Pythagoras showed that the golden ratio, phi ( φ) – 1.61814, used as the relationship of parts in a structure is amazingly pleasing. Physical dimensions in this relationship produce an order that is compelling and beautiful. The relationship of the successive chambers in a nautilus, the relative length of the tip of a finger to the tip to first knuckle, then to the length of the first two segments to the entire finger, then the hand, the relationship of successive vein length segments in a leaf all merge to the limit of φ . People know that symmetry is a characteristic of beauty, as you can see in my portrait, The Vitruvian Man by Leonardo da Vinci. φ is the “constant” of proportional symmetry in nature. Recognizing this constant and its derivation can bring order to a practical assessment of what makes things beautiful. (more…)

Individuals who write music, poetry, prose, stories, research science and culture, design useful implements, and all the other creative activities need support to give them an incentive to undertake the effort to produce these works.

How does a society provide these incentives and support to encourage the development of culture? (more…)