Structure and ordering

Structure and ordering in a system dynamic model.

During the development of a system dynamic instrument, in a first attempt the diagram, two notions in an intuitive manner came together, which were well appointed and worked out, but not yet investigated on all their possible implications: ordering* and structure. They are two key notions for the ground pattern. Ordering and structure form a contrary* and contrariety* relationship.

*Ordering: A condition of logical or comprehensible arrangement among the separate elements of a group. A condition of methodical or prescribed arrangement among component parts.
*Contrary: immediate thesis of reversing opposition
*Contrariety: mediate antithesis of contrasting opposition 

We defined structure as a perceivable traceable 'limited realm’ and ordering as the imperceivable untraceable ‘unlimited realm’ which in-form and or ex-form eachother. Implying that they are mirroring each other in their contrary as a contrariety. There is no structure without ordering and there is no ordering without structure.

The ordering in-forms the structure and the structure ex-forms the ordering and vice versa the ordering ex-forms the structure and the structure in-forms the ordering.

Neither are exclusive. The primal identity acts simultaneously as a primal antonym. Identity presupposes differentiation and vice versa. Similarities and differences presuppose each other just as connecting and disconnecting, as contrary and contrariety. It’s about the simultane autonomy of contraries that create the opportunity to relate in a non-simultane heteronomous contrariety; as contrary they are symmetrical and as contrariety they are a-symmetrical. The mediate relationship within the contrariety presupposes an immediate relationship as a contrary.

In the development of qualitative system dynamics, these two notions, structure and ordering, consciously or unconsciously played an important role, to inform you a brief summary. In our research we explored successively the diagram, the dynagram, the duogram, the dictogram and finally the hologram. The hologram is the latest and most hypothetical instrument. Many years of research are needed to bring its implicit dynamics to light. This is only possible after fundamental empirical and phenomenological research to shape a functional paradigmatic instrument as the hologram. The hologram enables us imaging complex processes.

The dictogram can be read fundamentally as a hologram, but because the dictogram includes the proverbial full and empty field, it only is and becomes "full-empty" by the empirical phenomenological research which can take place in it. In our work with organisations we use the dictogram as an in-forming field, possible to read from the diagram and or dynagram and if possible to visualize this imaging in a hologram.

Finally it is sufficient for the time being to qualify us to learn to think and work with the diagram and dynagram. So far these two are the keystones on which we founded a qualitative system dynamic framework. Both are exhaustively regulated by the ground pattern. In and from the ground pattern, they can be comprehended as a space-time, more diagram and as a time-space, more dynagram. Therefore structure is more a space phenomenon (diagram) and ordering more a time phenomenon (dynagram).

We could situate diagram and dynagram on possible different field positions, in this case in the vertical: the diagram on north and the dynagram on south. The diagram is more concentric and the dynagram is more discentric. However they form with each other a polarity in such a way that the resulting hologram could be constructed as their common center. A simplified antithetical contrariety can be found in the duogram situated on west. In a duogram the contrariety between space-time and time-space can be investigated and elaborated. A contrary could be found in the dictogram on east, the dictogram is both time-spatial and space-temporal.

When we want to read a model's structure for its ordering, we need on the one hand to understand the structure and on the other hand to comprehend the potential fundamental ordering.

Where we read the structure, we find fundamentally the structure of the ground pattern, here summarized with reference to its coordinates, connections, proportions and interfaces. Each part of this structure has a specific position in space, but this specific position in space can not be read without the manner in which can be moved in space from the one to the other or vice versa. With the structure appears ipso facto, the underlying ordering, they can not be disconnected, but can be differentiated as respectively the dynamic between composition (space-like) and configuration (time-like). Nevertheless, it is good to take into account of the therein discounted dynamic between the perceivable and the imperceivable, the material and the immaterial, between matter and spirit, both are inclusive within the functional paradigm and can only be understood as contrary and or in their contrariety further being investigated in both polarity as duality.

There where you perceive the structure of the ground pattern, and hence of each diagram and or dynagram, you find as a structure a composition in which the twofold dynamics unfolds itself into a further to differentiate fourfold, eightfold, sixteenfold and eventually sixtyfourfold dynamics. The last one is hypothetically a meaningful limit wherein the reality can be structured as to think. In the structure we find also mostly twofold dynamics, positive versus negative, wave versus particle, energy versus matter, clockwise versus counterclockwise, etc.

On the other hand, we see that also threefold dynamics can be thought in a twofold structure and you must even ask the question to what extent a twofold structure can only be completed by a threefold ordering. One position is not a position, two positions form a half connection and three positions form a whole proportion. Forms this threefold a base for the most simplex ordering of a ground pattern and therewith enables us to think out self-organizing complex systems?

Ordering is based on a cycle of interactions that may or may not move each other forward and or produce itself so that there arises a self-sustaining ordering. What number of connections would be sufficient for a network to develop a process in which a ordering will regulate itself. Thereby assuming that every interaction in principle is based on a duality of on or off, yes or no, may or may not. Only on this basis arise an reciprocity, an interaction. A grounded stable pattern of interaction is based on different research (Stuart Kauffmann) on a threefolded interaction. With one connection per position, nothing happens, with more than 2 connections per position, the system becomes unstable, with exactly two connections per position, the system behaves in a manner that is both complex and stable. Such triple stable relationships we can not only see everywhere in nature, but also in the ground pattern in which every position fundamentally stands in a threefold proportion.

This threefold we also can find in the symbolism, where for example an old Easter poem mentions it in a playful manner: one egg is not an egg, two egg is half an egg, three egg is a whole (Easter) egg. In more abstract words: any position in the structure of the ground pattern is threefold ordered, which makes that the threefold could be the fundamental phenomenon of any ordering, whereas the structure can be twofold understood.

Based on this consideration, we can ask the question to what extent within a system dynamically ordered field the ratio of 2:3 or 4:3 or 8:3 might be the constant relationship between structure and ordering, or to say it rudimentary, with 2 positions can a third party be involved, and together they form a threefolded field, whether or not to work out in threefolded proportions, with a manageable summit of 12 (4:3), for example, shaped in the hologram by drawing 4 threefold proportions in the diagram.

Two triangles on the horizontal and two triangles on the vertical, the two classic triangles symbolizing the dynamics between heaven and earth, mind and matter, male and female, Yang and Yin, etc. The two triangles on the horizontal symbolize the dynamics between appearance and disappearance, upstream or downstream, sympathetic or parasympahticus etc.

The two triangles on the vertical form a polar relation and the two triangles on the horizontal a dual relation, which implies that we see, for example, developed in the Chinese systematics behind the King Wen and the Fu Hsi, where both water and fire are positioned on the vertical dynamic ( king wen) in a polar and-and relation and on the horizontal dynamic (fu hsi) in a dual or-or relation. The first-mentioned is the oldest one so far in tradition, but it is also retrievable in the symbolism.

That makes that we can think a threefold ordering, even hypothetically, in a twofold structure. Though the ground pattern is a twofold construction from her defined coordinates, we can not escape from the middle between the eight coordinates of the ground pattern, and this center is the ninth appearing point and or disappearing point, but if nine, it forms a threefold triplicate. And as triplicate she is related to the phenomenon of the ordering and therefore to think as the structural source point from which the field can appear as it can disappear in an ending point, in-forming and or ex-forming. Ordering and structure, appearance and disappearance are interrelated and this appearing and or disappearing can only exist through structure and ordering with a simultaneous middle and or ‘in between’. Symbolically, the nine stands for the gate, providing support for passage or forming a passage between the one and or the other.

This means that the coordinates may function as respective source points (appearing) and or ending points (disappearing). Au fond in the field, pars pro toto, each part presents and represents the whole and vice versa. This means that in the ancient symbology on the ends of the dynamic cross (in the diagram as the static field), for example, was depicted a threefold dynamics in the form of three blades, and or three flowers, etc. (on the east, south, west, and north).

Thus, there is no structure without ordering and no ordering without structure. As each position as coordinate stands in a threefolded proportion with other coordinates, so also is each coordinate to understand as a threefold. That makes that the threefold eminently forms the instrument for ordering, life and spirit, as expressed in the flower of life, a threefold constructed hexahedral flower. If we want to visualize the flower of knowledge, it shall result in a twofold constructed octahedral flower. Analogous to the two primordial symbols of the tree of life and the tree of death, where the tree of death represents the tree of knowledge.

Structure, related to the flower of knowledge, and ordering related to the flower of life. We find in each a reflection of mind and matter: There where the mind is understood as a threefold and the matter as a twofold, in a twofold structure we can order mental and in a threefold ordering we can structure material. The reciprocity of obverse and reverse, ordering and structure as contraries, makes a threefold contrariety possible where the middle can appear and disappear, i.e. the field as the in-formative ordering and the ex-formative structuring principle.

We can find this observe and reverse in left rotating and right rotating dynamics of the diagram and dynagram and in many other phenomena, such as left and right, counterclockwise and clockwise, rotating stars, planets, quantum particles or lactic acids.

When we place diagram opposite to dynagram, respectively north (concentric) and south (discentrisch) positioned, whether or not similar to the northern and or southern hemisphere, we see simplified that the diagram rotates more to the left to win "depth" and structure and the dynagram rotates more to the right to achieve depth, structure and yin status. On the other hand the diagram will rotate more to the right to win 'height' and the dynagram rotates to the left for the same result. Is this a statement to venture? Depth and height, left or right serve here as a metaphor for the nature of every ‘to think out’ dimension.

Generally we see the dynagram clockwise in function, on the other hand the diagram includes a counterclockwise centripetal dynamic (from east to north) and a clockwise centrifugal dynamic (from east to south), which as an example is hypothetical analogous to the way in which, respectively, the dynamics of the low (left) and high (right) pressure areas are visualized in the northern hemisphere. In the southern hemisphere the other way, with regard to the low (right) and high (left) pressure areas. In which extent each hemisphere, for the direction dynamics in air and water is made up threefold, and over all the earth six membered, stands in this regard as an acquired observation, therefore, the question of why remains open.

What makes that we, intuitive and or in-formed by the field, chose for the respective positions of diagram (north / concentric) and dynagram (south / discentric) situated on the vertical polar axis? To note later that there exists a reflection of the sun's path in the northern hemisphere, clockwise from east to west, respectively rising and falling. In the southern hemisphere, counterclockwise from east to west, respectively ascending and descending. Similarly there can be found a reflection in the dynamics of the layers of air and water currents, sea currents or currents between the northern and southern hemispheres.

What we structure in diagram and or dynagram may be analogous to the ordering laws that we find in the earthly reality. One of them is the left and right rotating dynamic, in the ground pattern respectively antipathia rule versus sympathia rule, opposing and participating dynamics, object involved versus subject involved, centripetal versus centrifugal, imploding versus exploding, disconnecting versus connecting, disappearing versus appearing.

Which can be interpreted as a disappearing and or as an appearing field from the middle, respectively as an ending point or as a source point. Diagram and dynagram are related to each other as more space-time and or more time-space, more structure and or more ordering. The diagram gives as a structure the possibility to order thinking and the dynagram gives as an ordering the need to structure a process of thinking.

A dynamic cross in a static field and a static cross in a dynamic field. Obverse and reverse are always contrary and form a contrariety with each other, both on the vertical and horizontal axis, respectively the polar axis and the dual axis. This makes that the whole of all ordering can be traced back to the structure of twice two axis, on the one hand the vertical and the horizontal, the polar axis and the dual axis, respectively, the negative space and the negative time, and on the other hand the two diagonals, the impulse axis and the place axis, respectively, the positive time and the positive space.

So obverse and reverse can be found in the left rotating and right rotating dynamics, centripetal and or centrifugal, so we can also find this obverse and reverse in the function of the axes in the respective crosses, there where each cross makes both a quantitative as a qualitative space and or time dynamic visible. In the dynamic cross we find a qualitative negative space in relation to a quantitative negative time, on the other hand we find in the static cross a quantitative positive space (place axis) in relation to a qualitative positive time (impulse axis). This makes that quantity and quality as well as obverse and reverse function in defining space and time as a fourfold dynamics. Ultimately the positive space (place axis) and the negative time (dual axis) form the quantitative domain and the positive time (impulse axis) and the negative space (polar axis) form the qualitative domain.

Where we define the space as local and non local, so we define the time as diachronic and synchronic. We ascribe the local a diachronous character and the non local a synchronous character.

Obverse and or reverse, structure and or ordering, a system dynamic model is impossible to think without taking into account all these twofold to differentiate dynamics, au fond the reality is apparently twofold conceived and thus to think, but thinking transcends this duality by ordering her in a threefold. So that thinking can mediate between structure and ordering, from the structure more empirical and from the ordering more phenomenological, ultimately they have to be thought through and worked through in a functional threefold system dynamic connection. That forms the hypothetical system dynamic field on which man as widely as all reality can play. Finally obverse and reverse form the simplex of a complicated and explicated, in-formative and ex-formative, field on which enveloping and developing, involution and evolution as an ongoing dynamic produce eachother unremittingly. To this end form diagram and dynagram the first simplex building blocks of an in-formative and ex-formative field, both in her appearing as in her disappearing.

When we consult the ancient symbolism, we can see for example the image of the L-square in relation to the image of the (pair of) compasses. With the first you can draw rectangles and with the second circles. When you draw a circle from two intersecting rectangular lines you see when you use the intersections of the circle and the two intersecting lines to draw new circles a different division arise than when you start drawing a circle on a random position. If you use an intersection on the circle to draw a second circle with an equal radius, you can always use more points to draw more and more new circles from this one circle. This game of drawing circles was already shaped in ancient times and you'll find the example depicted in ancient Egypt. Working from the circle arises a hexahedral dynamic (the flower of life), operating from the rectangular L-square a triangular to octagonal dynamic (the flower of knowledge). What does this game with points, lines, planes and circles show?

In itself, not much if you do not look from the perspective that you can discern and or ascribe sense, meaning or significance to a symbol. Symbols are as old as mankind, apparently they orriginate from the human capacity to create and shape them, and ascribe and connect to those shapes meaning. Meanings that you have to detect, because symbols often merely are depicted in form and movement. Finding your way in the wealth of forms you begin to discover that certain forms are not accidental, apparently the man, shaping a symbol, saw something we empirically can not discern anymore. A form is just a shape or can a form link to somewhere, bring something into view, leading to that form and vice versa from that form unlock again that movement, sense, meaning or significance. In short the symbol as form represents in its structure a certain ordering, respectively a specific composition and or a specific configuration, one evokes another and vice versa.

This interaction between configuration and composition in a symbol can be read as a specific ordering in relation to a specific structure. Differentiated we could say that the structure and the composition are more determined and the ordering and configuration more indeterminate, it just depends on how you want to move the dynamics of space and time, composition and configuration, structure and ordering and that brings us to the question of who moves what. Or conversely, how can we read from or read back from the what the who, which is the question of any phenomenology that deals with the morphology of all life. We can not deny that all living things manifests itself in a form, even in a tremendous wealth of forms. In despite of, or just due to this huge variety of forms you can try to find the who that pronounce itself in a wealth of forms (the what). Looking at this wealth of forms you can not escape from the impression that many forms can be traced back into a geometric system that can also be found in the symbolic system. Apparently the form is doing something with the observer or creates the form something which is more than a random observation. Who in-forms, configures, orders the form to structure? The form remains silent unless as a phenomenologist you want to become proficient in learning to read this idiom.

So it is important to think to life this wealth of forms, which can be read in the form, is only possible if you read the form as a phenomenon, as a self-appearing, speaking entity (gestalt). Well, imaging of a given dynamic and or reading the dynamic from the form is a competence which we indicate as the ability of imaging, a competence distinguished from the ability of conceiving. Thinking uses these two faculties in every discipline or science. However, nowadays, from an emperic point of view, one has more attention for the what and less attention for the who, for the phenomenon, which wants to become image and can only be read if one wants to learn to understand again the imagery, which constitutes the realm for the phenomenology, the logos of the self-appearing, what speaks out the who and or who speaks in and from the what?

Can we see emerge a bandwidth between empiricism and phenomenology, which is also the bandwidth between the L-square and the (pair of) compasses, between a octahedral and a hexahedral imagefield? What speaks from a partially twofold and or threefold format of planes? A dynamic between matter on the one hand and mind on the other hand? A dynamic between matter and mind which among other things gives a twofold dynamic to think, for example through a diagram or a dynagram? Or a dynamic between mind and matter, that for example, among other things, can become visible through a threefold system, in multiple forms of life? Exploring this bandwidth might make it possible to learn to think the life and or bring again thinking to life?

Ordering and structure, the who and the what, subject and object as each other's contraries, form together an inseparable whole. Thereby the question arises who influences what or what influences who and or they influence eachother in their unceasing contrariety? We can approach them over the bandwidth of the horizontal / dual axis in an or-or relation and or over the bandwidth of the vertical / polar axis in an and-and relation.

In their duality they function in the contrariety as contraries, wich means on the one hand that they are related immediately, but on the other hand they mediate each other in the contrariety, based on who or what? Who or what has to be inserted in that mediation, what is the causa efficiens? (This is positioned on west in relation to the causa materialis on north, the causa formalis on south and the causa finalis on east, dynagram positions). Does the energy come from within the system or outside? Therewith the question arises in which extent open systems are in interaction with each other? If they are in interaction with each other then emerges whether or not an influence in the time. Is this then symmetrical and or a-symmetrical of nature; in an a-symmetrical relationship, there is a time arrow, and thus the formation of an increasing or decreasing order, order and or disorder. This brings us to the question of who or what influences ordering and or disordering, cosmos and chaos? Stand self-organizing critical systems (extending in the time) in a linear and or non-linear relation?

In their polarity they function as contraries in their contrariety as a self-organizing critical system whether or not in balance. What or who determines this balance, is it a passive and or active balance? When operates a system in a state of critical self-ordering? Has to be in the dynamic between ordering and disordering (extending in the time) either the structure, related to the space, as much contribute in this acting of a self-organizing system. Comes with the structure possibly the what into view and with the ordering possibly the who? Could the who in a self-organizing system be a matter of the mind (albeit still a mystery) so it appears that the what could be experimental related to the physical dimensions of the matter. Therein two fundamental factors play a decisive role, in particular size and shape. Size and shape are structurally the two key variables of a self-organizing critical system, regardless of the variety of these systems and regardless of their specific components that compose them.

In the ordering increasing or decreasing (dis)ordering play a significant role in any self-organizing critical system, the who is still subject of investigation, on the other hand the object, the what, the structure is determined by size and shape. Size and shape also co-determine as spatial parameters the nature and quality of critical states. With size and shape, we find an intersection with the symbolism, wherein archetypal patterns (sacred geometry) are considered as the hidden matrices of multiplicity. Also Benoit Mandelbrot searched for the hidden patterns in countless differing phenomena, which showed all kinds of fluctuations and irregularities. Form simplex harmonious relations a basis for complex chaotic phenomena? Mandelbrot named the building blocks of this patterning fractals: similar patterns in space and time, ranging in scale. Can the structure reveal the still hidden ordening?

The structure of a ground pattern needs to function as a fractal, a fractal which is determined by its structure, herein by size and shape. The size and shape of a ground pattern is defined as the smallest possible unity that can image the greatest possible multiplicity. How do we construct the ground pattern or how can we come to the irreducible structure of such a ground pattern, comes it from the L-square, the structure and or the compass, the ordering? Either the ground pattern forms the instantaneous center between structure and ordering, space and time, composition and configuration? Could the fractal nature of the ground pattern make it possible to image complex phenomena in time and space? For that purpose functions system dynamic research in numerous distinct phenomena; on the website we are imaging and conceiving this research.

Subpagina''s (1): Structuur en ordening