Language, Mathematics, and Linguistics

Claims (19)

• A form language able to produce life must be a system of transformations which allows living centers to be created, one by one.
  Defines the requirement for an effective form language.
• All eleven principles are, of course, embodiments of the fifteen transformations.
  States that the teaching principles directly instantiate the underpinning theory.
• Buildings made with an eye to the past will most often fail to have living structure, because the process of historical reproduction somehow turns vivid, living structure sour.
  Argues that copying historical forms does not produce living structure.
• Ensor, in his visions, used this language, the language not only of a true architecture, but also the language of our archetypal fantasy.
  Analysis of Ensor's painting as composed via the fifteen transformations.
• Even if all the conditions of chapters 6-15 are satisfied, it will still not be enough; without a form language that supports the living structure, the nearly-living process will fall down.
  Argues that living process alone is insufficient without a suitable form language.
• That such a simple form-language could produce such powerful results, was remarkable.
  Reflection on the eleven principles class, affirming that even a minimal form language can yield strong results.
• The apparent similarity of form language between Piano's cultural center and traditional huts is almost a trick—hardly more than an illusion.
  Argues that Piano's organic-looking building fails to capture the deep unfolded geometry of the traditional huts.
• The fifteen properties are the very simplest things which can possibly be used as a basis for assembly of a living thing, and it is from simplicity that they ultimately derive.
  Justification for using the fifteen transformations as a foundation.
• The fifteen transformations provide us with a natural 'alphabet' of living process.
  Asserts that the fifteen structure-preserving transformations can serve as elementary units for generating living form.
• The form languages of traditional societies helped people to work in living process and allowed them to form truthfully differentiated buildings in harmony with the whole.
  Argument that traditional societies had effective form languages for living structure.
• The forms of these buildings do not allow such an unfolding to occur; they patently do not.
  Critique of Renzo Piano's and Daniel Libeskind's buildings as incapable of unfolding.
• The geometric process of differentiation is the necessary underpinning of any building which is functionally well-adapted to its terrain.
  Links unfolding to functional adaptation, not just aesthetics.
• The schemata created by modern and modernistic architectural efforts in the 20th century are too crude to carry the load of creating living geometry.
  Critique of 20th-century modernism's inadequate form language.
• The sketches show precisely the kinds of forms which must in all likelihood follow from any program in which these fifteen transformations are progressively unfolded.
  Asserts that the chapter's sketches represent the necessary geometric character of unfolded buildings.
• The stair shown on page 436 has an unfolded form, visible as the trace of continuous stepwise adaptations.
  Specific claim about the illustrative stair example, supported by the probe.
• The step-by-step evolution of living centers, in a progressive differentiating process, is a biological necessity — an essential part of the adaptation of a complex system.
  Claims that unfolding is not a stylistic choice but a biological requirement for adaptive buildings.
• Their actual roughness, and the visible soft morphological character they have because of this roughness, are of the essence of the fact that they are living.
  Asserts that roughness is an essential quality of living structure, not merely a sketch artifact.
• Unless we have a form language that supports the necessities of living structure, then living structure is simply out of our reach.
  Central thesis of the chapter: form language is a prerequisite for living structure.
• We may even call form-language the repository of style.
  Defines form language as the source of architectural style.