Modularity and the Number of Design Choices

This paper tries to analyze one aspect of what is commonly understood as modularity in the architectural literature. We are referring to any building style that uses large, internally empty blocks or components such as rectangular panels of the same size. Where this idea is applied to define a structure's layout on the ground, or for an urban region, each unit conforms to previously fixed dimensions in a rectangular grid. At the heart of this approach lie two practices: (I) building materials are prefabricated only in a very limited number of sizes; and (II) one adopts a philosophy that subjugates design to empty rectangular modules. We compare here the number of choices available in different design systems. A simple model allows us to estimate the relative number of design choices in a free, non-modular design system compared to a rigid design system of empty modules. Modularity and the Number of Design Choices This paper analyzes one aspect of modularity in the architectural literature. Arguments can be made in favor of modularity, but the authors use mathematics to prove their argument against empty modularity. If we have a large quantity of structural information, then modular design can organize this information to prevent randomness and sensory overload. In that case, the module is not an empty module, but a rich, complex module containing a considerable amount of substructure. Empty modules, on the other hand, eliminate internal information, and their repetition eliminates information from the entire region that they cover. Modularity works in a positive sense only when there is substructure to organize. We also compare the accuracy of approximating a given design such as a curve. This serves as an easily-grasped metaphor for design in general, where the ability to represent a complex curve depends critically on having many different scales of structure. As a rule, architects wish to have available a large number of possible solutions, so as to enhance their ability to generate novel designs. Working within a modular system of design (with or without supplementary conditions such as internal structure in a module), however, restricts the number of possible results in a drastic manner. The restriction imposed by empty modularity may eliminate all of the possible designs that relate visually and functionally to human beings. We will argue that using empty modules reverses ancient practices that lie at the basis of humanitys connection with nature. The alternative to modular design is creating a form through subdivision or differentiation. In this way, a structure and its components can have any dimension or shape, and at the same time, the structure can utilize materials in a variety of sizes and shapes. Design can be freed up by subdividing the building materials to achieve a spatial coherence as determined by human functions, movement, the psychological perception of space, connectivity, etc. This is the opposite of rigidly fitting human functions into a geometrical frame that is determined primarily by the size of prefabricated construction panels. Today we try to fit ourselves into some arbitrary dimensions fixed by an architect without any regard for the complexity of our spatial and emotional needs. Modular arrangements often define the aesthetics of a style. Reasons for adopting a modular design system in architecture include those of economy of thought and action: it is easy to repeat a design unit that has worked before. It is true in almost all architectures, including various vernacular traditions, that a style is defined after a successful modular system has been developed, which is then formalized into a design canon such as the Classical orders. For example, the transition from wooden to marble construction in early Greek architecture occurred after the former material was developed into a successful system for building temples. The resulting style re-makes sensible wooden modules out of marble, which is not all that practical, even though the results are wonderful. Good and bad applications of modularity Classical, Romanesque and Gothic architectures are characterized by the repetition of large geometric modules such as bays, columns, windows, etc. These elements possess internal substructure (decoration, fluting, borders) even though some of the smaller modules such as the ordinary brick and smoothed stones are visually empty. Certain modular elements that are used in Classical and traditional buildings could be described as undecorated, yet there exists decoration on that and smaller scales elsewhere in the building. The result is a visual balance between substructure on many different scales, which follows from a fundamental mathematical rule on the relative number of subelements in a structure [Salingaros and West 1999]. Qualitatively, the result of the study by Salingaros and West [1999] may be stated as follows: Substructure exists in a hierarchy that follows an inverse proportionality: many smaller subelements; fewer intermediate ones; and very few larger ones. This multiplicity rule, derived for general complex structures, explains why contemporary neoclassical buildings dont always achieve the appropriate visual impact. Their forms clearly refer to classical forms, but the distribution of subdivisions is closer to the early modernists such as Mies van der Rohe and Le Corbusier. That is because substructure is cut off at a relatively large size; if smaller elements are present at all, they are not numerous enough for visual balance. For this reason, despite an obvious attempt to mimic Classical prototypes, recent neoclassical buildings tend to resemble in spirit the modernist buildings they are trying to contrast with. Looking at the architectural and urban failures of the twentieth century, modularity is one candidate for critical scrutiny since ugly, boring buildings look the same, and many of them consist of large empty rectangular panels or exposed untreated concrete, and lack ornament and color. The distribution of sizes is cut off at the size of the empty modules and so the scaling does not continue downwards. Thus, the mathematical connection of the structural scales to the scales of human perception and movement, all the way down to the minute scales present in natural materials, is eliminated. The worst urban mistakes are again characterized by rectangular blocks arranged in precise modular alignment. The more such buildings repeat, the more they create an inhuman habitat, the negative effect of which is proportional to the area covered by the modules. The deficiencies of uniformity become dramatic on the urban scale. The requirements of totally different functions would normally preclude mixed-use building groups from sharing the same module, yet the industrial production of the same modules encourages architects to create similar buildings and monotonous urban zones. The alternative is to abandon a pointless strict (...truncated)