Spirals
©Lorena Loo
©Lorena Loo
The spiral. In nature its manifest form can be seen ranging from seashells on the seashore to the spiral arms of galaxies far far away. Pineapples, pine cones and the heads of sunflowers are among those of the plant kingdom whose form embraces two oppositely directed spirals.
Even in our weather, a low pressure system combines with the Coriolis force to produce the exquisite counterclockwise spiral in the image below.
In 2002, samples of moss returned from a two week voyage aboard the Space Shuttle Columbia were discovered to have done something extremely odd: they grew in a spiral. On Earth, moss, like the typical teenager's room, grows in a chaotic tangle. But onboard the space shuttle, moss grew in a choreographed clockwise spiral like no moss on Earth.
(Click image to left to enlarge)
(Click image to left to enlarge)
© Copyright Lorena Loo
Cyclonic spiral storms have been detected on the surface of the 4th planet in our Solar System, Mars. In November of 2005, Science Magazine1 reported that Saturn's outermost ring, the enigmatic F-ring, was not really a ring at all but a spiral. Long thought to be comprised of a core ringlet and surrounding diffuse ringlets called strands, new data demonstrated the strands are actually connected, forming a single spiral arm that winds around the planet at least three times. (View a Quicktime movie of the "spiral ring" here)
Polar vortices were discovered at the south pole of Saturn and on Venus, a double vortex exists at both poles.
Polar vortices were discovered at the south pole of Saturn and on Venus, a double vortex exists at both poles.
The word "spiral" derives from the Latin "spiralis" meaning coiled and the Greek "speira" meaing coil. The image to the left is a bronzed coiled serpent from the Chou Dynasty of China circa 500-250 BCE. Joseph Campbell believed this to be evidence from pre-Buddhist China of knowledge of the coiled serpent of Kundalini in tantric teachings from India which came at a later period. Like the coiled serpent depicted here, Kundalini, the sleeping serpent in the muladhara (root chakra) was described as having 3½ turns.
Throughout the ancient world, the spiral (or the vortex in its three dimensional form) appeared in artworks. Said to be the entrance or tunnel into the spirit world, a shaman would go through the vortex and appear out on the other side in an entirely new spiritual realm.
Reputedly the early Christian monks drew their knowledge of the "spirals of life" from the teachings of the Druids. Yogis teach that the clockwise flow of energy is the enfolding into matter and the counterclockwise flow is the unfolding or dissolution of matter into energy.
Spirals are geometric forms and all geometric forms are but patterns of energy. The unexpected emergence of the spiral form/energy from various other geometric designs and arrangements is a field of exploration which delights mathematicians to no end. A square is a square until it square dances into nested squares out of which appears a spiral of triangles. Draw a square and then connect the midpoints of all four sides to form a smaller square nested within the first and rotated by a 45º angle. The new square is one half the area of the initial square. Form a nested square within the new square by the same procedure. Continue forming several such nested squares and you see a spiralling pattern of triangles within the configuration.
Spirals are geometric forms and all geometric forms are but patterns of energy. The unexpected emergence of the spiral form/energy from various other geometric designs and arrangements is a field of exploration which delights mathematicians to no end. A square is a square until it square dances into nested squares out of which appears a spiral of triangles. Draw a square and then connect the midpoints of all four sides to form a smaller square nested within the first and rotated by a 45º angle. The new square is one half the area of the initial square. Form a nested square within the new square by the same procedure. Continue forming several such nested squares and you see a spiralling pattern of triangles within the configuration.
But the spiral emerges from the nesting of any regular n-sided polygon, not just a square. A pentagon, hexagon, septagon, octagon, nonagon, and so forth. Whether of five sides, six, seven, eight, nine, ten or greater, as long as the sides are all of equal length, nesting of successive smaller n-sided polygons within the original one will give birth to a spiral of triangles.
There is more than one way to nest and generate a spiral or as in this case, four spirals. Here we began with a square. This time instead of forming the midpoint of each side, we moved an equal distance in the same direction from each corner of the square. Joining those four points formed a smaller square nested within the original square. Move the same distance in the same direction along the sides of the new smaller square to nest another square. Continue the process enough times and you see four spirals forming from nothing more than a sequence of lines.
This type of nesting and spirals can be done with any regular polygon, including an equilateral triangle.
The Mayans of Chiapas hold the symbol of the shell in reverence. In Spanish, the word for shell is "caracol" which also happens to mean "spiral." It is said the Mayans employ the spiral as a metaphor through which they understand abstract concepts which include time. Time is viewed as cyclic in nature, a spiral rather than a linear progression.
In the human anatomy, the spiral presents itself in the form of the cochlea, that part of our inner ear of which the Organ of Corti is the primary component. It is in the Organ of Corti where sound vibrations are converted into nerve impulses so that we can hear. Calculations have demonstrated that the snail-like shape of our inner ear serves to boost the strength of sound vibrations, especially for low frequencies. The word cochlea derives from the Latin word for, curiously enough, "snail shell." (Image to right)
A clockwise and counterclockwise spiral of triangles are shown from this successive nesting of regular pentagons.
Left: A square nested within a square. Area of each triangle is 1/8 of original starting square, ¼ that of the nested square. Right: A sequence of nested squares out of which emerges a spiral of triangles, in this case in a clockwise direction.
Combining 5 counterclockwise spirals (blue) with 8 clockwise ones (orange) produces a pattern of opposite spirals. Consecutive Fibonacci numbers (here 5 and 8) are known to turn up in such combined opposite spirals in the plant kingdom, though it is by no means unilateral. For some examples, see
Plant Spirals: Virtual Tour
Plant Spirals: Virtual Tour
The horns of a ram follow a spiral trajectory of growth as illustrated in the photo of a Battle Ram to the left. While (below) birds of prey pursue a spiral trajectory rather than the shortest path of a straight line (in green) when preying on their victims.
Double vortex at south pole of Venus. Single vortex at Saturn's south pole.
A low-pressure system swirls off the southeastern coast of Greenland. The counterclockwise spin owes to the Coriolis force in the Northern Hemisphere. In the Southern Hemisphere, the spin would be in a clockwise direction.
The coiled serpent of Kundalini is waking consciousness in the form of a spiral.