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Digital Design and Topological Control

At the turn of the 21st century, topology, the mathematical study of spatial properties that remain the same under the continuous deformation of objects, has come to invest all fields of aesthetics and culture. In particular, the algebraic topology of continuity has added to the digital realm of binary information, the on and off states of 0s and 1s, an invariant property (e.g. a continuous function), which now governs the relation between different forms of data. As this invariant function of continual transformation has entered the field of automated computation, the culture of binary digits has shifted towards a new level of calculation derived from the introduction of temporal quantities into finite sets of algorithmic instructions and parameters. This new level of topological computation, it will be argued, defines new operative procedures of control, constantly adding axioms at the limit of calculation through an invariant function that establishes a smooth or uninterrupted connectivity between distinct data. The establishment of a continual function between distinct forms of data is based on homeomorphism or topological isomorphism between data objects, of which parametricism, as the new global style for architecture and design, is a perfect example.