This writing is approaching the problem of discernible unit-assemblages as part of the overall interconnectedness in a holistic nature. Are"strata" and "units" our 'artifacts of science' or are they real, identifiable entities in nature?
Let us reach back to some ideas of a "naive" ontology:
Consider the existence as 'difference' - while indifference is the nirvana. Once the difference is acknowledged (by any means or observers), it becomes 'nformation'. Accordingly an information consists of three elements: the difference itself, which itself is a double take of the comparison of the 'making' of a difference, plus an 'acknowledger', where such difference is recognized. Information forms a bridge from originating to accepting. A "bit" stands for (indicates only) some difference and does not include the acceptance part of the bridge, nor the (qualifying) characteristics of it.
The 'yin and yang' of ontology consists of the dichotomy of the informations:
the yin part accumulates information-bridges, good for nature's survival into larger and more variegated complexes, while yang stands for the trend for a balanced existence, the control of the growth of such connection-complexes by dissipating extraordinary peaks and filling deep valleys (in the fitness-landscape) - for the survival of nature as well. The first part, in guarding against indifference, a dissipation, a homogenization indeed into ever increasing featureless symmetry, attracts differences as in an 'ontological gravity'. The second part, guarding against an overall accumulation into a similarly destructive "all-in-one" unification, can be visualized as an ontological trend of a maintenance, as an 'ontological entropy- production'. The balance of the two trends keeps nature 'alive' and secure.
In the pre-geometrical substance (expression from R. Zimmermann), in which our Big - and other unlimited Bangs - occur, the above ontological 'yin and yang' exist in an unlimited - nonlinear - dynamism of oscillating information-bridging among ALL, a system in a holistic interconnection, in a total symmetry of the variations existing without spatial or temporal limitations. 'Nonlinear' refers here to an overriding of (our) qualitative consistency and the quantitative proportionality, required within the 'causal' changes of 'our' world, to which we refer here as 'linear'. (Note: the term 'linearity' is applied here in a different sense from its mathematical definition). Within the holistic oscillation of differences (into the ever changing compositions-assemblages) no specified regularity is supposed (called frequently as 'chaordic': the 'order' of chaos. We avoid the term 'chaos', if possible, because of its entirely negative description). Considering such unlimited symmetry and connectivity, it is unavoidable that in 'spots' some (partial) linearity also emerges: transitionally some quantitatively proportional and qualitatively matching information accumulates - as an irregularity, which re-dissipates into the holism within the overall oscillation. Such spot-linearization, however, constitutes the emergence of an order (transitional in nature), in physical terms: a materialization. Linear characteristics (a physical system) emerge. Modern physics observed such occurrences in the quantum-vacuum: the disproportionation of the "nothingness " into a pair of emerging matter and antimatter particles, which recombine with a flash of 'energy-emission'. Theorists calculated a VERY short (!) lifetime for such an 'existence' - unless there are pairs undergoing divergent trajectories: a 'creation' of matter + antimatter. The lifespan of the recombining linearized pairs is considered short - in OUR observation, using OUR time. (See below).
Occurrences within such events are not accessible to our present observations.
Or are they?
There is one such 'occurrence' within our interest and observational reach: the one we live inside of, which we consider our universe. We call 'that' particular Bang the Big Bang, with all its linearization, freezing into a 'spacetime-mass-energy' system, with evolution and all, our world as we observe it FROM THE INSIDE. - We find the other spot-linearizations, the fulgurations called matter-antimatter phenomena - instantaneously dissipating - as seen in our time. If those spot-linearizations include worlds like ours, they may observe our Big Bang occurrence an 'instantaneous' event as well - in their time (if they have one). Whether our world dissipates by a 'swift' recombination, or lives on with a divergent antimatter-path we know not. Our 'inside information' does not disclose the answer. All our 'time' may be included in one transitional 'fulguration'.
Cosmic humbleness: not only are we on a minor planet of an insignificant star in one of zillions of galaxies - not only are we a sporadic event in the evolution of minor characteristics in the life of this planet, not only are we limited in our so venerated mental capabilities to but a fraction of understanding of nature's workings - our whole world may be a sporadic fulguration of disorder, to be restored from its 'existence' into the overall system of nature. Maybe, as we may say: instantaneously. Without any remaining history of our "greatness".
"what process is it...?" since nature represents herself as a process rather than static 'things'.
Science works reductionistically in separated items, layered according to the mind's handling capacity. The fundamental feature of our epistemic evolution (IMO): the abstraction, helps such fragmentation, individualizing the strata and units. Accordingly the attraction of the difference in information - linearized into a potential - works out in assembling of entities, a phenomenon named energy, to diminish the peaks and valleys in the fitness landscape.
This is a 'first glance' idea which may or may not work out. - End of introduction.
A big task: to identify complexity in the midst of the diversity in the literature. It became almost as undefined lately as is consciousness. Diverse researchers use their own definitions and there is no 'authority' to choose the 'orthodox' acceptable one.
From a tortuous path through a diversity of views it seems advisable to compose the most generalizable versions which do not exclude examples even of sideline characteristics.
Let us consider a 'whole' assemblage of ingredients. What makes it a complexity?
What introduces the difference from a handful of sand, or a page in a dictionary, both containing 'many' ingredients - sand particles or words - but not as a complexity?
Reaching back to Aristotle's 'whole': it may not be "more", but rather "different", - from a combined sum of the ingredients - unless we include all aspects into the "ingredients", not only the earlier recognized material-parts (and their quantities). Since we still do not know them all, it is advisable to say "different". What makes the 'whole' different? Georg Cantor's definition (borrowed from a mathematical concept) comes closer: "a many, looking like a one". The 'complexity' term, in its folk-usage points to a complicated system (of many(?) components), which may give a basis to calling it in a very generalized first formulation as
"an assemblage with unit characteristics of the total added upon those of the components".
Several considerations require a nonlinear emergence of the group-characteristics within the assemblage to make it a complexity. They concentrate on unpredictable unit-qualia, both qualitatively and quantitatively. Unpredictability, however, depends on the level of epistemic evolution: some "unpredictable" (mysterious, miraculous) items become predictable and straightforward as our cognitive inventory - and thinking capabilities - grow. Such temporary criteria should not be in a general definition. We may extend the allowance for a complexity into linear features as well, even if the group-formation is predictable. A mechanical device or a legal opinion may be a complexity as well as a living cell. Extending the classical, Aristotelian matterly component view, the 'components' we consider are beside the material parts: functions, even ideational features as well. So the "multiple components" term is applicable with maybe only ONE material component as well (with functional changes), e.g. one piece of thread can turn into a complexity: it can be woven into a textile, where the qualitative features (group characteristics) change susbtantially by the waeving/knitting and the new characteristics carried by that (same?) one thread.
Another view of identifying the complex is the process of the assemblage in which the new characteristic(s) emerge and create a novel (higher?) order. The complex unit includes the components consequently their order is part of the emerging one.
In an attempt to better define the term, we may expand into these considerations:
a complexity consists of an assemblage of components with novel characteristics of the total assemblage over the sum of the components' characteristics. The 'emergence" of the novel qualia in the assembling creates a new, higher order in the process.
There are no isolated items: everything is in connection with the rest of the environment. The environment is not limited, the neighbor's neighbor is also the neighbor of something. The component has components and the assemblage is a component of something of higher order. René Thom's catastrophe, an isolated spot, would have drastic consequences: independent evolutionary lines, parallel features, changing physical properties in diverse 'zones' would be feasible. The catastrophe concept refers to a certain - limited - aspect only: in one cartesian system there may be interruption, while in another aspect of the same entity the continuity still prevails. In extreme: the seemingly 'not interconnected' items are still members of the same landscape, space, or kind, 'connected' by the quality (at least: sameness) of the territory.
In the "pre-geometric substance" (see above) i.e. in nonlinear nature there is a postulated total, unlimited interconnection and an uninterrupted exchange of-and-into all possible variations. As stated: this must give rise to the spot-linearizations, as part of "all possible" variations. Except for these it does not make sense to consider strata, units, closed entities. Within such spot-linearizations, however, as e. g. within our universe, we may project an architecture, a limited order, unsatisfied trends of interconnection, units, a physical system with all its details - strictly as observed from the inside. From the outside, as for instance from "another(?)" universe, or in the hypothetical 'image' of the nonlinear nature, the spot-linearizations are fulgurations of some 'disorderly' appearance - and disappearance. Such disorder, however, belong really into the order of nature, as part of her unlimited variations. It is part of the "process" we call (the existence of) nature.
Let us enter the only presently accessible one of such 'disorderly' fulgurations - our universe - and take an inside look at the structure (architecture) as observed by our contemporary science. The image may be absolutely unique: we have no indications of any similar occurrences or events in connection with other spot-history in the nonlinear nature.
How do we account for the strata, layers, "units" of scientific inquiry? There is more to them than just the artificial chopping-off. Things, functions, ideations have their individuality, all within the interconnection, but individually discerningly.
To start 'top-down': the universe is part of the nonlinear nature, with a minor linear veneer on 'top' of the nonlinear substance. Below that linear surface we find (in the recent development at least) the 'chaotic' underlying characteristics. Unpredictable processes, fractalous architecture, nonlinear aberrations from the quantitatively established rules emerge, some are called self-organization, dissipative, tectological, complex adaptive/recursive systems, etc. The universe, however, is a 'unit' with its own enclosure: the process-difference, caused by the linear behavior. There is ample interconnection, the 'spot' is bound to resolve into the holism, we may speculate: how? by extreme entropy (the heat-death of past centuries), through the black holes, by virtue of the evolutionary increase of complexity into an overall 'chaotic' level, or some other way not yet thought of, - but the universe IS bound to revert into the holism. Even the unlimited harmonic cosmology is only an "inside" idea. There are certain processes with 'no return' in the evolution of inanimate (cosmic included) and our Earthly animate history, which (logically) point back to a starting condition and may lead to some end unknown. The ideas of 'restarting' the processes only prolong the prognosis, do not show a change in the trend.
Bottom-up we can expect a similar architecture and may find several examples. The hypothetical Big Bang story with its formation of the first photon may be ouside of our practical considerations, but we may start from the biologically better accessible units, the living cells. At the 1997 conference "From Simplicity to Complexity" in Bielefeld Germany (ref.: (proceedings) 1998, Vieweg ed.) where the above mentioned theory of Rainer Zimmermann (II. p.153) was presented, Gertrude J. Klauer spoke about the 'skin-effect' in living systems (II. p.99). - (In my partially paraphrased semi-quotes): "All organisms (including cells, elephants,and trees) are separated by a [borderline layer] from the surrounding environment... which regulates the very condition or state of the complexity of the cell and multicellular organisms. When observed from a topological point of view, such borderline is closed. But physically it is 'semi open' to allow flow of matter and effects passing through the borderline in both directions. The cell is enclosed by the (semi)permeable cell membrane, it provides an interconnection with the environment while separating the cell and its components into a unit of their own. Downscale: quite similarly the components (organelles etc. ) are surrounded by their (internal) membranes with a similar role. In the upscale: The living organism has a skin, with the same characteristics. A firm control of the skin-mechanism is necessary to maintain connections to the central 'control' of the organism: the brain. In cells, however, such central control is not detectable: the surface receptors are linked to biochemical cascades and signal pathways and thus to distinctive cellular reaction systems. (End of excerpts).
To generalize the biochemistry observations into inanimate material systems and into functional, even ideational complexity-units, we postulate a hypothetical 'skin' effect of a complexity, the differentiation-layer of functions between internalization and interconnection with the 'environment' i.e. adjacent other complexities (similarly encased into their own skin- characteristics) - we cannot help but visualize a hierarchical layer-system, where the components - with their own qualities - interrelate to each other and to the total of the complexity-unit, while the latter has its in- and out- relations with the surrounding totality. The quality of such interrelation depends on the kind of unit: ideational, functional (e.g. electric?) or material (gravitational? chemical?), or else, also beyond the existing inventory of so far discovered natural cognizance. The system is due to delinearization: in a growing scale of nonlinear characteristics (i.e. in the course of evolution, as we see it) the discerning skin-effects gradually dissipate and a stratification becomes more and more difficult, may even look artificial (e.g. the mind-aspect, consciousness, within the human complexity).
Conclusion of the present survey: the scientific startification and unit-identification of reductionist science is a natural helper of our observation-based inquiry, there are 'layers' and there are 'complexity-units' in our world - which is partially linearized within a nonlinear holism of nature). Every complexity shows a higher reliance on its own components than on effecs from the outside, although the latter may be controlling its condition of state, - even of its existence.
In the complexities of linear construct this is self-evident, a machine works with its own parts to fulfil its designed role, with a clear interaction to its environment. In nonlinear emergence cases, however, it is not so obvious for the human observer who is trained basically in the linear reductionist science. Most difficult systems are the ones with high "chaocity", like the human one, an intrinsic cooperation of ideational/functional aspects of nonlinear constructs and the linear material systems (neurons and other cells, linear functions etc.). We have a long way to go to set the record clear, first to identify (and create names for) the concerning elements, then to study them - and understand the ramifications. We need new sybolics and new words for the new aspects; if we want to put them in a new "math-like" system: a novel type of the computing is needed, which can handle 'equations(?)' including nonproportional quantitative(?) changes and inconsequent qualitative transitions in processes of unidentified probabilities e. g. - as in a novel way of causal progression - with a choice of unlimited available variants. And, of course, access to the nonlinear world beyond our physical limitations.
Then we can start studying the nonlinear world (if we have acquired information from it).
Madison, 10/24/1999