Preface: The Metrology of the Brochs

feature picture: Broch of Mousa. The broch on the island of Mousa is the best-preserved of the many brochs in northern Scotland. It is thought to be some 2000 years old
credit: Anne Burgess / Broch of Mousa / CC BY-SA 2.0

I wrote this preface for Euan MacKie who had resurrected his work on measures found within the brochs of Scotland. Euan was almost a lone voice in support of Alexander Thom’s work on metrology in the megalithic, and also the long distance alignments in the Western Isles of Scotland. When he met John Neal at the latter lecture in Glasgow, at which I was present, they appear to have entered into a review of the data and John Neal came back with an interesting theory which would make a full range of historic measures to have been employed in one area of northern Scotand, in the Iron Age. I sent Euan a summary of what ancient metrology appeared to be as a system of ratios and why Neal’s finding within MacKie’s data would be important. It became the preface for the article called The Roundhouses, Brochs and Wheelhouses of Atlantic Scotland c.700 BC-AD 500: Orkney and Shetland Isles Pt. 1: Architecture and Material Culture (British Archaeological Reports British Series) which I have recovered from a partial proof copy.

Preface

by Richard Heath

John Neal has demonstrated elsewhere [All Done With Mirrors, John Neal, 2000] that ancient metrology was based upon a “backbone” of just a few modules that each related as simple rational fractions to the “English” Foot. Thus a Persian foot was, at its root value, 21/20 English feet, the Royal foot 8/7 such feet, the Roman, 24/25 feet and so on. By this means, one foot allows the others to be generated from it.

These modules each had a set of identical variations within, based on one or more applications of just two fractions, Ratio A = 176/175 and Ratio B = 441/440. By this means ail the known historical variations of a given type of foot can be accounted for, in a table of lengths with ratio A acting horizontally and ratio B vertically, between adjacent measures.

In the context of what follows, this means that each of the differently-sized brochs analysed by Neal appear to have used a foot from one or other of these ancient modules, in one of its known variations. That is, the broch builders seem to have chosen a different unit of measure rather than a différent measurement, as we would today, when building a differently sized building. Furthermore, these brochs appear to have been based upon the prototypical yet accurate approximation to pi of 22/7, so that – providing the broch diameter would divide by seven using the chosen module – then the perimeter would automatically divide into 22 whole parts.

Thus, John Neal’s discovery that broch diameters divide by seven using a wide range of ancient measures implies that the broch builders had – (a) inherited the original system of ancient measures with its rational interrelations between modules and variations within these, from which they could choose, to suit a required overall size of circular building, often the foundations available: (b) were practicing a design concept found in the construction of stone circles during the Neolithic period.

These measures, used in the brochs, are not often found elsewhere in Britain, but are historically associated with locations hundreds if not thousands of miles distant. This suggests that the historical identification of such measures is only a record of the late use of certain modules in different regions, after the system as a whole had finally been forgotten, sometime after the brochs were constructed.

Such conclusions, if correct, are of such a fundamental character that they present a compelling case for ancient metrology and its forensic power within the archaeology of ancient building techniques.

—x—

Throughout Scotland and the Scottish islands there are in excess of 200 major broch sites. The following analysis is taken from, what I believe to be, the accurately measured inner diameters of 49 of them as supplied by Professor Euan MacKie. The modules are expressed in English feet although the original measurements were taken in metres and converted to feet at the rate of 3.2808427 feet to the metre. The range of diameters extends from the smallest, at Mousa, 18.897654ft, to the greatest at Oxtrow at 44.816311ft. John Neal’s original work on this can be found in this article, from this website’s earlier incarnation which also included a version of Appendix 2 of Sacred Number and the Origins of Civilization – soon also to be added, for reference.

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Sacred Number and the Origins of Civilization

Published by Inner Traditions

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ANCIENT MYSTERIES / NEW SCIENCE

“Richard Heath sweeps away the mechanistic and relativistic paradigm to reveal an earth-centered, celestial system founded upon the beauty of musical harmony and geometric symmetry.”
–Robert Lawlor, author of Sacred Geometry and Voices of the First Day

“Richard Heath effectively rewrites the book on the mysterious but accomplished megalithic cultures preceding ancient Egypt, Sumer, China, and India.”
–John Anthony West, author of Serpent in the Sky: The High Wisdom of Ancient Egypt

“. . . well-expressed, with a deep insight into the ancient science.”
–John Michell, author of The Dimensions of Paradise

The ubiquitous use of certain sacred numbers and ratios can be found throughout history, influencing everything from art and architecture to the development of religion and secret societies. In Sacred Number and the Origins of Civilization, Richard Heath reveals the origins, widespread influences, and deeper meaning of these synchronous numerical occurrences and how they were left within our planetary environment during the creation of the earth, the moon, and our solar system.

Exploring astronomy, harmony, geomancy, sacred centers, and myth, Heath reveals the secret use of sacred number knowledge in the building of Gothic cathedrals and the important influence of sacred numbers in the founding of modern Western culture. He explains how the Templar design of Washington, D.C., represents the New Jerusalem, and he identifies the role secret societies play as a repository for sacred numerical information. Those who attempt to decode its meaning without understanding the planetary origins of this knowledge are left with contradictory, cryptic, and often deceptive information. By examining prehistoric and monumental cultures through the Dark Ages and later recorded history, Sacred Number and the Origins of Civilization provides a key to understanding the true role and meaning of number.

Richard Heath is a Web developer with degrees in electrical and computer engineering. The author of The Matrix of Creation: Sacred Geometry in the Realm of the Planets, he lives in Scotland.

Sacred Number and the Lords of Time

Back Cover

ANCIENT MYSTERIES

“Heath has done a superb job of collating his own work on the subject of megaliths with the objective views of many other researchers in the field. I therefore do not merely recommend reading this book but can state unequivocally it is a must read.”
–John Neal, British metrologist and researcher and author of Measuring the Megaliths and The Structure of Metrology

“In Sacred Number and the Lords of Time we have an important explanation of how megalithic science was developed. This book is a long-overdue wakeup call to a modern culture that has abandoned this fully developed and astonishingly rich prehistoric model of the physical world. The truth is now out.”
–Robin Heath, coauthor of The Lost Science of Measuring the Earth and author of Sun, Moon and Earth

Continue reading “Sacred Number and the Lords of Time”

The Harmonic Origins of the World

“We have long known, thanks to Ernest McClain, that the ancients were obsessed with harmonic numbers and that the Bible encodes these from beginning to end. Now new evidence appears, as these numbers correlate with the planetary periods, and their discovery is pushed far back into the prehistoric era. Richard Heath’s work, based not on speculation but on objective data, challenges all accepted notions of cultural evolution and religious origins.”

–JOSCELYN GODWIN, author of Harmonies of Heaven and Earth and Atlantis and the Cycles of Time

As modern humans first walked the Earth roughly 70,000 years ago, the moon’s orbit came into harmonic resonance with the outer planets of Jupiter, Saturn, and Uranus. The common denominators underlying these harmonic relationships are the earliest prime numbers of the Fibonacci series–two, three, and five–the same numbers that interact to give us the harmonic relationships of music.

Continue reading “The Harmonic Origins of the World”

Sacred Geometry: Language of the Angels

Examining the angelic science of number, Richard Heath reveals how the development of human consciousness was no accident. The beauty and elegance we see in sacred geometry and in structures built according to those proportions are the language of the angels still speaking to us.

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Reveals how the number science found in ancient sacred monuments reflects wisdom transmitted from the angelic orders

• Explains how the angels transmitted megalithic science to early humans to further our conscious development

• Decodes the angelic science hidden in a wide range of monuments, including Carnac in Brittany, the Great Pyramid in Egypt, early Christian pavements, the Hagia Sophia in Istanbul, Stonehenge in England, and the Kaaba in Mecca

• Explores how the number science behind ancient monuments gave rise to religions and spiritual practices

The angelic mind is founded on a deep understanding of number and the patterns they produce. These patterns provided a constructive framework for all manifested life on Earth. The beauty and elegance we see in sacred geometry and in structures built according to those proportions are the language of the angels still speaking to us.

Examining the angelic science of number first manifested on Earth in the Stone Age, Richard Heath reveals how the resulting development of human consciousness was no accident: just as the angels helped create the Earth’s environment, humans were then evolved to make the planet self-aware. To develop human minds, the angels transmitted their own wisdom to humanity through a numerical astronomy that counted planetary and lunar time periods. Heath explores how this early humanity developed an expert understanding of sacred number through astronomical geometries, leading to the unified range of measures employed in their observatories and later in cosmological monuments such as the Giza Pyramids and Stonehenge. The ancient Near East transformed megalithic science into our own mathematics of notational arithmetic and trigonometry, further developing the human mind within the early civilizations.

Heath decodes the angelic science hidden within a wide range of monuments and sites, including Carnac in Brittany, the Great Pyramid in Egypt, Teotihuacan in Mexico, early Christian pavements, the Hagia Sophia in Istanbul, and the Kaaba in Mecca. Exploring the techniques used to design these monuments, he explains how the number science behind them gave rise to ancient religions and spiritual practices. He also explores the importance of lunar astronomy, first in defining a world suitable for life and then in providing a subject accessible to pre-arithmetic humans, for whom the Moon was a constant companion.

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Harmonic Explorer app

The work of the late Ernest McClain [1918-2014] was based upon a technique in which ever higher numbers appear to have been studied in antiquity as to the harmonic field of intervals possible within that integer limit. Such a single number reference can be mentioned en passant within texts like The Bible, Homer’s Illiad or the Sumerian story of Gilgamesh and be ignored today as a frivolous use of large numbers, such as great ages of the gods, the number of ships, or tithe goods and so on, when in fact the numbers were referring to a musicological field relevant to the narrative and its elements.

McClain’s work was very briefly introduced in  Precessional Time and the Evolution of Consciousness (2011) in its Chapter 3 on the Age of Aries, when such calculational musicology/theology seem to have replaced the megalithic activities in Age of Taurus. After then collaborating with Ernest for a few years, after his death I attempted to make an accessible book on Ernest’ work in my 2018 book Harmonic Origins of the World.

Ernest had a fine sensibility for the Ancient Near East (or A.N.E.), its number science and symbolisms. Through many email exchanges I wanted to be able to generate his tonal diagrams for myself; to both learn more and answer specific questions. I was able to make a web page so that people like myself could more easily enter his world of tonal yantras (that look like mountains) and their corresponding tonal mandalas (the octave circle); without having to learn the method of “limiting the products of powers of three and five and then doubling all numbers to the limiting number”. This Harmonic Explorer app enables ridiculous freedom over the previously required manual calculations, including walking through limiting number space with prime factor buttons, multiplying/dividing by 2, 3, 5, 10 or 12. It can also be very useful for screen grabbing when discussing a given tuning system as in:

TRY IT NOW HERE: Harmonic Explorer

Ernest’s website has study pdf’s of his books and papers plus other resources.