The modern theory of language

During the 20th century, the concept of “language” was given a precise formal meaning by several mathematicians, for example, by the mathematician Emil Post — and for the case of natural language by Noam Chomsky who coined the phrase transformational grammar. In both domains, the basic idea was this: a string-creating system was defined; the starting point was usually a null sentence consisting of a single character, or word, or the null string. The language provided a series of rules which allowed certain kinds of transformations which would elaborate a given string, and turn it into another string which was allowed (hence the term transformational grammar). Typical allowed transformations might include substitution, inversion, concatenation, etc.
The rules of the language were then these transformations.
A legitimate sentence in English was any sentence that could be derived by successive transformations. A legitimate proposition in arithmetic was any sentence (string of characters) which could be obtained by successive transformations of the base string.
You see how similar this is to the idea of differentiation as defined in chapter 7. In a transformational grammar, we start with a simple or empty string, and gradually elaborate it by successive transformations, until we get a completely differentiated structure, by substitution, inversion, concatenation, etc. In a form language for architecture, by analogy, we would then need a system of transformations which is able, gradually, to differentiate a previously less differentiated context, giving it more and more structure, until finally it becomes a completed building for that context.

More recently, members of another school of thought, have been trying to make progress with the idea of form language. George Stiny and his colleagues have made an attempt to develop what they call “shape-grammars” in a comparable way. So far, these latter studies have not borne as much fruit as one might hope, in terms which an architect would understand as useful. This has happened, I believe, because they have been undertaken, so far, within the context of the value-free, postmodern attitude, which almost by definition is not able to deal with problems of life and tries instead to study its subject within a purely neutral conception.
To be fair, I must say that these writers have, in all likelihood, not set out to do the job I have defined here. So far, their studies have been mainly academic, and they may truly not be interested in this question which I raise here. Nevertheless, they are dealing with the same subject.
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If we ask ourselves how we may construct a form language which can deliver (and help us create) living structure in buildings and communities as I have described it in this book, we are led to search, once again, for transformations: and of course the obvious place to start is with those transformations which appear naturally in the differentiating process. […]
Each of the fifteen transformations designates one way in which a structure may be transformed into another structure, while increasing its life. Any sequence of these fifteen transformations will therefore provide us with a basic, non-arbitrary scheme of differentiations that can be performed during the unfolding of a living structure. Thus, the fifteen properties, potentially provide us with the underpinning of a form language, in the exact sense understood by the modern science of mathematical linguistics.

It is possible to see the first outline of an adequate form language in the fifteen transformations themselves, and in their immediate impact on geometry. From this, we may see glimpses of a new style, that could emerge, in hundreds of culturally different versions, but one which is nevertheless quite recognizable geometrically, and utterly different from the geometry and style we became used to in the 20th century.

#book/The Nature of Order/2 The process of creating life/16 Form language and style#