Four-fold Reasoning

(also see creative quartets, meta-faculties, relationality and other keywords)

Why four?

• When we try to organise, or manage, at a meta level it is important to work at the right scale.
• For example, it is easier to work with the optimum number of ingredients - not too many, not too few.
• Oversimplifying things will make us miss opportunities. Juggling with too many variables will confuse us.
• We believe that thinking in fours is a good organisational compromise for a number of reasons.

Fuller's insight about 4

• In 1949, Richard Buckminster Fuller suggested that the mind works in a tetrahedral (four-fold) way.
• At the time this was a big claim, but later research into human cognition supports his contention.
• Here, Fuller was not referring to the geometrical aspects of the tetrahedron, but to its conceptual nature.

Some cognitive evidence

1. In 1956, George Miller claimed that few people can conceptualise more than 9 interdependent relations at once.
2. But in 2001 Nelson Cowan revisited Miller's assumption (see above), and found that our brains 'chunk' information in fours.
3. In 2004, Gobbet & Clarkson challenged Cowan's findings, suggesting that chunking in twos is more realistic.
4. In 2009, Klingberg & Torkel, 2009 confirmed this more cautious figure, perhaps because we tend to address a 'paired' set of tasks, then switch our attention to another pair of tasks.

Hearing the quartet

• Human beings initially find it hard to visualise how many relationships there are among FOUR things.
• One way to illustrate this is to represent the four-fold situation as a quartet of friends at a party.
• If they raise a toast to one another, a blind person would experience this as a series of 6 CLINKS.

six glasses clinking

Seeing the quartet

• Another way to represent a four-fold situation is by using Buckminster Fuller's tetrahedron.
• Some people find geometrical figures scary, but we find that they soon get over their initial fear.

• A tetrahedron is a polyhedron with 4 triangular faces, three of which meet at each vertex.
• It has 4 vertices and 6 edges. See Wikipedia or Wolfram for more information.

Four levels of usefulness

• 1. The tetrahedron's form is the simplest geometrical representation of a cell.
• 2. The tetrahedron's form can be used to map ideas in an optimally mnemonic way.
• 3. The tetrahedron's form expresses a higher consciousness compared with larger polygons.
• 4. The tetrahedron reveals intrinsic abundances that derive from the combination of things. 

Some practical examples

• John Ruskin (1819–1900) mapped benefits from the act of handcraft to show multiple beneficiaries.

• I have illustrated his model as a 'creative quartet' (see above).
• However, it is hard to find many other practical examples of a creative quartet(Wood, 2013).
• 'Creative duets' are a more common model. Nevertheless, they may inspire 'creative trios' or 'quartets'.
• By combining two problems (e.g. the training of dogs by prison inmates) can bring synergies.
• The Inter-generational Learning Center combines nursing home and kindergarten.!!!How does it help us?
• The number 'four' is helpful to learners because of
• This usually applies to the number of 'levels' we must orchestrate.
• E.g. mapping society, technology, ecology and semantics within a whole design.
• It therefore offers a framework of thinking that supports complex (i.e. manifold) innovations.
• 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?

 

• We have used this 'meta-tool' in at least 6 other tools.
  • 1) Our Triple Win Win tool shows that you can get twice as many abundances by combining 4 ingredients as you do by combining 3 (see above).
  • 2) We used it to define 4 interdependent working role/styes.
  • 3) We used it to orchestrate 4 interdependent ideas in our quadratic innovation method.
  • 4) It can be found in our learning-assessment tool
  • 5) This embodied a quadratic system of ethics.
  • 6) We also used it to manage other tools, in our system of four-fold integration

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).

 

 

• 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.

Acknowledgements

• 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)

Bibliography

• 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

Relevant web resources

• The fuller Map- an accessible online Buckminster Fuller reader by Paul Taylor
• Gorgias - Plato's tetrahedral dialogue that explores the limits of rhetoric.
• See how The Peer to Peer Foundationaddresses the issues of team, or 'network consciousness'

Relevant downloads

• Mapping Network Consciousness by John Backwell & John Wood (2009)
• Relative Abundance by John Wood (2007)
• The Triple Win-Win System by John Wood (2007)
• The Tetrahedron Can Encourage Designers to Formalize More Responsible Strategies by John Wood, (2004)

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