I learn through struggling with material I can't understand, pouring over it, going back to it, imagining ways I might be able to understand it, cursing it, creating inner Musculpt models of the relations between the unknowns I can't understand, walking away from it, finding it follows me wherever I might try to hide.  William Pensinger


The complementarity of wave and particle has become a standard metaphor used by many people to understand many things. The wave aspect emphasises continuity and wholeness while the particle aspect emphasises discreteness and partness. These two aspects have been contemplated through the ages. It is symbolised, for example, in Chinese coins that have the shape as shown here.

P3aThe circle represents the heavens and the square the earth. The heavens correspond to the continuous whole and the earth to the discrete set of parts. Both are real and the one cannot be reduced to the other.  Both are necessary, though some deny this.

Ralph Stacey denies the reality of organizations as ‘systems’ made up of parts. Instead, he insists that the only reality is that of relationships as in conversations. The organization is what emerges out of conversations (just as Freeman Dyson said that culture consists of conversations). Bohm was captivated by the idea of ‘holomovement’ and the unbroken wholeness spoken of by Krishnamurti. He rejected the ‘systems’ approach of Gurdjieff and Bennett.

We want to have both sides of the coin, but each has to be given its own kind of meaning. For example, it is counterproductive to model a system as a set of terms between which we draw connecting lines. Why? Because this is to turn the field of mutual relevance into yet another set of parts. It is far better to attend to the set of elements with something like a ‘feeling’ for the meaning of the gaps between them. The word ‘field’ invokes another metaphor, that Bohm himself used in his idea of a field of active information that ‘informed’ discrete reality, e.g. in the guise of the movement of particles or operations of brains.
Goban boardThe image of the Chinese coin associates with the ancient enigma of ‘squaring the circle’. This was not just a geometrical problem (how to draw a square with the same area as a given circle) but also a metaphysical one to do with how the spirit could coincide with a body (making our reality). Bennett spoke about this in Way to be Free.

The square also reminds us of a game board (such as in chess and Go) and so we are led to consider how playing a game with discrete pieces can enable us to square the circle, or realize the wholeness in a tangible form. In playing such a game we will not know what the wholeness is – as if we could look at the wholeness and translate it into pieces and moves – but we can know how to play and thereby allow the wholeness to emerge.

In yet another analogy, the square represents the conscious and the circle the unconscious and it is striking that Jung paid so much attention to mandalas as imaginative forms in which archetypes could be reflected. A game is even more interesting because it has a life while it is being played – in movement. It also can help us realise that no game is possible without gaps. When there are no gaps nothing further can be done and the game dies. Bennett drew attention to p3bthe significance of gaps in his series of talks on Hazard, the word deriving from the Arabic word for dice, which introduces another important element of uncertainty (there was an American cult novel called The Dice Man by Luke Reinhardt in which the hero runs his life through throwing a dice with six choices).
We want to consider playing a game of meaning. In such a game, the object is to bring wholeness into manifestation, or to marry the continuous with the discrete. For the game to be played, there must be both gaps and uncertainty. In our game, gaps are provided first of all by empty spaces and uncertainty by the fact that different people will do different things that will not necessarily correspond to  what is ‘rational’ in others’ eyes and which will also give unexpected results. The game is alive as it is being played. In this it echoes our idea of the Tao, for which the main symbol is water.

We will argue that a classical system of systematics will be like a snapshot of a part of the game. A meaning game is systematics at another level. A game also has several players and not just one person ‘doing the thinking’. Hence, it is embedded in dialogue. Classical systematics is somewhat authoritarian. It has the aura of saying that God has revealed the systems as truths. It is, as religion is, obsessed with oneness. In contrast, a meaning game invites us to co-create our reality. We have to agree about what is going on amongst ourselves, because there is no authority we can turn to (otherwise we stop playing). This corresponds to many insights developed in the realm of Group Analysis, for example, Patrick de Mare’s contention that ‘mind is between brains not in brains’  and Gordon Lawrence’s distinction between the politics of salvation (looking for authority) and the politics of revelation (allowing what we can see to emerge from us).

There is also a wealth of precedents, some of them contrary to our usual assumptions about games. For example, in the Mayan ball game the captain of the winning team is beheaded! Plato of course, equated philosophy with dialogue and in our own time, Timothy Leary called philosophy a ‘team sport’. In our political systems, we vote for a player rather than just for a representative.


For convenience, we distinguish three classes or phases of a meaning game.

  1. Game of Generation. This is how we produce molecules of meaning (MMs) that can be used as ‘pieces’ in the subsequent game. It can be something in its own right, but is usually preparatory.
  2. Game of Placement. This is playing the game per se, as we place (or move) pieces in a space that gives significance to where the MMs are placed.
  3. Game of Interpretation. This is peculiar to a game of meaning, in that how we understand the placements is an integral aspect of it. It can be taken as ensuing throughout the whole game or as concentrated in its last phase.

The three games merge into each other but usually concentrate into three phases (for this reason, they can be modelled onto an enneagram. An example of a simple ‘abstract’ meaning game is the Stone Game devised by Leslie Schwing and Janet Young. In the Generation game, the players go out and gather suitable stones with which they will play. In the Placement Game, they put stones one by one onto a black surface, guided by their feelings of meaningful togetherness. They can also draw in marks between and around the stones. When Placement stops, the stones are removed one by one to reveal only the marks and the Game of Interpretation can take place.

A major exemplification of the meaning game is LVT (logovisual thinking).

  1. Gather (game of Generation). MMs are produced by participants in response to a theme or question. They take the form of statements written onto the surface of magnetic hexagons. And they can derive from memory, imagination, written texts, conversation, observation, etc.
  2. Organise (game of Placement). The MMs are grouped together into subsets or otherwise arranged in relation to each other, each such arrangement signifying a new order of meaning (often then translated into a new set of written statements as a new class of MM).
  3. Integrate (game of Interpretation). The various new MMs are considered together for their mutual relevance.  This develops a new arrangement of symbolic and theoretical potential.

In Generation, elements are considered separately. In Placement, they are seen in their mutual relevance. In Interpretation, they are absorbed into a creative structure of meaning. The aspect of mutual relevance is of foremost importance. Here we must remark on the tendency in using words to split things apart (of the nature of words) so that many people look for definitions and whether this word means ‘the same’ as that word – both of which tend to take words as separate ‘things’. In the game of meaning (particularly in Placement), no word is taken in isolation. This approach was the basis of Bennett’s structural communication. He started from the view that no word (or statement) can be understood without seeing it in its relations with other words (or statements). In fact, we acquire our sense of what words mean just by this means.

The simplest approach we can take is to consider one MM as surrounded by a set of other MMs, each of which informs us of its meaning by their mutual relevance with it.  If we were using magnetic hexagons, the primitive case would look as below.



Each of the ancillary MMs could have its own penumbra of mutually meaningful MMs. We should remember that the reality is like a nexus and we can only represent a portion of it at a time and in just two-dimensional space.  An alternative form is that of a grid, and it is important to realise that such grids have a long history in the form of magic squares. The most well known is the 3 x 3 square in which the nine digits can be placed to add up to 15 in every one of the eight lines of three.


Magic squares can be dismissed as mere mathematical recreations, but not only can we argue a positive role for play but also suggest there is some useful principle in adding up to the same number in all directions. One possible correspondence between systematics and solving magical squares is as follows. Take the ‘sum’ of the terms along the various directions as signifying a triadic system; then we can consider the eight sets of three as equally well exemplifying this system, even though the terms they contain differ. Here we simply assume that the numbers 1 to 9 refer to members of a set with distinctive properties. The set might be a list of ingredients and the various triplets then acceptable combinations to make a type of meal. Reverting to the abstract numbers, item 4 can belong to three versions of the triad:  4-3-8, 4-5-6, 4-9-2.










Once we realise that the numbers used in magic squares can signify the content of any kind of set in which its members can be listed in a sequence, then we can utilise such squares for organising meanings, or MMs in our nomenclature.  The principle developed here is that of coherence between all aspects of the arrangement. There is a triadic coherence or agreement between the eight triplets: not only are all the terms conformable to a total set, but the members of this set can be combined in eight mutually consistent ways to give eight forms of essentially ‘the same’ triad.

The square form of game board gives us the series 1, 4, 9, 16 and so on which are the number of points of a significant class of N-grams that includes the enneagram. If we make a (non-magic) square as here with numbers in simple sequence, then the three vertical threes define three different aspects of the fundamental triad. In Richard Knowles’ application of the enneagram, these are three different kinds of leadership: 1-4-7 strategic, 2-5-8 command and control, and 3-6-9 leadership in self-organisation (see his book The Leadership Dance).


The game space can be regarded as a territory and the players as seeking to occupy it as much as they can. Once the game has developed, any unsanctioned move by a player can be felt as an act of aggression.  Such a moment occurred in the playing of our game, when one person altered the display while others were elsewhere.

The playing of games has always been associated with symbolisation of conflict and the games of chess and Go, for example, have often been conducted as if they were combat. This is largely because they are predicated on having a winner and loser and the winner acquires kudos or money. But it is also because players invest themselves into the pieces and their moves. At first it may seem strange that we do this. After all, the pieces in play are mere abstract tokens, which is highlighted in the case of the Stone Game, where they are reduced to extremely simple and seemingly neutral form. However, such innocuous elements have the capacity to attract into themselves our passions and self-identity. This was discussed by the Comix artist Scott McCloud in his comic book Understanding Comix when he pointed out that the simpler the drawing of a character, the more we were likely to identify with it and fill it with our own self-sense; in contrast with more realistic drawings that we will tend to see as Other.

Our pieces are MMs and because they involve written words are conceptual in nature. They stand between abstract simplicity and realistic portrayal. Nevertheless, they can go through a development for us as we invest them with substance from our own sense of meaning of ourselves. The metaphor we use for this is that they become charged with meaning. Initially, a written statement (or just name) of an MM is something ‘at a distance’ from us: we only have some vague sense of it and it can be treated as just an item we know about but has, as yet, little ‘weight’ for us. As the game proceeds, the MMs become charged up and their selection and placement is felt ever more strongly.

The game of Generation starts with the different players contributing their MMs. In our case, this was in response to the aim of identifying MMs that were significant for our understanding of the kind of thing systematics is. At the start, the players only have some sketchy ideas about this, so their MMs are provisional in character. Nevertheless, they reflect the individual knowledge, experiences and beliefs of the players; so there are contrasts between the MMs generated by different people. The MMs generated by other players stimulate each player to associate to new contributions. We call this  game in its own right because there is already a considerable interplay between the players. An MM put up by one player may challenge the points of view of the others. It may refer to something they do not know very much about, or even not at all. It may seem to be off the point and of no relevance. In this game, all contributions are allowed, so a typical response of other players is to ‘compensate’ for or offset for an MM they find problematic by generating other MMs of a different character. As we shall see when we come to a summary of how the game of meaning ensued, this meant that the players were driven to explore a complex meaning space for beyond what any one player would have generated by themselves. The MMs that appeared ranged over the mystical, artistic, technical, representational, and so on.

Initially, players identify with the MMs they have contributed themselves. But a dialogue is in process that leads beyond this to players embracing contributions by others as well. In a rough way, we can say that each player comes to feel a subset of the total set of MMs that contains more than their own but is less than the totality of them. Dialogue allows players to question and explain MMs, so that eventually there is an enlargement of perspective on the part of each player. His or her subsets are charged with meaning.

The game has already engaged in conflict and cooperation. Players have different views but they are prepared to allow some MMs outside of their preferences. An important rule is that – at least initially – all contributions are accepted; but we must remember that they are simply stored in a reservoir as it were, in a neutral space, and do not at this stage appear on the game board per se. At the end of the game of Generation, each player will have implicitly structured the total set of MMs into subsets relative to themselves. We say ‘implicitly’ because it is not explicitly articulated. It is artificial but maybe useful to consider that each player will have partitioned the total set into four categories (used in structural communication):

  1. Those that are regarded as essential
  2. Those that are accepted as relevant
  3. Those that are considered as irrelevant
  4. Those that are rejected as misleading

It is in the game of Placement that conflict is more energised. There is a restricted space and not all the MMs can be accommodated. In the early phases of this game, however, there are still some places open so that new placements can be made to adjust to and ‘correct’ for earlier placements. We can see that the implicit conflicts of the previous game are now being made more explicit. When the game space is fully occupied, the only moves open are (a) replacements, and (b) going outside the game space (thereby in some sense changing the structure of the game).

We can see this game as a fight over territory. Each player wants to bring what they see as the essential MMs into play and exclude those they regard as misleading. We can be reminded of the terrible things that ensue in the real world over territorial conflict, which involves a struggle over occupation by different groups (counted as number of bodies) but also a struggle over occupation by different beliefs or meanings. It is also reminiscent of family feuds, which can include struggle for control of resources but is essentially a struggle of power.

A meaning game allows us to move in a symbolic space to seek resolution and co-operation.  In the diagram here, we show three sets, including the intermediary one in which we play outside the initial framework.







The set of games – Generation, Placement and Interpretation – have their different centres of gravity even though they share to some degree in them all. That of Generation is more neutral or ‘monadic’ than the others because we have the principle of accepting all contributions into the collective space (the ‘reservoir’). That of Placement is more conflictual or ‘dyadic’ because it is territorial. That of Interpretation is more co-operative because we seek to integrate the emergent perspectives into a meaningful structure that can accommodate them without loss of their individuality.

A meaning game is situated in the middle region of the spectrum defined by paidia and ludus. Paidia is spontaneous play for the sake of itself while ludus is more formal and involves winning and losing [The Paidia/Ludus Continuum by Dakota Brown.]

Another important feature of a meaning game is that it is to some degree always a nomic game; it has rules that enable the rules to be changed. A game begins with a set of fixed and simple rules but, as it develops, these are modified. One obvious example of this we will discuss in the next section is coming to agree to work outside the initial game grid. In a strict nomic game, the changes of rule are the main focus and explicitly discussed. In a meaning game, they are emergent and it is then up to the players to acknowledge and clarify them.

4 X 14 board









Ancient Game Board carved in rock at Petra



The game began with a basic 3 x 3 grid. This was only the initial framework and gave way to a more complex and ‘organic’ form as the game progressed.

The theme of the game was the mutual relevance of systematics to other methods of making meaning (MMMs!). To this end, a set of MMs representing such MMMs was gathered as an initial step. There had already been discussions on the nature of systematics as a cultural element and in various perspectives, as was described in the previous section.  The set of MMs was not closed but added to as the game progressed and participants wanted to bring in new insights. Relatively little time was spent on expositions and explanations of the MMs and participants had to rely more on feeling than on any detail.
Hundreds of moves were made and what is shown in the following summary represents only a fraction of them. The moves were of the following kinds:

  1. Place an MM at a location of the grid (taking it from the available set)
  2. Move an MM to another position
  3. Remove an MM (back into the unselected set)
  4. Make a new MM (and Place)
  5. Change the format of allowable positions (de-restrict the grid)
  6. Develop ‘local’ realms of meaning
  7. Integrate local realms into a global pattern

Agreements had to be reached over the moves. These agreements were provisional and approximate. At all times, a compromise was being worked out between continuing the flow of the game and going through explicit negotiation procedures.

To begin with, participants took turns in making moves; but towards the end, this restriction also gave way to more free form dialogue. 
xSome sense of the progress of the game can be given in terms of two of the many stages it went through. The first image is of an early stage in the game (shown on its side to enable the words to be better read). The MMs that were then on the 3 x 3 meaning grid are shown here separately for clarity. 







At this stage, ‘Systematics’ was not in the original grid at all. The whole game area is show below. This MM is being seen rather as the ‘centre of the co-ordinate system’ of the grid and from it came two axes of reference encompassing the grid. The MMs on the right hand side are being held ‘in the wings’ and make their entrance later on. Also note that by this stage, the meaning grid had been exceeded by MMs placed to the right and below it.

In the final stage of the game, a very different form had emerged.
























In this form, the original grid has disappeared entirely and a complex whole shows itself. Nearly, but not all, of the original set of MMs have been brought into the picture.  The following photos give an impression of the series of stages connecting the two representations.



The placing of ‘Gaps’ marks a significant new departure from the original 3 x 3 grid and gives this MM strong emphasis.



New kinds of grouping appear, so that local regions appear with their own emergent organising principles.


‘Systematics’ has been brought into the main arena and appears as a major centre of gravity for its local regions.


The previous tendency continues even more strongly and an overall shape begins to appear.



iThe arrangement moves towards greater symmetry while a new and highly significant MM appears in relation to ‘Systematics’. This is ‘Animism’, which was intended to reflect an implication of the previous MM ‘Taoism’.

The final additional MM ‘Shit’ was only partly tongue in cheek. It was intended to acknowledge the ground material out of which what is living can be made.

The symbol that appears towards the bottom of the final structure was placed there because of a felt need for an MM to complete the vertical column. This was provisionally identified as language. Adopting this item, the vertical column then appears as a sequence of five MMs, the composition of which was surprising to the players themselves. In a word, it was truly emergent. ‘Hazard’, ‘Animism’ and ‘Shit’ are wild elements while ‘Systematics’ and ‘Language’ appear as domesticated ones.

We can adopt the principle of sequence (see next section) to correlate this set of MMs with elements of two schemes that Bennett developed. One is of the Essence Classes while the other is of the Energies. In the case of the Essence Classes we have a pentad in which the central ipseity is Animism (not Systematics). Animism came into view as a replacement for an earlier MM – Taoism – and was intended to convey the significance of taking everything as alive and meaningful in its own right. Systems are more abstract but bring into view what is beyond life. We can, therefore, regard Systematics as the ‘higher nature’ of Animism. But another surprise is that then Language appears as the ‘lower nature’ of Animism.

The pentadic order relates to the human body in an interesting way. The bottom term is associated with the anus, as the crude word Shit implies, but Language appears in association with the base of the spine, location of the ‘moving centre’ but also of Gurdjieff’s mythical organ of deception he called kundabuffer. Animism is centred in the belly and Systematics in the chest. Here we might remember the ancient Greek psych-physiology which located ideas or thoughts in the lungs, while the head – here as Hazard – was located in the head but as ‘beyond consciousness’, as sexual, creative and unpredictable. Any such correlation can be only suggestive. Another one might relate to: Head, Throat, Heart, Solar Plexus and Belly.

The diagram below conveys some sense of the correlations according to sequence and includes elements from Bennett’s twelve-fold scheme of Energies.














The detail of the exchanges that went on the playing of the game is not included here, but arriving at the initial set of MMs, engaging with each other over their placement, coming to change the space of play and arriving at interpretations was a rich and complex process and we faced such questions as:

  1. What could we take as the ‘final product’ of the game?
  2. How could we present the real substance of it to people who were not present?
  3. What has happened to us by playing the game?

The ostensible product was the final structure of MMs but the more essential result was a shift in the way we understood systematics. At the same time, it was thought (by some of us but not all) that we could take the structure and present it to a group and initiate a dialogue in which we could recapitulate and even develop the thinking that came about in the game.  The situation would be reminiscent of structural communication, where there is an already worked out set of MMs (content) and also a meaningful structure (form) but, to further the correspondence, we would have to create another kind of meaning game to enable people to enter into the experience. For example, we would have to take sub-features of the final structure and create questions that would elicit responses from participants to be expressed as subsets of the total set of MMs and also find a way of bringing out the structural relations between MMs. This was never obtained in structural communication, which remained in the domain of sets (see next section) and only speculated about sequence, let alone symmetry and so on.[ Amongst these speculations, we thought about three kinds of ‘programming’: A type concerning sets, B type concerning sequences and C type which may be related to symmetries. ] A major part of the power of the game and its results lay in the enigmas it produced, such as those briefly discussed in this section. The game of Interpretation never ends. It is akin to contemplation. As we progress through the meaning game we find that we become increasingly aware of more and more subtle ‘shapes’ of meaning. The more we articulate in explicit form the more we feel yet deeper levels in the implicate order. For every explicit representation, there is an inner reflection or complement that is implicit and thus only at the threshold of what we can name and describe.

The construction and playing of the game, as well as the reflections beginning to be expressed here about its implications, led to a new view of systematics as a discipline and we attempt to describe and discuss this view in the next section.

Magic Squares - a Method of Relevance Computation

Magic squares appear in many guises. One of them is in Euler Squares, which can be illustrated diagrammatically as follows. In the case of a 3 x 3 square there is a given set of three shapes which can take three colours (shadings):




One then looks for an arrangement in which every row and column contains all three shapes and they are each of a different colour. One such is shown below. There are nine different ones depending on which element is placed in the centre. The diagonals will always consist of one shape in three colours or one colour in three shapes.


These kinds of square give a different perspective on the triad, for example, because they use two dimensions and not just one.  The idea of magic squares can help organise our thinking about an idea (word, method, feeling, etc.)  by ‘placing’ it in the centre and arranging other ideas around it that have a ‘magical logic’ to their arrangements.











Geometry – symbolism
Set theory – transfinite numbers
Archetypes – Jungian psychology
Mythology – narrative form
Game theory – multi-player
xxxxxxTechnology - physical systems
Music – principles of harmony
Astronomy – reconciling cycles


Which of these would you play in the game? Where would you place them?