THE ELEMENTS OF ASTROGEOMANCY (II)

 Introduction to Sacred Metrology and its Geodetic and Harmonic Correlations

         © Xavier de la Huerga 2024

In the first part of this article, we have seen how four numerical sciences; arythmetic, geometry, astronomy and harmony were taught from the beginning of the Middle Ages and until the Renaissance under the name of Quadrivium. Disconcertingly, we can find these four sciences applied with a prodigious level of sophistication in megalithic monuments, thousands of years before Plato - and later Boetius - established them as the basis for the European mediaeval education system.

In this second instalment we will explore two more elements of the astrogeomantic canon put into practice by the megalithic builders: metrology and geodesy, the sciences dealing with measurement and with the shape and size of the Earth. Their use is evident in the architecture, dimensions, orientation and geographic positioning of all megalithic monuments. Although there is no record that these two were ever imparted together with the four liberating arts of the Quadrivium during the Middle Ages, there are profound connections between them and indeed they could be considered as directly related to geometry, if we attend to the very etymology of the word. All of this points to a primordial continuum of knowledge of which all of these disciplines seem to be inseparable facets. In fact, we are going to see later how the numerical structure of music - one of the Quadrivium pillars - is very much at the core of the ancient system of sacred metrology. 

The Miraculous Resurrection of Sacred Metrology

Nowadays, only a handful of nations hold to their ancient systems of measurement; Liberia, Myanmar and a few island states in the Pacific. In the UK, Canada and the US, a combination of the metric and the imperial system still coexist, the latter being a vestige of the ancient system of measurement. Other than that, the whole world nowadays uses the metric system exclusively and the ancient units of measurement are all but forgotten. In fact, for many centuries the overarching logarithmic structure that constitutes the numerical skeleton of ancient metrology was completely lost to memory until its miraculous rediscovery by John Michell in 1981, when he deciphered the core elements of the ancient system, and the subsequent painstaking reconstruction work done by John Neal over several decades. With this outstanding breakthrough, also came the realisation that the ancient system had once been used across the whole planet, by most if not all the peoples of the earth. This universality and the fact that it is a single unified numerical code are two of the great mysteries regarding its nature and origins.

Fig. 1 - "Cong tubes" belonging to the neolithic Liangzhu culture in China (5,300 years old) are among the oldest metrological artefacts known. Their markings register length units used in other parts of the world; digits, feet and cubits of various denominations.

Thanks to this timely rediscovery, we can again put into practice this forgotten prehistoric science that in contrast to the current modern international system is indeed deserving of being called a liberating art, since the Napoleon-imposed metrification is comparable to the suppression of all the languages of humankind in exchange for the adoption of a "lingua franca", whereas ancient metrology offers the whole gamut of the idiomatic spectrum, for it is in fact, an aspect of the primordial and universal language of number that preceded the metaphorical "confusion of tongues" at the Tower of Babel.

The Structure of the Ancient Metrological System

Figure 2, below (based on the work of John Neal, see bibliography) offers a very basic and incomplete description, but it is enough to show the underlying structure of ancient sacred metrology, which is a system of modules integrated by means of unit fractions. In the first column we see the names of some of the different feet, which are the basic units around which all the other modules develop. Their names only reflect an association with a geographic region or nation, it doesn't mean that they were invented by those nations, but have been associated with those parts of the world because of their frequent usage there. It is important to understand that all the modules are without exception part of one single integrated metrological system, utilised globally and whose origins go back to at least 7,000 years¹ and therefore predate any concept of nation.

 

Figure 2. The different micro-variations of the foot are always given by ratios that can be expressed as a series of unit fractions. For example, the Iberian and Assyrian feet are related as 63/64 (0,9 : 63/64 = 0,9142857), and the Iberian is 4/5 of the Royal Egyptian (0,9142857 : 4/5 = 1,1428571) 

In the second column are depicted the variations in length of the different feet, going from 0.9 to 1.16667, with the English/Greek foot determining the central value, or unity, of the entire system. In fact, the integrated structure and the exact nature of the system only makes sense and becomes visible when using values derived from the decimal division of the English foot, as seen in the above table. Using centimetre and millimetre, or the English foot in its modern duodecimal subdivision into inches will destroy the numerical coherence of the system, making undetectable the connective fractions essential for the understanding of its structure.

Moreover, each one of the feet is subjected to eight micro-variations governed by the fractions 175/176, 440/441 and 125/126. These fractions have the property of maintaining whole number integrity between diameter and perimeter of a circle when using values for Pi rationalised as 864/265, 25/8 or 22/7; as well as between the sides and diagonal of a square (√2) when using certain combinations of feet and cubits belonging to different modules. This property of the system satisfies a practical as well as a symbolic function, whole numbers are essential to the effective application of sacred geometry, which is the natural partner of sacred metrology. But, as we will see next, the fractions that determine the micro-variations have also a cosmological dimension. Uncannily, they are exactly the same ones that express the amount by which the shape of the Earth deviates from being a perfect sphere!

1 - Howard Crowhurst has found a mass of incontrovertible evidence that proves the use of the ancient metrological system in the megalithic complex of Carnac (France), whose oldest construction phase dates back to 7,000 years ago. See bibliography at the end of this article.

Sacred Metrology and Geodesy

As it has been said above, geodesy is the science that deals with the shape and dimensions of the Earth, whereas metrology addresses measurement and its applications. Both are inextricably related, as traditionally and universally the basic units of any measurement system are directly related to the size of the earth. Even the modern metre was originally and mistakenly defined as the ten millionth part of the Earth´s quadrant (the realization that this measurement was in error came too late, when the metre had already been adopted). In fact, it is the ancient Belgic yard of 3.284582ft that, thousands of years before the metre, embodied a perfectly accurate subdivision of the same ten millionth part of the quadrant that the French surveyors tried to unsuccessfully achieve at the end of the 18th century. 

Indeed, the ancient system of metrology is fundamentally a geodetic system. This not only makes sense, but possesses a profound philosophical dimension, since it is through the agency of measurement that both spiritual and utilitarian endeavours such as road-making, settlement-building, trading standards, secular and sacred architecture, or works of art become directly connected with the actual shape and size of our Cosmic Home and Temple, the Earth.

Terrestrial Harmonics

The shape of the Earth is that of a flattened sphere at the poles, which results in the different degrees of latitude becoming longer as they go from the equator towards the poles. We can see in the image below how these differences in size generate the very same fractions that govern the micro-variations between the modules of ancient sacred metrology. For example, parallel 38^o measures 364,126.032 feet and parallel 50^o is 364,953.6 feet long, when we divide these two between each other we get 0.9977324, which in fractional form is expressed as 440/441 (440:441 = 0.9977324).

Now, a geographic degree of latitude is always by definition 360,000 feet long, and if we divide the number of feet at, let's say latitude 38^o between 360,000, we get a foot of 1,0114612 English feet and this is the micro-variation known as Root Geographic. In the same way, when the 50^o of latitude is divided between 360,000 the result is 1.013760, another micro-variation of the English foot known as Standard Geographic. How is it possible that the logarithmic micro-variations of sacred metrology modules correspond to the variations in size of latitude degrees at the planetary scale? This is because the amount of flattening across the Earth spheroid "is not arbitrary in its numerical composition, but exhibits a numerico-geometrical regularity" (J. Neal. Ancient Metrology Vol. I). 

This type of "numerico-geometrical" resonance, or coherence that extends across different scales and a range of phenomena (the harmonic architecture of music, planetary orbital patterns, human anatomy, etc) could be defined as a fractal, or holographic property inherent in the fabric of the universe and stands as a proof that the megalithic metrological system, in its enormous multidimensional complexity, cannot have been invented, but must have been discovered (or as some millenary traditions hold; "received"). Perhaps through experimentation with number from a very different kind of awareness to the one we have nowadays, a mode of unified perception with the cosmos, that our ancestors could have accessed thousands of years ago. A perceptual mode that maybe can be regained through the study of the megalithic science as a unified whole and specially, through its practice.

Musical Harmonics

There is also a precise correspondence between certain musical intervals and the modules of sacred metrology. The following table (also based on J. Neal's work) shows a few examples.

As we see above, the values of the quotients (in green) between the harmonic intervals are identical with the values of the six metrological modules shown here expressed in fractions of the English foot. This impressive harmonic correlation would have been invisible if we had used the metre and suggests that the length of the Greek/English foot (30.479 cmts), was originally determined from the generation of a tone; a musical note. Perhaps through an instrument such as Pythagoras' monochord, whose mobile fret produces a series of correspondences between notes and physical lengths. On the other hand, the source of the original tone might be found in China, where the 5,000 year old tale about the creation of the ancient metrology system tells us that it was based upon the length of the huangzhong flute.

Practical Application

One of the obvious uses of understanding the numerical language of sacred metrology, is the ability to interpret the wisdom and knowledge encapsulated into the dimensions of the many monuments built with it, using it as a tool for archaeological and philosophical investigation. On the other hand, there is the option of transmitting that wisdom through its creative application in the arts, the design of objects, or the construction of spaces, buildings and whole settlements. Thus, helping to regenerate and re-sacralise our ailing societies.

It's been a daunting challenge to try to articulate coherently within the succinct format of this blog an accesible and clear description of the ancient metrological system, its complexities and intricate structure. This has been done in the hope to reach out to an audience that resonates with this subject, in order to arise their curiosity, inspire and motivate them to undertake its study and practice. Architects, artists, engineers, the mystic and the scientist, and ultimately all of humankind will benefit from the understanding and re-adoption of the ancient system of sacred metrology.

For those who already study and practice sacred geometry, sacred metrology is the missing link that can endow projects with a primordial potency that is impossible to express by using the metric system alone. Its integration with the other elements of the astrogeomantic canon will imbue any structure or space with the harmonic essence that our ancestors implemented through their vision of the cosmo-terrestrial order. Somehow, they perhaps intuited that their descendants, thousands of years later, would live in an age devoid of that vision and thus, codified it into their monuments in order to provide the keys that would allow us to remember, through the universal and eternal language of number, the way back home. 

References

John Michell - Ancient Metrology: The Dimensions of Stonehenge and of the Whole World as Therein Symbolised

John Neal - All Done With Mirrors, Ancient Metrology Vol I, Ancient Metrology Vol. II

Howard Crowhurst - Carnac - The alignments