A Quadratic Model of Consciousness

CHAPTER DRAFT by John Wood for The Divided Mind - a book edited by Dr. Jane Grant of Plymouth University.

Maurits Cornelis Escher 1943 Self Portrait

Self-portrait by M. C. Escher, 1943


This article describes methods and ideas that emerged from a continuing enquiry into 'metadesign' that led us to think about the role of 'consciousness' in teams, communities and the biosphere. In the West the notion of 'consciousness' has been shaped by humanism, industrialization and some strident forms of individualism. These have encouraged us to see it in strongly anthropocentric and solipsistic terms. The global economic system also reflects this individualistic ideology, given that 'growth', is driven by personal avarice on a collective scale. On the other hand, capitalism encourages enterprises to scale-up when they become successful. Both tendencies reduce the consciousness of organizations and communities. The article illustrates this idea by describing a 'quadratic' model of team consciousness that was developed to enhance practical developments that support personal, interpersonal, transpersonal and environmentally situated modes of awareness.


alienation, allopoietic consciousness, autopoietic consciousness, network consciousness, quadratic consciousness, solipsism, synergy

Local consciousness

For the first time in human history, scientists can sequence human DNA and map the activities of the living brain in three dimensions. However, these triumphs of science reveal little about the fundamental nature of ‘consciousness’. This article argues that, as part of our strategy for survival as a species, the popular understanding of consciousness should include the whole biosphere, rather than focusing on the individual mind. One of the paradoxical legacies of classical science is the belief that space and matter exist within different metaphysical orders. Indeed, Descartes is famous for promoting the solipsistic idea that body and mind exist as a 'divided totality', in which the soul is located in a specific region of the brain. This presumably inspired later thinkers (e.g. Locke, Schopenhauer and Nietschze) to theorize 'genius' in a way that prescribed 'consciousness' as a local phenomenon. The belief that consciousness is confined to individual minds, rather than existing within, or across, species, social groups, or regions of space-time has led to a number of other assumptions. It suggests, for example, that consciousness exists when the individual person, or mind, is able to reflect upon itself in a sufficiently knowing and explicit way. This individual-oriented perspective did not emerge spontaneously but emerged from a long trajectory of humanist thinking that also informed the ideology behind capitalism. It is perpetuated in education policies and practices that value the grading of lonely academic tasks more highly than the cultivation of collective wisdom.

Solipsistic consciousness

When we think of the key characteristics of western thought, Socrates (470–399 BC) is often cited as the originator of personal self-scepticism (e.g. Tarnas, 1991). However, it seems likely that he was inspired by Sun Tzu (544–496 BC), whose conclusions balanced the importance of self-knowledge with the need to understand one’s enemies. By the sixteenth century, in rethinking the moral conduct of dutiful Christians, Erasmus (1469–1536) became part of a movement to take moral responsibility out of the hands of church leaders and establish a regime of personal ‘self-regulation’. Indeed, the word 'consciousness' is allied to the moral concept of 'conscience'. However, by the seventeenth century, a growing interest in the citizen’s rights, rather than responsibilities, had inspired the idea of the 'self-owning individual' (MacPherson, 2010). The seeds of twentieth-century egoism can be found in certain key concepts, such as the 'presentation of self' (Goffman 1959), 'positive self-regard' (Rogers, 1961) and 'self-actualization' (Carland & Carland, 2015). These were already latent in Coleridge’s (1772–1834) notion of the 'self-conscious' individual. Around the same time, Lord Byron (1788–1824) was pioneering a stylish brand of performative self-observation and exhibitionism that he claimed as his most important achievement. By the late twentieth century, aided by the cunning fashion and toiletries industries, these trends had become absorbed into a ubiquitous culture of celebrity. It is tempting to satirise current notions of consciousness as a kind of privatized reality that can be acquired at the right price. This is not without some truth. Indeed, corporations not only design products and services to reflect the predilections of those who can afford them, but also to enable them to choose, create or bolster their self-image as a unique individual.

Machine consciousness

In the light of these advances of the digital culture it is not really surprising that we may discuss human intelligence using ideas borrowed from the computer industry. In recent years, PDAs, ‘selfie sticks’, Google search algorithms, social media apps and a mountain of other media accessories have facilitated new forms of solipsism and self-admiration. Sherry Turkle (2015) and many others have argued that immersive games and screen-based digital gadgets are increasingly reducing social empathy. At a time when our civilization faces the threat of extinction, this has become a serious issue. If we are to regain our attunement with Nature we need a language of consciousness that is as inclusive and perceptive as possible. Marvin Minsky, a pioneer of the digital technology revolution, has claimed that humans consciousness is weaker than computers. Significantly, he defines consciousness as a ‘low-grade system for keeping records’ (Minsky, quoted in Horgan 1994), presumably alluding to the frequency of self-polling algorithms within list-based programmes, such LISP. This is cute, but misleading, given that living human beings are autopoietic, rather than allopoietic. In other words, whereas digital programmes are designed to deliver a manifest outcome or product, living systems are self-definingly unique. Ian McGilchrist reminds us that our culture considerably overvalues the myth of self-control via the superego, whilst underestimating the importance of situated, embodied and self-reflexive knowledge (McGilchrist, 2009). Unlike digital intelligence, human wisdom derives, at least in part, from a set of analogue systems (e.g. neural, lymphatic and endocrinal) that work together using relatively sluggish biochemical processes. And the purpose of this wisdom is to facilitate the organism's own survival. As Polanyi puts it, ‘All knowledge is tacit if it rests on our subsidiary awareness of particulars in terms of a comprehensive unity’ (1969). This process is not mappable in algorithmic form. As Maturana and Varela explain, ‘… the space defined by an autopoietic system is self-contained and cannot be described by using dimensions that define another space’ (1980: 89). In short, human wisdom is somatic, interpersonal and transpersonal, rather than precisely definable and transferable.

Biological consciousness

Nonetheless, in our post-Enlightnment world of rational expediencies, it has been customary to trade wisdom for information, and to perceive information as data. This means that every event is reduced to a convenient alphanumerical chunk and stored in memory. Compared with analogue systems, this significantly reduces ambiguity, error, hysteresis and 'drift'. On the other hand, it is the capacity for making judgments in highly complex situations that enables humans to beat computers at Asian game of 'Go', even if they fail to do so at chess. In comparing the ways of the human mind with the workings of the biosphere, Gregory Bateson (1980) concluded that they shared aesthetic intricacies and subtle complexities, rather than bearing comparison to the simpler, more mechanistic resemblance. It is helpful to see successful living systems, not as individual 'things' and 'agents', but as complex fields of synergies (c.f. Corning, 1983) that organize themselves into a net synergies-of-synergies (c.f. Fuller, 1975). Yet, despite all of the above misgivings about the ideologies behind our digital culture, machine consciousness may be a useful stepping-stone to thinking about grander modes of consciousness. The notion of extra-human consciousness is not new, especially if we include theological thinking as an ultimately pervasive mode of consciousness. Vladimir Vernadsky (1863–1945) and Teilhard de Chardin (1881–1955) foresaw the evolution of ‘global consciousness’, based on the open exchange of information. But we have had a few related ideas, such as Anaxagoras's idea of the 'universal mind' (460 BC) and, more recently, Durkheim's 1893 term 'collective consciousness' (in Nemedi, 1995). Ray Kurzweil has suggested that, by 2045, developments in Artificial Intelligence will have produced a post-humanist, all-engulfing field of connectedness that he calls 'The Singularity' (Kurzweil, 2005). This is useful, as it offers a provisional theory of consciousness as an extensible field of informational connectivity, rather than a mysterious phenomenon of the individual intellect. It is interesting to note that the first cells were pre-biotic and could do three essential things: copy informational macromolecules, carry out specific catalytic operations and convert external energy into usable chemical form. It is likely that each capability was lost and re-discovered many times until all three coexisted within the first cells to evolve (Koch & Silver 2005).

Living systems

The fact that we are comparing words with slightly different terms of reference should not be seen as a problem, if our aim is to formulate new meanings befitting new situations. Indeed, it is possible that humans recreate records of a given event by accessing interference between different parallel perspectives, both creatively (Koestler 1964) and holonomically (Pribram 1991). What is more important is that the context of discussions should be framed in a way that promotes a greater awareness of ecological realities. Humberto Maturana and Franciso Varela define living systems in a very broad and systemic way. Indeed, irrespective of whether it is a bacterium, snail, corporate brand or sports team, all are subject to the same survival rules. For example, organisms only survive when they maintain an appropriate balance between their internal and outward-facing identities. Here, the term ‘identity’ refers to its integrity in terms of its outward persona (i.e. ‘maintaining face’) and its internal, structural formulation. The fable of Narcissus suggests that the hero of the tale is unlikely to survive for long because of his solipsism. This lesson applies equally well to communities, societies and species. According to Maturana and Varela, ‘living systems’ create themselves in a process they call ‘circular causality’ or ‘autopoiesis’, (Maturana and Varela, 1980). At the biochemical level, this entails the judicious and timely management of energy and materials flow within appropriate metabolic pathways, in accordance with the immediate environment. In corporations, similar operations apply, albeit via exchanges of monetary tokens, documents, goods and services. Loosely speaking, the synergy-levels within these systems can be seen as evidence of consciousness.

Organizational consciousness

In future, this aspect of organizational consciousness could have important implications for post-carbon economies, especially if energy supplies can no longer be taken for granted. Our society’s current profligacy is caused largely by the persistence of a linear economy that encourages reckless habits of mining, shaping, selling and dumping. While many non-experts can see that these business models are grossly expensive, they are propped up by reductionist methods of auditing and planning that apply 'economies-of-scale' methods to the management of highly complex, often fragile, ecological and social systems. For example, this explains why profitability is identified as problem, whereas soil erosion does not. Similar performance indicators ensure that we design cities for mobility and ease of construction, rather than ensuring diversity and local accessibility. Politically, radical lifestyle changes are deemed to be unthinkable, which leaves us no alternative but to burn more and more non-renewable fuels in order to maximize the throughput of homogeneous products to similar places. Another example of this mindset is the holiday industry, in which companies offer short-break amenities that are broadly the same, at the level of sunshine, flights, hotels and drinks, but compete mainly on the basis of price. The system therefore favours corporations who can higher rates of turnover by attracting customers from a wider catchment area and reducing diversity. As I have already said, the scaling up of organizations creates hierarchy and this reduces the organization's consciousness. One way to reform these wasteful habits would be to introduce a circular post-carbon economy (McDonagh and Braungart 2002) by designing a requisite set of fiscal and administrative 'switches' (c.f. Greyson 2014) to encourage this new paradigm.

Team consciousness

Another (slower) method is to teach students to think about their world using a relational language (Wood, 1992) based on synergy, rather than products and agents. At the level of urban planning and governance, this would encourage us see diversity as a primary asset, because it reduces the need for mobility. Following this logic, it is likely that future organizations would find it increasingly expensive to lose consciousness. In our research we therefore set up embodied team-experiments, and these led us to create a collaborative order that was flat-structured, rather than hierarchical. It required the design of a strongly open and democratic environment, together with a highly heterogeneous group of team members. We also used some of our many metadesign team tools try to encourage participants to sense, then to re-language subtle events that may not be noticeable from within the prevailing cultural-linguistic paradigm. As rigid hierarchical team structures systematically reduce team consciousness, we developed holarchic teams (Koestler 1964) to help individuals become less consciousness of their individual agencies and more conscious of their team's interpersonal empathies, transpersonal relations, shared identity, capabilities and volition. Teams therefore need to become aware of, and to interpret quite subtle, or intangible gut feelings, or other somatic and interpersonal phenomena. Team consciousness is a cultural phenomenon that enables team members to notice new experiences and to render them as 'thinkable'. These are prerequisites to revealing 'problems' as opportunities for synergies, rather than accepting received knowledge that sees them as intractable aspects of the prevailing paradigm.

Managing complexities

A key obstacle to making the necessary changes is the huge reluctance of educators, politicians and scientists to ask themselves radical questions about the purpose of their roles within the broadest ecological context, then to rethink the way we do things from within this new scenario. In the meantime, we are determined to develop metadesign tools and test them out in practical workshops. If we focus onto synergies, for example, it is important to achieve as many relations as possible. Here, use of the word 'relation' can be interpreted to mean a possible synergy. Synergies are additional to any existing resources, or assets. If they are socially or ecologically beneficial, they can be seen as a 'free bonus' that emerges from the combination of existing assets. They may even be more important than the human players (i.e. agencies), especially if they encourage more effective synergies within the team. Some of our findings can be mapped, albeit crudely, using mathematical methods. For this reason we have developed some simple mathematical and topological tools to help us optimize team size, team diversity and a minimum of cognitive complexity for facilitators. It is obvious, for example, that the ratio of agents to synergies in any system changes with the scale of the system. Where, for example, there is only one relation between two players, the ratio improves by adding a third player, as this creates three. This 1:1 ratio of players to relations can be improved by adding a fourth player, thus giving six relations (i.e. a ratio of 2:3). Beyond these numbers there are always more synergies than agencies.

Practical issues

Leonhard Euler (1707–1783) invented a visual schema, which was popularized in Harry Beck’s London original underground map of 1931. In this notation, agents can be represented by the circular blobs and relations denoted by the lines that connect them. Although, to some, the Euler-Beck schematic logic may seem dauntingly austere, it enables complex systems to be represented and discussed in a convenient and playful way. It uses simple topological principles to reveal previously unnoticed opportunities in a graphic way.

Triangle Tetrad

Figure 1: Triangle and tetrahedron

This is can be demonstrated visually in Euler’s law (1752) that relates to polygons (i.e. V+F=E+2). Euler showed that, in any polygon, the number of vertices (V) plus the number of Faces (F) equals the number of Edges (E) plus two. Buckminster Fuller has suggested that the additional two (i.e. relations) is Nature's abundance, because we can apply the same logic to methods that deliver more synergies (depicted as Edges) than the number of players, or agents, (depicted as Vertices) that created them. It is also a suitable form upon which to map interrelated things. What is important for metadesigners, here, is not the form of the tetrahedron itself (Wood, 2005), but the fact that it can be applied to any set of players, parts, or agents, whether it exists as a food recipe, zoo, team, community or garden, etc.

Quadratic consciousness

From the tetrahedron (Figure 1) it can be seen that a quartet has six times the number of possible inter-player relations than a duet and twice the number of relations in a trio. These methods cultivate co-creativity in order to synergize the collective knowledge within teams (Van Nieuwenhuijze & Wood, 2006). While it is important to work with small team numbers, a high level of diversity is also important and these criteria therefore are in contradiction to one another. The problem of 'designing' systems involving synergies is that many cannot easily or adequately be represented outside the imagination because they are emergent, quixotic and ineffable. More importantly, there is a very low threshold for the number of interrelated things that humans can grasp easily. We therefore need a system of representation that reduces complexities down to numbers that are optimally mnemonic. Miller (1956) claimed that few people are able to conceptualize more than nine interdependent relations at once. Subsequently, researchers found there to be different cognitive activities between left and right hemispheres, anterior and frontal lobes of the brain. Nelson Cowan (2001) revisited research on how our brains 'chunk' information. He confirmed that thinking in clusters of four is around the limit for the average person to grasp interdependencies. A useful compromise is to identify relations and try to map them in schematic form, even though this may make them over-simplified. I have applied this method to create a successful relational learning tool that has been adopted and used in Iceland since 2013 (c.f. Wood, 2015).

Autopoietic consciousness

Our team tool approach used four virtual roles that interact with one another to establish six interdependent relations. Together, they are intended to operate as a training model that simulates a 'living' autopoietic system. Designing the team as a cellular system meant looking for four roles that would be sufficiently useful when working interdependently. There should be the requisite level of diversity within the team and the ability of the participants to regulate the system without a permanent leader, either from within, or from the outside (c.f. Ashby 1956). Together, each should be able to play its part so that the whole team would manage its survival.

JW Fig 2

Figure 2: An autopoietic team

By mapping the four styles as a tetrahedron (see Figure 2) we were then able to identify their six relations as follows:

JW Table 2015

Table 1

Arguably, without appropriate interdependencies among the above roles, the organism would not survive for long. The Pusher & Doer, for example, represents the organism's connection to an outside world. Its purpose is to ensure that there is a flow of resources from inside to outside that would be appropriate and sufficient to maintain the external usefulness of the cell. The New Knower served as the sensory system whose behaviour was akin to a 'wise fool', or newcomer to an organization. This is important, because inwardly focused (e.g. solipsistic) organisms tend to lose track of what they have become, and the environment they have co-created. Sometimes, infants ask important questions that experts had not thought of. The Envisioner plays the role of the planner or strategist. Where each of the others are engaged in specific tasks, this role requires a more creative and imaginative process of thought. The Languager is an intermediary that attends to, and tries to understand what each of the other three are doing, or trying to do. On occasions, misunderstandings can threaten the survival of the cell, either because of internal conflicts or because the cell cannot adapt to external circumstances. This is likely, because each have different terms of reference that require their own mode of understanding. Its role may include re-languaging messages within the cell, with particular reference to the collective interests of the cell.


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See also our previous contributions to this series:

Network Consciousness 1download onlyJohn Wood & John Backwell(2009)
Network consciousness 2N/AJohn Wood & John Backwell(2011)
Network Consciousness 3N/AJohn Wood & John Backwell(2012)

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