Tag: John Neal

Working with Prime Numbers

Wikipedia diagram by David Eppstein :
This is an updated text from 2002, called “Finding the Perfect Ruler”

Any number with limited “significant digits” can be and should be expressed as a product of positive and negative powers of the prime numbers that make it up. For example, 23.413 and 234130 can both be expressed as an integer, 23413, multiplied or divided by powers of ten.

What Primes are

Primes are unique and any number must be prime itself or be the product of more than one prime. Having no factors, prime numbers are odd and cannot be even since the number 2 creates all the even numbers, meaning half of the ordinals are not prime once two, the first “number” as such, emerges.

Each number can divide one (or any other number) into that number of parts. In the case of three (fraction 1/3) only one in three higher ordinal numbers (every third after three) will have three in it and hence yield an integer when three divides it.

Four is the first repetition of two (fraction ½) but also the first square number, which introduces the first compound number, the geometry of squares and the notion of area.

Ancient World Maths and Written Language

The products of 2 and 3 give 6, 12, etc., and the perfect sexagesimal like 60, 360 were combined with 2 and 5, i.e. 10, to create the base 60, with 59 symbols and early ancient arithmetic, in the bronze age that followed the megalithic and Neolithic periods.

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The Integration of the Megalithic Yard

Above is a proposed geometric relation between Thom’s megalithic yard (2.72 feet), the royal cubit (1.72 feet) and the remen (1.2 feet). Alexander Thom’s estimate for it based on decades of work was refined from 2.72 to 2.722 feet at Avebury. If the origins of it are astronomical, then its value emerges from the Metonic period of 19 years which is 235 lunar months, making its value 19/7 feet or more accurately 2.715428571 (19008/7000) feet and this makes it 2.7 feet x 176/175 within ancient metrology. Another astronomical derivation is found at Le Manio as the difference between three lunar and three solar years, when counted in day-inches as 32 + 5/8th inches which is 2.71875 (87/32) feet. The megalithic yard of Thom’s first appraisal, of 2.72, probably arose from its megalithic rod (MR) of 6.8 feet since, the Nodal Period of the moon’s nodes take 6800 days which in feet would be 1000 MR. For a fuller explanation see my the appendix of my Language of the Angels book and my discussions of the Cumbrian stone circle, called Seascale by Thom and the only known example of a Type D flattened circle.

One can see that the Megalithic Yard is a tale of many variations, some of which might not consider how or why the megalithic might have come to adopt such a yard. I have come to trust simple integers and ratios to guide me to a possible megalithic pathway. To demonstrate, the above megalithic yard at Le Manio, of 32.625 inches is 29/32 of the English yard, and 32 lunar months (at Le Manio Quadrilateral) is 29 AMY. Such simple rationics is explored here.

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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

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A Pyramidion for the Great Pyramid

image: By 1200 BC, the end of the Bronze Age, the Egyptian map of the world (above) showed nine bows or latitudes, numbers 4 to 9 including the Nile Delta, Delphi, Southern Britain and Iceland, a map based on an ancient geodetic survey.

This post explores a pyramidion, now lost, which exceeded the apex height of the pyramid, so as to model the different reference latitudes established by geodetic surveys and encoded within their metrology and the Great Pyramid (by 2500 BC). This pyramidion would have sat on the flat top of the pyramid, 480 feet above the base of the pyramid.

In All Done With Mirrors, John Neal described how the full height of the pyramid, reaching to its natural apex, would have been just over 481 feet. Most pyramids probably had a pyramidion since a number have been found elsewhere that repeat aspects of or have a name carved on them, of a specific pyramid. Sitting on their apex, they often repeat the form of the larger pyramid, and are scale models of a specific pyramid. In the case of the Great Pyramid, exactly 441th of its natural apex is missing, and this is likely to be because a pyramidion once stood on the flat top the actual pyramid.

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Recalibrating the Pyramid of Giza

Once the actual height (480 feet) and actual southern base length (756 feet) are multiplied, the length of the 11th degree of latitude (Ethiopia) emerges, in English feet, as 362880 feet. However, in the numeracy of the 3rd millennium BC, a regular number would be used. In the last post, it was noted that John Neal’s discovery of such rectangular numbers to define degrees of latitude, multiplied the pyramid’s pointed height (481.09 feet) by the southern base length (756 feet) to achieve the length of the Nile Delta degree of latitude and, repeating Neal’s diagram relating the key latitudinal degrees of the ancient Model as figure 1, the Ethiopian degree is 440/441 of the Nile Delta degree. As shown above, the length of the 756 foot southern base is changed, when re-measured in the latitudinal feet for Ethiopia; it becomes the harmonic limit of 720 feet of 1.05 feet – normally called the root Persian foot.

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Ethiopia within the Great Pyramid

My last posting mentioned John Neal’s creative step of not averaging the Great Pyramid of Giza’s four sides, as had routinely been done in the past – as if to discover an idealized design with four equal sides. Instead, Neal found each length to have intensionally been different. When multiplied by the pyramid’s full height, the length of four different degrees of latitude were each encoded as an area. The length of the southern side is integer as 756 feet, and this referred to the longest latitude, that of the Nile Delta, below 31.5 degrees North. Here we find that the pyramid’s reduced height also indicated the latitude of Ethiopia.

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