The Geometry of Living Neighborhoods

by Christopher Alexander

Now, what do I mean by geometry? When we use the word geometry, we most immediately think of Euclid, of straight lines, rectangles, circles. This is a very narrow branch of geometry that deals with the mathematics of a few idealized shapes, which can be used, on occasion, to deal with human matters.

The world, the world of nature, the world of forests, of agriculture, the world of villages, the world of buildings – these things of this world, do not have the idealized shapes, and Euclid’s geometry comes nowhere near being able to describe them. Real things come about in part by accidental collision with other things – things that are adapted to the slopes of hills, fences that run across a piece of rolling country, houses that have roofs adapted to the light and to the sun, wind shelters, dovecotes, sheep pens, windows that are friendly to the light, the shapes of a piano or a Celtic harp, suits made for people, the arms of a favorite armchair, the full line of a woman’s cloak, the curves of a Porsche 365, or a Harley Davidson.

These are things we live with. They have geometry, but they have a more complex kind of shape, they have relationships with other shapes, and more harmonious lines and curves that make our world.

For the greater part, these things are all made by fitting – by gradual and careful adjustment – to the land, one room to another, a doorway to a beam, a vaulted ceiling to an odd-shaped room. In short they are generated forms. They cannot be described adequately by equations or by drawing straight lines. Most of them are far too complex for that. The same is true, of course, for the objects created by nature – rock, cliffs, sand dunes, trees and tree trunks, human bodies, animal shapes, the shape of a cat’s eye. It is the same with these things, as it is with things that human beings have built. So the language of these shapes must be a language of generative process, because it is only in the steps taken to achieve the shape, that we can record and capture the shapes and forms even to reproduce them.

Christopher Alexander