Nature

"With the cracking of the atom, and all other scientific developments of a similar tendency, we have had to start considering the world as made of things much more like vertebrates - soft on the outside, but with a solid skeletal structure within. The challenge one might throw out to painters is, how far can they express the underlying hard skeletal structure without sacrificing the great advances they have made in exhibiting the softness of the immediately apparent outside of fundamental elements of our experience?"(Waddington,1969)

Phi finds expression in inorganic matter in the form of the Golden Spiral. This is observed in the behavior of flowing gasses and liquids. Energy manifests itself in wave behavior. Watch a wave unfurl at the seashore. Can you see the Golden Spiral? This spiral can also be seen in the most far off galaxies and in traces left by subatomic particles as they lose energy.

Our own Solar System exhibits the properties of the Golden Mean. The distance between the planets reflects Phi. The approximate distance from Mercury to Venus is 1.61803 times the distance from Venus to Earth. It seems that the planets closest to the sun reflect Phi the most accurately. The ratio is seen to diminish as you travel further away from the sun, towards the outer planets.

Pentagonal Symmetry, or Phi's five pointed star follows the growth patterns of life forms. Life's smallest building block, the DNA molecule, exhibits Golden Mean proportions. One complete revolution of the DNA double helix measures 34 angstroms. (an angstrom is one 10-billionth of a meter) The width of the DNA helix is 21 angstroms. The ratio 34:21 is approximately the Golden Mean. A cross section of DNA has been found to form a star decagon.(This is a derivative of the pentagon whose ratio of radius to side is phi:1)

Phyllotaxis, is the botanical term which describes the distribution of branches and leaves on a plant. One key observation of those studying phyllotaxis is that the distribution of leaves around a central stem is governed by the Fibonacci Series: 3 Leaves in 5 turns, 5 Leaves in 8 turns...and so on.

The Human form fully expresses the Golden Mean. The umbilicus divides the body according to phi, the brow divides the head, and the wrist divides the hand and the forearm, all in approximately Phi proportion. Take a look at your hand. Your finger bones are in a 1:1.6 proportion to each other.

The golden mean can be found in other forms of nature where you find particular beauty, harmony in form, or intensification of function. It allows animals to grow larger while still maintaining a center of gravity. This can be seen in the Nautilus shell. Also, Phi is exhibited in the behavior of some animals. Swarms of insects, flocks of birds, and schools of fish, when dispersed, regroup into whirlpool spirals.

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