar year to the Saturn synod is 15:16. This is surprising new information since Jupiter has a ratio of 8:9 relative to the lunar year and, most significantly, these two ratios are both musical and correspond to a pure major halftone and tone respectively. The unit of time involved in the 15:16 ratio is *exactly *4/5^{th} of a lunar month, as can be seen by dividing 378 days by 29.53 to get 12.8 or 12 and 4/5^{th }lunar months.

The 22 hole ring seems obscure but the 38 ring hole, at 2 times 19, is reminiscent of the Saros cycle of 19 eclipse years between the recurrence of lunar and solar eclipses, lasting 223 lunar months or just over 18 years. In fact the decoration around these 38 holes is appropriate to indicating eclipses. The reason for 38 and not 19 holes was that the eclipse year is made up of two eclipse seasons. An eclipse season is the time between the crossings of the Moon’s orbit, by the Sun, the only time at which eclipses can occur during “seasons” lasting 34 days. [whilst solar eclipses are rare, there is usually one lunar eclipse per year]

If we divide the eclipse season period of 173.31 days by 22 we get a period of time 63/7 days or 7 days plus 7/8^{th }day. This period is exactly one third of 4/5^{th} lunar month, and so there is the implication that the 22 count contributed to tracking the eclipse seasons and that the 15 count showed in some way a relationship between Saturn and the Moon. (The 7 7/8^{th }day period is in a whole tone relation of 8:9 to the seven day week.) But if so, how was the counting done and what unit was being counted?

The remaining 62 ring seems very close to the number 63 found in 63/7. Indeed, if the 378 days of Saturn’s synod is divided by six, the result is 63 days. It seemed therefore that the unit of time, 63/7 days might be related to the outer ring of 62 if the central hole is included in the count to make 63 holes.

*The outer track of holes can simply count days.*

If the period sought had been 8 days rather than 7 7/8^{th} days, then 64 holes or days would give 8 periods, but the sought after period is 1/8^{th} of a day less than eight full days. By including the inner hole, the outer ring can count 63 whole days which, after one round would contain eight periods of the required length. Such a use of the central hole symbolises the end of one-sixth of the Saturn synod, a day that may have been special in this Saturn calendar – hence the central hole.

After eight days, i.e. 8 holes, the count should have lost 1/8^{th} of a day and by counting in an anticlockwise fashion, the time of day of this “falling behind” can be tracked exactly as if reading a 24 hour clock face. Figure 8 shows how after starting the count, the period of 7 7/8^{th} days looked for will end very close to where the marker now stands on the “24 hour” clock face. The marker will deviate from perfection in this regard but will generally always be showing in which three hour period the end of the 7 7/8^{th} day period occurs. This means there would be no need to show this explicitly in the decoration since it could be read accurately in this direct way. It also means that, theoretically, this ring can, with the central hole, measure the required periodicity *within three hours *without any further techniques or technology. Incidentally,this is an ingenious version of the Vernier technique, invented in 16^{th }century by Pierre Vernier, in which two slightly different scales interact to yield a more accurate reading.

This disk thus leads directly to a very complete and accurate calendar (see Figure 10) that can track the motion of Saturn, the Moon and the eclipse seasons. The calendar employs the simplest unit of measure available on Earth, the Day. It also employs units based upon the week, because Saturn’s period divides perfectly by seven days, that is

Our present seven day week would be the natural choice for people operating the Saturnian calendar.

This explains the seven day week’s adoption, both practically, as a calendric device, and evidentially, as an historical reality predating classical Greece. We know this calendar would have been contemporaneous with Egypt and other parts of the Minoan sea-trading network. It also connects to biblical history since Moses and Aaron could have encountered it in Egypt, and this could have lead to its adoption by the Jews alongside other knowledge including Jewish sacred measures and building techniques.

Other cosmic relationships appear within this new calendar (see Figure 10), relationships quite surprising in that they indicate that time on Earth is simpler that it should be. The main rival of Chronos, Zeus, the planet Jupiter, is shown to have a new relationship since their 378 day and 399 day periods have the ratio of 18 to 19 units of 21 days. This unit is exactly three weeks of seven days. (see Figure 9)

The chance of the only giant planets visible to naked eye observers both having periods that divide by seven seems unlikely and hence this would have seemed a significant fact to ancient peoples. The adoption of a seven day week would naturally be confirmed as a logical part of a sacred calendar.

In the mythology of Zeus, Chronos is accused of swallowing his own children and perhaps we can see in this a reference to *a system of time* that, if followed, effectively denied (swallowed) all the other celestial cycles/ planets. In fact the ancients could have “got hung up” on such a simple system of time. Zeus, a child of Chronos, is saved from such a fate by his mother and is brought up in a Cretan cave hidden from his father who might hear his cries. This implies that the drama is one being played out in Crete, with Chronos just down the road rather than in some heaven and routinely omniscient.

Most significantly, Zeus grows up to depose his father and become the god of the classical world from which western culture has largely evolved.

This calendar, implicit in the Disk of Chronos, evidently fell out of use and was replaced, probably with those for which there are historical records. It therefore seems likely that the overthrow of Chronos by Zeus was related to these calendrical practices and that Chronos was related to some fixed religious regime associated with the older Saturnian calendar. Since the calendar is simpler than it “should be”, that is, because time periods should not match so simply (in days) the periods of Saturn, the Moon and eclipses, then no further development of time was likely when living under such a calendar. The God of Time would have dominated thought and the religious precincts of the bronze age, until deposed and replaced.

All of this confirms the basic tenets, expressed in *Matrix of Creation*, that there was an ancient science that employed numerical arts to discover order in the world and also build monuments relating to their discoveries and that science. Lying behind it all was a world view that numbers actually defined how the world was built.

Such a belief in numerical creation could have been “seeded” in the fabric of the solar system as the numeric relations that are to be found, seen from Earth. In other words, our ancient awakening to the numerical relationships in the world could have been a cause for the evolution of human understanding itself. In the presence of an apparently designed world, a religious sentiment would have been a natural one. The original meaning of the word “religion” is, after all, not based upon *beliefs*but on *reconnection*, presumably to the truths of the cosmos.

It is obvious that there must be many artefacts and monuments with further facts to transmit to us from the past, facts that would restore our connection to the whole as Cosmos, and cause little understood traditions such as the week to become re-rooted in their original context.

For seven day week, try www.webexhibits.org/calendars/week.html

For a great book on calendars, try

*Mapping Time: The Calendar and its History*by E.G. Richards, Oxford, 1998

For more on the significance of numerical astronomy, read my book

*Matrix of Creation: Sacred Geometry in the Realm of the Planets*Inner Traditions Press, Vermont 2004

A Synod is always a repeat cycle time relative to the Sun, see from Earth. The Saturn synod is 378 (378.09) days whilst that of Jupiter is 399 (398.88) days.

- If the basic time period of 63/7 is being counted, then the Saturn Synod of 378.09 days is achieved as 6 times 8 times 63 divided by 8 as 378 days yielding an accuracy to the Saturn synod of 99.976%
- The Lunar Year of 12 lunations is then tracked as 15 times 3 times 73 divided by 8 equalling 354.375 days versus 354.367 days giving an accuracy of 99.998%
- The period between Eclipse Seasons is tracked as 22 times 63 divided by 8 or 173.25 days versus an actual period of 173.31 days giving an accuracy of 99.965%
- The eclipse season is plus or minus 17 days and 17 days corresponds to two holes of the 22 holes used for counting its periodicity. This means that the eclipse season can be expected in the area of fulfilment of the counting in the 22 hole ring, plus or minus two holes of the end of the count. If a lunar eclipse should occur with the marker outside this range, then the 22 hole marker could simply be moved to the nearest in-range hole, making the system self-correcting on the basis of simple observation.
- As stated in the text, the 63 hole count automatically gives an implicit reading of how many 1/8
^{th}days should be removed from the whole day, advancing the time of day at which the count is actually progressing. This does not effect the actual movement of the day marker, but indicates to high precision of a few hours, the exact moment referred to by all the markers in their different track rings. - Three periods of 7 7/8
^{th}days equal 4/5^{th}of a lunar month to the very high accuracy of 99.998%, repeating the result in 2 above.

We have to ask “Would this type of accuracy be useful?” and the answer appears to be that it would have been. The simplicity of it means that, once established,the level of skill required to track time, focused on the chosen time periods, would have been on a par with skills compatible with our knowledge of other bronze age activities.

]]>Using the lowest limit of 18 lunar months, the commensurability of the lunar year (12) with Saturn (12.8) and Jupiter (13.5) was “cleared” using tenths of a month, revealing Plato’s World Soul register of 6:8::9:12 but shifted just a fifth to 9:12::13.5:18, perhaps revealing why the Olmec and later Maya employed an 18 month “supplementary” calendar after some of their long counts.

By doubling the limit from 18 to three lunar years (36) the 13.5 is cleared to the 27 lunar months of two Jupiter synods, the lunar year must be doubled (24) and the 32 lunar month period is naturally within the register of figure 1 whilst 5/2 Saturn synods (2.5) must also complete in that period of 32 lunar months.

One can also see Plato’s World Soul in the Pythagorean Tetraktys (see Keith Critchlow’s *Foreword *and Robin Waterfield’s *Introduction *to *The Theology of Arithmetic*, Phanes, 1988), as a development of the Lambda diagram as per figure 2.

Keith Crichlow demonstrates that the Lambda diagram is none other than the *Tetraktys*, the latter probably a schematic missing in Plato’s *Timaeus* 35b&c, cryptically referred to by Plato since the uninitiated lacked it. The Tetaktys gives a beautiful organisation of the Pythagorean numbers involving only 2 and 3 as factors perfectly represented by an equilateral triangle growing organically out of ONE.

The Tetraktys of figure 2 differs from the mountain of figure 1 in that

- the vertical sense is not due to increasing multiplication by five, but rather decreasing multiplication by 2 or 3, and
- the elements were not normalised to a single octave.

The role of 36 within the Tetraktys of figure 2 corresponds to the number of lunar months chosen for the limit in figure 1, and so one can choose to normalise it, through doubling numbers where required, into the octave range 18:36.

On the bottom register, 27 already fits the octave whilst 12 and 18 must be doubled to 24 and 36, and 8 quadrupled to 32. At that point all that is above shares the numerocity of what lies in the bottom register, being dependent only on their powers of three.

The numbers 32:24:36:27 are identical to the white register of figure 1 and this may well indicate that the secret knowledge of the Pythagoreans, said to be summarised in the Tetraktys in particular, could well have been the astronomical harmonic relations to be found between the double and triple lunar year periods, the double synod of Jupiter and the 32 lunar month period which is also both 945 solar days *and* 2.5 Saturn synods long. This would have been a very simple means for the Demiurge to have employed, close to the harmonic origin story from one, two and then three.

If the right hand three elements are 12:18:27, and this is reminicent of the numbers generally used to designate three of the four Elements (water, air and fire) by the medieval period, and the four Elements were often shown then(after Plato), as is the case here, as being separated one from the other by fifths – exactly as Plato describes it in Timaeus (ref). However, most schemata differ from the allocation found in the decorated crypt of the Pope’s summer palace, the Anagni Cathedral (figure 4, right).

In the planetary matrix of synodic periods, Saturn is distinguished as the cornerstone having no other factors than the powers of two with respect to the lunar year. Hence it is harmonically commensurate (5/2) with the 32 lunar month period which is 8 merely doubled twice to fit the limit of 36. So it would seem that Saturn represents the Earth element. It is quite obvious that the lunar year of 12 lunar months is Water and that half the triple lunar year, of 18 months, is the element Air. The element of Fire is then the double synod of Jupiter (27).

**8:** Since 32 lunar months is 945 days,
then the earth which continually rotates towards the east is the cycle of
barrenness, according to Plato, is like the number 2 of octave doubling which
provides a container for intervals as a womb enables children to arise. Saturn
is also considered “plumbous” or “weighty” and so is naturally represents the
solid state of objects and, traditionally, the giver of boundaries being the
outermost visible planet.

**12:** The Moon’s links to water come
directly through the tides as first of many traditions such as that it fills
with water until “full” and thereafter starts to “empty”.

**18:** The lunar year also collaborates
with the near anniversary of three solar years equalling 37.1 lunar months.
This periodicity was studied by the megalithic astronomers of Carnac as a
right-angled triangle whose counted base was 36 lunar months symbolised by 36
stones in the kerb marking the base ay Le Manio’s Quadrilateral.

**27:** After two loops of Jupiter, the middle
of the retrograde loop will be punctuated by a full moon (at maximum retrograde)
since the Sun is then in line with the Earth and Jupiter. This fact enables the
loops of outer planets to be counted in lunar months, as required. The
association of Jupiter with fire seems natural since his primary weapon is
lightning, the cause of natural fires.

- The numerical Tetraktys,
- the account in Timaeus of a harmonic Creation and,
- the harmonic realities of Saturn and Jupiter relative to the lunar year,

are so closely related as to suggest the first two were a plan and description of the latter. The numbers referred to are the natural ones, in lunar months and this affects the history of ideas in sourcing Plato’s cosmology (influential in the Arabic Golden Age (800-1100) and subsequent western Quadrivium of numerical arts) on concrete astronomical facts ascertainable from simple observation and counting of time periods, inherited by the Pythagoreans.

The Pythagoreans considered themselves privy to a secret doctrine, and central to this was the school of “theoretical” harmonists in Greco-Roman times, recognizable today under the rubric “Harmony of the Spheres”. Whilst many cunning versions of such a thing have been proposed, the core of the matter rests in the simplicity of the numbers in figures 1 and 2, of the synodic periods of the outer planets in months relative to the lunar year. To think otherwise requires an explanation as to why this is not obviously a simpler and more probable fact. It is easiest to extrapolate megalithic astronomy as having observed and counted the synodic periods of the outer planets and, on comparing these with the lunar year length, discovering the planetary harmonic ratios, hence leaving a legacy of harmonic numbers referring to the heavenly world ancient literature and crafts.

The above is a further development of the theme of my recent book *The Harmonic Origins of the World*.

Jupiter reaches its maximum retrograde motion half way in the loop, after 60 days from its standstill in the sky. If, at that point, there is a conjunction of the moon and Jupiter then the moon must be full since the sun will be opposite both the moon and Jupiter. This means that, when a full moon is conjunct Jupiter at mid-retrograde, it will set to the west and one can start counting lunar months until the same phenomenon occurs.

We know a single synod of
Jupiter is 398.88 days and so there are *exactly*
13.5 lunar months in each synod since 398.88/ 29.53059 = 13.5073, just over 5
hours longer than 13.5 months. It is therefore true that, if one counts between
full moons occurring 60 days into successive retrograde loops of Jupiter, it
will be two whole synods before a full moon occurs in the same visual offset to
Jupiter at maximum retrograde in the sky. The lunar counting in between will be
27 whole months and at that point, the synod is known to be 13.5 months long
and 9/8 times longer than the lunar year.

In this way, not only could the Jupiter synod be found easily, using megalithic horizon astronomy, but knowing its length relative to the lunar year would reveal the remarkable harmonic ratio of the Pythagorean whole tone between Jupiter synod (9) and the lunar year (8 units of 1.5 months). This would have introduced the megalithic to that uniquely simple category of ratios responsible for the highly-ordered world of musical harmony.

The same procedure applied to the Saturn synod would require five Saturn synods (378 days) to complete since only then do 12.8 lunar months per synod yield an integer number of 64 lunar months. The loop of Saturn is smaller than that of Jupiter, 6.5 degrees compared to Jupiter’s 10 degrees. The reverse is true though, of the days spent by each planet in its loop, Saturn taking 140 days rather than 120. And the ratio of the Saturn synod to the lunar month is another crucial musical interval, the semitone of 16/15.

Tones and semitone are crucial to the formation of musical scales and so my proposal is that megalithic astronomy, once aware of these intervals, would have started to investigate practical music and instruments that make musical intervals. The best possible are string instruments where, if one uses a single string, one can measure the lengths of strings just as one can measure the lengths of synodic periods and find these ratios with which to form musical scales and a deeper musical tradition, inherited by the ancient Near East and other civilizations of the third millennium BC.

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