“Principles for the Development of a Complete Mind: Study the science of art. Study the art of science. Develop your senses – especially learn how to see. Realise that everything connects to everything else.” – Leonardo da Vinci
Everything in the Universe follows a blueprint or pattern. Aspects of our natural world, which may seem obscure and different from one another, are often shown to share common and basic patterns, e.g. clouds, flowers, crystals and even human DNA. But it is not just in our visible world that these patterns apply. There are many congruities between the patterns of nature, art, music and healing. Generally speaking, what we perceive to be beautiful and pleasing to the senses is so because of this patterning, e.g. the ratio of features on the human face and body, the leaves on a plant, and the rhythms and timings of a piece of classical music. This is the architecture of the Universe. Often something that we perceive to be random and yet beautiful is following an extremely complex set of fundamental rules that, from the smallest molecule to the largest planet, shape the reality we live in.
From the rhythms of our bodily systems to the movement of the celestial bodies there is a pattern that is instinctual and naturally balanced. ?It is commonly said that when we are in balance with the forces of the Universe that we are in a state of flow or abundance, and it is then that we come to the realisation that we are part of the whole, and that it is very much a part of us. Hermitic monks spending weeks in deep contemplation and meditation have often been able to explain what science is now only starting to, as they truly allow themselves to merge with and thereby know the unspoken silent forces of this Divine matrix.
The human brain is very advanced and often we follow our brain ahead of our instinct. Although we are very good at intellectualising how our Universe works, we don’t really fully understand every aspect of it, and so, by not listening to our inner voice or gut instinct we can often find ourselves struggling against this relentless force. This is when we start to experience pain and dis-ease. In order to be fulfilled, a connection with the underlying patterns of the Universe needs to be re-established and fortified within our hearts.
According to David Wilcock, in an interview conducted with Project Camelot in May/June 2007, there have been many recorded experiments done on the fruit fly (drosophila) where the DNA of the fly was mutated so that the eyes wouldn’t form. In every case, the eyes came back after five generations. He emphasised that nature can rewrite itself. In the same interview Wilcock goes on to speak about Dr. Francis Crick, one of the co-discoverers of the DNA molecule, who made an observation that the dust in the galaxy, if one were to look at it from where we are to the centre of the galaxy in a straight line, has all the spectrographic signatures and all the light waves that you would expect to see from living bacteria. Wilcock concludes at this part of the interview that life is the field and that this field is the energy that surrounds us and underlies matter. – Project Camelot interviews David Wilcock – Part 2 of 4, ?http://www.youtube.com/watch?v=0Bz9YPriDLo&feature=related
There are many different types of geometry that make up the world around us including sacred geometry, the three-dimensional platonic solids, the hyperbolic geometry of sea slugs and coral, fractal geometry, geometry in art and symbolism (phi/the golden ratio/the Fibonacci sequence), the geometry of sound and music, and the geometry of crystals.
What I love about this particular field of study is that it appeals to both the left and right side of the brain and that it can be viewed as science or art.
To say that everything in this life and reality is based on math may seem dull to some, but to me I feel it is a majestic and exciting prospect. It doesn’t make something less beautiful or fascinating if you know its origins, sometimes it can make something even more magnificent.
The Platonic Solids
The Greek philosopher Pythagoras was one of the first known to discover congruities and mathematical symmetries between art, music and nature. On further investigation he discovered three of the main shapes in matter: the tetrahedron, the hexahedron and the dodecahedron. What these three dimensional shapes have in common is that they are all made up of equilateral, equiangular polygons, which means that all the faces of these objects had the same number of bounding lines of equal length and of equal angles. It was years later that a student of Plato, named Theaetetus discovered two additional shapes: the octahedron and the icosahedron. These five shapes are collectively known as “the Platonic Solids” and it is understood that they are the basic structures of matter and form.
These perfect shapes are even visible in nature from the dodecahedrons of garnet and human DNA (see excerpt below) to hexahedrons of pyrite. When viruses are examined under a microscope their structures also mirror the shapes of the platonic solids. It is now widely believed that the very Universe we live in is shaped like a dodecahedron.
The standard model of cosmology predicts that the universe is infinite and flat. However, cosmologists in France and the US are now suggesting that space could be finite and shaped like a dodecahedron instead. They claim that a universe with the same shape as the twelve-sided polygon can explain measurements of the cosmic microwave background – the radiation left over from the big bang – that spaces with more mundane shapes cannot - (J-P Luminet et al. 2003 Nature 425 593 ) ?http://current.com/14b2u4c
The interesting thing is that the dodecahedron at all levels in all sizes can be found. When you dodecahedron consecutive stack, partly in each other, you can along the ribs spiral two lines drawn, called a double helix, which is exactly the geometric shape and proportions of the spiral staircase-shaped DNA molecule - Taken from article – DNA, Form Fields, Biometric and Resonance ?http://unhypnotize.com/health/1517-dna-form-fields-biometric-resonance.html
The platonic solids are also implied through sacred geometry and are especially highlighted in the concept known as ‘Metatron’s Cube’, which encompasses and unifies all five of the platonic solids. (More information on sacred geometry below.)
Since 1980 a science known as fractal geometry has been made known. A mathematical set known as The Mandelbrot Set gave scientists and mathematicians a function, which could explain the complexities of the formation of clouds, mountains, coastlines and other such seemingly random natural phenomena. It is a pattern, which is infinitely small and infinitely large at the same time, a pattern, which repeats itself and is self-organising, creating the same shape over and over again but to a larger or smaller scale. The pattern is so regular and repeating that scientists have been able to generate very real imagery of mountains and coastlines using only the maths of the Mandelbrot Set. Having studied the patterns the scientists were also able to discern the congruities between the Mandelbrot Set and mandalas, which are based on Sacred Geometry.
Although the concept of fractal geometry could only be explained in the 1980’s thanks to the development of computers, it appears to have been something that was in the collective unconscious for a very long time. A mathematician named Ron Eglash stumbled upon the fractal patterns in the layout of indigenous African villages and buildings relatively recently which led him to travel there to investigate further. When he pressed the people for an algorithm, which helped them to build in such a way and paint images that were of a fractal nature they merely told him that it felt right. It is as if the knowledge of fractals is innate to our very being. We now know that even our lungs are fractal. If you take a look at where your thumb meets the palm of your hand, in the wrinkles you see there a repeating pattern will become apparent. This is another example of fractal geometry. Fractal Geometry makes up the very clouds in the sky to the leaves on a plant and a corresponding mathematical function can be written to generate them.
The image below is the layout of a village in Africa and it is apparent how it resembles the Mandelbrot Set itself.
- picture taken from presentation by Ron Eglash http://www.ted.com/talks/ron_eglash_on_african_fractals.html
The way gas moves, the way cancer and the aids virus develop, the way our bones fracture and the way our hearts beat are all based on fractal geometry and can be mapped out using mathematical functions.
Sacred Geometry is known as ‘nature’s first pattern’. It is based on a pattern of interlocking circles of equal radius. The first pattern in sacred geometry is formed with two interlocking circles and creates the ‘Vesica Piscis’. This shape is very symbolic and mirrors exponentially in the sacred geometric patterns that follow. The Vesica Piscis is shaped like the human eye and some people correlate it to the all-seeing eye of Horus. The Vesica Piscis can be literally seen in many areas of our visible reality, the human eye for example, the petal of a flower and even some star nebulae e.g. the hourglass nebula.
- picture taken from http://www.jpl.nasa.gov/releases/2003/154.cfm
Another well-known shape that derives from this concept of interlocking circles is “The Tripod of Life” (a.k.a. Borromean Rings). It is formed when a third circle is added to the Vesica Piscis. This is a symbol which can be seen engraved in many sacred places and can represent: mind, body and spirit; The Holy Trinity – father, son, and holy spirit or The Triple Goddess – crone, mother and maiden. It is a pattern often seen in Celtic art and it is where the Wiccan Triple Moon symbol has its origins.
As the sacred geometry pattern expands and reiterates it forms concentric circles (other examples of concentric circles in nature include, the rings of a tree, the rings around Saturn, the orbits of the planets, and the waves that are created when a stone is dropped into a still pond). At each concentric circle in the pattern of sacred geometry a new formation occurs which holds deep spiritual meaning and also encompasses the patterns and meanings of the preceding patterns. Based on this theory, the next formation that stems from the Vesica Piscis in the pattern of sacred geometry is known as “The Germ of Life”.
“The Germ of Life” encompasses the six-pointed star, the hexagon, the Star of David, and even the peace sign.
The star of David which to the untrained eye is simply two interconnected triangles is actually a two dimensional image of a 3 dimensional principle, the Star of David is actually 2 inter-penetrated Tetrahedra, tetrahedra being the 1st in a set of the five platonic solids, this property has recently been found to occupy the centers of planets, contributing to the overall gravitational balance of the planet, it is hyper-dimensional phenomena, which has yet to be fully explained. But the 2 Tetrahedra depicted in the star of David are actually spinning in a counter rotating motion, one spinning clockwise the other spinning counter clockwise which I believe is emblematic of the centripetal relationship between the male and the female, you can see this phenomena depicted in the mysterious universal symbol of the yin and yang as well as in the swastika which is also emblematic of the centripetal rotation of solar systems. We now embark on a brief journey into sacred geometry where conventional rules don’t apply; you can find hyper-dimensional geometry in nature, in flowers, shells and more – Comment left on ?http://current.com/items/89329592_is-the-universe-a-dodecahedron.htm
“The Seed of Life” (the second concentric circle in the pattern) encompasses the Yin-Yang symbol, the Kabbalah tree of life. This tree of life is also mirrored in the grid lines layout that we use in crystal healing, incorporating the active line, initiation line, power line, and integration/manifestation line.
“The Flower of Life “(third concentric circle)
“The Fruit of Life” (fourth concentric circle) – encompasses the Tetractys (which is a triangle pattern that consists of ten points arranged in four rows). The Tetractys is a very important and worshipped symbol of the Pythagoreans. It is also said to correlate to the Kabbalistic Tree of Life. The Tetractys pattern is also apparent in tarot card layouts.
Although the ‘Fruit of Life’ pattern itself is two-dimensional it indicates and hints at the three-dimensional platonic solids. This sacred pattern along with the apparent three-dimensional representations of the platonic solids is known as Metatron’s Cube.
On viewing them it becomes apparent that these patterns are the ones used in many religious and spiritual mandalas which people meditate upon to gain greater insight, awareness and understanding into life. There have also been many incidences of crop circles around the world that mirror these patterns. It is believed to be a communication of some sort. Glyphs, again mirroring these patterns, have been found around the world in between layers of ice in frozen lakes and rivers, sand dunes, and engraved in ancient architecture and people have no explanation as to how they were created. The sacred geometry pattern is infinite in size in that it can be repeated both microcosmically and macrocosmically which is reminiscent of the root principles of creation itself.
Geometry in Art
The patterns created in sacred geometry are very aesthetically pleasing and can be interpreted into many different shapes and patterns by omitting certain parts of the pattern. There are infinite possibilities. One artist who has been painting sacred geometry for many years is Charles Gilchrist and his work is amazingly intricate. His reasons for creating such masterpieces, is that he feels it brings him closer to God. For him it is transcendental. Below is an example of his work:
– picture taken from http://www.charlesgilchrist.com/SGEO/Gal1201.html
In art and nature, there is a number known as ‘The Golden Ratio’ or Phi and it relates closely to the Fibonacci sequence. The Fibonacci sequence is a series of numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… It starts with the number 1 and then you take the next number and add that the number preceding it which is: 1+1=2 and then 2+1=3 and so on and so forth. It is the Fibonacci Sequence which is responsible for the ‘Spira Mirabilis’ (“the marvelous spiral”) which is a logarithmic spiral curve often found in nature from spiral galaxies to deep-sea creatures, from flowers to the human fingerprint, to the most common example, which is the nautilus shell. See picture below:
- picture taken from the website http://www.environmentalgraffiti.com/featured/fibonacci-sequence-illustrated-nature/10867
Most of the interesting things we find that relate to the Fibonacci sequence are actually more closely related to a number that is derived from Fibonacci, called the golden ratio. If we take each number of the Fibonacci sequence and divide it by the previous number in the sequence (i.e. 2/1, 3/2, 5/3, 8/5), a pattern quickly emerges. As the numbers increase, the quotient approaches the golden ratio, which is approximately 1.6180339887. Approximately. The golden ratio actually predates Fibonacci and has been breaking the brains of western intellectuals for around 2400 years. Applications for the golden ratio have been found in architecture, economics, music, aesthetics, and, of course, nature - Taken from article – Fibonacci Sequence Illustrated by Nature ?http://www.environmentalgraffiti.com/featured/fibonacci-sequence-illustrated-nature/10867
In art, many architects, especially in ancient times, have based their structures on this Fibonacci sequence such as the Parthenon and the Acropolis in Athens.
And in building the phi proportions, along with those of the other musical intervals, into the designs of cathedrals and temples, the architects also are building in the effects of the musical intervals upon which the sacred proportions are based. These effects, immediately experienced as harmonious, powerful, and centering, can be experienced first-hand when one enters a Gothic cathedral or an ancient Egyptian temple. Being inside such a space helps us to access other dimensions of consciousness. It is the same experience that is reached through listening to sacred music - Taken from article – Sacred Geometry and the Structure of Music? http://www.spiritofmaat.com/archive/jan4/williams.htm
More famously the Fibonacci sequence was incorporated into Leonardo Da Vinci’s Vitruvian man.
- picture taken from the website http://www.tendobenches.com/engelska/stretching-anatomy/
The human body is divisible in many ways by this golden ratio (a.k.a. Phi) in the way that the phalanges of the fingers are divided and compared with the hand itself and then the arm itself and so on and so forth. The Fibonacci series can even be seen in human DNA.
Geometry in Sound & Music
Through the ages, the sound of music in myriad incarnations has captivated human beings and made them sing along, and as scholars have suspected for centuries, the mysterious force that shapes the melodies that catch the ear and lead the voice is none other than maths… ?… Geometrical music theory represents a culminating moment in the longstanding marriage of music and maths. That marriage began when Pythagoras described pleasing musical intervals with simple mathematical ratios more than 2 600 years ago and further evolved during the Middle Ages when deep thinkers used those same ratios to model the “music of the spheres” – what many at that time believed to be the literally harmonious movements of the Sun, Moon and planets – Taken from article – Geometry Shapes Sound of Music? http://unicomm.fsu.edu/pages/releases/2008_04/18_geometrical_music_theory.html
I don’t think it’s any surprise to know that there are maths in music. The repeating sounds and patterns within the rhythms are apparent. Harmonies and octaves in music are all based on a number known as “the perfect fifth” which is the space between a note and the note seven semitones above it on the musical scale. Also, I’m sure you’ll agree that music can take you to many places mentally, emotionally and spiritually. Some songs are naturally soothing and relaxing, some (like heavy metal music) can help with the expression of anger and frustration, some can make you feel uplifted and others can stir memories which again can bring about a plethora of emotion in an individual.
Many cultures across the globe have their own tribal sounds and rhythms, from the tribal drumming in Africa, to traditional Irish music to the panpipes of South America, the sounds of silk and bamboo in China, Gregorian chanting, and the sounds of the didgeridoo used by the aborigines. These sounds are sacred to many and they are used in ceremonies to help connect with spirit and create greater self-awareness and insight.
Julian Treasure on TED
- The 4 ways sound affects us Open in new window
Natural sounds and music are often included in meditation tapes. These include rain, the ocean tides, a gentle wind, ambient forest noises and whale song. I lately came across some imagery that was derived through an application designed to convert sound to image using a process known as ‘cymatics’. The sound in question was whale and dolphin music. The images are amazing. The resemblance to the sacred geometry patterns is uncanny.
- picture taken from the website http://www.telegraph.co.uk/science/picture-galleries/6644756/Whale-song-art-dolphin-calls-turned-into-kaleidoscopic-patterns-using-wavelets.html
Legend recounts how Orpheus was given a lyre by Apollo. By playing his lyre, Orpheus produced harmonies that joined all of Nature together in peace and joy.?Inspired by this Orphic tradition of music and science, Pythagoras of Samos conducted perhaps the world’s first physics experiment. By plucking strings of different lengths, Pythagoras discovered that sound vibrations naturally occurred in a sequence of whole tones or notes that repeat in a pattern of seven.?Like the seven naturally occurring colors of the rainbow, the octave of seven tones — indeed, all of Creation — is a singing matrix of frequencies that can be experienced as color, sound, matter, and states of consciousness - Taken from article – Sacred Geometry and the Structure of Music ?http://www.spiritofmaat.com/archive/jan4/williams.htm
The Geometry of Crystals
The inner geometry of crystals is structured and uniform. It is because of this beautiful symmetry that crystals are so well able to reflect, hold and refract light. There are seven main geometric shapes or systems that crystal structures adhere to. These are namely, cubic, tetragonal, orthorhombic, monoclinic, triclinic, trigonal, and hexagonal.
Water itself is not considered to be a mineral (crystal) until it is frozen as ice. This is because unlike water, ice has a regular repeating inner lattice, which qualifies it as a mineral or crystal. Having this inner regular lattice causes ice to form beautiful crystals resembling snowflakes. Dr. Masaru Emoto has done studies into the healing powers of prayers and intention utilizing this crystallization process. People sit with some water and instill the qualities of a certain emotion through the power of prayer and intention and then the water is frozen and studied through a microscope. The results were phenomenal. Where the intention was pure and thoughts were strong and focused, the results yielded a beautifully symmetrical crystal, however in the presence of blasphemy or an intention of war etc. the crystals that grew were distorted and blurry.
The above text is merely an overview of the different types of geometry that make up the Universe we live in. Learning how to become attuned to this language we can learn to become balanced and connected.
Here is an amazing animation I came across on You Tube that illustrates the beauty in the maths of nature.
An interesting talk by Benoit Mandelbrot, the pioneer of fractal geometry, about fractals and the art of roughness.