## New levels interpolate between existing ones

## New levels organize the typological or topological requisite variety of the level below as messages for the level above

## New levels represent more constrained interactions among units at the level below

## New levels represent a filtering of information flow from constituents to supersystem, and a buffering of supersystem dynamics

## Level [N+1] loses informational access to level [N-1]; the total system gains the structural information of level N’s organizational specification

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The 3-level paradigm is not simply a description of
inter-level relationships, though it is very useful simple as
such. It is also a dynamical interpretation of the emergence of
new levels of organization in complex self-organizing systems. It
says, first of all, that new levels do not appear, or should not
be analyzed as appearing, at the top or bottom of a existing
hierarchy of organizational levels, but always as emerging **in
between** pre-existing levels of organization. Salthe's
original characterization of the inter-level relationships
(constituency and contraint, or in his terms, initial and
boundary conditions) already implies a set of informational
relations as well: the new intermediate level of organization
filters out information from [N-1] for [N+1], and informationally
buffers the dynamics of [N+1] against (normal scale) fluctuations
at level [N-1]. What I do here is to more formally assimilate
this to the semiotic paradigm (which leads to the principle of
alternation).

It is worth noting that Peirce's view of the sign as essentially triadic (i.e. X, R, SI), in comparison to Saussurean more dyadic views (signifier and signified), introduces the essential notion of the context-dependence of meaning which is somewhat backgrounded in other models of semiotics (though never absent). The SI here is not simply a formal system of correspondences or interpreting rules; it is a material system that does semiosis, that reacts to R's in ways that are adaptive to the underlying X's. (In Bickard and Terveen's terms, this is an interactive, not an encoding view of semiosis.) Two features of the mapping of organizational levels in complex systems onto the triadic view of semiosis are highly non-trivial (one can always map any triple onto another triple). First is the claim that the SI, in order to do semiosis, must be at a higher scale (either in spatial extension, or in temporal duration and reactivity, or both) than the scale of R's and of X's. To do semiosis you have to be able to assess difference in context, difference across space and/or across time. The scale relation of R-to-SI must be order-of-magnitude greater than the scale relation of R-to-X. The second non-trivial element is the principle of alternation itself: that the emergence of new levels of organization correspond to the re-organization of continuum variation from below as discrete typological equivalence classes with respect to the reactivity of the SI supersystem, and/or to the reorganization of discrete types at lower levels as continuously variable meaningful input to the SI.

What do we see in real complex hierarchically organized infodynamical systems?

I believe we can
discern a pattern that may be highly significant for any model of
the evolution, development, and emergence of semiosis in such
systems: **this****
pattern of alternation across levels of the re-organization of
typological information as topological meaning, and of
topological information as typological meaning ---**