Menkaure pyramid (all sides)
= 500 MY
Sahure pyramid (all sides)
= 380 MY
Could it be that the Ancient Egyptians created their own units by using the same ‘sacred’ principle as the world’s first workers in stone? They must have known that there is no other way to create a repeatable unit of measure other than to calibrate the spin of the Earth using the apparent motion of Venus or the stars – and the Egyptians were unquestionably fascinated by the heavens. Their use of Venus and stars in hieroglyphs shows how central they were to the priesthood.
The priests of Ra, the Sun god, may have sought an extra layer of encryption to hide the secrets of the master mason from the common man. One can imagine how they considered the length of the pendulum to be the circumference of the sun and then put a square around it. They would here be using the known Egyptian principle of ‘As above – so below’ as well as the ‘Russian Doll’ principle that was central to many early cultures, including that of the Megalithic builders. This meant that the same geometric principle would give them an infinite sequence of ½ MY, 1 MY, 2 MY to reveal multiples of royal cubits and remens.
The hieroglyph for Venus, which literally means ‘Divine Star’
The hieroglyph for the priesthood, showing Venus above the sun
We checked on whether there were any further grounds to believe that the Egyptians had used the principles of the Megalithic measuring system to create their own units. We found them.
In the Egyptian numbering system the circle was used as a hieroglyph to denote the fraction one quarter. In the sequence of circles within squares, the square that contains the circle with a circumference of a Megalithic Yard has sides that measure one quarter-remen. Furthermore, the Ancient Egyptians had a principle unit of area they called the ‘setat’ (later known to the Greeks as the ‘arouna’). This was most commonly used in its quarter form. We were amazed to find that the area of a setat is exactly 4,000 MY2 and the quarter-setat is therefore precisely 1,000 MY2. The chances of this being a coincidence are infinitesimally small.
The theory that there was interaction between the Megalithic builders of the British Isles and the Ancient Egyptians was starting to look extremely probable. It has already been noted by other researchers that the inner edge of the circle, or Sarsen Ring, at Stonehenge in southern England has a diameter of 1162.8 inches (2953.51 centimetres), which means that it has an area exactly equal to an Egyptian quarter-setat. Could the Egyptians also have adopted their units of area from the Neolithic people of Britain?
It appears that the early Egyptians were strongly influenced by the Megalithic builders of the British Isles. Such connections have been mooted before but have been rejected by mainstream archaeology because of the absence of cross-cultural artefacts at archaeological dig sites. The assumption that ancient cultures could not have had contact unless they left evidence appears to be unwarranted. The movement of a small number of master mason/magi priests between the British Isles and the Nile Delta could not reasonably be expected to show any trace of artefacts. The discovery of these interrelated measurement principles is far more conclusive evidence of a deep level of influence of one people on another than the digging up of Megalithic objects in the sands of Egypt.
Hidden within the working practices of all Egyptian mathematicians and builders the Megalithic Yard had been present, probably from the very start of the civilization. Megalithic ‘DNA’ in so significant a place as this surely points to the Egyptian system of measurements also possessing strong traces of the Great Underlying Principle – whatever its origin.
The plan of Stonehenge is designed on an area of a quarter Egyptian setat.
CONCLUSIONS
Many leading linguists accept that there was a single global language approximately 15,000 years ago. Our findings are showing that many cultures shared an approach to measurement and geometry that comes from an apparently single source more than 5,000 years ago.
The Indus Valley civilization or Harappa culture of the Indian subcontinent dating from about 2800 BC had a unit of length called the gaz that is very close indeed to the Megalithic Yard. We dismissed this as a probable coincidence until we became aware of the cube-shaped stone weights that this culture used. These weights correspond almost perfectly to the imperial system. The largest weight weighed 3 pounds and one of the smallest weighed just one four-hundredth of a pound. This was especially interesting as we had already identified that the pound weight is derived from a cube with sides of one-tenth of a Megalithic Yard (4 Megalithic Inches).
The Spanish vara is very close to being a Megalithic Yard as is the old Japanese measure known as the shaku. This is believed to have been imported from China more than 1,000 years ago and is almost indistinguishable from a Minoan foot. It follows, therefore, that 366 Megalithic Yards is the almost the same as 1,000 Japanese shaku, with a fit accuracy of 99.8 per cent.
Looking at Ancient Egypt, we noted that the basic unit of linear measurement, in use for nearly the whole of its history was the royal cubit. A related unit of length was the remen which had a Pythagorean relationship to the cubit. This was based on the square root of 2, which the Sumerians/Babylonians wrote down as 1, 24, 51, 10 (in their base 60 notation) but would be written today as the decimal number 1.414212963.
We found that the Great Pyramid of Khufu was built using a measuring wheel with a circumference of one Megalithic Yard and a diameter of a half royal cubit. All of the pyramids main dimensions are a combination of Megalithic Yards, royal cubits and remens, all to the value of‘279’.
The Ancient Egyptians also had a principal unit of area called the setat that was most commonly used in its quarter form. The area of a setat is exactly 4,000 MY2 and the quarter-setat is therefore precisely 1,000 MY2. The chances of this being a coincidence are minutely small. Further, it has already been noted by other researchers that the inner edge of the circle, or Sarsen Ring, at Stonehenge in southern England has a diameter of 1,162.8 inches, which means that it has an area exactly equal to an Egyptian quarter-setat.
1 Ruhlen, M.: ‘Linguistic Evidence for Human Prehistory’. Cambridge Archaeological Journal, 5/2, 1995.
2 Mackie, E.: The Megalithic Builders. Phaidon Press, London, 1977.
3 Kenoyer, J.M.: ‘Uncovering the keys to the lost Indus Cities.’ Scientific American. Vol. 289, No.1, July 2003.
4 http://www.harappa.com/indus/21.html
5 http://unicon.netian.com/unitsys_e.html#france1
6 Davis, P.J. and Hersh, R.: The Mathematical Experience. Penguin Books, London, 1990.
7 http://www.metrum.org/measures/dimensions.htm
CHAPTER 11
Music and Light
We had found that Megalithic ‘DNA’ is present in measurement systems spanning a broad period from the Sumerians and Ancient Egyptians through to those devised at the end of the 18th century. The first cultures to compile records of their civilizations have made it relatively easy to understand much about their lives and knowledge but the Megalithic builders left us little to puzzle over except their magnificent structures.
Generations of investigators have assumed that stone circles and other prehistoric monuments were built for some unknown pagan ritualistic purposes by otherwise unsophisticated Stone Age tribes. People with a more romantic bent have sometimes confused matters by speculating on what little is known of the much later Celtic peoples and attributing all kinds of inappropriate magic and mystery to the Megalithic monuments. These romanticists assume that great wisdom was held, almost instinctively, within the minds of a lost cult of nature worshippers. The evidence of Thom’s Megalithic Yard has demolished any notion of the naivety of its creators assumed by most archaeologists. We have to respect these forgotten people for the great astronomers and geometricians they certainly were.
The level of science achieved by the Sumerians, the Ancient Egyptians and the Greeks is well understood, but the knowledge of the Megalithic builders of the area around the Bri
tish Isles can only be reconstructed from a forensic investigation of their artefacts. Sadly, we can never know what myths and legends they handed on down the generations and we will never hear the music they played or the songs they sang.
Further accomplishments of the Megalithic people
As we have seen, however, it is entirely possible to reconstruct the mathematics these people understood and used, and this in turn might just give us some clues as to their other accomplishments. We have established that the number 366 was central to the Megalithic system because it is the number of Earth revolutions in a single orbit around the Sun (a year) and because one 366th part of a day is the difference between a solar and a sidereal day. The second important number in the system was 360, which was the number of seconds in a Megalithic Degree. Megalithic geometry works on a combination of these two numbers.
Alexander Thom had observed that those who built the stone circles and other monuments he studied seemed to have understood the concept that we call pi, the ratio of the diameter of a circle to its circumference. The length of the diameter of a circle fits approximately three and one-seventh times into its circumference. To be more exact we can express the number as 3.14159265, although the string of digits after the decimal point appears to be infinite.
Thom described how some stone rings were made up of carefully calculated parabolas that appeared to be designed to have a ratio of 3:1, instead of pi, for their principal diameter. In other cases, the builders of the circles had ‘flattened’ the sides of circles or had created ‘egg shapes’ in an apparent attempt to force pi into an integer relationship of 3:1 that it really cannot possess.
In order to explore more fully the long-dead builders’ knowledge of such matters, we decided to look closer at the key Megalithic number of 366 to see if it had any relationship with pi. Rather to our surprise, we quickly found a very important link. Imagine the following scenario:
1. A circle with a circumference of 366 Megalithic Yards is constructed.
2. The perimeter of the circle is then divided into half Megalithic Yards, giving 732 units around the circle.
3. The diameter of the circle will therefore be 233 half Megalithic Yards (732 divided by pi).
A surprising fact about such a circle is that it comes just about as close as possible to having both an integer number of units for its circumference and for its diameter. The difference between a truly integer circumference and diameter in this case is one five-thousandth of a millimetre, across a circle with a circumference of over 260 metres. This tiny fraction is far less than the human eye can discern. To any mathematician from the algorithmic school, this would constitute a perfect fit for all real-world purposes.
We found it fascinating that these Megalithic numbers could produce such near-perfect integer numbers for the circumference and diameter of a circle. So is this resulting diameter of 233 special in any way?
The Fibonacci Series
The answer is that it is very special indeed. While the Greek letter pi is used to denote the ratio of the diameter of a circle to its circumference, the letter ‘phi’ is used to denote the ratio found in a number sequence known as the Fibonacci Series. Leonardo Pisano Fibonacci (1170–1250) studied the mating patterns of rabbits and almost accidentally discovered the amazing ratio we now know as phi. The series is where each ascending number is equal to the value of the proceeding two numbers added together: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc. The sequence quickly settles down to the ratio scientists call phi, which is 1.618033989.
Phi is phenomenally important because it is the ratio associated with growth. From flowers to human embryos and from seashells to galaxies – everything in the universe that grows expands outwards according to this fundamental rhythm. The Fibonacci Series was known to the Greeks and to many other early cultures, though it was Finonacci himself who first studied the ratio in a scientific sense. In the fine arts the Series is often referred to as the ‘golden section’ or the ‘golden mean’ where it is usually expressed as a 5:8 relationship. The analysis of many Renaissance paintings will show how rigorously this principle was applied. Artists such as Leonardo Da Vinci and Michelangelo for example, would have learned about the golden mean as apprentices and used the principle in almost all their later artistic creations.
The Fibonaccian number of 233 from our 732 circle is composed of the numbers 89 and 144 added together. However, we had to face the possibility that the number 233 turning up in a Megalithic context was simply another coincidence and we certainly felt that we had to investigate the matter further. Then we noticed something rather peculiar when we brought the two irrational ratios of pi and phi together. Multiplying these numbers leads to another unimpressive looking number:
3.14159265 x 1.618033989
= 5.08320369
But if we divide our circle of 732 half Megalithic Yards by pi x phi we get an almost perfect result of 144. And this is the number before 233 in the Fibonacci series and again it is an incredibly accurate result. However, this is only a cross-proof of the first observation that a circumference of 732 half Megalithic Yards will produce virtually perfect Fibonaccian results for its diameter. We did find it very odd that the following is true to an astonishing degree of accuracy:
360 divided by 5
= 72
366 divided by (pi x phi)
= 72
It appears that there is a curious property of the numbers used by the Megalithic people that makes pi and phi work together to define the difference between 360 and 366. The tiny discrepancy in the mathematics described here is just one part in 400,000 – far beyond any engineering tolerance. By some mechanism we still do not understand, it appears that the Megalithic builders were in touch with nature and reality in a way that modern science is yet to achieve. We have extrapolated this relationship from Megalithic principles, but one question we had to ask ourselves was, ‘Is there any evidence to suggest that the Megalithic builders knew about this mathematical principle made famous in the 13th century by Leonardo Fibonacci?’ Our research had produced results that appeared to confirm their awareness of phi and our own observations were bolstered by the totally independent discoveries of Mona Phillips from Ohio. In the 1970s Dr Phillips had looked at Thom’s original data from Megalithic sites as a central part of her PhD thesis. She too identified the existence of phi within the Megalithic structures and she contacted Professor Thom, asking that he check her findings. Thom reported back that her results were indeed correct and he said that he found her observations to be quite amazing, calling them, ‘almost magical’.
We are sure that Dr Phillips and Professor Thom are correct in suggesting that some Megalithic sites do exhibit the ratio of phi. But did the builders deliberately use it or was it simply a natural consequence of using the number 366 in the building of circles? We had to face the possibility that phi may be simply somehow inherent to the manipulation of the number 366, which appears to have all kinds of‘magical’ properties.
We had some difficulty in imagining Neolithic people working with phi, but we decided to investigate other areas where there might be examples of the number 366, in conjunction with the Megalithic Yard, producing results that resonate with nature. After considering a few ideas we elected to look closely at the subject where mathematics meets art – music.
Mathematics meets art
Scientific interest in music goes back a long way. Pythagoras, the Greek remembered primarily for Pythagoras’ Theorem, lived between 569 BC and 475 BC and spent years experimenting with music. He is credited with being one of the first individuals to produce a really harmonious musical scale. Pythagoras experimented with stringed instruments to see which notes sounded better when played together. By way of an ingenious system of what are known as ‘musical fifths’, he worked out how to tune any instrument to produce good harmony. He knew that string length was very important and dealt with music as an exercise in mathematics.
As ever, it seems that the Greeks were g
reat re-inventors of already ancient knowledge and it is now accepted that Pythagoras was far from being the first to carry out such experiments. Sumerian texts indicate that scholars from the culture understood musical scales and tuned by fifths long before the Greek nation came into existence. We are particularly indebted to Fred Cameron, a Californian computer expert with a background in astronomy, who has spent years reconstructing Sumerian scales and then composing music that may be tantalizingly close to the original.
It seemed reasonable to assume that as the Sumerians had sophisticated music, the Megalithic people probably did as well. With this thought in mind we decided to take a completely new approach by returning to the basics of Megalithic mathematics, particularly the half Megalithic Yard pendulum, not just in terms of its linear length, but also with regard to its frequency. It was not long before we found ourselves being drawn into the fascinating world of sound and light.
It would not be possible to perform practically but if we theoretically fastened a pen to the bottom of a Megalithic pendulum and allowed it to swing freely while moving a piece of paper underneath it, we would end up drawing a sine wave (see below).
A typical wave showing frequency and length.
The pendulum ‘wavelength’ is the distance between two peaks or troughs on the sine wave and this would depend on how fast we moved the paper under the pendulum. ‘Frequency’ is the number of peaks and troughs over a given period of time.
Today we measure frequency in cycles per second, known as hertz, usually shortened to Hz. A simple example is a child banging a toy drum where a rhythm of one bang every second creates a frequency of precisely 1 Hz. If the child doubles the rhythm to two beats per second the frequency would be 2 Hz, and so on. The human ear can detect frequencies up to an amazing 20,000 Hz.
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