These three perspectives shared an awareness that number was an indispensable guide. Number is invariant; three is always three, and always one plus two. Mathematics is a realm of order, and recurrent patterns like the seasons or the harmonic scale call for mathematical descriptions precisely because such descriptions find stability in change.
As scoffers and skeptics like to point out, however, where there is pattern-finding, there is also often unconscious wishful human ingenuity. Moreover, because the astronomical, musical, and metrological perspectives were carried on sometimes in isolation from one another, their results diverged, and an apparent incommensurability emerged: how could they all be true? This gave scoffers an argument that was, on the face of it, difficult to answer: why not none of them instead? Perhaps the real answer was the skeptical shrug: the ancient myth-tellers and builders of stone circles were acting more or less haphazardly or moved by very terrestrial, local, and historical concerns. Was this not the simplest explanation?
Richard Heath for a quarter of a century has been building towards a case diametrically opposed to this. From the beginning he worked with Thom’s practical metrological results, bringing them into dialogue with Michell and John Neal; then later with a further expansion of astronomical results that far outpaced von Dechend and de Santillana’s speculations on the precession of equinoxes. In The Harmonic Origins of the World, Heath goes a further step, bringing McClain’s results into dialogue with his previous work. Heath provides ample demonstration that the results of these various perspectives can clearly be seen to not diverge from one another. Suddenly it is very plausible that they might indeed “all be true,” because they were never, for the ancients, separate at all.
According to Heath, there exists in our solar system a harmony of extraordinary beauty among planetary cycles. This harmony was observed by ancient astronomers, and enshrined in megalithic monuments; it was transmitted in oral and literary culture via a musical grammar of proportion, easily reproducible across various cultures, which informs scripture and speculation (in McClain’s phrase) “from the Rg Veda to Plato.” These assertions are of course controversial and deserve scrutiny. But they give the lie to any facile dismissal of ancient cosmological sophistication on the grounds that reconstructions are inconsistent. Astronomy, metrology (practical and theoretical), and music are all comprehensible under a single analogical system. They hang together in a coherent, living dialogue.
This book is the most recent chapter and the most comprehensive introduction to a vital adventure in ideas. It is a detailed account of how human beings on the ground could make sense of the sky by way of the octave. In it, rigor and common sense meet wonder and awe.
]]>Megalithic astronomy generated maps of time periods, using lines, triangles, diameters and perimeters, in which units of measure represented one day to an inch or to a foot. To quantify these periods, alignments on the horizon pointing to sun and moon events were combined with time counting between these events,where days, accumulated as feet or inches per day, form a counted length. When one period was much longer than another, the shorter could be counted in feet per day and the smaller in inches per so that both counts could share the same monumental space. In this article we find the culture leading to megalithic astronomy and stone circles, previously building circular structures called henges, made of concentric banks and ditches.
A previous article about the Thornborough triple henge in North Yorkshire, looked at its likely metrology as a time-factored artifact. That henge consists of three henges, oriented rather like Orion’s belt of stars, but it in fact it pointed to the maximum standstill of the setting Moon on the north west horizon. Its central henge is of particular interest, in providing the astronomers with a firm day-to-day grasp of the major cycles of the Sun and Moon using multiple counts between diametrically opposite points on the inner rings. Through counting time: the most elusive of all the time periods, the rotation of the Moon’s nodes around the Ecliptic (responsible for eclipses) was counted in-between the north and south henges, as per the previous article.
A Henge is a circular structure with at least, a ditch and raised ring marking its limit. Thornborough’s three henges each had three distinct concentric rings, this being the norm in Yorkshire’s henges (see figure 1). And since these other henges are also of a similar size, this implies that both their size and design were shared and related to some kind of function.
The outer ring defines the space of a henge and we note the two inner rings display a given ratio to each other, of around twelve to nineteen*** units. In other words when one looks at these diameters as a ratio, the nearest simple integer ratio that fits is 12:19. Since the rings are quite thick, and hard to measure between clear datums,the significant time periods relating to the sun and moon form two groups, of around twelve months and nineteen years.
*** This ratio is very interesting since it can be normalised through division of the shared difference into each of the two numbers. 12/7 = 1.7143 which in feet is the Royal cubit whilst 19/7 = 2.7143 which is the megalithic yard
From surviving engraved art near Carnac in Brittany, one can read that the megalithic counting of time (by 3500-3200 BC) had evolved inches to count days and the megalithic yard of 19/7 feet (the overrun of three solar years over three lunar years when counted in day-inches). In Gavrinis’ stone C3 we see engravings using divisions of 12/7 inches, within an astronomical diagram. From the centre of stone C3 (figure 2), seven divisions (times 12/7 inches) show the (so-called) English foot as seven divisions of 12/7 inches, running downwards from the centre. Also shown are 5 extra divisions, culminating in a phallic design, to reach a radius of 12/7 feet, the (so-called) Royal foot of the Egyptians. The stone C3 appears as a whole to have been composed within a circular framework of 19/7 feet, the (so-called) astronomic megalithic yard.
We therefore found at Gavrinis stone C3, two distinct measures within its engraved art, measures related by the ratio 12 to 19, numerators of the Royal cubit and megalithic yard over a common denominator of seven. My brother and I have already demonstrated how these measures emerged 4 Km west, at Carnac, through the astronomical invariance revealed by counting three years in day-inches. When lunar months per megalithic yard are counted, instead of day-inches, the three periods of eclipse year, lunar year and solar year, can be seen to form 19 year cycles. The foot naturally emerged from the fact that the solar year contains 12 plus 7/19 lunar months (equaling 12.368) so that a megalithic yard of 19/7 feet cancels with the 7/19 lunar months to leave an excess per year of one foot. In feet, the solar year is then 12 megalithic yards plus one foot, or 33.585 feet, and the lunar year of 12 lunar months 32.585 feet, the number of inches in a single megalithic yard.
This may seem impossibly fractional for a culture without decimal or similar arithmetic, but it is the measures themselves that enable counting to evolve natural denominators which divide into the found time periods in a simple and elegant way.
I believe the builders of the Yorkshire henges (figure 1), in building two rings in the ratio 12 to 19 were referencing (a) the three different years which are all about twelve months long and (b) the Saros and Metonic periods which take nineteen of the eclipse and solar years, respectively, to complete.
By counting the shorter year periods as a diameter in feet and the longer periods of 19 years in inches per day, made it possible for the eclipse, lunar and solar years (in feet per day) to be efficiently located within their anniversaries with the moon over nineteen years (in inches per day) resulting in the single compact henge monuments we find. These time periods, as diameters, could be used for continuous counting of years and anniversaries, in a calendrical fashion: major time periods would be seen as counts in progress so that at a given moment, each would be at a different stage of completion. Astronomers would learn many things such as, that the Metonic has a near relationship to the Saros in being 20 eclipse years long relative to the Saros’ 19 eclipse year duration.
Once the commensurability of the lunar month to larger cycles was established, that the Saros was 223 lunar months long and the Metonic 235, later monuments could employ a tally of full moons between eclipses (see Stoupe Brow) within a month counting scheme, or count lunar months per megalithic yard (exactly 32/29 larger than 29.53 day-inches) to form lengths used geometrically within monuments. The advantage of a counting tally is its small size and portability.
Harding, Jan et al. 2013. Cult, Religion, and Pilgrimage: Archaeological Investigations Thornborough. Council for British Archaeology: York.
Heath, Richard.
Heath, Robin. 1998. Sun, Moon and Stonehenge. Bluestone Press: Wales.
]]>Such patterns, called Cosmic Images by Halldorsson [3], seek to establish a geometric connection between places on the landscape and on the horizon, here in the south-western region near Reykjavik, the only Icelandic city. The spirit of a region or island was integrated through organising space in this way, according to centers (Things) of circles and their radius and diameter as numbers of paces, circles punctuated with places and alignments to other places, horizon events or cardinal directions. John Michell provided a guide to some of the techniques in his books [2, at end].
Palsson had noticed a number symbolism within Iceland’s foundation epic, involving geographical features. This resembles the situation where Ernest G. McClain interpreted Biblical, Vedic, and Babylonian mythic texts as involving harmonic invariance [4, at end]. Palsson intuited Pythagorean influences, where the 3:4:5 triangle could form a numerical myth of origin in Iceland, of a race of giants from the element Fire. This source of creation is seen in the bottom right of figure 1 where the “Primeval Hill” is located within such patterns. New creations arise from Fire and must surely return there, to formlessness; a myth conguent with the alignment of midsummer sunrise (top left) and midwinter sunset (bottom right).
The Primeval Hill, Fire, and the Number 27
If one accepts that the Primeval Hill in Iceland was based on the number 27, several otherwise unintelligible bits of information fall into place….
The Primeval Hill was based on Fire; the Earth was created through Fire and it is going to vanish in Fire. The pivotal event of Njals Saga is the destruction of the abode of Niall through fire. Its allegorical meaning is that of the fabulous phoenix bird, destroyed every 500 years after two periods or life-cycles. In the year 1000 Christianity was formally accepted as the state religion of Iceland. The seven ages of paganism vanished; Time, personified by Kari in the Saga, escapes from the flames and flies northeast to the land of the sunrise… the abode of the apostle of Christianity, Hjalti Skeggjason. Kari flies a precisely measured distance, 216 M (M = 1000 and 216 / 27 = 8), that of the diameter of the world as understood in those days.
The number 27 stands for Fire at the Primeval Hill. It also stands for kingship. It stands for the beginning and the end of time…
The number 27 is, of course, the number 3 multiplied three times with itself (3x3x3=27). The importance of the number 27 is typical for learning attributed to the Greek thinker Pythagoras. For Plato the soul of the world is divided according to a particular numerical series, which is thought to derive from the earlier Greek thinker. (It is called the Lambda-formula, so called because of its resemblance to the Greek letter, consists of two “arms “. One is 1-2-4-8 and the other 1-3-9-27.1 Multiplied together the 8 and the 27 make 216 – the basic number of the created world in pagan Iceland. Pythagoras and his followers are said to have believed that they would be reincarnated every 216 years.[2]
The Sacred Triangle in Iceland, page 26-27
John Neal discovered that the 216-nature of Palsson’s cosmogram (as per figure 1 and previous posting) was calibrated in Roman feet (24/25 = 0.96 feet) of a slightly increased (by 126/125) length of 24/25 x 126/125 = 0.9677 feet so that 216,000 feet are exactly 1/100 the mean earth radius of 7 x 12^6 = 20,901,888 / 100 = 209,018.88 English feet. By using the foot the Icelandic geometers had demonstrated two things:
This Roman foot enabled a fractional and non-regular number (209,018.88 feet) to be made regular as 60^3 = 216,000 feet. These two numbers are proximate and so the 126/125 ratio makes the size required a simple integer, made up of only factors 2 and 3 in its head number 216.
This type of Roman foot also has special properties as a diameter, illustrated most clearly by having a single foot diameter. As a fraction this foot is 3048/3125 feet long and this, times 22/7, leaves 3024/3125 x 22/7 = 3.0413 x 12 = 36.4956 inches. This looks like 36 inches and dividing by 36: 36.4956/36 = 1.01376 inches – the so-called geographical inch of the English/Greek module. The formula for 1.1376 feet is 3168/3125, the 3168 was symbolic as an ancient world norm for the perimeter of a sacred space emanating from the spiritual form of the Earth, its mean size.
To recapitulate: One Roman foot of this type on the diameter gives 36 (geographical) inches on the circumference. Multiplying 36 by 6 gives 216 on the circumference, a diameter of 6^2 gives (36^2) 1296 on the circumference and 6^3 (216) gives 36 x 216 = 6^5 = 7,776 (geographical) inches on the circumference .
The same is true with powers of 60, so that the diameter of Palsson’s cosmogram of 60^3 = 216,000 Roman feet gives 60^5 = 777,600,000 geographical inches around its perimeter. In terms of numerical symbolism, Ernest McClain found 60^5 = 777,600,000 is associated with the god YHWH (6.5.10.5 as 60^5 = 777,600,000) in the Bible, whilst that number of geographical inches corresponds the meridian length of the mean earth since 12^6 feet x 22 x 12 = 788,299,776 /1.01376 = 777600000 Greek geographical inches.
In Palsson’s figure 3 above, this property of the Roman foot appears to be employed to make a diameter two times the circles, of 432,000 to present an exact 1/100th scale model of the mean earth meridian, where the central Thing is the centre of the mean Earth, and the two subsidiary Things form a north and south pole, within the limitations of the landscape.
I first noticed that the meridian was 777,600,000 geographical inches in Sacred Number and the Lords of Time (LINK), page 194. But I had not guessed that there was such a smart diameter to circumference relationship involving a type of Roman foot and maintaining a pure-powers-of-60 relationship between the two. This illustrates how such relationships are inexplicably present within ancient monuments. One probably cannot know when such knowledge arose, or from whence it came but the monumental record and intuitions of later interpreters bring us to recover them: which is an important and objective outcome.
Whilst the Thing or primal centre, in Celtic, Nordic and other Ritualised Landscapes [2] is often found at the centre of a region or island, the interior of Iceland was and is inhospitable and so therefore the central place for the national assembly to meet is the center of a 432,000 foot length.
Ulfljotur’s, who had studied Norse traditions, formed a law involving 36 godar or law courts at 36 thing-places and his foster brother Grimur “Goatsfeet” was commissioned to locate the national Al-thing and subsidiary thing-places, after a year-long survey of the island. The resulting geometry of figure 3 emerges as multiplying 432,000 x 18 = 7,776,000. The miracle behind this is bound up with metrology but the outer symbolism is that 18 of 36 godar are transforming the mean diameter into the image of the meridian.
The actual geometries, according the Palsson’s protégé, Petur Halldorsson [3], are somewhat variable and Iceland might be a swan song for the tradition.
1 Palsson, Einar. The Sacred Triangle in Iceland. Mimar:Reykjavik 1993.
2. Michell, John. At the centre of the World. Thames & Hudson: London 1994. and also Twelve-Tribe Nations(both reprinted as The Sacred Center and Twelve-Tribe Nations by Inner Traditions.)
3. Halldorsson, Petur. Pattern of Settlements paced from 1 to 9. CreateSpace 2013. and The Measure of the Cosmos, 2007.
4. McClain, Ernest G.. The Myth of Invariance. Hays/Shambhala: 1976.
]]>In 2006 John Neal wrote,
Interestingly, the degree above the 52^{nd } parallel that lengthens by the factor of 441 to 440 would be close to the Arctic Circle. This is where, in western Iceland, Einar Palsson showed that the founding towns laid out by the first settlers had a distinctly geometric relationship. Not only this, but the foundation circle around which the towns were set out he gave as 216,000 Roman feet (about 64 km) in diameter. Had he used the Standard Canonical variant (Greaves’ Cossutian foot) of .96768ft then the resultant circle would be 209018.88 which is immediately recognisable as the hundredth part of the mean radius of the earth. Palsson did not see this fact, that 1.75 times the diameter is exactly the geographic degree at that latitude. This would be 365783.04 feet or 111490.57 metres, about 66° N.
The mean earth has each of its degrees of latitude equal to the actual degree length of 51-52 degrees on Earth (which is called the geographical degree). Neal is taking the mean radius and noting that, according to figure 2, 65-66 degrees (for Iceland) will be 440th part greater than the geographical degree length. See also my extracts on The Ancient Model of the World [new tab] if this topic is unfamiliar .
If Palsson’s diameter is one hundredth of the mean radius, one can say that the sacred image diameter has two relationships;
Neal takes (a) as of prime significance and here I consider (b) the interesting fact that the mean radius times 24/25 (roman foot) times 126/125 (standard canonical micro-variation) is one hundred times larger than the sacred image. Perhaps more important though is the fact that the diameter is then a harmonic number, 216,000 roman feet in diameter.
By making the diameter 6^3 x 10^3 = 216,000 SC Roman feet one can see the stade of 600 feet (a Roman stade is 576 English feet [NEAL. ADWM. 2000. 72.]) divides the diameter 360 times. The 360 x 576 (English) foot units of the diameter are also 336 Royal cubits (12/7 feet) which, when multiplied by PI, change (360 units of 600 Roman feet) into (360 units of 1056 royal cubits) and, all this being standard canonical, there are 360 units of 1056 Std Can Royal cubits of 1.728 feet (the Jerusalem cubit) on the perimeter.
Therefore, a 216,000 standard canonical roman foot diameter was easily constructed using roman stades of 600. And this diameter has a circumference immediately amenable in 360 segments of a rational nature, having the role of one degree on the horizon. Further, we can see in Neal [2000. 116] that 100 standard royal cubits as diameter give a perimeter of 360 feet. Many of the transformations available in ancient metrology can translate radial rationality into a rational circumference by using different modules and micro-variations of them, these cancelling unwelcome primes in denominators, of whatever rational PI is assumed, usually the prime number seven in 22/7.
Conclusions
A follow-on article can be found here
Data and Transformations
Feet are English unless named
Mean Radius of Earth | 7 x 12^6 = 20,901,888 feet |
SC Roman Foot | 24/25 x 126/125 = 0.96768 feet |
Palsson’s Diameter | 216,000 x 0.96768 = 209,018.88 feet |
Stade of SC Roman feet | 600 x 0.96768 = 580.608 feet |
Construction | 209,018.88 / 580.608 = 360.0 |
Degrees on Circumference | 580.608 x 22 / 7 = 1,824.768 feet |
SC Royal cubit | 12 / 7 x 126 / 125 = 1.728 feet |
Cubits per degree | 1,824.768 / 1.728 = 1,056 cubits |
Bibliography
Heath, Richard. Sacred Number and the Lords of Time. Inner Traditions: Vermont 2014.
Halldorsson, Petur. Pattern of settlements paced from 1 to 9. CreateSpace: Iceland 2013.
Neal, John. All Done With Mirrors. Secret Academy: London 2000.
Neal, John. The Structure of Metrology, its Classification and Application: a paper delivered to Ordo et Mensura IX Oct 20th 2005, Munich. Secret Academy: London 2006.
Palsson, Einar. Sacred Triangle of Pagan Iceland. Mimir 1993.
]]>It appears the ancient world had unreasonably accurate knowledge of the size of the earth and its shape: Analysis of ancient monuments reveals an exact estimate for the circumference of the mean Earth, a spherical version of the Earth, un-deformed by it spinning once a day. Half of this circumference, the north-south meridian, was known to be about 12960 miles (5000 geographical Greek feet of 1.01376 ft), a number which (in those Greek units) is then 60^5 = 777,600,000 geographical Greek inches. One has to ask, how such numbers are to be found very accurately within a planet formed accidentally during the early solar system?
John Michell’s booklet on Jerusalem found (in its Addendum) that the walls of the Temple Mount, extended for the rebuilding of the Temple of Solomon, was a scaled down model of the mean-earth Meridian in its length. These walls are still 5068.8 feet long, which is the length of a Greek geographical mile. This unit of measure divides the meridian into 12960 parts, each a geographical Greek mile.
12960 – the Greek miles between poles.
This is a harmonic number made up only of harmonic prime number factors; 2, 3 and 5. The mean-earth circumference is therefore twice this, or 25920 Greek miles and therefore equal in year-miles to the ancient duration of the ancient estimate of 25920 years for the Precession of the Equinoxes.
777,600,000 – the geographical inches between the poles.
This is Ernest McClain’s valuation of biblical god YHWH using the Hebrew letter-number values of 6.5.10.5 interpreted as 6^5 x 10^5, that is, as the fifth powers of 6 and 10, a head number (7776) thought to have also applied in the pre-Classical Greek world, to Apollo [Ion, John Bremer, 2000]. Head numbers such as 7,776 could be used for their harmonic content by losing the zeros of decimal notation and the power of 7,776 can be witnessed if the Lambda diagram of Plato, whose two powers of 2 and 3 are combined in 6, the “perfect number”, in figure 2.
Both these harmonic numbers apply to the meridian when seen through the Greek geographical foot, whose root value was the English foot we use today. (This fact, that the whole metrological system had the English foot as its root unit value, was discovered and documented by John Neal in 2000.)
4,320,000 solar years in day-inches around Equator
A similar geodetic fact was noted Joseph Needham (volume 3 of Science and Civilisation in China, volume 3, CUP, 1959) then by John Michell in Ancient Metrology, 1982), that the Equator of the Earth in English feet equals the number of days in the solar year (365.2422) times 360,000 English feet. I re-arranged this in Sacred Number and the Lords of Time, page 10 as :
“If the equator were divided into 4,320,000 parts then each would be 365.2422 inches long, the length of a solar year in day-inch counting. This would make the the equator 4,320,000 solar years long, the number of “years” in the Huindu cosmology of Yugas (‘ages of the world’) and the duration of one day of Brahma.”
This poses the unlikely scenario that harmonic numbers found in ancient texts by number and in buildings as their dimensions measured in ancient units, were referring to the dimensions of the earth (i.e. space) as well as to astronomical time: (a) the post-Vedic yugas referencing the length of the Equator and (b) the duration of the Precession of the Equinoxes in the Temple Mount referencing the (mean earth) Meridian.
For this to be the case, there has to have been an accurate model of the Earth’s key dimensions, and of the Great Year of precession whilst also; the units of measure, known as ancient metrology, had to have been already founded upon Earth’s dimensions. To evaluate this requires the ancient metrology of Neal and Michell (see 1982, 2000, and recent volumes on Ancient Metrology) and familiarity with ancient textual references and associated musical tuning theory (The Myth of Invariance, McClain, 1978).
I have summarised the ancient model of the size of the Earth (Michell 1982 and Neal 2000) with the above diagram. The model hinges on the Mean Earth and the English foot: I noticed its radius as being 7 times 12^6 feet so that its circumference using pi=22/7 is (2.pi.r) 44 x 12^6 feet. The composition of the geographical Greek foot (1.01376 ft) is 3168 / 3125 which is (288 x 11) / 5^5 so that it divides the mean circumference to give 129600000 Greek feet which divided by 5000 (a Greek mile) give 25920 miles as its circumference.
Three values of pi are employed in this model to characterize the shape and key dimensions of the Earth: 22/7 (best) 25/8 (good) 63/20 (not so good). These were used in combination both in the model of the earth and in the microvariations of ancient metrology (176/175 & 441/440) so that the metrology is tied to the size and shape of the Earth, as per Sacred Number‘s Chapter 3: The Model of the Earth.
Whilst there must be a unit of length that will divide up any given planetary length harmonically, that unit of length is very unlikely to be a known unit of length unless someone has defined it as a whole unit of length in the past, based upon measuring the size of the Earth. Indeed, the surviving English foot measure stood at the root of ancient metrology as the number ONE so that other feet, by being rational fractions of it, enabled geometric calculations to be performed in lieu of arithmetic and number notation.
Further to this, for a number of key dimensions to be coherently related to key measures within ancient metrology suggests that the above model of the Earth was built into the metrological system so that the ancient planetary model and ancient metrological toolkit were two facets of a single enterprise.
The simplicity of the model of the Earth is an achievement not paralleled until the last few centuries. In effect is was a geoid (meaning, the shape of the earth’s meridian) understandable in a far better way than the modern system which uses arbitrary units of measure and hence cannot see the three types of Pi implicit in the Earth’s geoid. The model of the Earth was an ideal construct belonging to the organising intelligence which formed it, alongside the Moon and Life.
Another approach to signifying the mean Earth was to work with the whole size of the mean Earth scaled down to a landform or a building like Stonehenge or Great Pyramid.
Returning to the north-south, mean-earth Meridian, John Michell discovered a landform 1/4 degree of latitude long between Stonehenge and Avebury. These monuments are both located in the 52nd parallel whose N-S length equals the length of every degree of the mean Earth. Cultures having the size-of-the-earth metrology could take the mean earth circumference as the prototypical boundary for temples and other sacred constructions, up to a level of scale where degrees of latitude could delineate distances between monuments, as that between Stonehenge and Avebury, to divide the whole meridian by that distance in degrees of latitude. A single degree of the mean earth divides the mean earth into 360 parts, making 51-52 degrees North is 1/360th of the mean earth. Quarter of a degree, at that latitude, divided the mean earth into 1440 parts.
John Michell interpreted Stonehenge, Avebury and Silbury as being an exact scale model of the three key earth radii, of the Equator, the mean Earth and the Equator [The Measure of Albion, p 103-115]. The metrological system measures latitude in the familiar 360 degrees in the ancient model of latitude, and so the distance between Stonehenge and Avebury additionally generates the harmonic number 1440 as a division of the mean earth. This number is found at the Parthenon (Harmonic Origins of the World, pages 72-78) and at Teotihuacan (ibid, pages 179-184), whilst being interpreted within the Bible, by Ernest McClain [ibid], as the number of Adam, again by letters equaling 1+4+40 = 45 but also, in position notation as 1440 – which is then Adam’s upper harmonic range within the Bible’s harmonic code: The number 1440 generates a fully chromatic tuning system in Just intonation, a tuning system where perfect fifths (interval ratio 3/2) are naturally tempered by perfect thirds (5/4). This number is naturally also found in the astronomical matrix, when the lunar month is divided by 80 so as to locate the outer planets Jupiter and Saturn to the lunar year (12 x 80 = 960, Jupiter synod is 13.5 x 80 = 1080 and Saturn synod is 12.8 x 80 = 1024). Adam is then 18 lunar months, the Maya astronomical period sometimes appended, as Supplemental Glyphs, to their Long Count dates.
The mean Meridian can therefore be seen in two ways, 777,600,000 geographical inches of YHWH or as Adam’s 1440 quarter degrees. 777,600,000 / 960 (YHWH / lunar year) equals 810,000 lunar years. The 81 = 3^4 is the number of powers of three between the lunar year and YHWH, and in powers of 6 this is 81 x 16 = 1296 (the number in the Meridian above) leaving four powers of five = 625 – the difference between the lunar year and YHWH in the vertical powers of 5. This vector of primes is then 6^4 x 5^4 or 60^4 = 12,960,000, which is the location on the astro harmonic matrix [or “holy mountain”] (rather than vector between locations) of the Venus synod, also Quetzalcoatl. 12,960,000 is Plato’s Nuptial number (see The Nuptial Number of Plato by James Adam, Thorsons 1985), and Plato’s dialogues a late text applying the same astro-harmonic numbers.
One comes to question how space and time are related and how the late stone age came to know the correct metrology, the accurate size and geoid of the earth and the consequent harmonic numbers that co-relate the space of the Earth and the synodic world of time, of its surrounding planetary system. The triad SPACE-TIME-HARMONIC resembles J.G. Bennett’s domains of Fact, Value and Harmony. He said in Dramatic Universe volume 3:
“It is no accident that recognition of the importance of structure has come, not by way of speculative philosophy or logical reasoning, but by the pressure of practical needs. We apprehend structures far more by the power of understanding than by knowledge. Knowledge is confined to Fact.
“The Domain of Fact does not include transformation, which belongs to the Domain of Harmony. In this sense, knowing and understanding are powers that belong to quite different regions of experience and this suggests the surprising, but correct, conclusion that structures are not objects of knowledge, and that their true place is in the Domain of Harmony. We do not know structures, but we know because of structures.
“Facts, that are no more than facts, are atomic and unrelated except by general laws. That is how the world was studied until the middle of the present century. Darwin’s Origin of Species (1859) and Clark Maxwell’s Treatise on Electricity and Magnetism (1873) were magnificent swan-songs of a dying age of science when it had seemed possible to explain the whole by the part and to account for the facts, without regard to the purposive action that makes them possible.
“We are now in the midst of a mental revolution, and as with all revolutions, its true significance escapes those most deeply involved. We are being forced to look at every kind of problem in a new way; that is, in terms of structures rather than of general laws. Scientists and philosophers are not alone in fighting a rearguard action against the revolution. In every department of human life, the ancient strongholds are being surrendered reluctantly and usually after they have ceased to matter. Men pay lip service to doctrines of ‘integration’, ‘unification’, ‘ecumenism’, and to the proposition that excessive specialization has become a menace to society; but, in practice, the changes come before the people concerned consent and usually before they realize what is happening.” systematics.org
It would appear that the stone age arrived through a form of understanding, of the most significant structures surrounding them: the sky, its time periods and the earth, its size and measures. We are now challenged in reading stone age forms of understanding, due to the popularity of the domain of Fact, and need to re-learn these forms “on the job”, to understand the earth and sky as the stone age evidently did. The cosmos appears to be no accident, yet technological science thinks all past religious cults and their divinely creative beings (in our oldest books,) were merely superstitious precursors to the prominent world view that mechanical laws alone led to the existing order.
]]>Ad Quadratum is a convenient and profound technique in which continuous scaling of size can be given to square shapes, either from a centre or periphery. The differences in scale are multiples of the square root
of two [sqrt(2)] between two types of square: cardinal (flat) and diamond (pointed).
When a square’s diagonal touches opposite sides sides of a larger square, the two squares differ by sqrt(2) and a square becomes a diamond or visa versa. By repeating this effect a continuum can be generated to form the large patterns found in sacred buildings such as the Vedic Angkor Wat, Christian Gothic cathedrals, Islamic Dome of the Rock and even Stonehenge. The technique is therefore very ancient yet still used. Subjectively such buildings express a high degree of visual order by employing what is called a geometrical progression. Objectively, such patterns appear to convey cosmic principles known to ancient builders but largely forgotten recently.
It is easiest, when maintaining a common centre, to define the outer square and then scale inwards, as was probably done at Ankor Wat (and at Stonehenge, where the Aubrey Holes existed before the Sarsen Circle).
Within the Indian traditions there are many texts defining yantra patterns in which square temples have their sides divided by small numbers, and their internal areas are then the squares of those side numbers. Typically 3 (9 in area), 4 (16), 5 (25), 6 (36), etc., also give a design able to define local units of measure used to measure them. Having identified an ad quadratum structure, it is important to find out how the local units of length correspond to its nested squares.
Whilst the inner core of Angkor Wat was square, employing ad quadratum in its design, the outer square was extended to the west so that the overall building was then rectangular, as below.
Some rectangles can be seen to express a rational ratio between their sides. The rectangle of Angkor Wat shares one side length with the outer square and, measuring the longer side results in the ratio 1.125 or 9 to 8 (9/8) which is a whole tone. As many of my other articles and books show, 9/8 is the counted time-length relationship between the lunar year and the synod of the planet Jupiter. This might be the reason why Angkor Wat was given this rectangular form, in which case the outer square form of the ad quadratum would symbolize the lunar year.
A following post (link to come) will investigate further the meaning of this ratio in Angkor Wat.
STONEHENGE: ASPECTS OF AD QUADRATUM GEOMETRY
Author(s): Rory Fonseca
Source: Journal of Architectural and Planning Research, Vol. 12, No. 4 (Winter, 1995), pp.357-365
It is said that we are transiting from the Age of Pisces to the Age of Aquarius in a backward precession through the 12 zodiacal signs. Examining the numbers that define these Ages is one of the core themes of this book. The basic premise is that stories – some of them handed down orally since Neolithic times – enable us to identify the inner spiritual aspects within our material world and participate in the evolution of human consciousness foretold by ancient myths. The author is greatly influenced by G.I. Gurdjieff and his Law of Seven, albeit with revisions of his own.
Readers such as myself, for whom mathematics is not their strong suit, need not be daunted by the many sets of figures presented in this book. They are important as supporting evidence for the theories presented, and their comprehension is made easier by the use of diagrams. Moreover, the fractions and ratios are often related to musical octaves and the Do-Re-Mi music-reading system.
The books subtitle is How Stories Create the World and the prose elegantly balances the numbers with profound insights. The link from Gurdjieff is established through his follower J.G. Bennett, who built on the former’s powerful ideas by incorporating philosophy and the science of his day; [then] onward to his student Anthony Blake, who in turn taught Heath the value of story making.
The combination of the author’s own numerical work on megalithic astronomy, Gurdjieff’s cosmology, and the ancient art of story-telling formed the idea of precession as a developmental cycle. The evolution of human consciousness through stories is a cornerstone of this book. While precession and the influence of planets is approached more from a mathematical than spiritual viewpoint, Heath acknowledges “that there is a form of intelligence within cosmic structures that arrives at certain types of solutions within the number field.”
Just as the notion of a Creator is natural to explain the highly constructive order in the universe, a Higher Self is the equivalent in human terms for the degree of order and structure found in the psyche and its life events. And this Higher Self can tell stories of meaning through life as a medium of communication to the selfhood located within existence.
The influence of the Moon is covered extensively. Together with the Sun, the seasons and periodicities or orbits of the planets, as experienced on Earth, it profoundly affects human life as well as giving a definite pattern to celestial time. For those who perceive that there is intelligence in our solar system but wonder why the lunar year does not coincide more closely with the solar year, it is interesting to learn that the Moon is also tied to the conjunctions between Jupiter and Saturn, called the Trigon period.
The length of one Age of the zodiac has been taken as 2,160 years since Plato’s time. The Ages of most interest in this volume are Taurus, which hosted the Megalithic period; Aries, when a specialised knowledge of musical harmony was encoded; and Pisces, when texts such as the Rig Veda, Homer’s Epics, and the stories of Semitic religions including the Bible, came to affect intellectual and religious life. The Bible’s Old Testament, we are told, was written using harmonic ideas such as purity, pure order, and an invisible and jealous God. Civilisation in the Age of Aries became an ideal of social order beneath God and king or emperor, according to principles of rulership.
Heath asserts: “Our modern ideal of free speech would horrify the ancient priests, whose purpose in articulation was the transmission of objective knowledge.” With the numerous references to harmonics and octaves, it is important to note that it is not considered that the numbers, vibrations and intervals are based on music – rather it is the other way around.
The patterns that were first recognised by megalithic peoples during Taurus formed the basis of the musical harmonies of Aries. While Gurdjieff’s teachings correspond to music in theory, the harmonic intervals involved relate to the processes found in the world itself. With music-making the vibrations are created by an instrument that can achieve various notes using functional apparatus. Gurdjieff, on the other hand, proposed that systems in the universe have vibrations, and that the energy of making the notes has to arise through the inner and outer transformation of their own vibratory level.
Heath proposes that the first half of an individual’s story manifests what is to become known to the selfhood during the second half. On a grander scale, our cultural history appears to evolve its consciousness within the dynamics of changing zodiacal signs.
The book assumes a starting point of 12,000 years ago, at the end of the last ice age, and follows the human journey as it first turned outward, toward an understanding of the visible structure of the universe, then turned inward to the structure of the number field that underlies creation. Our “information bubble” has been created, and from all the general knowledge emerges self-knowledge. In this way does the universe become self-aware through intelligent life.
]]>Interfaces with the Bible were subtle, with the introduction of the flood in Genesis brought on by the gods led by Enlil (5 or 50) and the creation of Adam (A.D.M = 1 x 4 x 40) as a letter composite sum in Hebrew of 45 and position notation 1.4.40. The god revealing his full name to Moses (=345) as YHWH (6.5.10.5 -) signifying the planetary matrix.
These numerical details were discovered by Ernest G McClain (The Myth of Invariance, 1976) but then I found planetary resonances pointed to YHWH as encoding a harmonic limit 6 x 5 x 10 x 5 = 777,600,000 or 60 to the power of 5. In contrast, the Sumerians had Inanna who became Ishtar of later Mesopotamian civilisations, who carried forward many of the Sumerian innovations. Ishtar, a fearful goddess was watered-down to become Aphrodite-Venus, and the planet Venus was her ancient planetary identification, the morning and evening star.
In my Harmonic Origins of the World, 2018, I located Venus at the head of the Maya feathered serpent of terrestrial planets and cycles, which the value of 60 to the power of 4 = 129,600,000; a harmonic Limit (based on units 1/80th part of the lunar month) sixty times less than YHWH who perhaps over-ruled Ishtar in the Bible as a limit outside the planetary creation. The lunar year in that arrangement is equal to 60, balancing the position of Venus relative to the range ONE (the cornerstone) to YHWH (the Limit).
Therefore, it is possible to infer the exile of elite Jews in Babylon circa 600 BC caused their writing of Genesis and Exodus to differentiate the Hebrew people and religion from the Ishtar and Marduk worshiping locals, whose astronomy was used for divination based on planetary gods. The path of ANU appears extended to subordinate the planetary world, giving supremecy to their God and simplicity, in Adam, to the religious.
]]>Osiris could have been seen as a/the god of Harmony and below I explain why harmony may have been thought technically significant at the dawn of our earliest texts, then found in Sumeria 900 miles to the East. The reason I believe musical ratios were significant at the dawn of history because they had naturally emerged from measuring the lunar and solar year and comparing these with the time between loops of the outer planets Jupiter and Saturn.
My work with celestial harmony grew from Megalithic monuments, interpreted as a culture defined by an astronomy using numbers as lengths to count celestial time periods and build numerate structures in the process. The words harmony of the spheres came through followers of Pythagoras who, for the West, conducted both a pilgrimage and origin work on the numerical origins of culture so, it was only a matter of time before I would connect with the ancient harmonists since, around 2000, I became aware that the lunar month was resonant with Jupiter and Saturn as tone (9/8) and semitone (10/9) interval. The lunar year was well studied by the megalithic with respect to the solar year – a relationship they captured in the right angled Lunation Triangle – so they were all fixed to compare time periods and are the logical choice to have first discovered Jupiter and Saturn’s relationship to the lunar year.
However, two intervals cannot make music since, at least, a melody is required with a larger range, most often the octave, in which a tone frequency doubles in the ratio 2/1. What then happens is one of the strange facts about music. The larger tones we call harmonious all emerge from the numbers less than 7, in a set call the senarius (“out of six”). Thus seven punctuates musical harmony leaving a second stage in which the tones and semitone (for Just tuning) emerge between the numbers 8 to 16 (itself a doubling) so that 9/8 is a tone and 10/9 is another tone that allows the semitone 16/15 to emerge. These tones enable music but also 9/8 and 16/15 are fixed relationships between the lunar year and Jupiter and Saturn.
I believe this pattern is what was shown in the tomb painting, within the side of Osiris’ throne. It is not just the smallness of the numbers in these ratios but also the fact that they differ by just one unit (musical ratios are superparticular). I noticed (below) the count of “eggs” within the larger golden frame is 15 across and 14 down, thus differing by one. The L-shape left, the outer golden frame, is familiar to sacred geometry with the Egyptians, who loved grids and arithmetic relationships like our arrays. Its ratio would be 16 across and 15 down, and could be seen as the semitone at the upper limit of relationships shown above.
The smaller L-shape (a gnomon) embracing the red square would then be 8 across and 7 down, the ratio of the Egyptian Royal foot, a ratio excluded from early Sumerian music for its use of the number 7 which separates the Senarius from the tones and semitone. Thus 9/8 then 10/9 grow top left of the gnomon for 8/7 and then bottom right are the lower numbers of the senarius, as ratios between the numbers 6 down to 1 – within the red square.
The growing tonal intervals are presented as superparticular rectangles with dimensions in proportion to the musical interval names we use today in table below
rectangle | interval |
2 by 1 | octave |
3 by 2 | fifth |
4 by 3 | fourth |
5 by 4 | maj. third |
6 by 5 | min. third |
It is the clarity of a wall rather than papyrus that reveals detail from which this interpretation seems likely. Such a design on this all-important throne could supplement or change what is known of this long lasting god and give new emphasis to musical theory as having been more significant to the Egyptians outside of the area of practical music but as a cosmological reality in the sky. The Kaaba’s rectangular portrayal of the senarius can be seen here, using adjacent odd numbers.
My book Harmonic Origins of the World (2018), now generally available, examines Osiris and other gods of mythology and scriptures, from their numerical and harmonic codes; using the methods of Ernest G McClain, methods believed similar to those known by Plato and possibly Pythagoras. These codes came to be there because of the same technical interest in a harmony garnered by ancient astronomy.
]]>Over 4.5 billion years ago the inner solar system was a jumble of would be planets and planetoids. It is thought that Earth shared its orbital zone with at least one other planet about the size of Mars, similarly composed of a heavy metal core and outer mantle. Both would have been mopping up smaller bodies but eventually the two collided with each other.
In a vast explosion, the Earth was severely damaged whilst the energy released caused vast amounts of both planets’ surface rocks to be vaporised or projected whole into space. This caused a ring to form ar ound the Earth that quite rapidly accreted (consolidated) into a single body which soon cooled to form a Moon orbiting every 20 days, a mere 2700 Kms above the Earth’s surface. The planet that struck Earth has been called Thea after the goddess that gave birth to the Moon, the latter being called Selena in Greek myth. Meanwhile the metallic core of Thea was not absorbed by the Earth’s core but instead, significant metal deposits were embedded in the surface layers – a fact that gave the Earth a rich “wedding ring” of workable ore deposits, significant to the later metal-working ages.
Such a massive satellite travelling over the Earth caused the whole surface to gravitationally deform below the Moon, but the Earth was then rotating every six hours so that this bulge would always be ahead of the Moon. Just as with tides today, but then much more strongly, the Earth’s rotation transferred energy to the Moon causing it to accelerate and take an ever-higher orbit. However, this was not before the Moon had kneaded all the surface rocks. This type of lunar influence then continued in an unusual way.
Around 4 billion years ago, the orbits of Jupiter and Saturn aligned so as to create a slingshot for solar system bodies that had not yet been incorporated into planets. This Late Great Bombardment proceeded to strike the Moon rather than the Earth and this protective role is thought to have saved Earth from damage to its nascent resources, such as the water present on its surface. The recognisable face of the Moon was largely created at this time, as craters and “seas” of molten basalt from this bombardment.
The Moon was further accelerated to an orbital distance of 320,000 Km by 3 billion years ago and this meant that its tidal effects were no longer strong on the mantle rocks but instead, the seas of that period experienced massive tides, hundreds of meters high. These must have been like continuous tsunamis racing around the globe. Meanwhile, due to the still great rotational speed of the Earth, these tides occurred many times a day and also, the early atmosphere was whipped up by the Coriolis effect so as to create continuous, hurricane speed winds. The extreme ocean tides caused massive erosion and mineralisation of the seas forming a massive number of chemical scenarios that could even have been responsible for the creation of life in the form of primitive replicating molecules.
Even today, volcanoes and Earthquakes are thought to trigger eruptions and release of seismic energy built up in the Earth’s unique tectonic plates. These plates themselves could be an artifact, in part, of the Moon’s kneading of the Earth and we can see that on Mars, any plate activity ceased billions of years ago as the mantle became stuck to a solidified core – probably through lack of a large Moon.
Whilst the original collision almost certainly caused the high spin of the Earth, it also created the tilt of the axis on which the Earth rotates. This tilt set up the seasonal conditions on Earth, so important for life’s varied habitats. However, this tilt would not have been stable without the large Moon that also resulted. Our large Moon stabilises the tilt by shielding the Earth from the small chaotic forces the Earth experiences due to the other planets. Mars is particularly vulnerable, and its tilt varies over millions of years by about 30 degrees. The Moon, by adding a large systematic component to the precessional forces, prevents planetary chaotic resonances from affecting the Earth.
The effect of the seasons, maintained by the Moon, is joined by the extra tidal effect it has on the seas and oceans. These tides create an extensive area of a very important habitat within the tidal ranges found on our coastlines. These are very bio-diverse and also have led to evolutionary changes as significant as the adaptation of marine animals into land animals.
In summary therefore, life on Earth would not have been possible without the Moon and the very special itinerary of its genesis and the gradual arrival at the conditions we find today. It all seems a little too special and this has lead to the general recognition that life such as found on Earth could not have evolved without such a special collision occurring at exactly the distance from the Sun capable of supporting such life. The precessional mechanism would not be stable without the Moon.
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