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John Neal makes a masterful job of considering the megalithic yard in the context of historical metrology, a metrology that he has managed to forge into a single conceptual scheme in which measures known to history from different lands all inter-relate.
Neal's book, All Done With Mirrors, is one of the most fundamental and significant contributions to the ancient understanding of numbers but to read it is no easy matter since he takes no prisoners and fully expects readers to resolve through calculation what he does not explicitly state. This makes his approach different to mine in which I try to present as easily a possible aids to the visualisation and registration of a pattern of facts. However, neither approach can really substitute for what one has to do for oneself in order to understand and John gave his "Secret Academy" idea the catch line "We can't give it away" because of the often deafening silence with which his work is met.
The aim here is to co-incide some workings based on Neal's book, to give others a taste of what lies beneath what is written and also to further my own interests in the Megalithic Yard. My brother's biography, Alexander Thom: Cracking the Stone Age Code, reveals that Thom's lack of metrological background led to both an original approach but also a disconnect to what is known about historical metrology. One particular mystery is how measures appear to propagate unchanged across millenia.
Neal says on page 47:
Thom made a comparison of his Megalithic Yard with only one other known unit of measurement. This was the Spanish vara, the pre-metric measurement of Iberia, its value 2.7425 feet. Related measurements to the vara survive all over the Americas wherever the Spanish settled, from Peru to Texas. Although the vara is exactly one of the lengths of the m.y. the fact that it is divided into three feet makes this relationship uncertain. These feet are thought to be Roman but this belief is also unlikely, and they would appear to be related to the earlier Etruscan-Mycenaean units. This is a good example of an intermediate measure being thought to be related because of a similarity in length, and illustrates the importance of considering the sub-divisions when sourcing a measure.
How units of measure are divided and aggregated follows strict rules. If these rules did not exist then the system of metrology would have no inner structure as a system. We don't expect measures to follow rules because today we simply measure things, and do everything else as a calculation following on from that. Metrology is an "ology" because it is a system of calculation that was used for building ancient structures when only limited calculation was possible.
Thus Neal can talk about the ancestry of the megalithic yard because the forensic tools are available through the system of metrology, in which a yard has three feet but that places the foot at close to the limits for a foot, at just over 0.9 feet, for the vara which would then be a yard of near Assyrian feet (9/10 feet). The Roman foot is far greater at 24/25 or 0.96 feet. A Mycenean foot would be 15/16 of the Roman which is in the region of 0.91 feet but the compounding to two errors, that the vara is a yard and that the Roman is its foot is the sort of confusion that only an exact metrology can ever recover from.
Why he [Thom] did not analyse the Megalithic Yard in terms of what was already very well known of ancient metrology, must remain a mystery. And why, after the Megalithic Yard becoming the most scrutinised measure in the history of measure, nobody else has succeeded in doing so, is an even greater mystery. The very simple fact of the matter is, that if as Thom claimed from the beginning, the Megalithic Yard has 40 sub-divisions, then it is not a “yard” but a double remen [1.25], or 2 and 1/2 feet, and the “megalithic inch” is a digit! If the Megalithic Yard is taken to be 2.7272 feet, which is within Thom’s parameters for thç value, the megalithic inch is .06818 feet, which is well within the range of the digits of all known ancient measurements. 16 of these digits are therefore one megalithic foot of 1.0909 English feet. This is a well-known measurement in ancient metrology, sometimes referred to as the Ptolemaic foot, and mistakenly, as the Drusian foot. His “fathom” of 2 m.y. is the historically well-known intermediate measurement, of a pace of 5 feet. Then, his “megalithic rod” [6.8 feet] is 6.25 Ptolemaic feet, which is also a measure known in antiquity as being 100th part of a furlong of 625ft or 1/8th part of the 5,000ft mile. The megalithic measures are not, therefore, peculiar to what is accepted as the megalithic arena, but are perfectly integrated with measuring systems found throughout the ancient world.
One should realise here that Neal is using the word "ancient" in an unquantified way because he believes metrology and other sciences of the numerical arts were inherited by the megalithic - a position that I question since there is no evidence for it. The megalithic could have generated a science of metrology in its earliest phase which then evolved into the greater system of many types of feet (Neal's modules) since the older megalithic monuments have not been well studied - the British monuments being from a later phase. The early burial mounds, if found to have employed this fuller system, would prove Neal's thesis. he continues,
Furthermore, the methods whereby Thom discovered [his megalithic measures], namely by careful surveys and comparisons, are the time honoured methods pioneered by Petrie and in no way are they [a] mistaken interpretation of the evidence, or invention.
The pattern of metrology comes in the ratios between types of unit. If a different foot is used these patterns remain constant and when metrology is used to analyse monuments then it this grammar of its usage that has remained invariant. This all seems like a load of geeky nonesense until metrology is resolved as a system within which the apparent babel of metrological signals become a direct communication from the past. Neal does not make this any easier by delivering a masterly analysis that prerequires most of the structural understandings to be in place.
But what doth this profit man? Is this simply a specialist field? For sure, by now, like Neal I am something of a specialist. It is true that no older language than metrology, other than language itself, has come down from such antiquity (perhaps art?). If there is a truth behind claims that the number sciences were sacred and contain mysteries concerning the spiritual world, metrology could be a philosopher's stone. It is also true that this system of prehistoric thought is a very powerful forensic tool for recovering their intended meaning of ancient sites and the types of measure found might reveal lines of metrological transmission in the ancient world.
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The relationship of the radius or diameter of a circle to the size of its circumference is governed by the irrational constant Pi = 3.1415... where the fractional part is endless. This means that, in theory, using a given number of length units to form the radius R will mean that the circumference (2 times Pi times R) cannot be made up of a whole number of the same units. Ancient metrology solved this and other problems by developing a whole range of interrelated units of length - a concept alien to our selves where our unit of length is usually just the metre or the English foot.
In other words, by having a range of units related to one another, a type of calculation was possible that today we would achieve using trigonometry and other techniques based upon the notational mathematics we now use. This makes ancient metrology a candidate for the prehistoric mathematics that is implied by megalithic monuments.
A number of rational approximations to Pi existed in the ancient world but the simplest accurate one is 22/7. which means that a diameter of a circle seven units in length will produce a circumference 22 units long. However, to be really useful, a metrology needs to be able to divide up a circle into any number as required, just as we do when we divide a circle into 360 parts and call the angle from the centre of each, one degree. If we can place 360 around a circle then a degree scale can be produced and how are degree scales made anyway?
Ancient metrology decided on a single unit and called this unit one - a fact revealed conclusively by John Neal in his All Done With Mirrors. Having worked for many years with this fact it continues to reveal the hidden nature of metrological buildings from the Megalithic to the Gothic period.
To build the system, the unit one is then extended or contracted into new units of measure that are a rational fraction of a foot, the English foot (as we call it today). Thus a Sumerian foot in its simplest form is 12/11 feet and this unit can be found in the vertical dimension of the Great Pyramid.
If we imagine one Sumerian foot as a radius, then the circumference will be 12/11 times 4*11/7 feet long and the elevens will cancel to leave 4*12/7 or what we would call four Royal cubits, again in their basic or root form - the unit of length most associated with the Egyptian builders. It is as if Pi has been transformed into 4 rather than being 3 plus something.
Matrix Diagram of mentioned Units of length
in their relationship to one another
Four Royal cubits might be called a megalithic rod of 2.5 megalithic yards by Alexander Thom and the common unit for the cubit and the megalithic yard is a 10 digit Palm, which is a tenth of a rod. All of this rich cyclicity within metrology was a functional idiom learnt by its practitioners.
The upshot is that one can build a radius with a required number of Sumerian feet in the radius and see that linear dimension translated into the same number of Royal rods on the circumference. A radius of 360 Sumerian feet would generate a degree circle in which an observer could see degrees on the radius as markers spaced one Royal rod apart.
One way in which metrology could calibrate a circumference
with 360 equal units of length
The choice of 360 for degrees comes from its similarity to the number of days in a year and its capacity to factor purely canonical numbers, the primes 2, 3 and 5. It is 5 less than the number of whole days in a year and 6 less than the whole number of earthly rotations in a year. 360 divides by 72 five times and 365 divides by 73 five times whilst 360 divides by 60 six times and 366 divides by 61 six times. The former gives us the Venus calendar with 73 day units and the latter gives us the Saturnian calendar with 61 day units whilst 360, the "common denominator", gives us convenience in aggregating degrees into 30, 12, 10 and so on yet gave many cultures a calendar with five extra days, the "Neters" in Egypt.
Calendars and degrees are therefore related and one use for placing a known number of divisions upon a circumference is to make that number resemble the days in a year, month, lunar orbit or whatever, since then you can enact the year as the re-entrant species it is, for every cycle is a snake that eats its own tail, every end is a new beginning - not just in self-development books but also in the sky!
Without ancient metrology this whole procedure is obscure and lack of metrological knowledge is holding back our cultural perception of what was possible and sophisticated in the techniques of the monument makers. Nothing can reveal what a pyramid or stone circle was doing without ancient metrology but the whole subject is locked out of official science and general knowledge for various reasons.
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