network theory .. explaining .. it goes beyond ..explaining .. the framework .. upon which .. all systems possible .. existing (past and present worlds) .. or destined to exist (possible and plausible future worlds) .. the origins of all systems .. their evolution ..
a framework .. that acts as a blueprint .. systems' evolving nature .. self-similarity availed .. bestowed upon ..
a powerful tool ..
For all of the initial intuitive appeal network theory ran into two problems. First it was too complex for 1970s computer technology to manage. (Anyone who has tried to construct even a simple neural-net model of a social process has similar complaints about 1990s computer technology).
..the initial intuitive appeal .. being described as such .. of network theory
initial .. to begin with .. at an early stage .. still to be revealed in its ..all-surpassing overwhelming dimensions .. dimensions that .. cover, have the capacity to include ..the reality itself .. all realities the human individual grapples with .. hidden within an immense potential .. near infinite in its boundaries ..
..intuitive .. comes from within .. intrinsic .. inherent .. the source of all spontaneous .. ground-breaking notions, ideas, conceptualisations ..
..appeal .. its attractive power emanating from deep in the very being of the human individual .. expressing fundamental primordial elements .. vibrate .. hit chords that 'dance' to the same tunes .. in ---
.. network theory .. providing the explanations required .. the blueprint nature organised its fabric .. to be used as the tool to discover .. literally un-cover the nature of all things ..
Connectionism arose in the field of computer science as a way of deal with parallel processes. Connectionist systems not only have rich interconnections (as all networks do) but the capacity to carry on more than one operation or set of instructions at a time (ie. in parallel). In connectionist systems the various processes are not only carried out simultaneously but often without reference to one-another. Another feature of connectionist systems is the tendency to regard 'information' not simply as whether a particular bit is on or off, but also as the pattern of network activation. In this second sense information can be understood as the pathway along which a signal flows.
..connectionism .. parallel processes .. abiding to connections .. connectedness .. self-evident in nature .. describing conciousness itself .. nature's ..nature ..an ever-evolving loop .. endless loops that generate connections .. makes nature .. nature exists by virtue of the connections .. nature can never be thought as anything else .. but an immense network of connected elements .. connecting the multitude of parallel processes undergoing in its entirety ..
..parallel processes ..envisaged .. nature networked to its core .. processes ongoing .. never cease to be .. in mind of what is called .. Conway's automaton .. the essence of ..emergence .. out of nature' state space .. in its entirety .. defined .. trodden by any process .. that comes to be .. and out of them .. selected few .. connect to build networks .. to present the information .. network building information .. fractally rendered ..
..connectionist systems .. systems .. what nature consists of .. nature is comprised upon .. the conceptualisation of 'system' itself .. can never be thought as anything else but .. as connectionist system .. any other conceptualisation severely lacking in definition .. ignores vital properties .. conceptualised notion rendered useless .. system thus conceptualised .. a useless tool in probing nature .. 'brings fruits' .. with no-avail ..
.. connectionist systems .. bear .. bring along two important attributes ..
.. the attribute referred in - connectionist systems not only have rich interconnections but the capacity to carry on more than one operation or set of instructions at a time -,
.. reminiscent of ..quantum computation itself .. envisaged and sparked the search towards materialising ..quantum computers ..as such .. the parallel processes .. at its heart .. availed by quantum superposition .. the ultimate expression of the afore-mentioned attribute of connectionist systems .. nature at its very core .. its quantum realm .. abides to that property ..
..and the attribute referred in - connectionist systems regard 'information' not simply as whether a particular bit is on or off, but also as the pattern of network activation,
.. the pattern of network activation .. bits .. what digital computers rely upon .. the pattern of network activation .. a network made out of bits, of positions .. in ..on and off states .. the patterns of .. the on/off states of all the positions/bits .. the elements that make up the network .. regarded as being ..activated .. active .. in action .. not in stasis .. not static ..but dynamic .. the flow .. the sequence of presented states .. by all the bits ..otherwise known as being positions ..otherwise known as being elements .. the elements visited .. once the including network is activated .. and their states (on or off) .. being recorded .. are taken into consideration .. provide the content of the information .. taking part in the flow .. along the sequential series of presented states .. run along .. recording the signal .. the numerous combinations between the included elements .. different flows .. with the potential to give rise to different signals .. but only a few(?) are selected which provide .. sense(?) information .. represent information
according to .. 'a whole that is more than the sum of its parts' principle .. the information .. that suits ..its environment .. suits its neighbouring elements .. the tendency .. towards it .. what drives 'wholeness' .. 'wholeness' achieved ..out of .. 'whole being more than the sum of its parts' .. actions ..
these 'wholeness' .. enabling actions .. overwhelming .. information rendered .. through such manner .. reality building .. continuous reality .. continuity .. measurable .. appearing in the form of ..measurable variables .. determine the conditions .. prevailing .. the use of formulas depicting laws of nature ..
the signal flows .. the signal .. the 'process' materialising .. flowing .. coherent .. information discernible .. compact .. made possible by the architecture of the lattice .. architecture established .. architecture enabling the flux pattern ..
activated .. collectively
A connectionist model allows two kinds of patterns to be studied. The first is the pattern of the signals, communications or other influences which flow through the lattice. This shall be referred to as the flux pattern. The Lorenz Attractor (Figure 4) has, for example, been used symbolically in clinical psychological practices to describe what might be happening in the brain of a person with a bi-polar disorder such as manic-depression. The two attractor foci represent the two mood-poles and the trajectory around these two poles is chaotic in two ways: first because the precise symptomatology from one episode to another is similar yet different since no point on the trajectory is encountered twice; second: because even though the transition from one mood-state to another is predetermined by the initial conditions the prediction of when these transitions will take place cannot be made with any accuracy.
.. flux pattern .. flowing pattern ..
.. attractor foci .. trajectory around these two poles is chaotic .. no point on the trajectory is encountered twice .. and .. mood-state .. predetermined by initial conditions ... prediction of when these transitions will take place cannot be made with any accuracy
..and in this sense human nature is chaotic ..
chaotic .. outwards .. but .. equivalently .. chaotic .. inwards .. flux pattern .. becomes ..rigid .. as the ..architecture lattice ..
architecture lattice ..pre-existing nodes .. lasts longer .. than .. flux pattern ..
The second kind of pattern which can be studied is defined by the architecture of the lattice itself: the pattern of connections among the various elements of the lattice and through which the signals propagate. This is known as the architecture, the matrix, or the lattice. The lattice places, for practical purposes, limits on what flux patterns are possible. The architecture allows us to differentiate plausible futures from implausible futures and, perhaps, from impossible futures.
..limits on what flux patterns are possible .. limits .. constraints .. which they may not be infinite .. in expanding ..outwards .. in its outward expansion .. but there is infinity ..inwards .. fractality's essence ..
Archimedes .. infinities in-between real numbers.. irrational numbers ..
more discreet .. discreet-isation .. discreet ..concepts .. to its ..lower limit .. to quantum ..elements .. realm ..
Using a connectionist model of a process (eg. Eiser, 1993) requires that we treat the phase-state as the current network location of the influence under study. The propagation pathway is not infinite but confined to orbits which follow the pre-existing pathways between various elements.
..propagation pathway .. not infinite .. orbits follow ..pre-existing pathways ..
The simplest kind of model allows only one kind of influence with one direction of flow. Each neuron in the human brain is susceptible to between 100 and 200 neurotransmitters, has multiple outputs and inputs, can create new connections, lose old ones, change their resistance to certain pathways, and die. The complexity of the human brain is significant (Harth, 1991) and one should at least be prepared to believe that human society is at least of equal complexity.
It is therefore the flux pattern chaos theorists explicitly study and it is in these patterns chaos theorists will ultimately be compelled to define their own notions of structures.
In other words they do not study structures qua structures themselves but their study of structures is geared to understanding the implications of the 'structures' which in the connectionist paradigm be understood as the flux patterns called social interactions.
Initially it is useful to draw a distinction between the connectivity pattern of the lattice (the architecture) and the communications which may or may not flow through this lattice. The lattice constrains what flow patterns might exist but does not require that they do. This constraining influences not only what channels and nodes but also what dimensions may be followed.
Using a more sociological description of these terms: the lattice may be likened to the actors, actresses, props and stage where a play is to be given. The flux or flow pattern is to be compared to the actual performance itself. Traditional uses of the term 'social structure' have - by paying insufficient attention to the time dimensions - made it rather more difficult than necessary to tell the difference between props and people.
The criticism Homans made can be seen not just as the requirement that sociological laws be rooted in physiological laws but that our conceptual paradigms should allow us to understand or express one set of abstractions in terms of another.
Connectionism however allows a different approach to theorising. Because connected networks can exhibit chaos the roles of individual elements cannot be discounted in advance. Because some networks can, under other conditions, exhibit highly predictable patterns, macro level analysis can be carried out and meaningful macro level generalities sought. Connectionist models lead us to consider the 'structure' of the architecture, the 'structure' of the flux, the temporal permanence of both. At this point we can join the debate over reductionism.