KARL JASPERS FORUM

TAGET ARTICLE 62

NETWORK OF NETWORKS
FROM REDUCTIONISM TOWARDS WHOLISM
by John A. Mikes
12 June 2003, posted 2 September 2003

[1]
ABSTRACT

This writing is about complexity, an attempt to transcend from our reductionist thinking into the wholistic view (frequently called "complexity-thinking"), the position of an all interconnected - interinfluencing world we live in. A 'narrative' is included about the origin and life of our universe linking logical (hypothetical) prerequisites to a world view based on natural science. An expansion of the 'network' concept serves for widening the horizon of the wholistic interconnection and total inter-influencing in the "complex" world.

[2]
THE POSITION

We 'believe' (this "religious" term referring to scientific statements as well if based on observations, their evaluations and interpretation of findings) - that the world we live in is a totally interconnected unity, combined of interinfluencing changes. Our present capabilities do not allow its assessing in total as a whole, only in parts as controlled by our actual (topical) observational skills. A more holistic view of nature is callable "complexity thinking", (inadequately), a better word is being proposed: "wholism" while the observation reduced to fragmented (topical) models and a study of such as substantial units, topical entities within their set boundaries is called the "reductionist way", or simply "reductionism". The latter is the way how our mind can work and how conventional science evolved in studies: reduced to such topically fragmented models, cut from the wholistic total by their topical boundaries.

The "Network of Networks" view is a compromise: it aims from a (mildly?) reductionistic view of the (impredicative?) 'complexity thinking', the wholistic view of nature, into a visualization that may provide applicability and a better understanding of the holistic totality within our present mental applications. An attempt to render the 'inapplicable' - more 'applicable'.

[3]
REDUCTIONISM

[3a]
Reductionism is identified, explained and applied in diverse ways in literature. It seems useful to review the way how it will be addressed here. The word is frequently used pejoratively, however it is the only way how human minds and human science could explore the world and could ever develop our technology. Ever since man observed nature, a topical interpretation served as a method of categorization and organization of the findings. The observed item was interpreted as an entity, a substantial unit in its topic, omitting features not connected to the observational goals and findings. The unit so observed is a model of an assemblage indeed having unlimited links, associations, but represented in its limited ways within the 'cut' topical boundaries of the actual interest. - Called a 'percept' (by Robert Rosen). Reducing the (unlimited interconnected) observables into such models is habitual in composing human information and very useful for our results and conclusions. Both the practical and the scientific efforts are based on this 'limited model' view. This is the way how our technology was (and still is) developed and how all of the ongoing cognitive inventory of natural sciences got together. This is also the only way how our actual mental capabilities can handle the knowledge about the world: using cut parcels - not too comprehensive for the present capabilities of the human mind.

[3b]
"Our knowledge" is in fact a reduced term, a 'cut parcel' from the whole, as the mind interpreted the perceptual (partial) impact as received from the wholism. (Upon a remark from Tim Gwinn). This is a reason why our understanding is not covering the 'total': from components we cannot perform the induction into the whole, especially, if we have only a limited content of them available. It is doubtful whether we can ever grasp the whole since the mind (a natural system above spatial and timely limitations), works by the brain, an intrinsic part of the complexity, limiting the overall functions by the mechanism of a material tool.

[3c]
The way how reductionism works is topical modeling, the models are selected with (chosen) topical boundaries, cutting content, magnitude, function to size. Included in the model are features satisfying the following points:

1) Whatever we know about the modeled topic in the cognitive stage at the time when the model is constructed (used);

2) Whatever we (science, the researcher, the formulator) find relevant to include into the model (topically);

3) Whatever we group together within the physical, ideational, functional boundaries as a "unit" - topically describing, maybe calculating it.

4) In most cases: to make it fitting into the quantized formalism of the conventional science using its established (available) quantitative units.

[3d]
Quantizing is feasible: since only the model, with the already known information can be included, the model serves as a (closed) quantitative item, prone to calculations. Consequence: a formalism was generated with fixed quantities and so named concepts, as a (reductionist) system of such entities. The rules and "LAWS" OF PHYSICAL SCIENCES were derived by such fixed formulations (models).

[3e]
Analysis is the method of studying reductionist models (top down): the model-components are identified and studied as (only) 'parts' of the larger models. Correlations have been established between the topical model-qualia of such parts and the similarly identified qualia of the larger model. Predicting the qualia of larger (more complex) so far not studied models from already known component-qualia (induction) is, however, not feasible. Examples: compound-qualia of a composition-material (e.g. acetylene C2H2) cannot be described by knowing the component H and C atoms, if acetylene has not already been studied and known. Or: the analysis of an acorn cannot lead to a description of an oak-tree. Or: from analytical data of metal atoms the quale of a computer-chip is not derivable. Aristotle's observation holds: the total is more than the sum of its parts, as long as he observed only the material components in an assemblage (also including connectional/functional and connective characteristics). Example: A triangle is more than 3 angles and 3 lines. If a model is part of a larger model, a verbiage may call the smaller one a map, the broader one the territory, (however still a reduced cut-off model).

[3f]
This lengthy musing about reductionist circumstances serves to show, how reductionist thinking - the knowledge-evolution of mankind - can lead to erroneous conclusions, to paradoxes. Findings due to unexplained features are deemed "givens" in nature (if not "mystique"). Understanding of the world requires a new way of thinking, different from the reductionistic way, which, however has been proven so successful in practical conclusions, calculations and categorization in our conventional "science" and the worldview(s) based on it.

[3g]
The next paragraph will attempt to speak about the unspeakable new: the impredicative wholeness, the world (nature, existence) in its total interconnectedness, even all-interinfluencing process. Models included. Unspeakable, because very little has been developed about it over the short time since such ideas practically surfaced in our epistemic development.

[3h]
The origins go back into earlier centuries (e.g. Plato, Goethe etc.) but nature's interconnectedness (complexity?) was first described by A. Bogdanov in the starting years of the 20th c. (Tektologhiya). Von Bertalanffy (~1930) soon picked up the idea for systems science and Köhler formulated it into his "Gestalt" theory (~1950). In the 1960-70s David Bohm's 'implicate order' gave some more physical description of the unknowable and Robert Rosen made it a philosophical system on biology-basis. (Although both were natural scientists, thinking 'about' their science resulted in new directions of human thinking - hence a new philosophy).

[3i]
The word "complexity" still haunts with its multiple, -loaded -historical content and inadequacy ("complex" as complicated). A better simple expressive word to 'express the all-interconnectional world view' has yet to be found.

[3j]
Before, however, we enter the discussion of a topic callable COMPLEXITY THINKING, (or even WHOLISTIC WORLDVIEW), - some details may require further clarification - or at least a short note, connotation underlying that chapter.

[4]
ABOUT THE UNIVERSE, OUR 'WORLD'.

[4a]
I will argue that 'The Big Bang idea' of the current physical cosmology is just a 'narrative' in a quantized formalism, requiring lots of 'faith' to justify whatever has been calculated. Physical concepts are explanations for observed phenomena - derived in times when the epistemic information was much less than accumulated later on, when those newly acquired variations were then fitted into the older views and justified - mostly mended, mended and mended (still into the old concepts/system). May I refer to the concept of the energy, or gravity, and some others, substantially unknown, except for 'their' observable activity and measurements on such activity.

[4c]
It is a viable position in human logic (not the only one, however) that the world needs an originating point (maybe an endpoint as well). The acceptance of such explanations require a strong (scientific?) "belief", since any experimental justification is quite unlikely. Hence my usage of the term: 'narrative'.

[4d]
Below I interject a chapter of a different 'NARRATIVE' for a "BigBang" (to mark the difference: written in one word) having as consequence the generation of our universe. It also carries a different view of evolution, a hint to the concept of energy and to some wholistic foundations for the "complexity-thinking". It is intended to be a concise updated description for essays in my Web site from the year 2000.

[4A]
INTERJECTION :

THE PLENITUDE - A "BIGBANG" NARRATIVE

[4Aa]
(the premises):

I CHOOSE the EXISTENCE of our universe, in a "naive ontology" within our (human) logic, based on ideas within the contemporary natural sciences.

I CHOOSE this interjected NARRATIVE about the "start-up" of the universe (and the same for the "end" of it) pertinent to this world view.

I CHOOSE an imaginary "PLENITUDE" (name originally from Plato), to serve ONLY as the initiative circumstance for BigBangs (= the generation of universes.) The Plenitude carries no description, only as far as necessary to support the BigBangs. It is 'a-spatial' (nonlocal), 'a-temporal' - an unlimitedly invariant dynamic symmetry, of unspecified "everything" (interchanging elements).

I CHOOSE two distinctive and quite different views in this narrative, one as viewed "from the Plenitude" and another one as viewed from the inside of the universe. The two are not connectable.

[4Ab]
THE PLENITUDE

is a 'zero information' concept (yet allowing all that was said above as necessary 'information' about it), with no specified 'content' acknowledged, no observation from this universe allowed, in a dynamic exchange of variations of everything that can be thought of or that cannot, in unlimited exchange, making it a dynamic invariant symmetry. The featureless dynamic homogeneity is a "simple system", since principally no complications (complex features) can be acknowledged in it. The 'unlimited variations', however, among the participating "all" elements do also include occasional groupings of 'identicals', which indeed are faults in the unobservability of the invariant symmetry: an observable - call it - complexity which dissipates as it occurs, in just a timeless fulguration. The fulgurational cluster, however, "exists" and this is what we call a BIGBANG, the occurrence of a universe. Considering the unlimited (I evade using the term "infinite") Plenitude, unlimitedly many such clustering may occur, all controlled in quality by the appropriate quality-composition of the clustering "identical? elements" and (including other, clustered-in, accompanying elements as well). The resulting 'universes' are as different as are the elements of the individual cluster-forming fulgurations. We can speak only about our own one, since in our so far known, developed capabilities there is no provision for us to contact other universes. (Which does not exclude such capabilities from the part of other universes.)

[4Ac]
This is the BigBang narrative from the "PLENITUDE-VIEW". It shows a generation of universes (Multiverse?) and their re-dissipation into the invariance within the - timeless and spaceless - fulguration. It also shows a 'tendency'(?) within the 'informationless' Plenitude to maintain (recover?) its invariance, as per the limitless ever-symmetrical interchange of everything. The fulgurational clustering, however, forms obstacles to this trend and so it 'means' some sort of a strain. This is part of the BigBang cluster facilitating its re-distribution. In the occurring universe it still MAY(?) represent something we would call a force, (or energy), what we may observe in the INSIDE, - within the "universe-view". (This 'stress' idea is still in a vague developmental stage, just as the other one of the capabilities of other universes to contact us.) Such characteristic is not just 'assumed'. The universe is still a part of the Plenitude and what we observe the interconnectedness and interchange among the 'elements' of it, observed as mattery, functionally, ideationally modeled complexities. We also can see a tendency for (re?)dissipation e.g. in the black holes. The textural play of the cluster is the universe-system, as its life.

SO FAR WE VIEWED THE NARRATIVE FROM THE "PLENITUDE-VIEW".

[4Ad]
Let us change perspective and step in the inside of the cluster, to '(re)view' our developing and expiring world by itself: in "THE UNIVERSE VIEW". Plenitude and its view are excluded from it, only the characteristics (processes) within the cluster remain. A "system" evolves - in our case a space-time physical system, with concepts like 'extension' and 'duration', Observable complexity is building up and dissipating away, as long as (in the inside (ie. universe) view of course) the entire construct will dissolve back into the Plenitude.

[4Ae]
THE UNIVERSE

is a process and we are part of it. All of its aspects are connected within the framework of the 'total' universe: the changes of all DO influence the changes of them all, it is a dynamic interconnected unit: the WHOLENESS itself. The process enfolds by extension in 'space' and duration (time spans) in 'time' (both concepts so far poorly defined), it has a history (we call it evolution) and is based on observable differences. Acknowledgement of the differences (information) generates a response, a sensitivity, (consciousness?) in the system, a chance leading to further processes (both building up or dissipatively). In the course of this history (evolution) we, humans, evolved at some point, - no indication if it occurred at the early formative or the decadent stages. The snapshot we observe (being) does not identify the position in the process. It is not knowable either, whether the history is a monotonous, consecutive process with increasing complexity building, or a parallel work-through of diverse levels of the complexities up and down. Our logic is not at all binding nature, she is not anthropocentric/metric/logic. We see only fractions of the "becoming". Another possibility is that the dissipation is continuous, not a 'one shot' ending. We have no way to know from the snapshot (the 'being') we see. It shows in a continuation of the 'becoming' (before and beyond the status of 'now').

[4Af]
We should keep in mind that 'process' and 'system' are all only within the universe-view in form of observable changes. Although in our conception the universe is "wholeness", of unlimited variations - in our horizon - it has a beginning and an end - within the BigBang - two 'distant' occasions in the universe-view, however one single timeless fulguration as seen from the Plenitude-view. The system 'universe' consists of the inside view "changes" in 'natural systems' and 'natural processes' (the latter called here as 'evolution', - the entire inside history (ups and downs) of the universe). More than whatever our observations can cover at this stage. Our reductionist models are within the 'universe' framework, consisting of the topical cuts and the topically cut views of selected, identified mechanisms.

[4Ag]
The 'real' (complete) Wholeness, however, is in the Plenitude-view which is outside of both our observation and attainable information, even of our proper cognitive identification.

[4Ah]
As a consequence of the time/space system generated within the universe the question "what was before the Big Bang" is unidentified. Similarly the marvels which physical cosmology theory assigns to the uncannily small fractions of the 'first second' into the BigBang are understandably the occurrences with the generation of TIME itself - transmuted by physical thinking (and the instrumental capabilities) into a calculable time-span. The other marvel of cosmology, the 'inflation' of space into vast extensions is similarly a transmutation: with the BigBang: "SPACE" is generated in the universe-view, meaning a transition from the (plenitudinal aspatial) "no-space" into (universe-)"space", called (identified) in the physicists' terms: an increase (from zero to vast).

[5]
COMPLEXITY-THINKING - - WHOLISM

(as it is presently - inadequately - called.)

[5a]
The difficulties in writing about "complexity" (even worse: "complex"), go beyond finding a usable, appropriate title. Identification (a basis for an adequate definition) is just as difficult: the elements are vague, as will be seen: not even "all-listable'. Most writings resort to 'negative distinctions', saying: "what it is NOT". The aim of this part is to find 'positive' identifications, maybe usable for formulating a suitable definition, for finding a suitable 'title'-phrase (a better wording) representing "IT" - whatever the 'it' may be.

[5b]
A major obstacle is the historically attached (loaded) meanings of the words 'complex' and 'complexity'. The connotation of being un-simple, multifaceted, composite, convoluted, complicated etc. haunts even in texts dedicated to our topical versions, e. g. in Robert Rosen's writings proper, as 'complex systems' are used inadvertently in the literature - for the compositions fitting the above vague historical meanings. As will be obvious later on, a "system" is a reductionist assemblage having topical content, boundaries, interrelated (listable) components, synthesized only from its known components. Such 'assemblage' is what Rosen called: "a machine", a predicative aggregate of listable components, in most cases a human design, a cut-off, reductionist (simple? see below- rather callable incomplete) model. R. Rosen does not use a term that refers to the uncut whole (wholeness). "All systems in Rosen's view are human designs (modeling is ALWAYS an "art", systems are always subjectively defined). (Rem. by T.Gwinn)". "Systems" in general fall into categories, as boundary-enclosed topically defined (formal?) organizations of its elements within the existing cognitive inventory. However Rosen uses the uncut (holistic? yet topically identified) complexity as 'natural system', including its (wider?) impredicative connections and influences as well.

[5c]
A Rosen based definition, published by Donald Mikulecky, uses 'complex' for the holistic - and 'formal' for the topical aggregates as well:

(As will be mentioned later, 'real world' is a distinction I use with care.)

[5d]
Another common feature in literature based definitions comes from the notion that a "complex" system (in the holistic sense ) is different from a "simple" system. Rosen's definition of the "simple" and the "complex" systems (from: RR's 'Essays on Life Itself'):

(Simulable in this sense is usually equated with "Turing computable").

Further down we will meet another connotation for 'simple': the - plenitudinal - featureless simplicity, different from Rosen's definition).

[5e]
As Tim Gwinn's notes (quotes from R.R. with my emphasis) include:

"A subtle, yet important, item to note is that complex systems are defined essentially in terms of WHAT THEY ARE NOT (i.e., simple systems). THIS IS DONE BY SPECIFYING AS MINIMAL A CRITERION AS POSSIBLE (HAVING AT LEAST ONE NONSIMULABLE MODEL) in order to provide a precise, yet unrestrictive, distinction between simple and complex. The realm of SIMPLE SYSTEMS are well-understood to the extent that all their models are restricted to Turing computability, and thus the characteristics of simple systems are likewise restricted. In contrast, COMPLEX SYSTEMS are, in a sense, open-ended: there is no apparent upper-limit to how complex a system can be constructed, and therefore, no apparent limit to what characteristics such systems might have. Accordingly, COMPLEXITY ITSELF IS DEFINED BY ROSEN IN AN OPEN-ENDED FASHION.

[5f]
Gwinn also tabulates a comparison of characteristics of 'simple vs. complex' systems (after R.Rosen). Extracted from this comparison, here are some of the positive features of the 'natural systems'(R.R.) complexities (paraphrased by me):

- They (may) contain impredicatives - ALL components are not restricted to be 'listable' and predicative.

- They (may) contain non-fractionable aspects - in our present knowledge some aspects are beyond our present detailed (analytical) explanation.

- They can be modeled in 'complex' and 'simple' ways - their identification (modeling) can be just topically cut, as in a "natural system", or more reductionisticly restricted, (cut to a 'simple system'-RR*).

- They (may) have both non-computable and computable models - if topically modeling the feature, there may be models not algorithmic (i.e. not suitable for Turing machine application).

- They (may) have closed loops of entailment - this writer would apply it to the universe proper, as one closed loop, hence: "endogenous" in the universe-view, unlimited or topically fractionated.

- Synthesis is generally distinct from analysis - a rather inductive buildup of the impredicative "complex" includes unknown factors as well. 'Synthesis' in such inductive buildup is different from the term in the natural sciences: the resulting process is usually called 'emergence'. The listable, known components and the usual processes, provided by conventional analysis may be insufficient to explain such emergence.

[5g]
All these characteristics are true and make sense - however they can only be assessed if we "analyse" parts of the totality (into, - well - reductionistic partitioning to get to the listed features).

The listable (assumed?) elements of the holistic, all-including, totally interconnected and mutually interinfluencing nature-view are incomplete. In Rosen's expression: "there is no largest model".

In reference to the ambiguous usage of "complex(ity)", I will use the word

[6]
WHOLISM (AS IN 'WHOLISTIC')

as long as no better expression can be found. I definitely want to get away from the 'complex' and it variations, not only because of the many mis-meanings, but also for and important topical reason.

[6a]
The 'wholism' world view is the result of the fulgurational transmutation in the BigBang from certain plenitudinal elements into a universe, which is then observable in the 'universe-view'. Consequently it is still an expanded (into time and space) part of the plenitude, a dynamic invariance of all participating elements included, dynamically interchanging, consequently a dynamically homogeneous closed loop of its own. In the universe-view, however, observables occur and form associations usually called complexities. We cannot observe the 'total' as such, only in a modeled fashion, (as Rosen's 'Perspects') in partial views. This involved a vocabulary calling such partial compartmentalized models "simple". In fact these are the complexities, the discernable complex groupings, while the entirety of the wholism (the plenitude) is still quite 'simple', an infinite dynamically homogeneous aggregate - a total, an entity, - and not even observable as a 'total assemblage' being composed of ("complex"?) parts.

[6b]
In other words: the universe starts from its original plenitude- simplicity as long as the UNIVERSE-VIEW expands it into observable complexities. The 'expansion' in our case occurs by the evolving of our (physical) system of time and space. The "plenitude simplicity" refers to a different feature from Rosen's 'computable model' what he called simple, this one refers to the featureless state of the dynamic invariance, simple in the common sense meaning of the word, since NO 'complexity', not even any observable can be identified within. (See this dichotomy and an attempt for its resolution in the musings under the subtitle 'Network of Networks'.)

[6c]
In this sense THE TOTAL UNIVERSE (A UNIT) IN ITS WHOLISM IS SIMPLE, only the models we observe are 'complex'. I cannot 'clean up' completely the vocabulary, the RR-terms "simple models" and "complex models" are still workable, in the sense of 'machines' and 'unlimited wider model views' also called 'natural systems'. This is the other term still unavoidable: a SYSTEM is a topical model, a network in topical interaction, usually with a definable content (reductionist cut-off!) while the "natural system" refers to an aspect WITHIN the wholism, - yet identified topically, indeed a 'smuggled-in' form of reductionism, (as is the concept of the 'network of networks' as well). Rosen usually did not work in wholistic terms, just topically identified (natural?) systems assumed to be extended into the unlimited.

[6d]
A way to approach a suitable identification is the above "wholism". The difficulty comes from the ways how we think: we think reductionisticly. It seems useful at this point to interject some remarks on concepts and the ways as they are used in this essay (with no claim or proposal of a general acceptance).

MIND: used as the mental aspect of the 'complexity human', (as a (RR)-natural system, with no further (widely) agreed categorization so far. It includes the functional material tool, the neuronal brain as an essential part of the "complex assemblage" (as an aspectual model). The mind-content can transcend both space and time limitations, hence: nonlocal and atemporal, while the material tool is restrictive in functions.

REALITY refers to nature itself, of which we receive impacts only as appropriate to the actual epistemic level we are at. We have one way only to acknowledge such information: through the interpretation of the mind. What many usually regard as reality is indeed such (virtual) representation.

NETWORK is an artefact, a model composed itself of models limited in topical and functional content, called 'nodes' - connected by 'links' of influencing factors within boundaries of its topical content and function. Both organizations and systems are potential networks.

OBJECTIVE refers to 'object-oriented' view. Since all our 'objects' are representations of the mind, what we consider 'objective' is indeed the subjective variation of something we have no direct access, only via our mind. Our instruments are extensions of models of our senses, our computers are the extension-tools of limited models within our 'computing' mind function.

MIR (Mind Independent Reality) is an oxymoron : since we, as our mind, are all part of the world, nothing can be called independent. We can distinguish between mind-included, accessed, discovered features and David Bohm's implicate, still waiting to be discovered. Once, however, the informational enrichment of the cognitive inventory (epistemic development) engulfs those features into our knowledge, they will be interpreted (see under 'objective').

EVOLUTION is applied for the 'total' history of the universe, from the BigBang till the complete re-distribution - all in the inside "universe-view". (It represents the inside happenings in restoring the plenitude invariance within the timeless fulguration - as viewed in the "plenitude-view"). In this sense evolution includes also the segment in which Darwin pioneered: the process of the carbon-water based 'life' processes in the biosphere of this planet. As mentioned above, we have no way to discern, whether the 'snapshot' we see of this history is in an early phase of the universe's course, or rather close to its end. We also cannot distinguish if the distinct phases occur successively or in parallel, as judged from this one phase 'being' we are in and what we just see. The total of the 'evolution' is a space-time expanded process within the 'formation and demise' of a single (plenitudinal) fulguration, the occurrence of this universe.

IMPREDICATIVE means in the mathematical sense of Kleene a closed loop undefinability. In this essay it is used as the general meaning of the word: something beyond our capability to properly define in all detail, a composition which we cannot 'predicatively' describe, although lots of predicative characteristics can be listed. As a metaphor it can be called the "The Edge of Wholism" - a 'word-pattern' taken from the 'Edge of Chaos'. A semi-simple, semi-complex concept.

ENDOGENOUS is used by St. Kercel as impredicative (math) applied for material systems proper. In this essay it is used as the general meaning of the word: as a feature "gen"-erated by and within itself ("endo-"). I apply it to the universe-view, IN which the (physical) system is generated by the aspect of the inside observation (not by us as armchair-spectators, but by the system - call it a "conscious universe"(?) formulating its own rules 'within'.

MODEL is a topical representation of the target of observation. It includes composition, function, ideation of relevance - pertinent to the actual topical cut. Boundaries are identified for a model, which limit the target, cutting off connections to the wider world. A closely identified 'model' is the unit of the reductionist studies (observations), which can be widened by taking further connections into consideration. Such increasing of the model may go all the way to include ALL connotations wholisticly unlimited, when the model turns into the "real thing", not a model anymore, yet 'cut' to a consideration of a 'topically directed', wholistic view. (As in Rosen's "natural sytem").

[7]
NETWORKS

[7a]
Topically oriented models are connected by links of influences, in other words the routes of change, of information, within the overall changing environment in the wholism. Such groups of models are called variably organizations, systems, or a less 'loaded' concept: networks. The name points to less hierarchical arrangement than organization, less function-oriented than system, although allowing both aspects to prevail with the image of 'unspecified connections'. So are the topics: unspecified within the wholeness: ideational networks, operative networks of the living (frequently called: organizations) as well as 'lifeless' model networks (frequently called systems). Examples to these three types: philosophical systems, political parties, electrical distribution systems. The variations are broad and unlimited: whatever topical distinction is chosen, network formation is available. We may extend this statement into: whatever aspect we choose in quality, inter-topical variations, quantitative scaling, time-frame, size, etc. all aspects are usable for network-forming. A pattern of "network in a physicist's view" is described in A. L. Barbasi's book "Links". Let us take a closer look at one (beside another example below), the air-traffic pattern, the network of airports. Limited access (local traffic) ones are called "nodes", while the bigger ones with broader connections are the "hubs". Another of his examples we look at closer, comes from the 'board members' of big corporations, with persons included, most of them participating in several corporate boards simultaneously, thus connecting an array of large corporations into networks of coordinated interest-adjustments - coordinated goals. As can be seen, the 'nodes', the single connected features in a network, are all networks themselves, Rosenean percepts though, identified limited (topically matching) models with the connectivity within the topical 'plane' of the named network. The 'hubs' are not so obvious, although in a network of a living organization, e.g. the human body, with cells as nodes, the more involved organs may represent hubs. In a country-wide distribution system of electricity, water, or highway traffic (or even taxation) the quantitative aspect of hubs is obvious. (As will be seen, the restrictions as the hub-node difference will disappear in the wider (unlimited?) connectivity of the 'networks of networks' view.)

[7b]
This writing does not go into details of a quantitative treatise on networks, i.e. the one-plane identified reductionist constructs, mostly within their quantized theoretical formalism of mathematically based sciences (starting with the graph-theory of Peter Erdös and Alfred Rényi). The aim with networks in this writing is to use them as a potential route from the general, reductionistic model, the ubiquitously observable simple, topical networks into an approach to understanding of wholistic connections in nature.

[7c]
NETWORK of NETWORKS

Since the nodes in networks are considered networks themselves, the title may sound redundant. Every network IS a network of networks anyway. This chapter intends to expand from the formalistic (physicalist?) view of the graph-theory based networks, (characterized by the number of links in the given 'topic' of the network) into wholistic (super?)links (I apologize for the pretentious name and will not apply it further on) of the nodes connected with networks of different qualities (topics) as well. The physicalist(?) 'network' concept in the reductionist scientific view of topically selected nodes connected by (counted and accounted for) "links" is reductionist itself, a topical (cut-off) model of connectivities. In nature, however, (meaning the wholeness) the connections of items (nodes in this case) is unlimited, both in number and quality. We want to add some explanatory words to this point: firstly: 'unlimited' is not 'infinite'. Since the nodes have a variety of quantitatively discernable links (diverse 'strength' as frequency of use, preference of interconnection over other links, etc.) and qualitatively an unlistable variety (to topically, maybe qualitatively 'other type' networks), the interconnections - directly or indirectly - are expectably unlimited. Through chains of (series of?) links of unrestricted quality no (remote?) nodes can be excluded from being connected. Those links may fade away from our topical (physical) observation, or may come as 'negligible' concerning our physically recognizable strength-scale, (i.e. not limited to 'practical' orders of magnitude), which, however, does not exclude them from existence: in some aspect they may indeed jump into activity. Remoteness is not used here in the sense of a spatial distance. It refers to the out-of-boundary status in the network-model quantitatively and qualitatively. It adds a topical incoherence to the model, even through indirect connections (through other connecting links or networks). Such 'outbranching' connection-image makes the wholism unfathomable for the capabilities of our current mind and not simulable. The idea of the "networks of networks, however, may let us try to step one step forward and identify at least the way how to approach the wholistic realm. It might give a glimpse of the totality, maybe not yet provide a clear 'understanding' of it.

[7d]
Let us review the two networks mentioned above, the networks of board - members and the networks of the air-traffic distribution - observed in the (physicalistic?) way: by number of links and let us expand it still by some quantitative distinctions between nodes and hubs within the scope of the number of the connecting links to the individual nodes. The topic of both models (=nodes, forming such networks) is defined in a single-aspect view, in a 'one plane' observation. In such view the 'board member' is only a figurehead, - the airport-node is a landing and taking off place of aircraft. We may call both types 'mathematical points' in the wholeness view. Well, in real life they are not.

[7e]
1) Board members network

Even in this restricted view the stereotyped links are not identical: there are differences in strength, how the individual board-members are tied to 'other' (linked) companies as well, where they also have 'some' interest/influence. They have in cases a strong managerial authority (with the financial reward) in select companies they participate in. I others they just 'sit' on the board. In these two aspects there will be observable differences beyond just the number of the involved companies. A board member's monetary interest in a company where (s)he participates can vary from superficial to substantial and so changes the mode of activity invested at the appropriate board. Different links.

[7f]
Air-traffic network

Suppose a small airport is only connected to the big city close-by by daily 2-way flights each week-day. Another similar small one has also only one such connection, but in a strong commuter traffic, 8-10 two-way flights daily. Both have "one link", but obviously no identical connectivity. The situation is similar at the 'big hubs', connected to dozens of airports maybe internationally, by diverse number of flights in the select "links", however deemed as "one link" each. It is a superficial view of the network, even at this "one-plane" view (no pun).

[7g]
Our choice of considered qualia of connected networks and the chosen strength of the links helps our view to recognize distinctions in the total interconnectedness of unlimited networking. A reductionist choice.

[7h]
Both cases are in the restricted-model viewing, observing the 'main topic' of the "network" proper. The 'nodes', however, have other connections, in connection with less restricted aspects. A board member has health, family, friends, background, studies, vacations, employees, finances, hobbies, girl friends, etc.etc., and all of them have many aspects to participate in networks with (indirect?) 'links' to the board member as an individual. These aspects (all of them) influence the personality-decisions of the board member directly, or indirectly. A final outcome in a particular case is way beyond any possible scientific analysis - many call it unrestricted "free will" decision, - because we don't know all possible circumstances (networking connections) involved.

[7i]
An airport, in turn, is much much more than a landing and take-off place of aircraft: it has people working there, travelers, authorities involved, finances, construction projects, fuel, food, etc. supplies, communication galore, merchants, airlines, and a little million others, all involved in the life-activity of the airport and involving their connections into it. All are networks with outbranching connections, effective, however, - directly, or indirectly - into the activity proper of the airport - now network of networks.

[7j]
This view is still topical and still reductionist, but in its prospectives may point to a view of the 'wholistic' interconnectedness in the world we live in. These two examples are from our everyday's life, but similar compositions are available in every aspect of the world, in philosophical systems as well, as in biological units or cosmic development.

[8] CONCLUSIONS:
BEYOND our NETWORK - VIEW

[8a]
Let us return to the starting position of the universe: the fulguration of a cluster of 'similar elements' with their accompanying "environment", to give rise (in our case) to the space-time universe view we live in. The space- and timeless fulguration is EXPANDED in this view - call it 'reality' ? - into processes for building and dissipating complexities. Physical sciences study and (in the reductionistic way:) explain the observations, which are indeed part of the plenitudinal invariant symmetrical dynamic exchanges. There are build-up steps and destructional steps, in no discernible sequence (I refrain from calling them "random", because they fit into the pattern we called "evolution" (of the universe total). There may be an intermittent dissipation process what we see as black holes, maybe the extremities of an expanding universe (if it expands indeed) are lost to the rest of the plenitude. These points are (so far) beyond our explanational capabilities.

[8b]
These lengthy musings serve one important purpose : to distinguish between the SIMPLICITY of the natural (plenitude based) content of the universe and the COMPLEXITY of our reductionistic views. We left out two characteristics, so common to most topical groupings in our universe view models: THE SPACE AND TIME RESTRICTIONS. Most networks we identify are time-bound : valid only in a niche of the lifespan of the universe. That may also be the case for the space-bound networks. Exceptions may be some ideational 'topics' which may be 'nonlocal', i.e. aspatial-atemporal. These topics may include some transitional links to the plenitude-view just as those may have in which we try to eliminate the timed boundaries. The same may happen if some other restrictions are lifted, however 'One quale we recognize is the scale-factor, select the orders of magnitude we restrictively think in as the granulation. As we cannot detect the network characteristics of a car-engine in the scale-framework of atoms, or living cell connections in cosmic measures, we cannot consider an economic setup (network) for the past 5 millennia. Our untold boundaries include the space and time frames. This makes the network thinking definitely reductionistic. This may also be the reason, why we cannot think otherwise, only reductionisticly (more or less, of course). Another reason is our (nonlocal, atemporal) mind, the mental aspect of us, our network as human beings, functions as a unit operation with its material tool, the neuronal brain. Consequently we cannot "cut out" completely the material restrictions of the universe-view, we cannot approach a 'real' plenitude-view.

[8c]
These restrictions make our thoughts about Wholism so vague. We are anchored in a reductionistic view and try to think beyond it. We are at the beginning of this study, we have no vocabulary for the not yet well-identified concepts, not even the ideas are clearly formulated. It will take a lot of effort to develop this field.

[8d]
The "Networks of Networks" thinking points to one way to approach the impredicative wholeness we live in. It is still the reductionist model system expanding to more and more, not the wholeness, to cut it into a model. The "...and more" makes the patterns uncalculable, unsimulable, not like a "fuzzy" variation, which is based on a quantized formalism, using added uncertainties. It is a thought-experiment as a fist step to overcome the thought-obstacles.

Barabasi, A. L.: 'Linked' [Perseus Publ. Cambridge MA USA, - 2002]

Bogdanov, A.: 'Tectology' [ Moscow, - 1920 ] (1st English translation): Dudley, P.: 'Bogdanov's Tektology' [Centre for Systems Studies, Univ. of Hull UK, - 1996]

Bohm, D.: 'Wholeness and the Implicate Order' [Routledge and Kegan Paul, - 1988]

Gwinn, T.: http://www.panmere.com/rosen - and private communications

Kampis, Gy.: 'Self Modifying Systems in biol. and Cognitive Sci.' [Pergamon Press, - 1991]

Kercel, St.:

http://www.unc.edu/nci/endogenous.html - and private communications

Mickulecky, D.:

http://views.vcu.edu/~mikuleck/PPRISS3.html , http://www.people.vcu.edu/~mikuleck/index.html (and others)

Rosen, Robert, most books out of print, new edition in the works.

John Mikes website ref. :

http://pages.prodigy.net/jamikes/tectology.html - (1997)

http://pages.prodigy.net/jamikes/plenitude00.html - (2000)

http://pages.prodigy.net/jamikes/SkinJuly00.html - (2000)

http://pages.prodigy.net/jamikes/homeindex.html - (1999)

John Mikes Ph.D.,D.Sc.

Madison NJ USA

John Mikes obtained a Ph.D. in chemistry and a Dr. of natural sciences in polymers with admission (called 'candidacy') to the National Academy of Sciences in Hungary. His professional work extended from synthesis and structural study of special polymers into liquid-treatment and pollution control, later in the controlled release medicine development. He lectured and consulted on three continents, obtained 38 patents and published a hundred papers, wrote/edited some books and a scientific magazine (Ion Exchange). His theoretical work in cognitive domains covered mainly internet-discussions over the past two decades after some fundamental philosophy and psychology courses in college. He retired from Ciba-Geigy as Senior Research Fellow.