From Sacred Geometry: Language of the Angels

from Sacred Geometry: Language of the Angels, Appendix 1.
(Available: first few weeks of 2021)
This is relevant to many on-site posts.

Metrology has appeared in modern times (phase five below) in reverse order, since humankind saw the recent appearance of many measures in different countries as indicative that past cultures made up units of measure as and when they needed them, perhaps based upon lengths found in the human body. But this soon breaks down under scrutiny because the measures called after different regions all have systematic ratios between them, such as 24/25 feet (which as a foot is the Roman) and 6/5 feet (which is an aggregate unit, a remen), and the size of humans is quite various between regions and within populations. As stated in the main body of this book, the notion of measures from different regions was called historical metrology. This framework began to break down when answers appeared as to why the different regional feet were related, not only to the English foot as equalling one for each ratio, but also to the fact that the units of measure were often seen to divide into the size and shape of the Earth (leading to our phase four)—then called ancient metrology.

Another aspect of measures was their ability to approximate important, otherwise irrational, constants (our phase 3), such as π, √2 and even e in the form of megalithic yards, which are close to 2.71828 feet, the numerical value of e—the exponential constant. The earliest megalithic yard was almost exactly that number of feet—derived from an astronomical count over three lunar and solar years in day-inches (chapter 1) leaving a 32.625-inch difference between these years (our phase one); those 32.625 inches equal 2.71875 (87/32) feet.

The gap between the first and second phases of metrology seems to be the gap in time between the megalithic in Brittany and in Britain. Only as the metrological purpose of more megalithic monuments becomes clear might one be able to know more accurately, but British metrology, in choosing a megalithic yard of 2.72, was able to factor the nodal prime number of 17 within its counting. While Brittany could, at Le Ménec’s western cromlech, use a radius of 17 megalithic rods (6.8 feet) to have a count of 3400 megalithic inches across a diameter, Britain could use 12 such rods to model the lunar year of 12 months while also counting 15 rods as 3400 shu.si, a small digit known to historical metrology as dividing the 1.8 foot (the double Assyrian foot of 0.9 feet) into 60 parts, while the shu.si (0.03 feet) divides into many foot modules (see p. 112), and the English yard contains 100 shu.si, and 68 yards contains 6800 shu.si enabling the nodal period to be counted at Balnuaran in Scotland.

There is a particular need to regularize this subject through the gathering of more examples of metrology’s past applications. One must recognize that those responsible for our present knowledge of it have largely passed away, and those in academia are not going to rewrite history in order to impartially reassess whether their own approach to ignoring it can still be justified, especially when they are not preserving the metrology within monuments because they can’t see it as a signal from the past.

Overview of Megalithic Units of Measure

At least five specific MYs have emerged from the counting applications within megalithic monuments:

1. The proto megalithic yard (PMY) of 32.625 day-inches, emanating from an original day-inch count over 3 solar and 3 lunar years (at the Manio Quadrilateral) as the difference in their duration (chapter 1). This is therefore an artifact of the world of inch counting.

2. The Crucuno megalithic yard (CMY) of 2.7 feet: We saw that, by the factorization of 32 lunar months as 945 days long, the lunar month (as 29.53125 days long) can be represented by 10 MYs of 2.7 feet (27 ft) where the days in such a count are the Iberian foot of 32/35 feet. This I call the Crucuno megalithic yard, though, in the historical period, this foot came to be called the root foot (27/25 feet) of the Drusian module, which, times 25, is then 27 feet. The astronomical megalithic yard AMY (next) is 176/175 of the CMY.

3. The astronomical megalithic yard (AMY): In Britain, this is 2.715 feet (32.585 inches) long, giving N = 32.585 for the actual N:N + 1 differential ratio between the solar and lunar years. When representing lunar months over a single year, the excess becomes the English foot of 12 inches—a megalithic, now-called English, foot. From this one sees that every AMY on the base of the Lunation Triangle defines an AMY plus 1 inch on the hypotenuse above it (length N + 1 = 33.585 inches – a Spanish vara), as the duration 1 mean solar month. The AMY can appear as an integer when the CMY defines a radius because it is 176/175 of the CMY.

4. The nodal megalithic yard (NMY): Used in Britain. Thom’s Megalithic Sites in Britain gave the megalithic yard as having had the value of 2.72 feet as “the” MY, based on integer geometries within stone circles and some statistical methods applied to some of the other inter-stone distances Thom had measured. Its value evidently derives from its relationship to the nodal period of 6800 day-feet because 2.72 =6800/2500, where 2500 feet is half a metrological mile of 5000 feet. For this reason, I now call it the nodal megalithic yard (NMY), which contains the key prime number 17 in its formula 272/100, 272 being 16 times 17. Its megalithic rod (NMY times 2.5) of 6.8 feet factorized the nodal period of 6800 days: 15 rods gave 102 feet (3400 shu.si) and 30 rods gave 204 feet (6800 shu.si – e.g. Clava and Avebury), the shu.si being 204/6800 = 3/100 feet. It therefore appears that the NMY, its rod of 6.8 feet, and the shu.si had a raison d’être in the British megalithic period that was focused on the later problem in astronomy of counting the days of the nodal period.

5. The later* megalithic yard (LMY): Seen at Stonehenge and Avebury. Thom in 1978 published a new estimate for the MY as 2.722 feet. Unbeknownst to Thom but lurking within his own error bars was a further development of the AMY which, times 441/440, would locate his value within ancient metrology as 2.716 feet, 126/125 of the CMY. The CMY is clearly the root value (in Neal’s terminology 2.5 root Drusian of 27/25 feet) and the AMY the root canonical value, while this LMY is the standard canonical value.
*in the context of Thom’s work.

All of these different megalithic yards had their place in the megalithic people’s pursuit of their astronomical knowledge. Noting the role of the shu.si in compressing the length of a nodal count to a mere 204 feet, Thom’s NMY of 2.72 is the key to how its length of 3/100 feet was arrived at. The shu.si of 0.03 feet (0.36 inches) surprisingly divides into many of the historical modules of foot-based metrology.

Historical
Module
Foot Ratioshi.siNotes
Assyrian 9/1030Carrying the sexagesimal (base-60)
system of the Sumerians.
Roman42/2532
Inverse Byzantine99/10033Times 3 gives 99, a yard minus one shu.si.
English133.3Times 3 gives 100 shu.si in a yard.
?51/5034Divides into the nodal period.
The difference between 80 and
81.6 feet and between 90 and
91.8 feet at Seascale, where 91.8
locates the Jupiter synodic period.
Persian21/2035Its remen (6/5) is 42 shu.si.
Drusian27/2536The CMY is root of the AMY and
the LMY.
Remen6/540Half-remen of 20 shu.si as ideal
form of the equal perimeter model.
Some units commensurate with the shu.si

Five Phases for Metrology

MetrologyThe application of units of length to problems of measurement, design, comparison or calculation. as a single system was based on the number 1, which was then realized astronomically as the English footThe standard prehistoric foot (of 12 inches) representing a unity from which all other foot measures came to be formed, as rational fractions of the foot, a fact hidden within our historical metrology [Neal, 2000]. as an excess over one year [Robin Heath, 1998; Heath & Heath 2010], which then became related to all the foot modules of the ancient world—through a range of simple fractions. There were, therefore, phases in the evolution of ancient and then historical
metrology. I can see five right away.

Phase One: An Inch-Based Metrology for Astronomical Counting*

Primordial measures arising from the conduct of astronomy in the megalithic period included the English inch used to count days at Le Manio, CarnacAn extensive megalithic complex in southern Brittany, western France, predating the British megalithic.; the Proto Megalithic YardAny unit of length 2.7-2.73 feet long, after Alexander Thom discovered 2.72 ft and 2.722 ft as units within the geometry within the megalithic monuments of Britain and Brittany. (PMYproto-megalithic yard of 32.625 (261/8) day-inches, generated at Le Manio Quadrilateral as the difference between three solar and three lunar year counts.) of 261/8 inches arising from Le Manio’s three-year count, forming the Lunation TriangleThe right-angled triangle within which the lengths of the two longer sides are the relative proportions of the solar and lunar years.; and the English foot arising from counting the Lunation Triangle over a single solar year as lunar months using the PMY per month.

To form the English foot required definite steps that were necessarily taken
through megalithic astronomy and findable in the monumental record as (a) the use of the inch to count days over 3 solar years,† (b) the use of the differential length over 3 years to count lunar months rather than days, and (c) the counting over a single year to find an excess length of the English foot, which still has 12 inches because the lunar year has 12 months.

*Corresponding to the work of Heath and Heath (2011) and Heath (2014)
†See “Reading the Angelic Mind” in chapter 1, p. 14.

Phase Two: A Foot-Based Metrology for Astronomical Counting‡


Using ad hoc simple foot ratios based upon the English foot, in the service of
astronomical counting such as: 27 feet representing the lunar month at Crucuno (near Carnac) enabling days to be counted in parallel, using Iberian feet of 32/35 feet; nodal units such as Thom’s early megalithic yard of 2.72 feet; and the yard of 3 feet containing 100 shu.si.§ Nearby, the use of feet per day can be seen at Erdevan, over the SarosThe dominant eclipse period of 223 lunar months after which a near identical lunar or solar eclipse will occur. and MetonicGreek: The continuous 19 year recurrence of the moon’s phase and location amongst the stars. periods. The full system of Ancient Metrology was not yet developed.

‡Corresponding to the work of Alexander Thom (1967, 1971, 1978, 1980)
§More on the types of megalithic yard and the shu.si can be found in the box above (p. 237)
called “Overview of Megalithic Units of Measure.”

Phase Three: A Foot-Based Metrology for Handling Mathematical Functions

Using ratios of the English foot to approximate to irrational and geometric functions: measures are able to map feet to √2 or its reciprocal, to π, or to other measures related to the models in chapter 2.

The English foot was long enough to form fractional ratios in which the number field could be expressed as a calculating tool, since the measurement of a length using a different ratio of foot length gives a result in which the original measurement has been multiplied by the denominator of the fraction and divided by the numerator. Thus, 9 feet becomes 8 feet of the ratio 9/8. The initial approach to such ratio-based feet was to build right triangles using English feet so that the foot of 9/8 feet emerged from a base length of 8 feet and hypotenuse of 9 feet. Above each foot on the base were 8 demarcated feet of 9/8 feet (see fig. 2.1, p. 34), and there are strong reasons to suspect grids of unit squares were in use to form triangles since the right angle is native to such grids, which are also conceptually adapted to studying pure numerical interactions in space.

Phase Four: A Metrology of Foot-Based Modules and Microvariations*

Foot modules evolved as a general-purpose toolkit involving only the prime numbers {2 3 5 7 11}: the systems of root measures using right triangular ratios from the common English foot standard; a common grid of microvariation within each module, applicable to geodeticUnits of measures and monumental measurements relating to the numerical definition of the shape of the Earth by the late megalithic. surveying and modeling; and some less common microvariations such as 225/224 and 81/80.

*Corresponding to the recent books about ancient metrology
from John Michell (1981, 2008) and John Neal (2000, 2016, 2017)

Phase Five: The Foot-Based Metrology Discovered from the Historical Period†

The historical measures were found through exploration of the geographical regions after which they were named, such as measuring sticks, anthropomorphic sculptures, objects whose size was noted in antiquity, modern-era survey measurements (e.g., by Petrie and Thom), and through inductive metrology, measuring surviving sites and artifacts.

†Corresponding to Petrie (1877) and Berriman (1953)

BIBLIOGRAPHY

  1. Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
  2. Heath, Robin, and John Michell. Lost Science of Measuring the Earth: Discovering the Sacred Geometry of the Ancients. Kempton, Ill.: Adventures Unlimited Press, 2006. Reprint edition of The Measure of Albion.
  3. Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
  4. Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
  5. —-. Ancient Metrology. Vol. 1, A Numerical Code—Metrological Continuity in Neolithic, Bronze, and Iron Age Europe. Glastonbury, England: Squeeze, 2016.
  6. —-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
  7. Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.

Le Site Mégalithique du Manio à Carnac

by Howard Crowhurst

Perched on a hill in the forest north of the Carnac alignments, a megalithic site has escaped the fences that have littered the landscapes of the region for several years. These are the menhir and the quadrilateral of Manio. From the outset, the large menhir impresses with its dimensions. Nearly 5m50 high, it is the highest standing stone in the town.

More discreet, the quadrilateral caps the top. 90 upright and contiguous stones, varying in height between 10 cm and 1m60, make up an enclosure approximately 36 meters long and 8 meters wide on average, because the long sides converge. The stones at the ends draw a curve. Four stones to the northeast form the remains of a circle. Two menhirs, much larger than all the other stones in the quadrilateral, open a kind of door in the south file. This particular form questions us. What could she be used for? Was it a meeting place, maybe an enclosure for sheep? In fact, what we see today is probably only the outer skeleton of a larger monument, a mound of stone and earth that contained a chamber inside. Other remains complicate the whole, unless they help us solve our puzzle. Hidden in the brambles and brush, we can discover a stone on the ground of rounded shape. These curves are reminiscent of the belly of a pregnant woman. She is nicknamed the “Lady” of the Manio.

Day-inch counting at the Manio Quadrilateral

It is 10 years since my brother and I surveyed this remarkable monument which demonstrates what megalithic astronomy was capable of around 4000 BC, near Carnac. The Quadrilateral is the earliest clear demonstration of day-inch counting of the solar year, and lunar year of 12 lunar months, both over three years. The lunar count was 1063.125 day-inches long and the solar 1095.75 day-inches, leaving a difference of 32.625 day-inches. This length was probably the origin of a number of later megalithic yards, which had different uses.

Continue reading “Day-inch counting at the Manio Quadrilateral”

pdf: Astronomical Musicality within Mythic Narratives

Ancient musical knowledge came to Just tuning long before Greek music, in Babylonia. It now seems likely that two sources of musical information, were involved in an early tradition of musical tuning by number: firstly, the early number field is the original template upon which musical harmony is based; and secondly, the prehistoric geocentric astronomy which preceded the ancient world had been comparing counted astronomical time-periods, and had discovered the rational tone and semitone intervals between the lunar year, Jupiter and Saturn . Ernest G. McClain identified a harmonic parallelism within ancient texts in which the anomalous numbers found within mythic narratives inferred a unique array (a matrix) of whole numbers, shaped like a mountain, which could explain plot elements, events and characters of the narrative, as intended parallels to such harmonic mountains. McClain’s matrices allowed the author to locate the harmonic intervals found between planetary synods as a reason why religious texts should have employed harmonic numbers, these relating to planetary time as gods alongside ancient systems of tuning. Based on a talk delivered at ICONEA2013, 5th December at Senate House, University College London.

Le Menec: Start of Carnac’s Alignments

The Meaning Of Le Menec

“Alignments” are long rows of stones, that run in parallel for long distances through the landscape. The alignments in Carnac, Brittany, often have a starting point in what the French call a cromlech. Based upon a circular geometry, these monuments are made up of stones following arcs to form a single compound shape. The stones of a cromlech can be touching or they can be spaced out and in some cases, stones might have been removed during the historical period but in some cases also, gaps in the “walls” of a cromlech were probably intentional and are there on purpose.
Originally published July 2012

Continue reading “Le Menec: Start of Carnac’s Alignments”

Units within the Great Pyramid of Giza

There is a great way to express pi of 22/7 using two concentric circles of diameter 11 and 14 (in any units). Normally, a diameter of 7 gives rise to a circumference of 22, when pi is being approximated as 22/7 (3.142587) rather than being the irrational number 3.141592654 … for then, the 14 diameter should have a circumference of 44, which is also the perimeter of the square which encloses a circle of diameter 11.

The square of side 11 and
the circle of diameter 14
will both have the same perimeter.

Figure 1 The Equal Perimeter model of two circles, the smaller of which has an out-square of equal perimeter to the greater circle
Continue reading “Units within the Great Pyramid of Giza”