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I take my initial example here within the hierarchy of levels of organization that we normally take as representing the evolution of bio-semiosis, that is, the levels of organization that undergird the recognizable case of human semiosis, human meaningful and adaptive organismic response to signs (i.e. to representamina, R, as signs of conditions X, for the organism = SI). Clearly there are many intermediate levels between the organism-in-its-environment and our most microscopic quantum levels of analysis of material systems. I cannot be sure that I am able, or in some cases that anyone may yet be able, to identify all the relevant, intervening levels of organization in these systems,
but it does seem to be the case very frequently, that there is an alternation across levels of typological and topological semiosis, and I believe that this is fundamental to our notion of what constitutes "emergence"; as when we say that quantitative change has produced a qualitative difference.
I believe that the principle of alternation is fundamental to what we mean by emergent levels of organization in complex systems. We do not recognize a new level of organization if there is only a local re-organization of one gradience into another; we see this as a simple causal process on a single level of organization.So (topo) to (topo) does not appear to us as emergence. Thus a change in temperature which leads to a change in pH does not require any new level of organization for its interpretation; but a change in pH that leads to de-naturing or re-naturing of a protein, or to new possibilities for stable syntheses of new macromolecules does.
Likewise, a simple typological re-coding from one medium to another may represent a transfer of information, but it is only when a new scale of dynamical organization also emerges as an ultimate SI interpretant (the third level in the 3-level paradigm) that the system as a whole is seen to be using the information in a new way, to be building informational complexity. So one would not consider simple transfer of codon information between DNA and RNA to be semiosis, but macromolecular changes in 3-dimensional conformation patterns which depend on codon sequences, and also on wider cellular conditions could be (see analyses to come).
Explications of examples of semiotic alternation in the biological hierarchy