Quantum units at the scale of atoms or ions represent discrete, categorial, typological variety. An atom is either a Carbon type or a Nitrogen type or some other element; there are no intermediate degrees of Carbon-ness, no normal atomic or ionic species with a fractional number of protons. As we look at a biological molecule on a scale somewhat larger than the atomic scale, the variety available to be organized is the set of discrete differences from one atomic species to the next. We may increase this repertory somewhat by considering the different bonding arrangements and allowing that a nitrogen amidst one set of atomic neighbors does not behave as exactly the same intra-molecular species as a nitrogen in some other atomic environment, but still the set of possible types is finite and discrete. However, as we begin to consider the molecule as a whole as an emergent unit of organization at a new level, and we ask what properties of the molecule over longer many-atom stretches are relevant to how other molecules react to it, then we see that it is the electrical charge distributions in space, which have a quasi-continuous representation, which matter. Molecular organization represents a re-organization of the discrete, typological variety of atomic species into quasi-continuous spatial distributions of electrical charge, as a function of the interactions among the species in various combinations; and this new toplogical variation in electrical charge is what conveys information to the next higher level of organization: intermolecular interactions.
We see this most strikingly in the case of proteins, where the discrete units are compounded from atoms to repeating amino acid units (again slightly different in different neighboring AA environments, but still a finite set of types), but what matters in terms of the action of the protein as a whole in the larger-scale environment is a spatial conformation, the folded-chain, which is a collective effect and presents us with emergent properties on a larger spatial scale, which are properties that matter to a still larger scale, as below. Typological variety is emergently reorganized at a larger spatial-material scale as topological variation that is meaningful for phenomena at a still higher scale.
What is this next scale? The topological variety, regarded as information, represented by the conformations of macromolecules (e.g. folded proteins) and their associated (interactively functional) spatial charge distributions matter to a still higher scale, the chemistry of the cell, only by way of, for example, their interactions with intermediate-scale cellular structures such as membranes. The membranes, of many kinds in the cell, have in common that they respond to biomolecules as ligands, that is, as potential binders to membrane sites. These sites are formed by the interaction of the membrane-constituent molecules and represent, in their own spatial conformations and active charge distributions, an emergent level above that of the individual biomolecular species. These active sites define equivalences classes for other biomolecules, ligand classes, effectively those which will or will not bind to the site and produce some effects. In some cases binding may be partial, and some ligands may produce more pronounced effects (say the opening or closing of a membrane pore), but what has happened here is that, so far as the next still-higher level is concerned, all that matters about a biomolecule is which ligand class it belongs to relative to this membrane site. The topological variety of the folded protein of the ligand, or of the site itself, does not matter in its quantitative detail, but only via these equivalence classes and discrete effects. Topological variety has been reorganized at a new emergent level as typological meaning for still higher levels.(Note that obviously there are still some quantitative effects that are matters of degree, but the new organizational level as such fits what is expected from the principle of alternation.)
Suppose we now move up again in scale, from a view in which we see individual molecules interacting to one in which we see only statistical distributions and average concentrations. In between, there is the interesting regime of what is coming to be known as pauci-molecular chemistry, where the assumptions of the law of mass action and macro-chemistry are not met. There may be further emergent levels of relevant organization at these intermediate levels, but they are not well understood yet. Nonetheless, it is quite clear that in this regime we are in transition from typological phenomena in which there are again quite discrete reaction pathways dependent on local conditions, to a higher level of global or gross cellular chemistry at which the law of mass action is a better or very good approximation. Global level cell chemistry has its own emergent properties, such as overall pH and other average concentrations, and these variables are now topological in nature, because to good approximation they are continuously variable.
The molar chemistry of cells, representing topological variety, can again be reorganized at still higher levels into typological vareity, as in the well-known case of nerve cells that 'fire'; certain quantitative thresholds are exceeded leading to global chain reactions throughout the cell, and we know that still higher level brain processes depend on configurations and sequences of this now typological variety: cells that do or do not cascade or discharge. Whole multi-cell synaptic sequences are built, which are, like molecular species built from atomic ones, again of discrete identifiable types (each recurrent pathway is a type in this sense).
But how do these synaptic cascade pathways matter to larger brain processes? in part at least they matter by way of global, coherent electrical excitation of the brain, such as the alpha wave patterns and others of similar kind. These wave patterns, while themselves discrete types, carry information in a topological form: continuously variable amplitudes. We should also note here that it appears that there are many other such global, or at least 'volume' effects of neurotransmitter concentrations, such that neurons may not actually 'fire', but only carry slow-wave changing potentials, influenced by peptide concentrations and modulating the graded release of neurotransmitters that affect many neurons in the local volume. Here too we find higher-scale topological effects of lower-scale typological variation, and vice versa.
It is at least possible in some models of brain functioning that topological, meso-scale brain dynamics, in the form of propagating waves of electrical activity, whose effects matter through degrees of intensity, whether of chemical concentrations or of electical polarizations, interact at a still higher scale of brain activity to produce emergent levels corresponding to elementary "percepts" or to "phonemes", which are frequently or regularly typological in their informational variety. This presumably happens through the emergence of new attractors in the dynamics of the meso-scale functioning, each attractor in effect classifying its basin into a type.
Clearly there is an intimate interdependence between perceptual and motor functional elements in such as scheme, and we can again see a transformation or re-organization in the production of smooth motor behavior, which functions in terms of its topological characteristics (timing and coordination, gross and fine movement in space), which are in turn emergent from the discrete, typological elements that correspond to dynamical attractors in the neuro-muscular system. Ennervations and innervations of particular nerve elements and muscle fiber bundles (typological and discrete) emerge as overall continuous motion in space (topological, characterized by continuous degree and change). This is surely a miracle of emergent organization at a very high level (slower processes, on larger spatial-extensional and matter-energy scales).
Finally, I will end here with the last step of the link from physics to language and human social semiotics that I promised, namely the smooth motor actions (topological) are re-organized by learned processes of organisms in communities to be produced and interpreted as signs, such as word-utterances and gesture-productions, which are classic instances of typological signs. The SI here is not just the organism, but the organism in a community, and not just a community of other persons, but an ecosocial system that includes all the relevant nonhuman agents or actants as well. The time scales here are not just those of cognition, but those of language and culture learning, and indeed implicating the next higher scale: historical change in the social meaning systems for words and gestures. [On ecosocial systems, see here.]