Christopher Alexander on Simplicity and Symmetry

“… Complexity (in the bad sense) consists of distinctions which unnecessarily complicate structure. To get simplicity, on the other hand, we need a process which questions every distinction. Any distinction which is not necessary is removed. To remove a distinction we replace it by a symmetry … Gradually we get just that syncopated system of local symmetries … that is typical of all real life.

… This means that the geometry of a wholesome living structure will be almost entirely made up of LOCAL symmetries, while yet being mainly asymmetrical in the large.

Very often, when we look at something, we have an immediate, intuitive sense of its rightness or wrongness. This … comes directly from the symmetries we see and our sense about these symmetries.

The essence of this rightness or wrongness hinges on the issue of necessity … Everything in nature is symmetrical unless there is a reason for it not to be. When this law is violated, we feel that something is unnatural, and that is the way in which symmetry plays such a fundamental role.

… Imagine you are looking at the sky … see a cloud which is perfectly square. Without even thinking, you would that is was not a natural cloud.

… the symmetry structures in the world are very close to us. We perceive them instantly and subconsciously, without even knowing it. This mode of perception gives us an intuitive sense of which symmetry structures are appropriate or not appropriate in various situations.

… Each thing in the world is subject to various influences. It has various degrees of similarity and difference compared with other things, according to its situation. And in itself it also has various degrees of similarity and difference. This is what we call its symmetry structure. Symmetry is a precise way of talking about similarities.

We observe that in any thing, there must be just the right amount of similarity and difference …

When we make something which is just right, we have hit the degree of similarities ad differences … just right. On the other hand, when we are wrong we can also analyze the wrongness … Either the symmetries are less than the situation requires … or … more. To understand the idea that the symmetries in a structure are “just right”, consider for example the flow of electricity in two parallel wires. Other things being equal, the current will flow equally in the two wires. Why is this? If we want to, we can invoke some rule like Ohm’s law or the principle of least action … But the deepest explanation, the most profound one, is simply this: There is no reason for the two wires to carry different currents, because the situation is symmetrical … Asymmetries occur only where there are reasons powerful enough to generate them.

… things which are similar must be similar, and things which are different must be different …

Successful life which creates unity in a building and hold it together is generated by the balanced, syncopated, off-beat quality that the natural system of symmetries creates…”

Christopher Alexander – The Nature of Order – Book 2: The Process of Creating Life