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"Boundary Functions shows us that personal space exists only in relation to others and changes without our control. ...

By projecting the diagram, the invisible relationships between individuals and the space between them become visible and dynamic. The intangible notion of personal space and the line that always exists between you and another becomes concrete. The installation doesn't function at all with one person, as it requires a physical relationship to someone else. In this way Boundary Functions is a reversal of the lonely self–reflection of virtual reality, or the frustration of virtual communities: here is a virtual space that can only exist with more than one person, and in physical space.

The title, Boundary Functions, refers to Theodore Kaczynski's 1967 University of Michigan PhD thesis. Better known as the Unabomber, Kaczynski is a pathological example of the conflict between the individual and society: engaging with an imperfect world versus an individual solitude uncompromised by the presence of others. The thesis itself is an example of the implicit antisocial quality of some scientific discourse, mired in language and symbols that are impenetrable to the vast majority of society. In this installation, a mathematical abstraction is made instantly knowable by dynamic visual representation."

(Scott Snibbe, 1998)

Fig.1 Scott Snibbe (1998). "Boundary Functions".

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"When considering the relevance of Kant's transcendental position on Euclidean space, one widespread complaint goes something like this: In what concerns the transcendental validity of mathematics in experience, Kant failed to distinguish between pure and applied geometry the way we do today. Pure geometry, as Hilbert showed, is a mere mathematical multiplicity, an axiomatic system interwoven by means of formal relationships where a priori intuition plays no role at all. Its claims have no empirical content whatsoever. Applied geometry, on the other hand, as exemplified by the use of non–Euclidean geometries by Einstein, has to do with the application of a formal geometrical structure as a means of depicting the empirical world. This application is done under certain theoretical assumptions and the postulation of an empirical spatial congruence. Once the coordination of the geometrical structure with the empirical phenomena is established, it can be empirically tested. There is no place for the idea that Euclidean geometry is a priori and synthetic, a transcendental constitutive of experience. Euclidean geometry is just a possible 'mathematical multiplicity', a formal structure whose correspondence with the physical world is not imposed. Thus, the transcendental a priori validity of geometry for all possible experience as implicitly ascertained in the mathematical principles of the pure understanding appears to have been refuted."

(José Ruiz Fernández, 2003)

Essays in Celebration of the Founding of the Organization of Phenomenological Organizations. Ed. CHEUNG, Chan–Fai, Ivan Chvatik, Ion Copoeru, Lester Embree, Julia Iribarne, & Hans Rainer Sepp. Web– Published at www.o–p–o.net, 2003

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