Abstract
Drawing on the Luhmannian reading of objects as self-referential constructs, this theoretical reflection explores some possible synergies between topological thinking and Social Systems theory, in order to account on the issue of object formation from a spatial perspective. By discussing the dynamics between different modes of observing and the emergence of systems’ functions, I argue that the operative space of systems, mobilised as a communication medium, channels the emergence of particular object configurations, while obstructing others. I elaborate on this perspective to provide a possible way of addressing the interplay between objects and the operative space of systems, through a topological understanding of observation. There is a brief conclusion pointing to the main challenges and potential of further developing these ideas.
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Notes
- 1.
Cited in Van Stigt (1979:395)—The rejected parts of Brouwer’s dissertation on the foundations of mathematics.
- 2.
In the first formulation of his duality theorem Henri Poincaré introduced the analysis of Betti numbers, as topological objects that describe ‘the maximum number of cuts that can be made without dividing a surface into two separate pieces’—see: http://mathworld.wolfram.com/BettiNumber.html
- 3.
Albert Lautman points out that the result of Alexander’s duality theorem applies in the case of polyhedra embedded in Euclidean space ‘provided that they are allowed to be expressed by Betti numbers and torsion groups’ (2011, p. 124).
- 4.
Oxford dictionary definition—Mathematics entry.
- 5.
Brouwer’s Fixed Point Theorem reformulated by Dave Richeson (2011)—see: http://divisbyzero.com/2011/01/12/beautiful-theorems-about-dynamical-systems-on-the-plane/
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Barba Lata, I. (2015). Topology and Object Formation. In: Beunen, R., Van Assche, K., Duineveld, M. (eds) Evolutionary Governance Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-12274-8_11
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