Lesson 3: Making a circle from a counted length

The number of days in four years is a whole number of 1461 days if one approximates the solar year to 365¼ days. This number is found across the Le Manio Quadrilateral (point N to J) using a small counting unit, the “day-inch”, exactly the same length as the present day inch. It is an important reuse of a four-year count to be able to draw a circle of 1461 days so that this period of four years can become a ouroboros snake that eats its own tale because then, counting can be continuous beyond 1461 days. This number also permits the solar year to be counted in quarter days; modelling the sun’s motion within the Zodiac by shifting a sun marker four inches every day.

Figure 1 How a square of side length 11 will equal the perimeter of a circle of diameter 14

Our goal then is to draw a circle that is 1461 day-inches in perimeter. From Diagram 1 we know that a rope of 1461 inches could be divided into 4 equal parts to form a square and from that, an in-circle to that square has a diameter equal to a solar year of 365¼ days. Also, with reference to Figure 1, we know that the out-circle will have a diameter of 14 units long relative to the in-circle diameter being 11 units long, and this out-circle will have the perimeter of 1461 inches that we seek.

Figure 3 A general method, using the equal perimeters model, applied to a 4 solar year day count of 1461 day-inches, found as a linear count at the Manio Quadrilateral. A square, formed from this linear count, can be transformed into an outer circle of equal perimeter using the simple geometry of π as 22/7.

For this, the solar year rope (the in-circle diameter) needs to be divided into 11 parts. Start by choosing a number that, when multiplied by 11, is less that 365 (and a 1/4). For instance, 33. A new rope will be formed, 11 x 33 = 363 inches, marked every 33 inches to provide 11 divisions. Through experience, we discover we need 2 identical ropes so as to make practical use of the properties of symmetry through attaching ropes to both ends of the solar diameter rope.

Place one rope at the West side of the in-circle diameter and swing it up until it touches the in-circle. Place the other rope at the East side of the in-circle diameter and swing it down until it touches the edge of the in-circle. Now connect the 33 inch marks between the 2 ropes. This will divide the 365 1/4 diameter into 11 segments.

Seven of those segments are the new radius to create the 1461 inch outer-circle.

Figure 3 Division of the in-circle into eleven equal parts so as to select 7 units as a radius rope to then form the circle of diameter 14 units and perimeter 1461 inches.

This novel application of the equal perimeters model, rescued from Victorian textbooks by John Michell and applied by him most memorably perhaps to Stonehenge and the Great Pyramid (in Dimensions of Paradise) is a general method for taking a counted length and reliably forming a radius rope able to transform that counted length into a circle of the same perimeter as the square, easily formed by four sides ¼ of the desired length.

The site survey at the start, drawn by Robin Heath, appeared in our survey of Le Manio.

Sacred Number and the Origins of Civilization

Published by Inner Traditions

Back Cover

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.

Publisher Pages

Description

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.

Pre-publication format
(view picture in new tab for detail)

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.