Trans-organization across modes

Level N-1 Typology to Level N Topology

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... and then we have also those cases which take us from typological variety to topological ...

Here it is perhaps most evident how scale plays a role. If we have large number of tokens of a small number of discrete types, in order to treat them quasi-continuously we need only regard them from the viewpoint of an SI of much greater scale. Individual events, over long time intervals, can be analyzed as continuously varying frequencies. Individual items, over large spatial scales, can be analyzed as continuously varying densities.

Or we can actually regard, from higher scale, the results of the interactions among such items, as when monomers produce polymers; ions, lattices; actants, networks. Here we can look at macro-properties, which may be more continuously variable, even though the underlying microproperties are discete. This is especially evident when we consider global macro-scale phenomena, as with lattice propagation phenomena such as waves (phonons) and molar properties (e.g. elasticity).

In time, discrete events which form interdependence sequences also constitute higher-level systems, as in the case where patterns of discrete neuron firings come to be organized as smooth motor movements, through co-ordination and temporal coherence.