Civilization One: The World is Not as You Thought it Was (24 page)

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:

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:

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.

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 great 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.

When we hear a note played on a musical instrument, both frequency and wavelength are involved in what our ear registers. The note we choose to call ‘A’ on a modern piano keyboard, three notes below middle C, has a frequency of 440 Hz, which means there are 440 peaks and 440 troughs, of the sort shown in the diagram above, for every second of time. The note A also produces a wavelength, which in this case is 78.4 centimetres. The next note up on the piano keyboard, B flat, has a frequency of 466.16 Hz and a wavelength of 74 centimetres. As the frequency increases, the wavelength decreases.

We had previously discovered that the modern second of time (plus its double counterpart) was first used by the Sumerians, but we could equally well adopt Megalithic units of distance and time to specify musical notes in exactly the same way.

The Earth turns once every sidereal day of 86,164 seconds and according to Megalithic geometry the equator can be divided into 366 degrees, 60 minutes and 6 seconds of arc. Because the planet bulges a little at the equator its equatorial circumference is larger than the polar circumference and therefore the distance of one second of arc is longer, at just under 366.6 Megalithic Yards. It follows that the Earth will rotate through one Megalithic second of arc every 0.65394657 seconds – which is a period that we might reasonably call a ‘Megalithic Second of time’. Therefore, if we had a musical note with a frequency of 366 cycles for every Megalithic Second of time, it would be ‘in tune’ with the turning Earth because there would be one vibration for every Megalithic Yard of planetary turn at the equator. In reality it is very slightly more than a Megalithic Yard because of the equatorial bulge. The difference between the polar and equatorial circumferences is equivalent to 36.6 Megalithic Minutes of the polar circumference! We decided to call this theoretical unit of Megalithic sound a ‘Thom’ (abbreviated to Th) in honour of Alexander Thom whose work is at the root of our investigation. In standard terms, a frequency of 366 Th would be 560 Hz, which places our Megalithic note slightly above C sharp in modern concert tuning.

Once we had our primary note, it would then be possible to tune an entire instrument, or even an entire orchestra, to that note. Since all the notes in a scale are harmonious and therefore have a mathematical relationship with the starting or ‘root’ note, and because the Megalithic Yard is geodetic, it would follow that any piece of music played in this Megalithic C sharp would enjoy a mathematical relationship with the turning Earth, both in terms of the planet’s dimensions and its spin.

Alan, a keen musician, began building a series of musical instruments tuned to this Megalithic root note. In particular he decided to create a Megalithic C sharp didgeridoo, the native Australian instrument which is basically just a long, fairly wide tube varying between three and eight feet in length. The didgeridoo is essentially a low-pitched drone-pipe where the player maintains the drone using circular breathing. Originally they were made from straight eucalyptus branches that had been hollowed out by termites but as Alan did not have access to either eucalyptus branches or termites, he used bamboo instead. The exercise worked very well indeed and the resulting sound had a very authentic feel to it so Alan created a second didgeridoo to give to Chris.

Chris had been to Australia, where he had noted a number of ancient Aboriginal myths for his research when writing
Uriel’s Machine.
It is known that some of these myths are 10,000 years old – nearly twice as old as Sumerian stories. Chris suggested that we should try and find out if this particular ‘Megalithic’ didgeridoo really existed amongst the aborigines and was surprised when Alan replied that he had a good friend who was an authority on the subject. Gordon Hookey, an indigenous Australian, had stayed at Alan’s house for a number of weeks when he was visiting Britain to give talks on Aboriginal art and music. Unfortunately, every attempt to contact Hookey for research purposes failed, as he appeared to be permanently on the move. By a quirk of fate, at almost exactly the same time as Alan had given up hope of tracking down his friend the doorbell rang and one of those magical moments of beautiful serendipity occurred. As Alan opened the door a beaming stranger introduced himself saying that he had come to borrow the key to the local Civic Centre, held by Alan and his wife. As the conversation developed Alan was soon open-mouthed.

‘I’ll come and open up the Centre for you with pleasure. Are you running some course or other?’ asked Alan.

‘Yes. I’m just beginning a music course with a difference – I teach the didgeridoo.’

‘What?!’

Alan stopped in his tracks, staring at the stranger in disbelief.

‘I know it sounds pretty weird but it’s actually a fascinating subject,’ replied the stranger in self-defence.

‘No, no, I don’t think it’s strange at all. It’s just that I can’t believe that you have turned up on my doorstep at this precise moment in time,’ Alan said, shaking his head from side to side in disbelief.

The visitor was carrying a long bag, which he then told Alan contained a number of authentic didgeridoos. It transpired that he had spent considerable periods living in the Australian bush with Aborigines. There he had manufactured his own instruments and had ultimately become one of Britain’s few non-Aboriginal experts on the subject. Alan dived right in with the $64,000 question.

‘You wouldn’t happen to know if native Australians ever use a didgeridoo that produces a note a little over C sharp, would you?’

The reply stunned Alan.

‘Something a little over C sharp?’

Hookey paused momentarily as he thought.

‘Yes, they certainly do – it’s considered to be the most sacred of all tunings and is reserved for playing music to the Earth.’

‘Playing music to the Earth!’ Alan shouted back at the surprised stranger. ‘That’s incredible. When you say ‘Earth’ – do you mean the ground or the entire planet?’

‘It’s the same thing to native Australians. The note from that didgeridoo harmonizes them to every aspect of their environment. The sound it makes thanks the world for all it gives them and playing it binds them to all of nature. It’s a kind of prayer of thanks offered up the planet and, at the same time, the music they make merges them into the whole of creation.’

This was incredible information. It had been a long shot that such an instrument existed at all, but to find out that the Australian Aborigines used an ‘Earth’ note with a frequency of 366 Th was simply wonderful. One again it could be a huge coincidence and it seemed completely impossible that there would be any calculated connection with Megalithic mathematical principles.