addenda: Tables of basic concepts

Basic concepts

A process is an actual event. The structure of processes is an abstraction, an apparatus for our capacity of discernment. The abstract structure should contain all elementary potentialities, she serves as a framework for the potentialities. The intrinsic own character lies in the relations between the potentialities. The concepts which indicate the different potentialities should be general, in order to allow the structure to serve as a frame when working with various specific processes such as animals, mountains, theories, human actions, politics, and such.
The universe is an ordered and creative compound of processes.
 

Cosmological and geometrical data

A point is a concept of space and time, it contains no parts.
A line is a relation between two points.

A point can form a relation with itself: the line which links a point with itself can be thought of as a circle (360 degrees). The beginning and the end are connected in that single point, the contact with the actuality of space, time and movement.
The circle allows us to distinguish relations between points which have been projected on this circle.
The line which connects a point on the circle with another point on the circle is a straight line. Such a straight line divides the circle, or part of it, in two parts. The number of divisions possible approaches the infinite, things will be more clear if we lift out some defined groups of straight lines:

1. The straight lines which link two points vis-a-vis one another within the symmetry of the circle form oppositions of counterparts (distance of 180 degrees);
2. Two straight lines of related counterparts, positioned perpendicular to each other, form quadrangles of four straight lines inside the circle (distances of 90 degrees);
3. Three lines which connect three points, lying at equal distances on the circle, form equilateral triangles (distances of 120 degrees);
4. Six lines which link six points, lying at equal distances on the circle, form hexagons (distances of 60 degrees);
5. Twelve straight lines which connect twelve points, lying at equal distances on the circle indicating undulation, form a dodecagon (distances of 30 degrees each),
6. Twelve lines which link twelve points, at distances of 150 degrees each, form an ongoing cyclic movement forward or, at distances of 210 degrees each, an ongoing retrograde cyclic movement.

These are the basic proportions, the basic measure for the twelve phases of the process is 30 degrees.
 See figures at : structure #6/2 and at the additional page,
Individual space-time thanks to a unique system of co-ordinates - structure #9/3,
Events co-ordinated and connected in space and time - structure #13/4,
ZIGZAGZINE 26, A complex network 1,
Structure #26/8x tabellen van basisbegrippen,
Development and limits of processes in interaction - structure #33/10.
 

The network of relations

1. The relation of co-ordinate unity is the relative position of a unique point in space, time and movement.
   From the original position of the point several points of orientation can be established, that is to say: one as standard applicable background pattern and a number of points of reference which in the course of time and with regularity shift against that background  see figures and animations at : structure #9/3.
   The (terrestrial) construction: the calendar date is converted into the Julian number of the day and the standard time at the Greenwich meridian. From there Local Time is computed: the MC, the tip of the South-North axis, records the rotation of the earth, the local time. Thereupon the local horizon is established: the Ascendant represents the position of the point in space. With the coupling of the framework, the process structure with its undulation in the phases, to the Ascendant, this becomes the indicator of the starting point of the process. When the MC-IC axis and the points of reference are put in place the characteristic pattern / viewpoint of this process of development has been laid down in the symmetries of the circle. The cyclic structure of the process both permits repetition and demands feedback; in the point between two cycles interaction with other processes, and thus co-ordination, can occur.

Thus the relation of co-ordinate unity, at this macroscopic level (where processes comprise more than one cycle), is supplied with the three structural relations - with their own place against the background - within the circular form of the process:

2. The Ascendant - Descendant axis is the relation of interaction with the environment.
   It is the horizon which divides the circle in two halves. The lower part encloses the capacities for dealing with itself, the upper half encloses the capacities for dealing with the other, the environment. The axis represents flexibility and openness in inconstant environments.
3. The MC-IC axis is the relation of direction in the environment.
   She represents the application of the own inner space and time, the expression of the identity, in the environment.
4. The points of reference together form the relation of identity which develops itself historically and spatially.
   Together with the two axes they represent the uniqueness of the process.

Link to
an individual system with a unique system of co-ordinates - structure #9/3,
 see figures and animations at : structure #13/4 and its additional pages -1-, -2-, -3-.

  ^  

A network within a nested network

From the relation of co-ordinate unity, the universal relation, originate: from E to H, four groups of structural relations between parts of the structure of the process; from I to Q, nine groups of functional relations between two or more points of orientation, including P and Q, two groups of relations of relative motion between functions.
Functions can interfere with other functions (potentialities). The effect of the interference depends both on the relative positions in space and time and on the duration (more exact: the number of interactions or cycles). Interference comes about both inside the process, that is in mutual functionality of the functions within the network, and with processes in the environment. The interaction between different processes takes place as interference between their potentialities.
 

Structural coherence; four groups of relations within the structure

5. The relation which has come into being with the placement of the Ascendant and its frame of the phase structure upon the background with its points of reference is the structural pattern. The background is, just like the phase structure, devided into twelve equal parts with different character which indicate the working methods of the points of reference.
   The twelve relations of pattern or viewpoint are:
   1. the pattern of trivial beginning, the frame starts in the first part of the background,
   2. the pattern of private values, the frame starts in the 2nd part of the background,
   3. the pattern of differentiation, the frame starts in the 3rd part of the background,
   4. the pattern of stability, the frame starts in the 4th part of the background,
   5. the pattern of essence and play, the frame starts in the 5th part of the background,
   6. the pattern of functioning, the frame starts in the 6th part of the background,
   7. the pattern of interaction, the frame starts in the 7th part of the background,
   8. the pattern of refusal, the frame starts in the 8th part of the background,
   9. the pattern of extension, the frame starts in the 9th part of the background,
   10. the pattern of autonomy, the frame starts in the 10th part of the background,
   11. the pattern of diversity, the frame starts in the 11th part of the background,
   12. the pattern of surrender, the frame starts in the 12th part of the background.
6. In the second group, the relations between two consecutive segments of 30 degrees, the phases of the circle, the private is located next to the other in the environment, and vice versa. The phases carry the driving undulatory motion of the process, supported by the also driving differences in the background.
   The twelve relations of contrast:
   1. the contrast of mandate with trivial beginning,
   2. the contrast of begin with interest,
   3. the contrast of value with swift knowledge,
   4. the contrast of distinction with the stability,
   5. the contrast of preconditions with essence/play,
   6. the contrast of overview with functioning,
   7. the contrast of capacity with supplementation,
   8. the contrast of interaction with rejection,
   9. the contrast of selection with extension,
   10. the contrast of ideal with restriction,
   11. the contrast of limits with diversity,
   12. the contrast of society with transfer of the result.
7. In the third group, the axes of oppositions or counterparts, two segments find themselves over against one another of 180 degrees. In these axis-relations the spatial pole is combined with the temporal extreme, or vice versa, and the private is confronted with or mirrored in the other/the environment. The polarity they represent also emphasizes the cyclic property of the structure.
   The six axis relations of counterparts or symmetries:
   1. -  7. the axis of contact with the environment connects the mandate with supply,
   2. -  8. the axis of inner values connects private interests with rejection,
   3. -  9. the axis of difference in the environment connects swift knowledge with extension,
   4. - 10. the axis of inner stability connects preconditions with limits,
   5. - 11. the axis of the position in the group connects the individual with diversity,
   6. - 12. the axis of inner unity connects functioning with transfer of the result.
8. The relations of resemblance are founded on the analogy of the qualities of the parts the structure of the process, the background, and the functions. In this way a certain phase (field of work) shows similarity to a certain part of the background (manner of work) and to a certain function (instrument):
   1. actual beginning: opening phase, energy background, initiate function,
   2. the value: reference phase, interest background, attention function,
   3. flexibility: knowledge phase, distinguish background, relate function,
   4. the precondition: hold phase, bonding background, stability function,
   5. intimacy & playing: testing phase, overview background, self-governing function,
   6. the capacity: work phase, utility background, analyse function,
   7. interaction: supplementation phase, harmony background, attraction function,
   8. the rejection: resist phase, selection background, remove function,
   9. extending: exploring phase, idealising background, interpret function,
   10. the autonomy: limiting phase, anticipating background, consistency function,
   11. diversity: acceptation phase, contexts background, renew function,
   12. the purpose: resignation phase, assimilation background, integrate function.
       

  ^  

Functional coherence; seven groups of relations between potentialities

In order to realize the seven groups of relations at least two points of reference or functions are needed at a time. A function not only has its own dynamics at its disposal (see under H), but also the dynamism of the phase and the part of the backgroud in which it is located. The functions (orientation points) together realize the overall function of the individual process.
The description of these relations is based on the structural parts of the pattern of beginning involved (see: E); to this the functions add more possibilities (e.g. their relations with other functions) which are naturally more individual.
Nota bene: Some of the following descriptions are only tentative. In the last three parts of the themes line I plan to further investigate the relations K, M and N.

9. The conjoining relation unites two or more functions which are located very closely together, usually within the same working area and with the same manner of working. The relations between working areas and manners of working have been described under E: the patterns of beginning.
   The conjunction literally adds up to one function with such a mixture of qualities that the constituent parts cannot be distinguished clearly.
10. The twelve contrasting relations with a smoothly flowing character, as described under F, can be activated when brought together by connections between two or more functions.
    • the twelve half-sexts between 1 and 2, 2 and 3, 3 and 4, up to and including 11 and 12.

    The relations of 30(6) degrees amplify the under N mentioned emancipating relations of 150(6) / 210(6) degrees.

11. The two times six dimension adding relations with a relaxed supplementary character bring about a connection between the space- and the time-poles of either the inner world or the environmental world. Again, the character of phases and that of the manner of working is combined, dependent on the combination in the pattern of beginning (see: E).
    1. the six sextiles of the environment's space and time:
       • the 1-3 sextile of beginning with swift knowledge,
       • the 3-5 sextile of distinction with essence/play,
       • the 5-7 sextile of overview with supplementation,
       • the 7-9 sextile of interaction with extension,
       • the 9-11 sextile of ideal with diversity,
       • the 11-1 sextile of community with the mandate.
    2. the six sextiles of the internal space and time:
       • the 2-4 sextile of value with stability,
       • the 4-6 sextile of preconditions with functioning,
       • the 6-8 sextile of capacity with rejection,
       • the 8-10 sextile of selection with restriction,
       • the 10-12 sextile of limits with transfer of the result,
       • the 12-2 sextile of purpose with interest.

    These relations of 60(6) degrees are complementary to the under M. described specialising relations of 120(6) degrees.

12. The three groups of dialectical relations with a strong dynamic character span the four structural parts: inner space, inner time, outer space and outer time. The parts are located perpendicular to each other, at a distance of 90(6) degrees. The character of phases and that of the manner of working is combined, dependent on the combination in the pattern of beginning (see: E).
    1. the four hypothetic square angle relations of presence and initial fact.
       Two symmetries, the axis of contact with the environment can be combined with
       the axis of inner stability, via
       • the 1-4 square of beginning and stability,
       • the 4-7 square of preconditions and supplementation,
       • the 7-10 square of interaction and restrictions,
       • the 10-1 square of limits and the mandate.
    2. the four antithetic square angle relations of observing differences.
       Two symmetries, the axis of inner values can be combined with
       the axis of the place in the group, via
       • the 2-5 square of value and play,
       • the 5-8 square of essence and rejection,
       • the 8-11 square of selection and diversity,
       • the 11-2 square of community and private interests.
    3. the four synthetic square angle relations of seeking a resolution.
       Two symmetries, the axis of difference in the environment can be combined with
       the axis of inner unity, via
       • the 3-6 square of distinction and functioning,
       • the 6-9 square of capacity and extension,
       • the 9-12 square of ideal and transfer of the result,
       • the 12-3 square of purpose and swift knowledge.

    These relations of 90(6) degrees are complementary to the under G. and O. described confronting relations of 180(6) degrees and thus actually strengthen them.

13. The four groups of specialising relations with a self-evident and self-strengthening character associate at least two of the three dialectical aspects (hypo)thesis, antithesis and synthesis, and are directed in the same way at the same type of working area. The character of phases and that of manners of working is combined, depending on the given pattern of beginning (see: E).
    The parts are connected like the sides of an equilateral triangle at a distance of 120(6) degrees:
    1. the three trine relations of physical certainty.
       The relations of the inner space in a state of subjectivity
       • the 4-8 trine of preconditions and rejection,
       • the 8-12 trine of selection and transfer of the result,
       • the 12-4 trine of purpose and stability.
    2. the three trine relations of inner coherence.
       The relations of the inner time in history, actuality and becoming
       • the 10-2 trine of limits and interest,
       • the 2-6 trine of value and functioning,
       • the 6-10 trine of capacity and restrictions.
    3. the three trine relations of physical presence.
       The relations of the contextual space in inconstancy and entanglement
       • the 1-5 trine of begin and play,
       • the 5-9 trine of overview and extension,
       • the 9-1 trine of ideal and the mandate.
    4. the three trine relations of social communication.
       The relations of the contextual time in situations of objective difference
       • the 7-11 trine of interaction and diversity,
       • the 11-3 trine of community and swift knowledge,
       • the 3-7 trine of distinction and supplementation.
14. The twelve bridging relations with a comparative or emancipating character bring about a connection between the four structural parts: on the one side a polarity of the private inner space and time, on the other side an adjacent polarity of the space and time of the context. Thus two or more functions conjoin an axis of counterparts or symmetries (G) via amplification, counterbalance or shift of perspective with the private or with the social of an adjacent axis. This is in fact a movement towards an asymmetry, a possibility to break through a rigid symmetry. The character of phases and of manners of working is combined, depending on the given pattern of beginning (see: E).
    Thus a connection of either 150(6) or 210(6) degrees can, amplified for instance with a complementary relation of contrast (F and J) of 30(6) degrees, put the extremities of the opposition cyclicly in perspective, harmonize or transform (O) them with a second, adjacent, relation of 180(6) degrees (G):
    • the 1-6 inconjunct of beginning and functioning,
    • the 6-11 inconjunct of capaciy and diversity,
    • the 11-4 inconjunct of community and stability,
    • the 4-9 inconjunct of preconditions and extension,
    • the 9-2 inconjunct of ideal and interest,
    • the 2-7 inconjunct of value and supplementation,
    • the 7-12 inconjunct of interaction and transfer of the result,
    • the 12-5 inconjunct of purpose and challenge,
    • the 5-10 inconjunct of overview and restrictions,
    • the 10-3 inconjunct of limits and swift knowledge,
    • the 3-8 inconjunct of distinction and rejection,
    • the 8-1 inconjunct of selection and the mandate,
      or of 210(6) degrees, in the other direction:
    • the 1-8 inconjunct of beginning and rejection,
    • the 8-3 inconjunct of selection and swift knowledge,
    • the 3-10 inconjunct of distinction and restrictions,
    • the 10-5 inconjunct of limits and challenge,
    • the 5-12 inconjunct of overview and transfer of the result
    • the 12-7 inconjunct of purpose and supplementation,
    • the 7-2 inconjunct of interaction and interest,
    • the 2-9 inconjunct of value and extension,
    • the 9-4 inconjunct of ideal and stability,
    • the 4-11 inconjunct of preconditions and diversity,
    • the 11-6 inconjunct of community and functioning,
    • the 6-1 inconjunct of capaciy and the mandate,
15. The six confronting relations of counterparts or symmetries as described under G develop, when brought together in relations at a distnce of 180(6) degrees between two or more functions, a more or less polarising character. The character of phases and of manners of working is as always combined, depending on the given pattern of beginning (see: E).
    1. - 7. the opposition of beginning with supplementation,
    2. - 8. the opposition of value with rejection,
    3. - 9. the opposition of distinction with extension,
    4. - 10. the opposition of stability with restrictions,
    5. - 11. the opposition of identity with diversity,
    6. - 12. the opposition of capacity with surrender to the mandate.

In groups of relations which are closed or nearly closed, for instance a quadrangle (K), triangle (L) or any other combination, frequent repetition is obvious. Such a situation can concentrate, intensify and develop into a vicious circle.

Link to
the complex network of relations within (and between) processes - structure #36/11,
 see figures and animations at :  structure #36/11.
 

Relative motion; two groups of relations between functions

The points of reference or functions are recorded on a place in the circle, in reality they moved at that moment with different and for each characteristic speed. Naturally they all move in their own orbit constantly in forward direction, seen from the earth however, most of the points show regularly an apparent retrograde movement.

16. The two relations of relative speed; the faster function is located behind or in front of the slower function:
    1. the ingoing relation,
    2. the outgoing relation.

17. The three relations of relative direction:
    1. the forward direction,
    2. the stationary position,
    3. the retrograde direction.
        

Mutual functionality of functions

The mutual relation of the orientation points is one of mutually relative functions. There are at least twelve orientation points - functions - available which each, from their own point of view, carry out their own development purpose and -process with the help of the entire network of their own process. An example: function A is active within the pattern of function B in area 8 but within the pattern of function C in area 3, and both are in their manner functions within the pattern of A.

Links to
examples of functional relations in - the themes line.
 

Limitations, questions and other additional remarks

Via the single point of contact with the actual environment a process generates subsequent learning cycles as well as new events which both receive their specific purpose and character from the actual moving world of space and time. A process thus finds itself, with its unique properties in all sorts of complications, between its own unknown preconditions on the way to its own unknown purpose, its function for the environment which is a cyclic process as well. In that situation certainties cannot be all that certain. Some examples:

• The accurate establishment of the relative position of the unique point in space and time depends on the accuracy of the established space and time of beginning. In case of doubt they are - by reversing the method, that is by interrogation - in principle reconstructable.
• The location of the points of orientation varies somewhat breadthwise. The effect on its functioning as characteristic property of a process should not be great but it is nevertheless a point in question.
• The relation between Ascendant and MC marks the tilt of the earth which correlates with the time of the year, therefore the relation between the earth's local horizon and the Sun. Upwards of the polar circles this relation is by nature very particular. There the Sun for some time in winter disappears under the horizon, the Ascendant - Descendant line. The MC, the marker of time (at 12 o'clock Local Time coinciding with the Sun), also disappears for a period of time beneath the horizon. In the other extreme, when in summer the Sun remains visible all the time as does the MC, the MC can continue marking the highest point of the Sun. But this would invite some questions too.
• All relations between functions of a process are sliding scales as all other factors always join in to determine the character of that single property. The pure form of a property, its potentiality, can in practice not be established with certainty, at best be approximated statistically or intuitively. For these reasons the general definition can never be more than a debatable approximation.
• By definition potentialities of a process, the unique combination of functions, develop in the course of time into individual properties.
• In case of direct contact between two processes interaction can occur between one or more functions of both. The condition is that on both sides one or more functions are located at places (in the background) between which one of the types of functional relations is practicable. Relations between processes are active if and in so far as functions between both can interfere.
• Cyclicity must guarantee both the openness (discontinuity) and the autonomy (continuity) with the environment as the feedback and the changes of level of that process itself. Cyclic openness: the environment has (both on the macro as the micro level) access to the events which the process generates, the world or the process 'spirit of the time' provides its actual purpose there and then.
• Insight in the own purpose demands a close study of the history of the proper preconditions and capacities.
• The number of all possible relations is many times larger than offered here (I think for instance of functions which do not use the same manner of working as the phase in which they are located); for meaningful survey it was necessary to set a limit.