Johanna Irander

Studio Irander
johanna.irander@studioirander.com

Dimensions

https://www.doi.org/10.66966/COTAA.2025.21

Dimensions can — aside from physical quantities that are measurable in units of length, width, and height — also refer to abstract dimensions of space, which in quantum physics refers to possible states of a quantum system that exist depending on a subjective level of perception. Using a methodology of deconstruction and disassembly — in a continuation of Kandinsky’s deconstruction of pictorial elements in art, and the exploration of urban components by Tschumi — the investigation examined the fundamental structure and system behind dimensionality. Based on scientific facts, and philosophical theories and observations by, amongst others, Euclid, Plato, Hypatia, Descartes, Deleuze, Rancière, and Steyerl, the investigation found that what constitutes the underlying mechanism of the universe on a fundamental level does not appear to be vectorial composition or angulation, but pulsation, alternating oppositions, and level of energy. This enables the establishing of a new classification system in a redefinition of spatial and abstract dimensions — or planes of perspective to distinguish and differentiate the word dimension relating to the Cartesian coordinate system, and other aspects and meanings of the same word, including philosophical and mathematical definitions — based on level of energy, and frequency level. The planes are organised as strata of energy / frequency levels, where each plane operates as a polar opposite of previous planes, thereby forming a sequence of active, or positive (+), and passive, inert, equilibrial, or negative (-) oppositions, and thus reflecting the rhythm of a sine wave oscillating between polar coordinates. This theorem expands on the definition of dimensions as a theoretical complement to the vector based Euclidean space, which originally was intended to represent an abstraction of physical space, and the Hilbert space system, which in mathematics is used to define infinite abstract dimensions.

Keywords: abstract dimensions; space-time continuum; planes of perspective; Kandinsky; Tschumi; Euclidean space; Hilbert space.