D’Arcy Thompson explains in the article the inter-relationship between mathematics and form. The study of form may be descriptive or analytical but lacks precision. But when form is defined with respect to mathematics the quality of precision is imbibed.
D’Arcy Thompson goes on to explain the various methods of incorporating mathematical precision into form. The method of study for this article is plotting of the form on co-ordinates of the Cartesian system to generate proportional diagrams. Thompson’s initial intentions were no more than trying to translate the form of a curve into numbers and words. However, the next step he took intrigued most morphologists, as he went on to analyze the deformation of the form on the co-ordinates, as well as, study the transformation the form inscribed in the co-ordinate network. His analyses makes it likely to discover hidden identities by using mathematical synthesis. This method provides the necessary computations and abstractions and moves from static form to the analysis of dynamic forces underlining this form.
This method of co-ordinates became the foundation for D’Arcy Thompson’s theory of morphological transformations. Using this theory he was able to create related forms. He found that if he referred to the same mathematical function in transformed systems of co-ordinates, these identities are of the same ‘genus’ and variation that occurred in the form due to the “law of growth”.
He concluded the article by stating that if an organic form is studied mathematically it offers a better understating of the relationship between species, their deformation and evaluation cycle.
1. What is the scope of error in this method from collection of data, analyzing the data, plotting the data and then creating deformations?
2. Does the data plotting method vary depending in the size and scale of the species?
This article talks about the theory of natural history and its association with language. Foucault defines both natural history and language as a framework of thoughts as both are spontaneous and always in a state of evolution. He goes on to state natural history in the classical age is not merely the discovery of new objects of curiosity, but it covers a set of complex operations that introduce the possibility of constant order. Classification and speech have their place of origin in the same space thus can be scaled on the basis of time, memory and reflection, while natural history may be defined as a non-scalar quantity.
Foucault explains why natural history in the classical period could not be established as biology, however by the end of the 18th century this changed, nature had now become the universal distribution of beings. For example:
Minerals: capable of growth, but not of feelings and movement
Vegetables: capable of growth and susceptible to sensation
Animals: capable of spontaneous movement
Foucault concludes by explaining how natural history can be scaled when it is spanned by language, and stressed that in order to understand nature the “true language” has to be established based on the root language.
1. Does the definition of nature change in respect to the language that we apply to it?
2. How important is the role of “blind resemblance of imagination” in Foucault’s definition of natural history?
This article discusses the importance of typology and notion of type. Quincy defines type as the “idea of an element which should itself serve as a rule for the model”. While Argan explains type as a legitimate process of design in general.
Argan begins by explaining how most modern critics deny the validity of an architectural typology altogether. He then contemplates the similarities between typology and iconography. He maintains that typology may not be a determining factor of the creative process, but is always evident much as iconography is in figurative art.
Argan claims that type may just serve as an outline that aids in stimulating the design process. Architectural typologies are an abstraction of particular characteristics of an individual building, thus type may be defined as the reducing of a complex formal variant to a common root form. Type can be explained as a principle which contains the possibility of infinite formal variations. The influence of architectural typology is seen in three areas:
• The complete configuration of the building,
• major structure,
• decorative elements.
Thus typology may be understood as a guideline for the architect to follow in the process of conceiving a building. Every architectural project has an architectural typology whether the architect consciously follows the “type” or wants to depart from it; or even the sense that every building is an attempt to produce a new type.
Argan concludes the article by stating that “type must be treated as a scheme of spatial articulation which has been formed in response to a totality of practical and ideological demands”. Hence following a typology does not lead to duplication of the build form.
1. Does architectural typology of built form differ depending on the function of the built form?
2. How can we really know if a new typology is ideal in an existing urban setup?
Paul Rudolph introduces the Theory of The Six Determinants of Architectural Form. He claims that all six determinants vary in relative importance with respect to individual problems.
- Relationship to other buildings and the site: for a building to be acknowledged it must truly blend in and relate to its neighbouring surroundings in terms of scale proportions and space between the buildings.
- Functional aspect: the principle that a building should be designed keeping the function and purpose of the building in mind. Form must follow function.
- The environmental conditions: while planning a building the climate, landscape and natural lighting conditions of the region must be examined and incorporated into the design solution as much as possible.
- Materials: each material has its own inherent properties and should be used for buildings that need to integrate the same properties based on the function of the building.
- Psychological demand of space: such requirements are met through the manipulation of space and the use of symbols.
- Spirit of the time: this is the last and the most important determinant as this shall lead us towards richer architectural expression.
Having stated the six determinants, Rudolph goes on to state that most architects need guidelines to follow so as to maintain a discipline in the built form that is being produced. He concludes the article by leaving an open ended question, “Modern architects fought hard against the restraints of the outworn styles; the day is won; but the visual disorder of our cities still abounds. Can we enlarge our vision sufficiently to meet the challenge? “
1) Rudolph states: “when architects depend on their sensibility and imagination architecture has always gone downhill” would that hold true for the Modern Movement?
Form and Figure
The article by Alan Colquhoun talks about considering the stylistic quotation as a single phenomenon and examines it in relation to both the historical tradition and to modernism.
The use of dramatic elements seemed to be in direct consideration of The Modern Movement of that time. The primary principle of this movement was the prohibition of all dramatic references from the past. In the second half of the nineteenth century avant garde came up with a new definition of style which re-established the relationship between nature and reason. There work usually revolved around the relationship between form and function.
Colquhoun defines the avant garde works as a breakthrough from older works in terms of natural expression. He goes on to define form as “a configuration that is held to have either a natural meaning or no meaning at all “ and figure as “a configuration whose meaning is given by culture, whether or not it is assumed that this meaning ultimately has a basis in nature”.
The origins of what he calls figure lie in the classical tradition of rhetoric. The rhetoric principle states that there is a difference between what can be imagined and what can be thought. This suggests that a figure represents an idea.
Despite their fundamental differences Colquhoun talks about the concept of figure and its implications both to Gothic and Renaissance architecture. In the last quarter of his article he discusses the notion of pure form and its expression. He further talks about a group of American architects of whom Charles Moore and Robert Venturi were the most visible faces. They were the Neo-Realists and Aldo Rossi of the Italian Neo-Rationalists. Neither of these groups were able to recreate the notion of the pure form.
1) Is a break from the older tradition in terms of natural expression or the prohibition of all direct stylistic references the only way to lead a modern movement?
Elizabeth Grose in her article discusses about space that lies in between- the relationship between the virtual and real. She defines this space as a focal space for social, cultural and natural transformation. She states that” The position of the In-Between Lacks a fundamental identity, lacks a form. Yet it is that which Facilitates, allows into being, all identities, all matter, all substance”. And argues that this space is not defined as “the in between space” but is of consequence and not just a resultant of its surrounding spaces. “It is the space of the bounding and undoing of the identities which constitute it”
After comparing in-between space to Plato’s choric space she concludes that in-between space is not a space without boundaries of its own but is space that is defined with the parameters of the form that surround it from the outside. Thus by default the space is constitutes of in between space.
The in-between plays a significant role in architecture as allows for evaluation, alternation and progression in form, content, nature and culture. Nature, as defined by opposition, “is the stuff of culture and this of architecture” meaning that it exists between each and is a result of permutations and evaluations. Both in architecture and culture.
In the last quarter explores the of power of in-between space. She asserts that power is necessary for the becoming and is what “proliferates”. And defines power as the ability to overcome and absorb obstacles in its part, to use them as part of its own self-overcoming.
1. What is the real use of the in-between space other than acting as a buffer zone for expansion for the other surrounding space?
2. Is the in-between space considered virtual or real?
The reading discusses the logical interpretation and application of diagrams and mathematical code to architectural form to understand and prove Lar Spuybroek’s prediction: “the death of the diagram at the hands of a biological digital code”. He discusses ontological abstractions through idea, schema, diagram and code, and he traces through history how the explanatory schemes have become generative from reductive. While reductive theories are restrained by the need of an external activation, generative theories needed self organization machinery and idea mobility.
Spuybroek explains with the base theory of Plato the abstraction of an idea of form “not considered real but an imperfect projection of an ideal state of being” and elaborates on the theory that the real form cannot be experienced by sense but can be understood by the mind, through Kant’s theory that in order for real to exist it must pass a schematic state. He goes on to argue that these theories failed to describe the relationship between the abstraction and the real form.
He then explains how generative ontology is understood through a active and dynamic process where material particles themselves organically seek organization an can thus be interpreted. He explains how the basic parameters of an architect to define tangible spaces are diagrams.
He states that an act of visualization where information is collected and organized into a virtual machine. Machines are discussed as a progress of the diagrams, there qualitative and quantitative information and is processed together.
Expansion is an act of materialization where the organizational diagrams obtain qualities of quantity, matter and structure. He concludes by setting out to make a diagram as real as possible.
The article is opened by quoting Winston Churchill “we shape our buildings there after they shape us”. David Orr articulates that architecture is not a abstruse subject but needs to be placed in a larger context so as to formulate into ecological design. Orr discusses the urban problems, such as traffic congestion, poverty, climatic change, pollution, biotic impoverishment and land degradation and traces it back to the our neglect in the past, he goes on to optimistically states that the “obvious solution is better design”.
Orr explains that the problems in the past had only risen because of the miscalibration between human intentions and ecological results, and thus resulted in the display of design as failure. He also raises the concern in how technology has distant man from nature that in turn raised the concern that will people who no longer believe that they need nature be willing to protect it .
Orr then discusses Albert Einstein’s theory as the solution: “the same manner of thought that created problems could not solve them”, and define ecological design in the words of architects Sim can der Ryn and Steward Cowan did that is any form of design that causes minimal environmental destruction by integrating its self with the living process. Orr writes about to bring us back to a world that takes a second look at the world we are living in
He studies the relationship of our health and stated that it was deeply connected with our nature and that it was important to bond with other life forms, thus it is necessary to create designs that resembled our evolutionary past.. The article is concluded by emphasizing how it is important to link human behavior and restructuring our daily lives that tower above by reconstructing the urban setup.
The article by Stan Allen discusses the notation, diagrams and their role as mapping methods in architecture, which help architects to “conceive, visualize, calculate, and implement their work”.
According to Allen notation uses universally understood symbols for communication and diagrams on the other hand are purely graphical in representation that capture the attributes of the process in a way that is immediately comprehended to the onlooker.
Allen’s interpretation of notations suggests them to be “reductive and abstract” and translate basic instructions like mathematics and time based arts. He goes on to explain how notations universally may be understood and interpreted, while diagrams are impure and unclassifiable and may be interpreted in multiple ways. Allen then moves on to separate notation from diagram, he concludes that all notations are diagram but not all diagrams are notations.
He goes on to explain diagrams as “schematic and graphically reductive” that may be developed as a language of architectural expression so as for architects to convey and catalogue information. Notations on the other help on mapping existing objects alone a time line.
In the last quarter of his article Allen describes “diagram architecture” as a form of architecture that has the ability to derive a response to the diagram. He states that diagram architecture has the “ability to multiply effects and scenarios” and “behaves like a diagram”. He closes the article by proposing that diagram architecture has the promise to add meaning to an increasingly disconnected urban setup through the fine arts.
1. Is there a particular scale at which this method of architecture may fail?
2. Are notations and diagrams the only way to perceive the architecture expression of the built form?