We all know how intricate are the relationships between a single tree and the forms of life that live with it, and around it. But why are trees so important to human beings who are after all–as forms of life–so distinct and different from trees? Though distinctive and different, human beings are part of the same heritage of life.
The reason that trees and forests are so important to us, as human beings, has to do with the natural geometry of the universe. We must therefore distinguish between man-made geometry, stemming from Euclidean geometry, the geometry we learn at schools, from the natural geometry, especially the geometry of the living forms.
When Euclid was inventing his geometry, which has become the basis for man-made forms, the Greek reason was already corrupted by Aristotle’s analytical and classificatory approach to the world. With Socrates and Plato the Greek world is still held in unity and harmony. With Aristotle, we begin to divide and chop and atomize–put things into separate compartments, where they are identified by special labels called definitions.
Euclid and his geometry only reinforces the tendency to atomism, separatism, thinking in neat logical categories–here are the axioms, here are the rules of derivation, here are the theorems derived from the axioms through the accepted rules of derivation. All very neatly and rigorously defined. A triumph of the rational Western mind which is going to depend so much on the power of formal reasoning, on the meaning of axioms which will become the ultimate bricks out of which other things are to be constructed.
What should not escape our notice, in particular, is Euclid’s emphasis on the importance of the point, and of the straight line. Let us be aware that we never see the point because the point as such is invisible; we hardly meet a straight line in nature. Yet the architecture of the human world, or to be more precise of the world as constructed by modern man, is founded on the straight line and those invisible points.
Let us put the proposition in general terms: the geometry that dominates our lives, when we live in a city, in a modern house, or when we drive an automobile, is the geometry derived from the abstract system of man-made geometry. It is a geometry which, after a while, constrains and suffocates us.