Chapter 5 The revival of
an ancient science
At the other end of the scientific spectrum of contemporary science an ancient science is being restored. For ages it has been preserved carefully. It is more or less an art form and it is called ‘sacred geometry’. Why sacred, what is so sacred about geometry? In spiritual mystery-schools of the past it was taught that sacred geometry has been used by God to create the universe. We now know that sacred geometry contains many mysterious elements that elegantly describe many phenomena such as the growth of plants, the proportions of the human body, the orbit of the planets, light, the structure of crystals, music. The list goes on and on. We’ll give a few examples in this chapter.
Now why do we introduce sacred geometry in a book that is about contemporary and groundbreaking science? The reason is that sacred geometry seems to be the key to a new post quantum physics that is emerging that better explains the existence of the zero point field. The new physics that is emerging is a revival of 19th century aether physics.
The archaic science of sacred geometry can be traced back to the Egyptian civilization but may well be a heritage from the civilisation of mythological Atlantis and we’ll provide sufficient clues in this book to sustain this claim. Sacred geometry contains elements that are crucial in understanding a new aether physics that will be introduced in the next chapter.
Surprisingly enough sacred geometry also shows up in many crop circles that have been appearing in the last two decades all over the world. It seems that someone somewhere is teaching us meaningful lessons. I will not go into detail about the source of crop circles whether or not they are extraterrestrial; I personally think it they are, because this cannot (yet) be proven.
What is far more interesting is that crop circles contain intelligent embedded geometry. The fact is that hundreds, thousands of crop circles appear each year and that their design is of a much higher intelligence than that of people who may have found it interesting enough to create hoaxes! There is abundant evidence that apart from the crop circles that were indeed identified as hoaxes; the majority of crop circles are genuine. It was proven that the stems of the crops are bent in a peculiar way by an excessive heat produced by a hitherto unknown energy source since no burning marks were found. Strong energy fields can be measured hours after the crop circles are formed in and around the crop circle.
In my opinion the significance of crop circles is that contemporary scientists are getting hints to seek for more understanding of geometry in physics in general and in the zero point field in particular.
In the ancient teachings of sacred geometry it is believed that the sacredness of everything in the universe can be described in terms of geometrical patterns coming from the hand of God. As unbelievable as that may seem, it can be illustrated with ample examples that indeed many unexpected things have a hidden geometry that is not obvious at first sight.
It is now believed that the Egyptians applied sacred geometry in the construction of the Great Pyramid and many other monuments. The Egyptians had two mystery-schools; one was called the left eye of Horus. This school taught the female principles of creation, about love and compassion. The other school was called the right eye of Horus and taught the intelligent male principles of creation; sacred geometry was a main subject.
Sacred geometry has also left its traces in other cultures such as in the gothic architecture of European churches and cathedrals (Chartres), the Parthenon in Athens, paintings by Leonardo Da Vinci and the Hindu classical dance. Sacred geometry has been preserved in circles of Freemasonry in utmost secrecy.
The Freemasonry symbol is a carpenter’s square and a pair of compasses, the two only instruments needed in sacred geometry. The golden rule is that if you have to use any other instrument than these two to prove something applies to sacred geometry, it may be geometry but it is definitely not sacred!
Thanks to people like Robert Lawlor, Bruce Rawles and Drunvalo Melchizedek, the art of sacred geometry is now being restored and thanks to the enormous success of the book the ‘Da Vinci Code’ by Dan Brown that became very popular in the year 2004, the awareness that seemingly important knowledge has been secretly preserved throughout history is now within the public domain.
Now let’s take a quick course in this sacred art form and I’ll show you some amazing things in the end.
Flower of life
Now this is a very important figure in sacred geometry:
It is called the genesis pattern. We must remember that what we see here is a two dimensional representation of what are actually three-dimensional spheres! Depicted in the picture you also see the hexagram formed by the two equilateral triangles, it’s the Jewish symbol known as the star of David. The star of David in this picture is actually a three-dimensional star tetrahedron or interlaced tetrahedron. It is formed by two interlaced three-sided pyramids, one pointing upwards and one pointing downwards. If you’re looking for an example of a star tetrahedron, have a look at the cover of this book.
Now the next creation story was taught in the right eye of Horus mystery schools and is also the basis of the Hermetic tradition (the wisdom of Hermes Trismegistus alias the Egyptian Toth). This creation story was most likely also familiar in Freemasonry circles.
In the beginning the universal mind of God created from a total void or nothingness from the focal point of God’s awareness a single central sphere. The first sphere was all around God on the first day of creation. The next day God created another sphere, the center of this sphere is located on the surface anywhere of the first sphere. The intersection of the two spheres is called the Vesica Pisces:
Symbol of Christianity
Did you ever see the symbol on the right? You see them often as a bumper sticker on cars; the symbol is probably derived from the Vesica Pisces.
The Holy Bible mentions that God created the light on the second day, the Vesica Pisces as we will explain at the end of this chapter is now believed to be the geometry of the photon- the particle state of light!
God’s creation continued for 7 days, each time the center of a next sphere is projected on the surface of the previous sphere. Now count the number of spheres in the Genesis pattern, they add up to 7, exactly the number of days it took God to create the world as mentioned in the first book of the Bible, Genesis. This is why it is called the Genesis pattern.
If we continue God’s creation in the very same way but just a little longer than 7 days, we get the following figure:
The flower of life
This figure is called the Flower of Life, note the double outer circles that were added here, this figure is found all over the world, decorated on ancient buildings and sacred monuments. It has been found in temples in Egypt. No symbols were found that continued the creation process beyond the Flower of Life pattern, that’s why the outer circles were added. Somehow in ancient times, the ancients wanted to limit this creation pattern to the Flower of Life, maybe they wanted to hide something?
So let’s joyfully continue this creation pattern and look for what is hidden in these patterns that was discovered by Drunvalo Melchizedek.
Let’s add the just the next outer round of spheres. What we now find is called the Fruit of Life, I marked the significant spheres that make up the Fruit of Life red to distinguish the pattern, remember that what we see is actually a three-dimensional picture of spheres:
Crop circle Wiltshire, 22nd July 2003
Now the Fruit of Life is called a female form because it only contains rounded forms, spheres, just like a female body that is curved. The male counterpart can be constructed if straight lines are used to connect all the centres of all the spheres in this picture. The result is called the Cube of Metatron.
Cube of Metatron
The Cube of Metatron is very important since it contains the solid geometrical forms that have become the focus of a new aether physics that we will describe in the next chapter!
Philosopher Plato described these forms that we find in the Cube of Metatron 400 years BC, hence they are called the Platonic solids.
In fact the Platonic solids can be found in the Metatron twice, the smaller versions of the solids are repeated in the inner 7 spheres. One of the five Platonic solids is the well-known cube. If you will, you can try and find the cube in the Cube of Metatron. I will help you a little bit with this one, here it is:
Cube in the Cube of Metatron
The green spheres are the corners of the cube. One corner in the back is hidden from view though.
The five Platonic solids are named after Greek philosopher Plato who first described them 350 years BC in his book Timaeus. Here they are:
Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron.
Crop circle, West Overton, 24th
June 1999 octahedron projected in 2D layout.
All of these five forms are in the Cube of Metatron, it may take a little while to discover them but they are all in there. The Platonic solids have very remarkable characteristics, for one they all fit perfectly within a sphere. The vertices of the solid are on the surface of the circumscribing sphere! Also they perfectly fit inside each other and can be perfectly nested. All forms have a double, an opposite form that can be created from the other. The cube and the octahedron are doubles for instance. If we take the centers of the faces of the cube and connect all the lines between these centers we get the octahedron. The same process can be reversed creating a cube from an octahedron. The tetrahedron has itself as the double. The dodecahedron and icosahedron are doubles. Every line, face and angle in a Platonic form is identical to every other line, face and angle within the same form. In other words the Platonic solids are extremely symmetrical!
Another puzzling symbol that is derived from the progression of the Flower of Life is the Tree of Life. The Tree of life is central subject of study in the mystical Jewish Kabbalah. The Tree of Life can be overlaid with the Flower of Life and they will perfectly match. The Tree of Life is an extraction from the Flower of Life, leaving out a number of spheres of no interest.
Tree of Life
pattern Jewish Kabbalah
Jewish Kabbalah, Tree of
In the next picture we show that the Tree of Life also perfectly overlays with the Genesis pattern. Do you start to grasp the geometrical beauty of symmetry that is involved in all these symbols and how all of them evolve from a simple progression of the Genesis pattern?
In the next picture we show that the Tree of Life also perfectly overlays with the Genesis pattern. Do you start to grasp the geometrical beauty of symmetry that is involved in all these symbols and how all of them evolve from a simple progression of the Genesis pattern?
Tree of Life overlaid by the Genesis
The Tree of Life is the mystical symbol used in the Jewish esoteric Kabbalah. The Tree of Life is mentioned many times in the Bible as the tree next to the Tree of Knowledge of Good and Evil in the center of the Garden of Eden. Ancient traditions thought that these geometrical patterns were very important and preserved them in mystical esoteric sciences..
The torus is also a very important geometrical three-dimensional form and we’ll bring it up here because it is the building block of matter in the new aether science of the next chapter. It is best compared with a doughnut or the smoke ring from a cigar. Here’s it is:
It is a sphere, curving inwards on top and bottom, such that it has a hole in the middle! It also resembles an apple. The torus is the result of rotating the Genesis pattern 360 degrees around the center.
Maybe the most important subject of sacred geometry is the Golden Mean. The Golden Mean is a very special ratio and is expressed by the Greek letter Ф called Phi.
= ½ * v5 + ½
Phi like Pi is an irrational number, meaning you can never calculate its exact value, you can only approximate it.
The Phi ratio is expressed in the Golden Section. The Golden Section is a the length of let’s say a rope when it is divided such that the ratio of the longer part of the rope to the whole is exactly the same ratio as the shorter part of the rope is to the longer part. (Read it again)
When the Phi ratio is applied to a rectangle whereas B = 1 and A has length Ø, the rectangle is called a Golden Rectangle.
The Golden Rectangle can be used to create a spiral, the Golden Spiral. Starting with one Golden Rectangle, a second Golden Rectangle can be attached to the first using the longest side of the rectangle, side A as the shortest side B of the next rectangle. To this end the second rectangle is constructed 90 degrees perpendicular to the first rectangle. If this process is continued, called the spiralling of the Golden Rectangle, a curved line can be drawn through the corners of the rectangles creating the Golden Mean spiral. The spiralling of the Golden Mean spiral continues indefinitely in inward and outward directions, it’s getting smaller and smaller spiralling inwards and getting bigger and bigger spiralling outwards.
Golden Mean spiral
A variant of the Golden Mean spiral is the Fibonacci spiral. The difference with the Golden Mean spiral is that is does not spiral in indefinitely but starts with a Golden Rectangle of which one side has length 1 and the other length Phi.
Gradually when the Fibonacci spiral, spirals outward, there will be no distinction noticeable any more between a true Golden Mean spiral and the Fibonacci spiral.
The Fibonacci spiral is based on the progression of the Fibonacci sequence.
Crop circle, fractal spirals, Milk
Hill, Wiltshire august 12th 2001
Leonardo Fibonacci (1175 AD), a great mathematician of the Middle Ages discovered the Fibonacci sequence by studying nature. He studied the growth of rabbit populations and the growth of leaves and petals and discovered a well-defined mathematical sequence in all of this.
This is the Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc.
Each number in the sequence is the sum of the two preceding numbers starting with the root number 1. The Fibonacci sequence progresses towards the Golden Mean if we divide two successive numbers in the sequence.
1/1 = 1
2/1 = 2.0
3/2 = 1.5
5/3 = 1.667
8/5 = 1.60
144/89 = 1.618
The Fibonacci sequence propagates towards Phi (Ø) but never reaches it since it is an irrational or transcendent number.
Fibonacci spirals and Golden Mean ratios appear everywhere in the universe. The spiral is the natural flow form of water when it is going down the drain. It is also the natural flow form of air in tornados and hurricanes. Here’s another beautiful example of a Fibonacci spiral in nature, it’s the Nautilus shell and every book about sacred geometry contains one:
The Golden Mean ratio is all over the human body, in the ratios between the bones, the length of your arms and legs. The Golden Mean is also the ratio in the distance from the navel to your toe and the distance from your navel to the top of your head. Michelangelo has beautifully hidden these Golden Mean ratios in his fresco on the ceiling of the Sistine Chapel in Rome:
Michelangelo and the Phi ratios in the human hand
(Courtesy of Frank van den Bovenkamp, www.frankvandenbovenkamp.com)
Greek philosopher Pythagoras discovered a wonderful mathematical relation between the harmonic notes in music. He noticed that by depressing a string in different positions on the fingerboard of a guitar like string instrument that harmonic sounds were created. Some notes sounded better than others. At each depression of the string the string is divided in two different lengths and the ratio between these lengths were measured by Pythagoras. He marked down all the ratios that sounded harmonically well together. In this way he found the following ratios:
1:1 (open snare)
1:2 (depressed at 1/3 of the length of the string)
3:2 , 5:3, 13:8, 21:13, 34:21
What Pythagoras had discovered is called the Diatonic musical scale, named after the fact that the string is divided into two lengths (Dia = two).
These ratios correspond with the frequencies of the notes produced by the white keys of the piano when attuned in the Diatonic scale. After the 7th note the octave of 8 notes is repeated only this time the first and the eighth note are doubled in frequency! The next 7 notes of the white keys on the piano follow the exact same ratio!
Now if you have been paying attention you may already have noticed that the musical ratios discovered by Pythagoras are the same ratios of the Fibonacci sequence! Simply take a number out of the Fibonacci sequence and its successor and you have the musical ratio found by Pythagoras.
The Fibonacci sequence is the sequence that gives us beautiful harmonics in music. The diatonic scale is not the only musical scale, there are many more, in fact no piano today is tuned in the Diatonic scale. But the principle relation between harmonics in music and mathematical progressions of the Fibonacci sequence is real.
Now let’s pretend that we’ve tuned a piano in the Diatonic scale and that we have extended the piano’s keyboard with keys to provide for 49 octaves! That would be one hell of a piano and it would certainly no longer fit into your living room!
But suppose that we could actually play on this piano. When we play the notes in the last two highest octaves, the keys on the furthermost right side of this piano, will correspond with the frequencies of the colours of light!
There are seven keys in the highest octave that are the frequencies of the 7 primary colours of the spectrum of light, the 7 colours of the rainbow!
So not only does the Fibonacci sequence define the ratios of harmonics in sound but also in the electromagnetic spectrum of light, it defines the 7 colours of the rainbow!
Music and color, the same harmonic
We now know that many musicians like Beethoven, Mozart, Chopin, Bartók, Schubert and Debussy used the Fibonacci sequence and the Golden Mean ratio deliberately not in the notes but in the composition itself. For instance Beethoven used the Golden Mean in his famous Beethoven’s Fifth. His famous opening motto not only appears on the first and the last bar of the symphony but also on the bar that represents the exact Golden Mean point of his symphony! Bela Bartók used both the Golden Mean and the Fibonacci sequence deliberately in his compositions using the measures 5, 8, 13, 21, 34, 55 and 89 to introduce new instruments such as strings, cellos, percussion etc. The question is why did these composers add sacred geometry into their music? Maybe they were not only famous musicians but also Freemasons?
Squaring the circle
A classical mathematical problem dating all the way back to Plato is called ‘squaring the circle’. In the last three thousand years mathematicians have tried to come up with a solution using only a pair of compasses and straightedge on how the construct a circle and square such that they have the same perimeter. In 1882 Lindemann proved that there is no solution to this problem. Since Lindemann’s proof is rather complex, we will show in simple terms why the circle cannot be squared. The circumference of the circle with a radius of one is 2 * π and π (Pi) is an irrational number (a transcendent number, π can never be measured only be approximated!). But when Pi is irrational and cannot be measured so is the circumference of the circle! However the square’s circumference is a real number since it equals 4 times the side of the square that is a real number that can be measured. Hence the circumference of both circle and square will never be equal in the mathematical sense; however they can become infinitely close.
Now here’s an interesting drawing from Leonardo Da Vinci. What he is showing in this sketch is that the human body ‘squares the circle’. When man stretches his arms and holds them horizontally, man’s body will perfectly fit into the square. On the other hand, when he spreads his legs and raises his arms as in the sketch, man’s body can be perfectly circumscribed by a circle. The circumference of the square ‘equals’ that of the circle.
A lot has been written about this sketch alone, it contains a whole lot of hidden sacred geometry. We will not go into all the details here, but I want to show you some very amazing things. Ancient wisdom, the Hermetic tradition tells us that the human body can be regarded as a blueprint for the universe by means of all the ratios that are found within the body. This may indeed be true. Let’s have a look at the following picture:
This is the same picture as above, in the picture there are now two red circles added. The biggest red circle fits perfectly and is inscribed by the square. The smaller red circle’s is centered between the outer circle and the inner red circle and tangentially touches both.
Much to our surprise, the upper red circle represents the moon and the lower red circle represents the Earth! In mathematical terms: The ratio of the diameter of the smaller red circle to the bigger red circle r / R equals the ratio of the diameter of the moon to the diameter of the Earth! Now let’s prove it:
Radius of the moon : r
Radius of the Earth : R
Side of the square is : 2R
The perimeter of the square is : 8 R
Radius of the outer circle is : r + R
The circumference of the outer circle is : 2 p ( r + R )
Now ‘squaring the circle’ makes the perimeter of the square equal to the circle:
8 R = 2 p ( r + R )
8 R - 2 p R = 2 p r
R (8 – 2 p) = 2 p r
r / R = (8 – 2 p) / 2 p = (4 – p) /
Earth radius = 6,370,973 m
Moon radius = 1,738,000 m
Moon to Earth ratio = r / R = 0.27279977
r / R = (4 – p) / p = 0.273239544 (p = 3.14159265)
Quod Erat Demonstrandum!
There is another mysterious relation to be discovered in the sketch of the Vitruvian man by Leonardo Da Vinci. The Great Pyramid at the Giza plateau in Egypt called after the pharaoh that is supposedly buried there named Khufu (Cheops in Greek), holds a perfect geometrical relation to the squaring of the circle and the Vitruvian man as depicted by Leonardo Da Vinci!
Look at the picture below:
Great Piramid at Giza in relation
to Vitruvius man
The triangle in the picture is the exact geometrical proportion of the Great Pyramid at the Giza Plateau near Cairo, Egypt. The angles between the base and the apex (top) of the pyramid are exactly 51 degrees and 51 seconds. (51º 51’).
The Great Pyramid and in fact the complete layout of the Giza plateau with all its pyramids, sacred temples and the sphinx contains a lot of hidden sacred geometry of which we will reveal more in this book. The point I want to make here is that the Egyptians were aware of the art of sacred geometry and how it relates to the universe, as the Giza plateau and in particular the Great Pyramid proves.
Let there be light
While explaining the Genesis pattern of sacred geometry we mentioned that on the second day of creation God created the Vesica Pisces and that the Vesica Pisces is the geometry of the light particle the photon. The Holy Bible mentions the second day of creation as the creation of the light. By the way did you notice that the Vesica Pisces has the shape of the eye?
It was discovered by Buckminster Fuller, who did a lot of the groundwork in re-establishing sacred geometry, that the geometry of the photon must be two tetrahedrons joined at a common face.
Now the geometrical shape of the double tetrahedron is perfectly circumscribed by the Vesica Pisces whereas the vertices of the tetrahedrons neatly touch the face of the Vesica Pisces. This has been confirmed by Drunvalo Melchizedek another sacred geometry architect!
The tetrahedron is also the hidden geometry in the electromagnetic wave (wave form of light) itself. The electrical and magnetic fields are perpendicular to each other and a spiral can be drawn connecting the electrical field with the magnetic field that exactly traces over a tetrahedron!
Tom Bearden, the inventor of the MEG machine has proof that James Clerk Maxwell must have known this but that Oliver Heaviside removed the knowledge of the hidden tetrahedron in the simplified version of electrodynamics.
Notre-Dame de Chartres
The knowledge of sacred geometry has been preserved in the architecture of churches and cathedrals all over Europe. The cathedral of Chartres is famous for its sacred geometry that was used in its design. Sacred geometry can be found for example in the layout of the ground plan and the stained glass windows that contain the Phi ratio.
West rose window of the Chartres Cathedral and ground plan
In the Gothic nave of the cathedral we find an enigmatic labyrinth on the floor made out of white stone and set within dark marble. The labyrinth measures almost exactly one tenth of the interior length of the cathedral and it is used as the central point, the focus of the whole geometric construction of the cathedral. Obviously the designers thought it to be very important
The diameter of the labyrinth measures exactly the size of the west rose window shown in the picture above. At the same time the distance from the center of the west rose window to the floor is the same distance as the distance from the center of the labyrinth to the west portal wall of the cathedral. In other words the west rose window and the labyrinth form a perfect equilateral triangle.
Labyrinth on ground floor of the
I personally visited the Chartres Cathedral a few times. During my last visit, in the summer of 2004, I noticed a young couple, a boy and a girl. The girl kneeled down at the center of the labyrinth and went into a meditation, hands held high into the air. The boy sat beside her. The couple were totally undisturbed by the crowd that passed by although they drew a lot of attention! I was intrigued. Obviously the couple knew something more about the sacredness of the labyrinth and they had chosen this spot for their meditation. But what could it possibly mean?
If we meander through the labyrinth we have to make these alternating left and right turns. At the same time we turn inwards and outwards until we enter the center. According to Daniel Winter, whose physics we will study in the next chapter, the labyrinth is the two dimensional symbolic projection of the Phi spirals that make up a torus. The torus is assumed in his aether physics to be the building block of matter and the atom. The labyrinth according to Winter is a symbolic projection of the twists and turns the Phi spirals of light take while centring into the nucleus of the atom.
The Chartres cathedral secretly contains knowledge of sacred geometry; however it took many ages before it was discovered. Sacred geometry was used in many more cathedrals and churches throughout France such as the ones of Rheims, Sens, Arras, Amiens, St Quentin, Bayeux and Toulouse to name a few. All of them contained labyrinths quiet similar to the one in Chartres. The labyrinth obviously was very important.
France was the home of the Merovingian Kings a bloodline that were believed to be the descendants of Jesus Christ. Many authors now claim that Jesus had children with Mary Magdalene and that the Catholic Church kept this fact secret for many ages. The idea has gained a lot of public awareness since the book the ‘Da Vinci Code’ by Dan Brown was released in the summer of 2004. The descendants of Jesus are the bloodline of the Holy Grail. Traces of this bloodline lead to Rennes Les Chateaux in France and Roswell Chapel in Britain, the homeland of the Knights Templar and King Arthur. This secret of Jesus’s his marriage to Mary Magdalene and of his offspring was carefully preserved in secret societies.
It is now believed that these secret societies also preserved scientific and Gnostic knowledge that can be traced back to the mythological Atlantis. The Atlantean knowledge was supposedly passed on to the Egyptians and from the Egyptians to the Greek Hermetic tradition. In modern times it was preserved in secret circles of Freemasonry that have existed throughout the ages. Leonardo Da Vinci was a member of such a circle that gave him access to the science of sacred geometry and his membership explains why he used it in his paintings. The importance of sacred geometry especially the meaning of the Golden Mean has been used in many art forms in modern history, from the paintings of Leonardo Da Vinci to the architecture of churches and cathedrals and in music such as Beethoven’s Fifth symphony.
This chapter was a lecture in sacred geometry. I would not have introduced it in this book if it didn’t play such a significant role in a new physics that is unfolding. Science is discovering the geometrical and fractal patterns described by sacred geometry in our physical universe, the gravitational and electromagnetic energy fields of the Earth, the structure of the atom and the energy fields of the human body.
In chapter 3 we showed that the separation once suggested by René Descartes that there is a strict segregation between the physical and the mental dimensions is false. The human mind is very powerful and has powers of mind over matter. Quantum physicist Amit Goswami suggested that consciousness is primordial and that the physical realm is created from it.
In chapter 4 we discussed the zero point field that was discovered by quantum science. The zero point field is an unlimited inexhaustible energy field that is present everywhere in the universe. We suggested that the zero point energy might be the spiritual energy required to sustain Amit Goswami’s claim.
In this chapter we studied sacred geometry an ancient science that is being rediscovered by contemporary scientists.
In the next chapter we will use sacred geometry, the zero point field and our understanding of consciousness and show how scientists today assimilate it into a new model of physics, a theory of everything that explains both the physical and the mental domain. We will also see that contemporary science is rediscovering what Plato 2350 years ago suggested: that the world of the atom is constructed from the Platonic solids and discover the importance of the Golden Mean in waveforms.