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Fibonacci’s Rabbits, the Golden Ratio and da Vinci's Vetruvian Man

(extract 1 from The Human Antenna.) Buy now from amazon_3.jpg BarnesNoble_3_1.jpg

lfib.jpgLeonardo Fibonacci (b. 1170AD in Pisa, Italy), perhaps the most influential mathematician of all time, spent much of his early life as a merchant working for his father. While stationed in Algeria, he traveled to many countries in the Middle East and Europe, where he became interested in each country’s differing currencies and mathematical techniques. Fibonacci has been credited for introducing the Hindu –Arabic numbering system to Europe – 1 through 9 – which the Europeans were to find much less cumbersome than the Roman numerals.


On returning to Pisa in 1200, he became a full time mathematician writing four books. His work was the first documented record of simple maths equations using today’s numbers. He also set himself many practical problems, which he then attempted to solve. The answer to one, involving the breeding pattern of rabbits, proved to have a profound effect on generations of artists, architects and scientists for centuries to come.

Fibonacci tried to estimate how quickly a rabbit population would grow in ideal circumstances. As in all maths problems, certain assumptions were made. Firstly none of the rabbits would die, secondly that each pair of rabbits did not produce more than one pair of off spring each month. Finally, it was assumed that each rabbit only reached sexual maturity in their second month.












Thus, the Fibonacci sequence was born. As we have all observed, a rabbit population grows exceedingly rapidly, with the number of pairs per month being shown in the following sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597 etc.

Each number is the sum of the preceding two numbers; as the number become larger the ratio of the last number to the one before approaches 1.618 – known as the Golden Ratio.

As we achieve adult hood, the ratio of the length of our body below our navel to that above is 1.618 to 1.

This of course could be regarded as an irrelevant isolated coincidence –was it not for the Golden Ratio or Mean, and Fibonacci’s series, revealing themselves within every corner the natural world from the smallest microscopic structure to the largest mammal, from the simplest algae to the largest tree. A nautilus shell grows, and a fern unfurls, ‘mindful’ of the blueprint first observed by Fibonacci. Note that each line is divided below according to the Golden Ratio of 1.618.









The distribution of seeds in the sunflower is governed by this spiral, based in turn on the Golden Ratio. The daisy family will also only have a number of petals from the Fibonacci series. The branching of shrubs, trees and even the bronchial tree in our own lungs also follows these ‘divine’ rules.

Leonardo da Vinci ( 1452-1519) used the proportions of the Golden Ratio in his masterpiece the Mona Lisa. His Vetruvian man displays the sacred geometry of the human form based on the proportions and divisions demonstrated three centuries earlier by his fellow countryman and name sake Leonardo Fibonacci. The relationship between the length of bones in the human finger, hand and arm are examples that are easily
demonstrated on any medical student’s skeleton. On the microscopic level, every double helix spiral of DNA measures 34 angstroms long by 21 angstroms wide. You can see these numbers in the Fibonacci series above; their ratio is 1.619.

The renaissance artists introduced perspective to art. They observed that all of nature followed the same rules of form – the Golden Ratio was a measurement of proportion that linked the smallest simplest life form with the most complex.

Architects such as Sir Christopher Wren incorporated these universal proportions into their churches not only for aesthetic and religious reasons –there were also aware that they contributed to excellent acoustics. The harmonic of sound and music are also based on this sacred geometry.

I can only give you a taste of this extraordinary subject that could easily fill a lifetime of study. It represents a measurable link between many times and cultures, between art science and spirituality. It touches on everything from the mundane to the mystical, from labyrinths to whirling Dervishes, from DNA to black holes and even galaxies. Spiral dynamics , a new discipline arising from this living geometry, is applied increasingly in the business world to predict financial markets, and help direct sustained growth within companies. Evolutionary and sociological trends are now plotted in spiral form, suggesting a collective morphic field effect -similar to the concept of Carl Jung’s “collective unconscious.”

For my part, I began to realize that the numbers themselves weren’t so important; for me this was all to do with proportions and relationships. Describing this geometry as sacred seemed to me to be no rash overstatement. Not only was it strong confirmation of the holographic nature of the universe, it also suggested that that everything within this
universe shared something very special at the most fundamental level. An unseen organizing, interconnected intelligence that gave birth to energy and form. A benign pure consciousness that for many would be the very essence of God.

In Leonardo Da Vinci’s day, openly expressing this abstract view of a divine force would have been nothing short of heresy. He was wise to keep his secrets locked securely away within his work in code form; sacred secrets concealed within the knowing smile on the face of the beautiful Mona Lisa.



Out of the Darkness. (extract 2 from The Human Antenna.)

"Just as the world was created from dark chaos through the bringing forth of the light and through the separation of the aery firmament and of the waters from the earth, so our work brings forth the beginning out of black chaos and its first matter through the separation of the elements and the illumination of matter."
- Sir Isaac Newton

newton_by_blake_1.jpgSir Isaac Newton, the 17th century founder of the Laws of Gravity, was an alchemist. Alchemy is not simply the mystical process of extracting gold from base metals – it literally means “out of the darkness.” So the one man mostly strongly attributed to setting the Western world on a course of mechanical materialism seemed to be as much aware of levity, as he was of gravity.

'Newton' by William Blake

Newton’s Laws explained how we all are bound to this earth, why the moon is bound to the earth in orbit, as the earth is to the sun. Yet it appears that Sir Isaac knew that this was only part of the story.

One of Newton’s influences was Robert Fludd who died five years prior to Sir Isaac’s birth. Fludd was a doctor, a philosopher and scholar whose seminal work had been based on the concept that the workings of our bodies somehow reflected those of the universe itself – a unifying theory in line with Eastern Taoist thought – as above , so below.. In the 20th century this understanding of the basic nature of ourselves and our universe was rediscovered by physicist Dennis Gabor, who first demonstrated the nature of holograms, and neuroscientist Karl Pribham who then applied these principles to the nature of our human brain.

Others influenced by Fludd were his friend Sir William Harvey, the physician who
mapped the human circulatory system, and Newton’s contemporary Sir Christopher Wren the architect who designed St Paul’s Cathedral - and many other magnificent buildings within whose sturdy walls, and upon whose solid foundations, generations have continued to experience the divine.

So when William Blake, the visionary poet, somewhat despairingly exclaimed in 1802 in a letter to his friend Thomas Butt : “May God us keep, from single vision and Newton’s sleep,” he may well have been paying Sir Isaac a gross disservice.

We’ll never know whether Newton envisaged how great an influence his discoveries
were to have on the history of the Western world. How they would help spurn the Age of Reason, the Industrial Revolution and a deep understanding on the mechanical workings of our bodies and our world. To such an overwhelming extent that, by the end of the nineteenth century, many Western scientists confidently exclaimed that they had learned everything that could be learned about science.

And then along came Albert Einstein. Fifteen generations after Newton, Einstein’s Laws of Relativity added subjectivity to the laws of nature. He declared that just what we observe may depend on us, the observers. And that our mass, our physical being (in fact all ‘things’), could regarded equally as energy.

Then, one single generation later, came the startling theories of quantum physics;
Heisenberg’s theory that all matter exists fundamentally as probabilities, only coming into existence when we observe it. And like light itself, all matter can be also viewed as wave forms. That the reality conveyed to us by our senses may only be part of the story. That all we touch, see and hear is in fact an apparently chaotic kaleidoscope of interfering fields of information, converted into our space/time model by our very selves.

It is not surprising that even Einstein himself initially found this all rather too much.

But what exactly are the implications of this new quantum awareness – a state where, as Buddha was to declare, ‘all is illusion.’ ?

How, for instance, does it affect our understanding of life itself?

….of love?…. of healing?… of death?

But it is also important to remember that the mechanistic world of gravity is as real as it ever was for us – it is responsible for our days, our nights and our months. It secures each and every one of us to our home, Mother Earth – allowing us to see the light by day, and reach for the stars at night.

So maybe only now we have been so thoroughly grounded, we are ready to share the true glory of Sir Isaac Newton’s vivid alchemic vision. The light emerging from the dark, a state of levity from gravity.

And I am beginning to suspect that if, as William Blake inferred, Sir Isaac had fallen asleep, one of his eyes remained firmly open.

At times, I am convinced it continues to watch over us.

Printed with the kind permission of Zenith Publishing. New Zealand.

The Baby in the Ear (extract 3 from The Human Antenna.)

For many years, I had been treating people with acute neck and back pain by placing tiny needles in specific tender points their ears. In many, the relief was so rapid after a single needle that it appeared instantaneous. I followed the map charted by the famous French doctor Paul Nogier, who had started to treat thousands of patients with this method in the 1950’s. Remarkably all the information held by the body was being portrayed within the few square centimetres of a human ear.


The points are very specific – and are found by using a small blunt probe over the area of the ear that corresponds to the painful part of the body. The correct point, no bigger than a pin head, is acutely tender. The electrical resistance of the skin is reduced at the precise point, so the acupuncturist may also use an electrical detector as a guide.

Such was the simplicity and safety of this procedure that I had been using it every day in my practice. Not only was the method relieving a lot of suffering, it was also cutting thousands of dollars off the country’s annual drug bill. I was curious to research the science behind such a strange and wonderful healing technique, but for several years any logical explanation alluded me.

Then one Saturday, I attended an exhibition of holographic images in Auckland. These weird ghost like 3D images of every day objects fascinated me. Beneath one of the displays – a transparent apple - was a detailed explanation of how a hologram came to be formed. Apparently a laser beam was first split into two, with one half rebounding off the apple and the other deflected by a mirror. The two beams met up again and blended like ripples on a pond. This was recorded onto a special flat photographic plate.

When another laser beam was shone on this plate, a three dimensional matrix of the apple appeared on the other side. Somehow, human beings had discovered how to reduce a three dimensional object into a two dimensional form, only to convert it back again into a three dimensional, but weightless form.

If this wasn’t startling enough, the best was yet to come. A scientist, Dennis Gabor had won a Nobel Prize in 1971 for discovering that if a tiny corner was cut from the plate, and subjected to another laser beam, the image of the whole apple appeared again. And if another small corner was cut from this sample, the same thing happened. And so on and so on.

The penny began to drop. Here at the frontiers of science was a glimmer of an
explanation for my observed effects of ear acupuncture. Here was proof that information conveying three dimensional form of a structure could be stored within the tiniest fragment of that structure. Of course this shouldn’t have seemed so revolutionary –we had known for fifty years that all our genetic information is encoded within microscopic strands of DNA.

And that for centuries Chinese doctors have gained information about the whole body by observing its map on the surface of the tongue, and by gently palpating the character of the arterial pulse at the wrist.

In the Auguries of Innocence, William Blake invites us to:

To see the world in a grain of sand
And heaven in a wild flower
Hold infinity in the palm of your hand
And eternity in an hour.

Somehow one and a half centuries before Dennis Gabor’s remarkable discovery, William Blake had decided we lived in a holographic universe. Within a world of patterns whose origins existed beyond the reach of our five senses.

Printed with the kind permission of Zenith Publishing, New Zealand

The Growth of The Human Antenna


Printed with kind permission of Zenith Publishing, New Zealand.