"The tree which moves some to tears of joy is in the eyes of others only a green thing that stands in the way. Some see nature all ridicule and deformity...some scarce see Nature at all. But, to the eyes of the man of imagination. Nature is imagination itself."
"To see a World in grain of sand
A Heaven in a wild flower,
Hold infinity in the palm of your hand
And Eternity in an hour."
- William Blake, Auguries of Innocence
DA VINCI'S VITRUVIAN MAN
"For the human body is so designed by nature that the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part of the whole height;.............The other members, too, have their own symmetrical proportions, and it was by employing them that the famous painters and sculptors of antiquity attained to great and endless renown.
Similarly, in the members of a temple there ought to be the greatest harmony in the symmetrical relations of the different parts to the general magnitude of the whole."
- Vitruvius, De Architectura (The Ten Books On Architecture) Book III Chapter I "On Symmetry: In Temples And In The Human Body."
Vitruvius believed in the human form as the ideal manifestation of nature providing the perfect proportions for the Classical architectural orders. Da Vinci's above sketch was in honour of the master architect. An epitome of depicting the micro-cosmic significance through the human body in reference to the macro-cosmic workings of the Cosmos can be traced to the underlying presence of a Divine symmetry or a Cosmic harmony so profound yet so subtle which entangles itself expressing through all forms of nature and life.
Jim's presence can be felt from the following lines. The first consecutive lines Not to touch the Earth - Not to see the sun is taken from one of his favourite book Frazer's The Golden BoughAnd are titles of its sub chapters...
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Not To Touch the Earth
Not to see the sun
Nothing left to do
But run run run
Let's run
Let's run
The house upon the hill
Moon is lying still
Shadows of the trees
Witnessing the wild breeze.....
Run with me
Let's run
Run with me
Run with me
Run with me
Let's run
.......We should see the gates by morning
We should be inside evening...
Sun sun sun
Burn burn burn
Moon moon moon
I will get you soon soon soon
Another Jim's favourite..........
"Tyger! Tyger! Burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry? "
-William Blake, Songs Of Experience
THE FIBONACCI RESONANCE
The Fibonacci sequence in mathematical terms is derived following the integer sequence, starting from 0 or 1 it continues adding the two consecutive numbers deriving the third for example ( 0+1=1; 1+1=2; 1+2=3; 2+3=5; 3+5=8; 8+13=24;.....) resulting in the following sequence
0, 1, 1, 2, 3, 5, 8, 13, 24.......
The most intriguing and interesting presence of the Fibonacci sequence can be found in nature itself. As the Law of Nature binds itself within the resonance of the Fibonacci, sprouting from a leaf to 2 leaves then to 3 to 5 to 8 to 13 to 24....so on. From the petals of a yellow chamomile to an unfurling fern, from shells to earthworms and from a spiral galaxy to the human form all bear the Fibonacci number. Mysterious as it can be, nature sure knows its miracles......as Adolf Zeisig puts forth
“in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form.”
THE GOLDEN RATIO OR THE DIVINE PROPORTION
Above image showing the Fibonacci symmetry in a pink daisy.
The Divine Section or Sectio Divina in Latin or Sectio Aurea is the golden ratio occurs when two quantities share the same ratio as to the sum of both quantities shares to the larger quantity. For example if a> b then a:b=a+b:a that leads the mathematical calculation to the
Greek constant phi φ =1+square root of 5/ 2= 1.6180339887....
where a+b/a=a/b= φ
Architects and Artists like Le Corbusier or Dali used the golden section forming the golden rectangle to achieve artistic and aesthetic perfection
Above image showing the Fibonacci symmetry in a pink daisy.
The Divine Section or Sectio Divina in Latin or Sectio Aurea is the golden ratio occurs when two quantities share the same ratio as to the sum of both quantities shares to the larger quantity. For example if a> b then a:b=a+b:a that leads the mathematical calculation to the
Greek constant phi φ =1+square root of 5/ 2= 1.6180339887....
where a+b/a=a/b= φ
Architects and Artists like Le Corbusier or Dali used the golden section forming the golden rectangle to achieve artistic and aesthetic perfection
IN ART & AESTHETICS
In 1509, Da Vinci's close friend and collaborator Luca Pacioli penned De Divina Proportione a three volume collection based on the use of Divine proportion and classical architecture of Vitruvius, the use of golden ratio and its role in art and aesthetic harmony. The above image shows a sketch of a polyhedra by Da Vinci depicting regular solids done for his book. Below is an image of the original text.
The Sacrament of the Last Supper by Dali also highlights the use of the Golden ratio. Inspired by Matila Ghyka (a Romanian Poet,Mathematician, Diplomat and Philosopher) Dali uses his canvas as a dodecahedron background with the sides and edges forming the golden ratio as depicted below.
Debussy's Reflets dans l'eau (Réflections in water) uses keys in the Fibonacci integer sequence of 38, 21, 13, 8 respectively with its musical climax reaching the phi or the Golden Ratio.
THE GOLDEN AND FIBONACCI SPIRALS
The spiral nebulae or Mollusks shells all grow to form the Golden spirals which are logarithmic in nature with their growth factor phi or the golden ratio. Hence when these structures be it spiralling galaxies or conch shells grow outward further from thee central point they make an unique sequence of the phi or the golden ratio to every quarter of their turn. Thus creating one of the most immaculate beautiful patterns in nature.
VESICA PISCIS THE MOTHER EARTH
Sketch by Walter Russell, an American polymath.
Mandorla in Italian meaning the Almond and Vesica Piscis in Latin meaning the bladder of a fish is a very ancient esoteric sacred geometric symbol consisting of a pattern formed by two intersecting circles of the same radius adjoining at the perimeters with its circumferences passing through the center of the other circle forming an almond shape within. Since antiquity it has been associated with feminine forces of the World Mother, Mother Nature or the Mother Earth due to its nestling, nurture, fertility and protective aspects as all things are born and grow from the Mother.
The use of the Vesica shape can be traced back to antiquity as depicted below in a Manuscript Evangelistar Von Speyer Um 1220 in Badische Landesbibliothek Karlsruhe Germany Circa 1220 showing Christ in a Vesica shape surrounded by the four Evangelists represented by the four animal figures.
THE GOLDEN RATIO IN THE QUANTUM WORLD (Excerpts from an article released by Helmholtz Association Of German Research Centers)
HIDDEN SYMMETRY FOUND FOR THE FIRST TIME IN SOLID STATE MATTER
In 2010, the Helmholtz Z Berlin Fur Materlien in association with Oxford and Bristol Universities and also Rutherford Appleton Laboratories found a discovery startling the world of science as we know it....
The quantum world detected for the first time a nano-scale hidden symmetry latent in the atomic structure of a cobalt niobate. This magnetic material was pushed to a quantum state of Uncertainty employing Heisenberg's Uncertainty Principle and the results were baffling human understanding...
Following is an excerpt from the article...
Prof. Alan Tennant, the leader of the Berlin group, explains "The system reaches a quantum uncertain – or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical."
The spiral nebulae or Mollusks shells all grow to form the Golden spirals which are logarithmic in nature with their growth factor phi or the golden ratio. Hence when these structures be it spiralling galaxies or conch shells grow outward further from thee central point they make an unique sequence of the phi or the golden ratio to every quarter of their turn. Thus creating one of the most immaculate beautiful patterns in nature.
VESICA PISCIS THE MOTHER EARTH
Mandorla in Italian meaning the Almond and Vesica Piscis in Latin meaning the bladder of a fish is a very ancient esoteric sacred geometric symbol consisting of a pattern formed by two intersecting circles of the same radius adjoining at the perimeters with its circumferences passing through the center of the other circle forming an almond shape within. Since antiquity it has been associated with feminine forces of the World Mother, Mother Nature or the Mother Earth due to its nestling, nurture, fertility and protective aspects as all things are born and grow from the Mother.
The use of the Vesica shape can be traced back to antiquity as depicted below in a Manuscript Evangelistar Von Speyer Um 1220 in Badische Landesbibliothek Karlsruhe Germany Circa 1220 showing Christ in a Vesica shape surrounded by the four Evangelists represented by the four animal figures.
THE GOLDEN RATIO IN THE QUANTUM WORLD (Excerpts from an article released by Helmholtz Association Of German Research Centers)
HIDDEN SYMMETRY FOUND FOR THE FIRST TIME IN SOLID STATE MATTER
In 2010, the Helmholtz Z Berlin Fur Materlien in association with Oxford and Bristol Universities and also Rutherford Appleton Laboratories found a discovery startling the world of science as we know it....
The quantum world detected for the first time a nano-scale hidden symmetry latent in the atomic structure of a cobalt niobate. This magnetic material was pushed to a quantum state of Uncertainty employing Heisenberg's Uncertainty Principle and the results were baffling human understanding...
Following is an excerpt from the article...
Prof. Alan Tennant, the leader of the Berlin group, explains "The system reaches a quantum uncertain – or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical."
By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the chain of atoms acts like a nanoscale guitar string. Dr. Radu Coldea from Oxford University, who is the principal author of the paper and drove the international project from its inception a decade ago until the present, explains: "Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture." Radu Coldea is convinced that this is no coincidence. "It reflects a beautiful property of the quantum system – a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material", he explains.
THINGS HAPPEN BEYOND OUR CONTROL
-Jim Morrison
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