In the 1960s, John Bennett and a group of young researchers addressed the problem of enabling quality education beyond small numbers of privileged students. They developed a method called structural communication, which simulated the work of a small tutorial group without the actual presence of an experienced tutor. It was far beyond the simplistic and mechanical devices then in view based on multiple choice and linear teaching machines. It was based on a strong distinction between knowledge and understanding. Knowledge could be acquired bit by bit and was largely right or wrong, but understanding could only be acquired as a whole and would embrace multiple interpretations.
SC was underpinned by strong psychological and philosophical ideas, particularly holistic and systems thinking. It translated these ideas into a method that relied on structure and two-way communication. In this method, understanding is generated by an activity of the student who has to reconcile what he knows with what he does not know. He does this by engaging in a two-way process through an active interface: in order to receive information he has to give some.


The ‘not-known’ side included the simulation of the tutor and his understanding of the topic. The active interface enabled quite complex ‘messages’ to be exchanged and it was the realisation and design of this interface that was most profound and yet simple.
There is a universe of discourse. In this universe – as in a particular topic of study – there is contained a set of recurrent meanings – which later were to be called MMs or ‘molecules of meaning’ - that need to be known in order to begin to be able to enter the discourse at all.  What the MMs are depend on the topic and its treatment. While the student can learn what they are semantically – as might be tested for through multiple-choice – he may not understand how they are related to each other and, even more importantly, how their meaning changes with context.
The visible part of the active interface was called a Response Indicator. The example below is taken from a Study Unit on thermal physics. 

The student will know what these statements are about but not why they are significant in relation to particular purposes and in different contexts. He is then faced with a set of questions that have to be ‘answered’ by a selection from the array of MMs in the Response Indicator (numbered to expedite and simplify the process). In the case of physics the questions could be based on the design of experiments or apply to the requirements of explanation (the MMs shown in the example relate to temperature scales). The art of writing such materials very much depended on constructing questions that could be answered by the simple device of selecting a subset of MMs from the array.

The active part of the interface was a diagnostics that operated on student responses in terms of and, or, and not logical functions and supplied apposite comments on particular responses. Every MM in the Response Indicator was given a value of ‘essential’, ‘relevant’, ‘irrelevant’ or ‘misleading’ by the author-tutor in relation to each question.

The main principle of structural communication was that meaningful communication involves not only information but also the structure of information, or ‘information about information’. In general terms, we can communicate both content and form. The diagram shows the idea better than it can be defined.


In the original educational context the left hand side relates to ‘student’ and the right hand side to ‘tutor’. But the model can be extended in many important ways, the most general being to identify the left side with knowledge and the right with understanding. Allied to this was the step actually made of metamorphosing SC into LVT. In LVT there is a process that begins on the left and ends on the right with an intermediary stage relating to the ‘active interface’. The three stages became established as Gather – Organise – Integrate.

Structural communication metamorphosed into LVT over many years.
Students became participants who, instead of talking ‘at a distance’ to a tutor could profitably discuss things with each other.
The content of the Response Indicator could be generated by the group itself.
MMs were made as physical objects that could be moved around on a surface.
Selections in response to questions were superseded by assembling clusters of MMs and then giving them meaning.
Diagnostics were replaced by dialogue.
A structure of process was articulated whereby knowledge could be transformed into understanding through a cycle of work.
It was an application of meaning technology or ‘logotechnology’


MEANING TECHNOLOGY – power of combinations

The critical component of structural communication and its development into LVT and beyond is the MM, a discrete unit of meaning that can be combined with other units to produce new meanings.

The meaning equation         M(1) + M(2) = M(3)

followed the Aristotelian formula the whole is more than the sum of its parts  because there is ‘something more’ in M(3) than in the addition of M(1) and M(2). The principle is extended to a set of N MMs such that every combination of any number of MMs up to and including N has a potential of meaning. An illustration of the principle is provided by modern sciences: there are the standard sciences such as geology, biology, chemistry but there are also relatively new sciences such as biogeochemistry rising to prominence as a science of the biosphere. Such new sciences arise in relation to a purpose and context and are not undertaken abstractly. With just 5 MMs, there are 25 possible combinations; with 20 MMs the combinations run into thousands.

Using analogies from natural science, some combinations will be more fruitful (e.g. as a science) or more stable (e.g. as a chemical compound) than others. But it has been learned that all possible combinations can be made and many turn out to be useful in unexpected ways, even though many combinations may remain ‘unthinkable’ for us.

The properties (=meaning) of a combination cannot fully be deduced from its components, but to some degree anticipated, if we have knowledge of other similar combinations. This is a principle of systematics. Therefore, understanding can be seen as a developing grasp of the meaning of all possible combinations in relation to each other.

The term ‘combination’ means the condition of mutual togetherness that is more than an addition. Bennett distinguished this state by the term coalescence and contrasted it with the state of mere addition which he called compresence.

There are many pathways between the extensional plane of compresence – illustrated very exactly by the example of a Response Indicator given above – and the intensional unity of coalescence, which we take to be a state of understanding within us. These are symbolised in the figure below, suggesting various intermediary staging points or hypotheses.


The term meaning technology can apply to the naming and organization of MMs involving physical objects. If the compresent points or MMs (shown on the bottom line) have names then the intermediary points are MMs of another order and can have names also. The requirement of these names changes in going from compresence to coalescence rather as from description to conation, or aspiration.  The movement through the pathways can also be seen as analogous to metabolism, in which case the upper regions are more connative as in the sense of ‘being born with’ the person.

A combination or grouping of a number of MMs can be given a name as a compresence, as a label or classification. It can also be given a name that is a realisation of a truth, a genuinely new emergent meaning.

NOTE: The combination A, B, C, D, E is a cluster of MMs on a level and not a vertical arrangement.

TOPONOMICS – meaning of placement

The word derives from topos place, and nomos rule. It means the ‘rules of placement’ and refers to a type of visual logic, or grammar.  If we have a rectangular grid onto which MMs can be placed we can picture any particular MM as proximate to eight others. The arrangement can be seen as to 8 directions, along four axes, or in two dimensions.


The first proposition in toponomics is that closer proximity means a higher degree of mutual relevance than less proximity.
The second proposition says that the meaning of placing an MM in different directions is different.
This is to make spatial arrangement meaningful. It draws on the general instinctive sense we have of up-and-down, left-and-right, within-and-without. 
The pattern of arrangement repeats, as in this 5 x 5 grid. Evidently, the structure is fractal in a way similar to designs found over thousands of years from ancient times, related to genealogy.



The topological features of meaning are additional to those of combination. Each line, each area has an inherent meaning. Regions with similar shapes can be expected to have similar meanings, or correspondences. Toponomics is the structural basis of visual thinking, which has roots in early conceptualizations of art, as in the Vasusutra Upanishad.


We dance round in a ring and suppose,

But the Secret sits in the middle and knows

Robert Frost

If toponomics relates to the spatial aspect of meaning, ring composition relates to the temporal, as in narrative. The British anthropologist Mary Douglas has established that ring composition is a feature of most ancient texts and was used into the Middle Ages in Europe and the Middle East.

The original conception of structural communication included two types of programming. A type dealt in sets of MMs while B type dealt in sequences. Sequences are represented by linear orders, that is as lines; but this includes circles. 

Circles allow for wholeness and pattern. The most obvious pattern divides the circular sequence into two halves, which then leads to making pairings across the circle. Such correspondences played a considerable role in ancient texts. This form of representation was introduced into LVT by the year 2000. It obviously leads to making use of many kinds of symmetry and lends itself to representing the multi-term systems of systematics.

This form of representation leads to interesting results since the agent has to decide where to start and what the rationale of the sequence is – and also to bear in mind the two halves of the circle, which makes the mid-point most significant. This is extended into having three, four, five, etc. critical points or nodes. In the simple dyadic form the top point is called the ‘latch’, because it unites beginning and end, while the lower point is called the ‘turn’ because that is where the process changes.


What then emerges is articulated sequence or structured process. The assumption made is that symmetrical patterns of connection tend to be harmonious (in balance). The depiction corresponds with the view that reading a text is both diachronic and synchronic – sequence and form.



A magic square is composed of numbers which add up to the same total in any direction. The most widely-known exemplar is the 3x3 square using all nine digits of the decimal system.


The concept is applied by analogy to meaning squares by seeking to establish an arrangement of their constituent MMs such that they make sense in all directions and regions (cf. toponomics). In the most sophisticated and subtle application, one has to establish that the triplet meanings along all eight directions are equivalent in some significant way. These requirements have to be interpreted according to purpose and context and there are no formal algorithms for doing so.


This example is the meaning square used in compiling this presentation of meaning games (logo-games), produced by one person.

The squares can be extended to any number, usually with 5x5 being the largest of convenience. Typically, the meaning square is situated in the centre of an arena of play, the grid being filled and changed in an interaction between several players. MMs will be taken from a reservoir around the board. Number of players can range from one to several (cf. n-logue).


Though the most usual form of the meaning grid is square, circular and triangular forms have also been used. The triangular form lends itself to three perspectives, while the circular favours a view of centre-and-periphery.






More complex variations can be produced when the form of the meaning grid is allowed to transform in response to the progress of a game, as in these tessellations.



Meaning, or logo games are a natural outcome of the accumulative interplay of structural communication, toponomics and meaning squares. They were first developed in relation to systematics. It was later found that some features of meaning games had also been addressed in independent developments by others based on the Glass Bead Game of Herman Hesse. In a meaning game, there are usually 3-5 players and a grid with capacity for 9-16 MMs. The most concentrated game is with 3 players and a 3x3 grid.

It is another type of ‘game’ to generate the set of MMs on which the play will draw. Given this set – larger of course than the available spaces – the players take turns starting with the following rules of play:

  1. They can place one MM in the grid
  2. They can move an MM from one place in the grid to another
  3. They can remove an MM from the grid

The grid becomes filled and the rules then allow for

  1. Replacing an MM with another one (from the store)
  2. Exchanging two MMs in the grid
  3. Creating a new MM and placing it

A further stage is when placements are allowed outside the grid.

All rules have to be agreed by the players and changes can be negotiated. There is thus some aspect of what are called nomic games – games mainly concerned with how rules can be used to change rules. This allows the format of the game space to transform, as shown in this example, which started as a 3x3. The original grid served, in a quite literal sense, as a matrix or womb.

Meaning games are art, because there are no logical rules for calculating what MM should be placed where. The substance of the meaning game is mutual relevance, which is another expression of the meaning equation. When two MMs are placed in proximity, then this indicates a mutual relevance between them that can be understood not only in terms of their separate content but also of their relative position.
A logoic game allows for different levels of meaning.

The ten MMs which can be placed in the triangular game should all have equal weight or a similar level of meaning, even though this is difficult to define. Then there are nine triangles, each specified by three MMs and such triangles can be taken to signify a new level or type of meaning thus enabling the arising of nine new MMs. The matrix of the game becomes a generatrix(strictly speaking: a geometric element that generates a geometric figure, especially a straight line that generates a surface by moving in a specified fashion). Other new types of MM can be generated, for example: by paying attention to the three main lines of the triangle, or to the central hexadic figure. There is an interplay between the meanings of points, lines and areas.


Although restrictions of time and energy put limits on the process, there can be some asymptotic sense of the whole meaning.

 The representation of structure in this method goes far beyond what is attempted in standard systems diagrams, which are typical of habitual ways of representing structure. There is immense mental inertia that restricts thinking to object-like terms of one thing acting on another. This not only restricts thinking to mechanical causal lines but also determined that elements of whatever kind are only considered linking in pairs. Logic gates offer some possibility of going beyond this but are rarely used save in simplistic yes/no mode. The diagnostic tests used in structural communication such as ‘if members of set A or members of set B are included and also members of set C, then . . .’.correspond with the structural thinking expressed by toponomics.
Consideration of the reality of new meanings emerging from a combination of previous meanings is a main feature of systematics.  





The idea of a coalescence of MMs to make a new coherent meaning has its roots in Bennett’s systematics, which he worked on for some decades before the development of structural communication. Bennett’s formal definition of a system was

A set of independent but mutually relevant terms

This was extended to postulate that the dominant attribute of such a system derived from the number of its terms. Bennett articulated these attributes for the first nine (or twelve) systems and discussed their applications. He used Greek terminology for the systems, namely Monad, Dyad, Triad, etc.

Every system also has a structure which is constituted by the set of coalescent combinations it realises: these are the ‘strong’ mutual relevancies of the terms with each other. Take the example of a four term system or tetrad. There is first a set of four terms with the possibility of coalescence. They are compatible. We know that the terms are mutually relevant but not in what way – that is, we do not yet understand the meaning of them taken together. There are six pairs of terms, each of which can become coalescent; and six triads also. The final state of a fourfold coalescence must integrate all the lesser ones, as in this linear picture:

            4 terms – 6 pairs – 6 triads – 1 whole

It relates to a more general linear model of understanding, which Bennett referred to as progression and expressed as the series of number systems as such:

            Monad – Dyad – Triad – Tetrad – Pentad – Hexad - - - -

Significantly, a similar conception is to be found in the Russian methodology of innovation known as TRIZ as movement towards Ideality, here shown in abbreviated and paraphrased form:

            State of affairs – contradictions - innovative principles - - - Ideality

For both systematics and TRIZ the linear picture is insufficient, because it is also possible to ‘start from the end’ and work backwards. In systematics, moreover, the starting point can only be determined by the end point. That is to say, we can only know what the terms are in the light of the whole system. The pictures can be amplified by use of ring composition.

First the simple picture. The two aspects ‘whole system’ and ‘terms’ are placed together because they arise equally in some unknown way. The circle represents a cycle or ‘story’ to do with making combinations and testing them for meaning, and thereby changing our understanding of both the whole system and its assumed terms. The lower small circle signifies ‘the turn’ and it is construed that in one direction is the clarification of what the terms are, while in the other is understanding of what the system means.



A more complex picture gives space to a process of generating the terms, which becomes the first half of the cycle. It is identified with LVT and terms are made from MMs




Many different kinds of whole emerge and, allowing one step further than what is shown in the last image, there are at least four:


Where we use the word quality to signify a wholeness beyond systems.

This kind of extrapolation is an analogous mode of the thinking that obtains in meaning games, when a ‘shape’ of meaning is repeated and transposed (another analogy being the transposition of melodies into different octaves). The first three systems are shown merely as an indication of possible transpositions.

Systematics is an explicit form of analogous reasoning based on number and form. These are exactly the features exploited in structural communication and LVT and developed by the methods of squares, rings, toponomics in general and logoic games.

‘Ordinary life’ is widely felt to be characterized by conflict and competition, linear process and repetitive behaviour. The systems of systematics offer a world that contrasts with the ordinary one we presume. They represent several elements acting not in competition but in mutual accord; things happening together without confusion, and maintaining stability while allowing for the emergence of new things. In this respect, systematics is idealistic.   A similar picture is given in TRIZ, but with the concept that systemic harmony canbe realized because there is an inherent trend or trends that move processes and devices towards Ideality, both in nature and in technology.

The qualitative sense of such ideas as harmony and coalescence can be abstractly expressed by the requirement to have each term of a system of equal value to all the others as well as being of the same kind as each other. This is a paradox in terms of classical logic, because if the terms are not the same, how can they be equal? In practical life, it is simpler to see. For example, in a heterosexual couple who live together in love the man and woman are not identical while both being human, such that they are equal in presence, value and meaning etc. The example shows how we can believe in such systems (as the loving man-woman couple) but not be able to observe or measure the harmony of equality from outside: it is up to the two people involved and even they may not be able to know. The example also brings into the picture the question of values since the mode of togetherness of the two people is more than factual.

The postulate of equality of value leads on to the prospect of co-creation and the question of how a coalescent harmony may be realized.  


In N-logue the meaning of the whole system is equally produced by each of its N members. In more specific terms, an N-logue is a dialogue of N people, each with a distinctive role, but with equal value. N-logue is a logoic or meaning game played through speech without the support of any visual display or action with objects. It was developed in the 90’s to foster creative thinking in small groups and as an implementation of systematics: the nature of an N-logue is largely derived from the number N. 
N-logue is implicit in logoic games and made explicit in certain kinds of game. Below are the structured spaces used in 3-logue and 4-logue ‘board games’.

In such games, the players are not distinguished in role and it is only the requirement of equality that obtains. In speech form, there are also distinctions of role or specified relations between the players. This is best exemplified in the application called trialogue. There are three players: one asks questions, one gives answers and the third makes comments. They speak in a prescribed order, usually Question – Answer – Comment, reiteratively. Players can change roles but only with mutual consent of all the players. An important feature of the method is that deviations from the order of speaking are inhibited (players cannot argue back, ask for clarification, etc.) This constraint is crucial. It bears on how it is possible for a ‘system’, a multi-term harmony, to enter into manifestation in time and space.

Only one person can speak at a time (in order to be heard). However, what is heard – or in the mind – can embrace more than one utterance. It is postulated that N-logue obtains when, in the ‘listening mind’, N utterances or one cycle is apprehended or felt as one whole.

In relation to any given utterance in a trialogue, there will be one person who makes it, another who listens and then has to speak, and another who listens to both the previous and then has to speak. Of course, as the process continues, this effect travels round the circle of three people. The cyclicity of the process engenders coalescence, creating a consciousness of the whole system over and above the sequential awareness of one utterance after another. This is tantamount to creating a larger present moment than can be sustained by any one of the participants by themselves. The size of this greater present is associated with one cycle, hence with recurrence.

In Bennett’s cosmology of three kinds of time, the sequence of elements belongs to successive time, their mutual presence to eternity and the cyclic action to hyparxis. (The idea of three temporal dimensions is now being explored independently by Peter Caroll.)

There appears to be a general function we can identify with understanding: it acts to reconcile the conflicting natures of the realm of space-time-causality and the realm of greater freedom and all-inclusiveness, variously projected as ‘spiritual’, ‘imagination’, ‘higher dimensional’ and so on. One of the projections is as the unconscious. In the treatment of the unconscious in Matte-Blanco there are two ‘logics’, one of the conscious mind and one of the unconscious. The latter has contrary properties to the former. Thus: asymmetrical relations are symmetrical (e.g. the relationship of child equals the relationship of parent); the part is identical with the whole (the arm is not just part of the body, the body is part of the arm), and any member of a set is identical with any other and with the whole of the set. Applied to systematics, all relevances are mutual, a term of a system is equivalent to the whole of the system and every term is the same as any other.  From this point of view, systematics represents the integration of unconscious mind into consciousness.