Is everything chaos and chance? The Greeks deeply influenced Western philosophy by elaborating a consistent system of numbers and proportion in art to measure order and harmony in human life, nature and the finest artifact.
The Meaning of Numbers for Ancient Greeks
Pythagoras first defined musical harmony, the intervals between notes, by the lengths of strings of the Lyra, as opposed to the frequencies of the tones (both are actually inversely proportional). Interestingly, the meaning of numbers (Arithmos) and rhythm (Rhythmos) comes from the same root: rheîn = to flow. Plato then generalized the geometric proportion to all forms of aesthetic under a broader Metaphysic: “all these kinds of things received their shapes from the Ordering One, through the action of Ideas and Numbers” (Timaeus), “Numbers are the highest degree of Knowledge” (Epinomis).
The most important numbers for the Pythagoreans were the Five and the Ten. Five was the number of Love, uniting Two, the first even – female – number, and Three, the first odd greater than one – male – number. Five, the number of love, became later the symbol of humanity represented by the regular pentagon or pentagram, while Ten or Decagon symbolizes the universe. Ten was chosen as it is the sum of the first four numbers: "1," the spiritual level + "2" for woman + "3" for man + the "4" elements (Earth, Air, Water and Fire).
1.618 or the Golden Ratio Beauty
With the geometric representation, comes the calculation of proportions and the idea, still very modern, that you can model everything, including the ultimate harmony of the world. The geometrical proportion (a/b = c/d) is called continuous when b = c, which reduced the proportion to three terms: (a/b = b/c). A further simplification to two terms is obtained by setting c = a+b, i.e. (a/b = b/(a+b)) or (b/a)2 = (b/a)+1. This b/a ratio is known as the “Golden Ratio” or the “Divine Proportion” and is equal to Φ = (1+√5)/2 = 1.618.
Fibonacci sequence in nature (0, 1, 1, 2, 3, 5, 8, 13, ...), Hoax or Reality ?
Approximation of this ratio has been discovered in some living forms (known as the Fibonacci sequence in nature) such as the optimum angle between leaves or branches on a stem to obtain the maximum exposure to vertical light. There are also claims that the human body integrates some golden ratio proportions. For instance, the bones of the fingers approximate a diminishing series of three terms (1, 1/Φ and 1/Φ2), with the longest bone equaled to the sum of the two following ones. However there are no normalized way to make the measurement and, more often than not, the technique used is stretched to confirm the initial golden ratio beauty theory.
Beware of Golden Ratio | Respect Golden Rule
All this becomes very scary, when the model is used to measure beauty, especially in human face. Can really beauty be defined by the dictatorship of a mathematical model? We are again losing common sense and bow in front of this powerful cult that has survived millennia. At the end, beauty is in the eye of the beholder and you don’t want
to judge others’ beauty in ways that you would not like your own to be judged! Treat others as you want to be treated. That’s a golden rule, not a golden ratio.