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April 12, 2011

Good Shape: A Recursive Rule

Stone framed windows, Haifa, Israel. Photo by Tom Kubala.

“It is easiest to understand good shape as a recursive rule. The recursive rule says that the elements of any good shape are always good shapes themselves.”

Christopher Alexander, p. 179, Book One, The Nature of Order

“In addition, we note that the simplest and most elementary good shapes are made from elementary figures.”

Christopher Alexander, p. 181, Book One, The Nature of Order

Recursive Rule? Throughout Alexander’s opus The Nature of Order, the idea of recursion appears often. At my first reading, the idea seemed to get in the way of Alexander’s explanations of the living quality of buildings, the concept is difficult to understand and wrapped in an impenetrable mist of mathematics. However, a little persistence pays big dividends in this case. Remember back to early math in school when you were asked to find the square root of a number? It sticks out in my memory because of the unusual method required to answer the question. There was no formula that could be applied to a number to find its square root, instead, we were shown a process to solve the problem. First: guess what might be the square root, second: multiply your guess by itself, third: determine how close you are to the number for which you are seeking the square root, fourth: adjust your original guess to correct for how far off you were the first time. Repeat this process until an acceptable level of accuracy is achieved. This is what a calculator does when you push the square root button, only so very quickly that it seems instantaneous. Back in school it felt like such a ‘messy’ way to get an answer, so very un-mathematical. Little did I know that I was being introduced to a recursive non-linear dynamic system. So what does all this have to do with ‘Good Shape’? As it turns out, there is no formula for making a good shape either, but there is a recursive process! No shape exists in isolation, in making a good shape, one is constantly seeing things at various scales, moving recursively between larger and smaller shapes.

Here is a definition of recursive from the world of computing that might make a connection for some of you…”relating to or involving a program or routine of which a part requires the application of the whole, so that its explicit interpretation requires in general many successive executions.” (The italics are mine.)

In other words, making a good shape depends on your ability to progressively employ good shapes to make good shapes. Apply your intuitive faculties, they just so happen to work recursively.

The topic deserves a future blog post or two.

posted by: Tom Kubala
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