diagram / abstract

see abstract / concrete
A prisoner, in his cell, kneeling at prayer before the central inspection tower.
N. Harou-Romain, Plan for a penitentiary, 1840. From: Michel Foucault, Discipline and Punish.

Michel Foucault recognized the panopticon as the diagram of modern power. In Discipline and Punish, he described the major effect of the Panopticon: to induce in the inmate a state of conscious and permanent visibility that assures the automatic functioning of power. (p.201) The perfection of this architectural apparatus was to render its actual excercise unnecessary and independent of the person who excercises it. The Panopticon "automatizes and disindividualizes power" It is "a marvellous machine which, whatever use one may wish to put it to, produces homogeneous effects of power. " Thus, for Foucault, the Panopticon functions as a kind of laboratory of power, a generalizable model of functioning. It must not be understood as a dream building: it is the diagram of a mechanism of power reduced to its ideal form...a figure of political technology that may and must be detached from any specific use. "it is a type of location of bodies in space, of distribution of individuals in relation to one another, of hierarchical organization, of disposition of centres and channels of power, of definition of the instruments and modes of intervention of power, which can be implemented in Hospitals, workshops, schools, prisons."(p.205) For Foucault, the panoptic schema is the general principle of a new "political economy" whose object and end are the relations of discipline. (what Deleuze would call the factory work model.)

In his book on Foucault, Gilles Deleuze aligns his own terminology with Foucault's, while bringing Foucault more in line with his own metaphysical project and production of concepts. According to Deleuze, "A diagram is a map, or rather several superimposed maps." (Gilles Deleuze, Foucault, p.44) He calls the "diagram or abstract machine ... the map of relations between forces, a map of destiny, or intensity, which...acts as a non-unifying immanent cause which is coextensive with the whole social field. The abstract machine is like the cause of the concrete assemblages that execute its relations; and these relations take place 'not above' but within the very tissue of the assemblages they produce." (Deleuze, Foucault, p. 37)

For Deleuze and Guattari, language, or more generally, regimes of signs formalize expression on one side and formalize content on the other. "But a true abstract machine has no way of making a distinction within itself between a plane of expression and a plane of content because it draws a single plane of consistency." ( plane of immanence.) It"makes no distinction within itself between content and expression, even though outside itself, it presides over that distinction." (Thousand Plateaus, p. 141) "The abstract machine connects a language to the semantic and pragmatic contents of statements, to collective assemblages of enunciation, to a whole micropolitics of the social field." Thousand Plateaus, p.7 "The diagrammatic or abstract machine does not function to represent, even something real, but rather constructs a real that is yet to come, a new type of reality." (p.142)

According to, Brian Massumi, "The abstract machine is interpretation. It is the meaning process, from the point of view of a given expression." (Brian Massumi, User's Guide to Capitalism and Schizophrenia ) Félix Guattari compares abstract machines with the Noam Chomsky's concepts "...of the abstract machine inhabiting linguistic or syntagmatic concepts," presumably alluding to Chomsky's theories of competence. where is the "field" of competence?
For Hardt and Negri, the world market "might serve adequately -- even though it is not an architecture but really an anti-architecture --as the diagram of imperial power." (Empire, p. 190)


"A fractal process can be stopped and diagrammed at any point in its dividing. Every stop will yield a different diagram, each of the same fractal. The overall identity of the fractal is enveloped in each diagram, but is not manifestly present in it. It cannot be, since the fractal's identity (becoming) is at one with the generative process that must end for a given diagram to be produced." (Brian Massumi, p.37) The abstract machine is the equation. In their capacities for emulation, computers "realize" abstract machines. (see Langton, p.11)

Is a computer program an abstract machine? The formalization of machines by Gödel, Turing, von Neumann separated its "logical form" from its material basis of construction. Algorithms are thought of today as abstract machines. (see also c omputation)


Christopher Alexander: "Any pattern which, by being abstracted from a real situation, conveys the physical influence of certain demands or physical forces is a diagram." (Notes on the Synthesis of Form, p. 85) For Alexander, the diagram is "the starting point of synthesis."

Alexander's examples include: stroboscopic picture of splash of milk, Le Corbusier's Ville Radieuse, the sphere, the texture of bathers on a crowded beach, the arrow, representations of molecules, an engineer's sketch for a bridge ...
For Alexander, diagrams can summarize formal characteristics, or functional properties, but "constructive diagrams" provide a bridge between requirements and form. Thus the diagram illustrated above presents information on the traffic flow requirements for a traffic interchange in condensed graphic form in such a way as to indicate directly what form the new intersection must take. (p.88)

Mathematics / Physics:

Scientists have increasingly come to represent the behaviour of a system in " phase space." Is a "phase portrait" a diagram? or is the "phase portrait" the plane of consistency ? What is the relation of these analytical models to architectural diagrams?

"The shapes of mathematics are abstract, of course, and the shapes of architecture concrete and human. But that difference is inessential. The crucial quality of shape, no matter of what kind, lies in its organization, and when we think of it this way we call it form. Man's feeling for mathematical form was able to develop only from his feeling for the processes of proof. I believe that our feeling for architectural form can never reach a comparable order of development, until we too have first learned a comparable feeling for the process of design." (Notes on the Synthesis of Form, p. 134)

What is a form? "The first move is, if not to define it, at least to see the model for it in contour or diagram." (Jean Molino, introduction to Henri Focillon, The Life of Forms in Art) According to Molino, Focillon's work is a critique of iconology, as it considers matters of form to be separate from matters of signification. Specifically formal signification (which iconography helps identify) is allusion to other forms and is more motivated -- meaning more necessary and natural-- to use a linguistic term, while the relation of the nonformal signification of iconology is largely arbitrary. (p.24) For Focillon, forms are caught in a perpetual metamorphosis.