abstraction

Theory

"It is the theory that decides what we can observe." (Einstein)

"It is more important that a theory be beautiful than it be true." (Paul Dirac)

In Greek, theoria originally meant a looking at or viewing and theoreo, a spectator. In this sense, theory and Visuality are metaphors of each other.

Is the theoretical attitude is that of the disengaged observer? Does theory require a distinction between the illusionless observer and the gullible participant, or to put it more mildly, between theory and observation? Does theory always entail what John Dewey derided as the "spectator theory of knowledge"? Perhaps to theorize is to create the impression of something that existed already (or, even better, always already) (see metaphor) In the Pragmatic tradition, theory is the critical reflection on "belief." William James calls it "an appetite of the mind," what Frank Lentricchia calls "the need to generalize" and "to obliterate differences." (quoted in Cary Wolfe, Postmodern Theory and the Pragmatics of the "Outside" )

But according to the Greek conception, theory is not a knowledge but touching (thigein ).

Read More

abstract/concrete

The etymological origins of "abstract" are the latin abs trahere , to draw away from. Thus the abstract is separated from body, object, or application. It can describe qualities apart from any object or thing. In Archaic Greek art, the genre of particular things outweighed their specific, individual qualities in artistic representation. Hence abstraction, expressed through the geometricization of natural forms, dominated Archaic art. A Greek polis , when understood as a particular pattern of life and not just a geographical grouping of people and their belongings, was essentially an abstract conception, just as a nation "is today. (see J.J. Pollitt, Art and Experience in Classical Greece.) When we describe a culture in terms of categories such as "religious," "economic," etc. we are not describing real subdivisions, but are making abstractions for our convenience. In the study of "structures" the practice of analysis consists in constructing "models" that replace the study of concrete phenomena by that of an object shaped through its definition. 

Read More

Analogy/Homology

Analogy/Homology

The concept of homology, or morphological correspondence, was the central tenet of philosophical anatomy. It was used to define structural similarity. Homologies, which are now defined in terms of evolution, were formerly interpreted in a transcendental sense. Whereas homologous parts are now considered to have descended from a common ancestor, in the pre-Darwinian era they were usually looked upon as evidence of an ideal pattern imposed on nature, or a blueprint in the mind of the creator.

Read More

Attractors

Attractors are geometric forms that characterize long-term behaviour in the phase space. Roughly speaking, an attractor is what the behaviour of a systems settles down to, or is attracted to. They are globally stable in the sense that the system will return if perturbed off the attractor, as long as it remains within the basin of attraction.

Read More

bachelor machine

bachelor machine

The term "bachelor machine" was first used by Marcel Duchamp around 1913 in connection with pieces of work that would later be assembled in the Large Glass of 1915-1923. (Also known as the bride stripped bare by her bachelors, even) For Duchamp, the term refers specifically to the lower portion of the glass, the realm of the bachelors, which contains, among other things, the chocolate grinder, the cemetary for uniforms and liveries -- Priest, Delivery Man, Gendarme, Cuirassier, Policeman, Pallbearer, Footman, Stationmaster and Page Boy -- and the témoins oculistes. The Large glass consists of two distinct realms, the realm of the bride above, and the realm of the bachelors below, both desiring and imagining one another without any possibility of mutual comprehension. (one is here reminded of the real / imaginary distinction and the discussion of cyberspace)

Read More

being / becoming

For Cassirer, " Form thinking" belongs to being, while "causal thinking" belongs to becoming. But strict knowledge is only possible of the always-being. That which is becoming can only be described, if at all, in the language of myth. Or rather, myth is already familiar with both the question of the "what" and the question of the "whence." "It sees everything that it grasps (the world as well as the gods) under this double aspect." (The Problem of Form and the Problem of Cause, in The Logic of the Cultural Sciences, p. 87) 

Read More

fold

"In the late work of the painter is the fold / of that which comes to presence and of presence itself / become simple, 'realized.' healed, / transfigured in an identity full of mystery. / Does a path open up here, that leads to the co- / belonging of poetry and thought?" From Martin Heidegger, "Cezanne." in Gedaches, quoted in Agamben, Stanzas, p 158, n.)

"A structure is a regularized infolding of an aleatory outside." (Brian Massumi, p. 58) (see inside / outside ) For Gilles Deleuze, the Baroque is an operative function endlessly producing folds. These operations occur on two levels: the pleats of matter and the folds of the soul. What is the connection between the two? Correspondence, communication, or a fold between two folds?

Read More

form

Is there an independent problem of form, for which biology must develop its own concepts and methods of thought? The Pre-Darwinian project of rational morphology was to discover the "laws of form," some inherent necessity in the laws which governed morphological process. It sought to construct what was typical in the varieties of form into a system which should not be merely historically determined, but which should be intelligible from a higher and more rational standpoint. (Hans Driesch, 1914, p. 149) 

Read More

fractals

fractals

The classic example used by Benoit Mandelbrot to introduce the fractal geometry of Nature is the question: How long is the coastline of Britain? Imagine measuring the coastline with a meter-long stick. This act of measurement would make an approximation of the coastline consisting of a finite number of meter-long straight lines and would give us one result. If we went back with a 50cm long stick and remeasured, we would get a total more than twice the first. As our unit of measure became smaller, the total length would increase without bounds. Our answer to the question would be that the length is scale dependent and increases without bound as the scalar unit becomes smaller. However, the "roughness" of the coastline seems to remain constant at every scale. Fractals have the same degree of irregularity at all scales of measurement. This roughness can be calculated as the log-log plot between the measured length and the reciprocal of the measuring unit, between "count" and "step" (see fractal dimension)

Read More

Gestalt

The word "Gestalt" is usually translated as form, although it might be better understoond as "organized structure," as opposed to "heap", aggregate, or simple summation (what Max Wertheimer called "and-sums.") 

Read More

hypertext city

hypertext city

As a conceptual framework, Hypertext provides a specific means of configuring issues sourrounding the confrontation of cyberspace and the city. It does so by embracing the advent of the electronic realm and the proliferation of networked links while at the same time interpreting these technological transformations as part of the project of writing. More specifically, studies of hypertext have focussed on the history of writing as technology, on the potential for hypertext to change the relationships between reading and writing, to alter the demarcations between the inside and outside of the text, and to change the nature and role of narrative. For its proponents, hypertext is the mode of writing that articulates the sociality of the network, that promises democratization and the empowerment of the individual, and that rearticulates themes that writing and the city have been seen to share: in the construction of memory, in the relation between movement and the subject, and in the production of space through abstraction and narrative. 

Read More

logical type

"This statement is a lie." true or false? 
Bertrand Russell' s theory of logical types arose in the early part of the twentieth century as a result of contradictions and paradoxes in the mathematical theory of infinite sets. For example, "the class of all those classes that are not members of themselves" was self-contradictory. One such contradictory entity within mathematics endangered the self-consistency of all mathematics, so that Russell came to the conclusion that all such paradoxical statements had to be ruled out. He devised a hierarchical "theory of types" in which the legitimate members of a set at one level all belong to the level just below. 

Read More

mapping

mapping

A "map" takes points in one space (the source space) to certain points which the map identifies as the "corresponding points" in another space (the target space). Wittgenstein calls these "logical spaces." Symbolic structures which obey a system of rules for translation are isomorphisms, structural homologies. Thus the mapping amounts to a distorted image of the source space on the target space. Language maps thought on to sound. An input/output function can be understood as a mapping. Thus the toaster executes a function mapping from bread to toast, and the groove on a gramophone record maps to the sounds. The psycho-physiological problem in mechanistic psychology becomes a problem of point-to-point mapping of mental functions such as language and memory on to the brain. (see mind /brain )

Read More

Mandlebrot set

Mandlebrot set

The Mandlebrot set has been described as the "most complicated object in the world." The figure represents the boundary of the domain of attraction of the behaviour of a simple equation in the complex plane. It is not the domain of attraction of a single system but rather a map of a family of systems, based on a single criterion.

Read More

neuron

neuron

Neurons are rather different from most cells. Mature neurons do not move about, nor do they divide. If a mature neuron dies, it is rarely replaced by a new one. Neurons have a more spikey shape than most cells, and the axon of a neuron can be very long -- as much as several feet. Neuroscientists today believe that the brain records an event by strengthening the connections between groups of neurons that participate in encoding the experience. (see engram)

Read More

population/typological

One of the changes in biological thinking brought on by Darwinism is the replacement of the typological thought of the morphological rationnalists by the "population thinking" of the current neo-Darwinist synthesis.

Traditional Biology seeks to be a science of forms. The Linnean hierarchy, which is more empirical that rational, seeks to classify forms through a structure of nested classes (taxa) of the traditional, Aristotelian kind, whose members are individual organisms. In this system, a "higher" taxon can be said to be more 'abstract' in relation to a lower one, requiring fewer properties for membership and with a greater extension. But according to Driesch, the Linnean hierachies of genera and species were only related on the basis of empirical abstraction, not on the kind of fundamental concepts that carry principles of division and allow for a rational systematics. In the latter case, according to Driesch, "The so-called ' genus' ... then embraces all its 'species' in such a manner that all peculiarities of the species are represented already in properties of the genus." (The Science and Philosophy of the Organism, p.245)

Read More