The Quartets Toolbox

Blue Square see other Creative Publics Toolboxes Blue Square

FOUR reasons why FOUR is auspicious

  1. Relations are more plentiful (and valuable) than things.
  2. Relationships are the very essence of synergy.
  3. The human mind struggles to visualise more than FOUR interdependent entities.
  4. FOUR is the lowest number in which the sum of its relations is bigger than itself

Quartet square-50cm-spacer.jpg Tetraeder-Animation.gif square-50cm-spacer.jpg tetrad3-colours.jpg
Fig. 1 - A musical quartet square-50cm-spacer.jpg Fig. 2 - solid tetrahedron square-50cm-spacer.jpg Fig. 3 - tetrahedral framework

OVERVIEW - Organisations can become more adaptable when they cluster and recombining more of their assets at an optimum scale. There are several advantages of organising these assets in clusters of around 3 to 5. For one reason, the organisational consciousness of small teams is very high, compared with large, multilayered organisations. Combining existing assets can create new synergies and the ratio of synergies:assets is higher in clusters of more than 3. On the other hand, the human mind finds it hard to envision the simultaneous combination of more than 4 interdependent parts.


The quartets tools help organisations to map out and/or design an optimum number of synergies at a scale that is manageable for the human mind.

A DEFINITION - by 'quartet' we mean any group of four, whether persons or things. We are particularly interested in the broad principles behind it, rather than in, say, its musical or theatrical associations (see figure 1). For the sake of visual clarity we often represent it in the form of a geometrical figure (see figure 2). We use it to map the (4) 'players' (or 'assets' ) which are represented by the silver spheres. The relations between them are thus represented by the (6) coloured rods. See Wikipedia or Wolfram for more information. (Bucky Fuller)


How it Works

We might think of inventing as an activity that fulfils certain unspoken rules or assumptions. Thus, the stereotypical act of invention is that which culminates in a single gadget or product and either reduces the workload, or makes life more convenient. In this sense we might describe this stereotypical activity as a 'genre'. However, it is generally accepted that all creative acts come about as the result of combining at least two sources of data or understanding (e.g. Koestler, 1964). The same mathematics applies to the creation of synergies. We need at least two assets to combine, before we achieve one synergy. But this sum (1+1=3) appears to be a relatively poor deal if we regard it as putting two existing assets together to produce only one additional outcome (see the Synergy Toolbox). The #Synergy6 Framework seeks to improve on this format by re-inventing the paradigm of invention. Instead of starting with two assets it advises organisations to cluster at least three together to produce additional outcomes.
The tetrahedron shows that four assets can combine to create 2 additional 'relations', or 'combinations' than we started with. If these combinations are useful, they are then regarded as synergies. By clustering at least four well-chosen assets we can begin get more synergies than assets. The aim is to human mind is not very good at visualising (and mentally juggling) very many elements at the same time. In our view, the quartet has an optimum number of interdependent 'players' or 'ingredients', or 'parts'.

How it Works

Combining many edible ingredients when cooking is relatively easy when the recipes have evolved over a long period of experimentation and note taking. However, the logic of recombination shows us that, hypothetically speaking, anything can be combined with anything. hings work better with the optimum number of ingredients. Juggling with too many will make us confused. But if we work with too few we may miss opportunities. Innovation in complex situations (e.g. teams, communities) can easily become difficult to comprehend. This may be because change defies the familiar boundaries of language. While thinking in 'fours' may not always show us how things 'really' are, it can inspire us to work beyond the 'thinkable'.
It shows how the number 'four' is helpful within creative thinking and planning.

  • This usually applies to the number of 'levels' we must orchestrate.
  • E.g. mapping society, technology, ecology and semantics within a whole design.
  • Four-fold innovations can become viral concepts, or memes that can propogate themselves.

How does it work?

When trying to grasp a given system in a simple way, choose four interdependent (or co-creative) elements. Visualise, or represent them as four, colour-coded nodes (vertices) on a tetrahedron (e.g. see above). In a working situation it may be reasonable to consider including yourself in this 'world model' (see quadratic ethics).


  • 1 - Use the model to show how each node (e.g. one of the green letters) links directly to the other three letters (i.e. along the tetrahedron's edges).
  • 2 - Identify what each of these (six) numbered edges represent, within the logic and purpose of your system.
  • 3 - Remind yourself that each of the six 'links' are bi-directional - i.e. all four players may 'give' and 'receive'
  • 4 - Incorporate these (twelve) standpoints in you understanding of the whole system.
  • 5 - Remember that any shift in one of the twelve standpoints is likely to have an effect on the other eleven.

How have we applied it?

Moving from 2D to 3D

  • Many designers feel comfortable in playing with a 3D model.
  • The tetrahedron well illustrates the optimal values of a non-hierarchical team.
  • Its (4) nodes can represent interdependent agents, or players.
  • The tetrahedron works in the same way as the square whose corners are linked with diagonals (above right).

euler-tetrad1.jpg tetrad-balls-numbered1.jpg

  • Another way to visualise it is by thinking of adjacent atoms (e.g. 'collaborators')
  • Just imagine four equal spheres in the same working vicinity
  • When they are close-packed, each will touch all of the other three, simultaneously
  • This is special among spheres - i.e. if you add another sphere it will not touch all
  • This is an optimum, non-hierarchical representation using 3D forms
  • If you imagine lines connecting the centres of the spheres you have a tetrahedron.
  • Each of the vertices in a tetrahedron is a 'neighbour' of all the others

The Tool's Context

Human history has made us so accustomed to social/organizational hierarchies that we tend to assume they are 'natural'. When we speak of 'democracy' (e.g. ancient Greece or Iceland) we usually overlook the enormous scaling-up of national superpowers that are democracies. With the growth of hierarchies comes a reduction in what we call the consciousness of the network. (download article on Network Consciousness. Where some network theory explores what happens in social groups of over 100 ((e.g. Dunbar's number) is approximately 150) this tool explores much smaller groups, or teams, of participants.


  • Plato wrote about the tetrahedron (one of his 'Platonic' solids).
  • It has 4 faces, 4 vertices (corners), and 6 edges
  • It is also non-hierarchical (Fairclough, 2005; van Nieuwenhuijze, 2005; Wood, 2005).
  • Buckminster Fuller was inspired by the '+2' in each case (see Amy C. Edmondson's interpretation of Euler+Fuller).
  • He called this constant relative abundance and used it in his idea of Synergetics (1975)
  • I am indebted to Paul Taylor, Otto van Nieuwenhuijze and Ken Fairclough, all of whom continued to develop and promote Buckminster Fuller's work
  • In 2005 ds21 researchers found that, by dividing design teams into 4 different groups we might produce interdependent sub-groups
  • In September 07 we realised that this might be a useful tool for achieving holarchic collaboration
  • The advantages of this approach resemble the computer system's peer-to-peer configuration
  • Heidegger (1964) spoke of a 'fourfold' state of being. 'These are characterised by
    • 1. being "on the earth" - but this also means:
    • 2. being "under the sky". Both of these also implicate:
    • 3. "remaining before the divinities" and:
    • 4. a "belonging to men's being with one another".
  • By a primal oneness the four-earth and sky, divinities and mortals-belong together in one...
    This simple oneness of the four we call the fourfold.' (Heidgger, 1964: p327)
  • Even when mortals turn "inward", taking stock of themselves, they do not leave behind their belonging to the fourfold.
  • When, as we say, we come to our senses and reflect on ourselves, we come back to ourselves from things without ever abandoning our stay among things. Indeed, the loss of rapport with things that occurs in states of depression would be wholly impossible if even such a state were not still what it is as a human state; that is, a staying with things. (Heidegger, 1964: p335)


  • Cowan, N., (2001), The magical number 4 in short-term memory: A reconsideration of mental storage capacity, in Behavioral and Brain Sciences (2001), 24: 87-114 Cambridge University Press Copyright ©2001 Cambridge University Press doi: 10.1017/S0140525X01003922. Published online by Cambridge University Press 30 Oct 2001
  • Fuller, Buckminster, (1949) "Total Thinking", reprinted in "Ideas and Integrities: A Spontaneous Autobiographical Disclosure" (1969), Ed. Robert W., Marks, Englewood Cliffs, NJ: Prentice-Hall.
  • Fuller, R. B., (1975), “Synergetics: Explorations In The Geometry Of Thinking”, in collaboration with E.J. Applewhite. Introduction and contribution by Arthur L. Loeb. Macmillan Publishing Company, Inc., New York.
  • Heidegger, M, (1964), 'Building, Dwelling, Thinking'. Basic Writings. London and Henley, Routledge & Kegan Paul.
  • Klingberg, Torkel (2009). The Overflowing Brain: Information Overload and the Limits of Working Memory. Oxford: Oxford UP. pp. 7,8. ISBN 0195372883
  • Miller, George A. (1956), ‘The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information’, originally published in The Psychological Review, 1956, vol. 63, pp. 81-97

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