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Four-fold Reasoning

(also see creative quartets, 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

One White Bit Tetrad Graph

  • 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.

One White Bit
One White Bit Glass Clinking Tetrad

One White Bit 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.

One White Bit Noun Cyrstal 575753

  • 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

Some practical examples

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

One White Bit Ruskin 4 Fold Map

  • 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 propagate themselves.

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

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