Abstract
Simon's famous ant metaphor points to the possibility of two alternative representations for the same complex phenomenon: the ant's convoluted path on the beach may be described as complex behaviour against a simple background, or as simple behaviour against a complex background (or as a little of both, of course). The metaphor also supports the intuition that complexity is largely in the eye of the beholder – a fruitful philosophical position to take, as it encourages the observer to seek the representation that is the most useful for the purpose at hand rather than engage in a wild goose chase for “the” correct kind of representation. However, the ant-on-the-beach scenario falls short in one important respect: it views phenomena as consisting of a system of interest and an environment, whereas in fact every system description also involves a (usually tacit) underlying spatio-temporal framework.
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Notes
- 1.
Original emphasis, cited in O'Driscoll and Rizzo (1985, p. 52).
- 2.
In economics this distinction was made by Knight in his seminal dissertation where he used the term ‘risk’ to describe the first case from the perspective of a decision maker, reserving the term ‘uncertainty’ for the second case. See Knight (1921).
- 3.
This section on historical time draws on the work of the TimeMap project (www.timemap.net/timelines) by Johnston et al.
- 4.
This indeed seems to be the modus operandi of insects (including ants!): “…the insects write their spatial memories in the environment, while the mammalian cognitive map lies inside the brain.” See Chialvo and Millonas (1995).
- 5.
This works as follows: If O a is the selective operator that selects out of U whatever answers to the description of A, then O a U is a representation for the set of entities A . Now, A itself may comprise several other kinds of entities, among which those answering to the description of B may be of particular interest. In this case, if O b is the operator that selects the B's, then O b A= O b (O a U) is a way of representing B as a function of A and U. This procedure can be iterated for as many steps as necessary, so that if we have a hierarchy of entities A, B, C, D,… such that D \({\subset }\) C \({\subset }\) B \({\subset }\) A \({\subset }\) U, we may represent these as: O a U = A, O b O a U = B, O c O b O a U = C, O d O c O b O a U = D, and so on (see Larsen 1970).
- 6.
Zeigler's hierarchy of system specifications comprises the following four levels: Input–output relation observation, input–output function observation, discrete event system, discrete event network. Couclelis (1986) specifies four models of decision of increasing complexity in term of that hierarchy.
- 7.
There may be some connection between prior structure as discussed here and Bunge's notion of “determination” as the basis for causality. If so, my idea would stand on fairly respectable philosophical ground! See Bunge (1979).
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Couclelis, H. (2009). Polyplexity. In: Reggiani, A., Nijkamp, P. (eds) Complexity and Spatial Networks. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01554-0_6
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