Tool no. 20 - Quadratic Ethics

A four-fold, self-inclusive, 3D modeling system for mapping ethical relations

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The Underlying Issues

The Ten Commandments (in Hebrew)

  • Today, consumer-oriented, individual rights-centred codes tend to be humanistic.
  • How can ethics work beyond the oversimplified language of 'individual rights'?
  • Many people still follow religions that present moral codes as simple imperatives (e.g. one 'ought' to, or 'must' do x or y).
  • At worst, these fundamentalist doctrines are commandments in which the context has been lost or forgotten.
  • This means that they have also lost their 'dimensionality'.
  • The tacit, situated, or embodied relations on which the stories were based has been flattened into one dimension, i.e. the individual's obligation to a rule, or code.

The Tool's Purpose

  • While a context, purpose, or beneficiary can often be inferred, they are seldom stated.
  • What is needed is a method of mapping more dimensions that reconcile all the salient factors.
  • This tool can be used to enrich existing codes of morality.


  • By reducing a vast array of agents to four relational elements it is easier to manage them (why four?).
  • It enables professionals and citizens to visualise their situation in a self-reflexive way.
  • It is a subtle tool that needs careful explaining and reflection.
  • It has proved highly successful, especially when used in design education at graduate level.

Tool Context

  • Looking at relations between things is a more systemic approach that may enable better results.
  • But this level of description is usually too subtle and complex for creative individuals, and teams
  • Western codes, and discussions, of morality usually become deontological, therefore one-dimensional
  • This has been unfortunate, because actions tend to be discussed in terms of propriety, rather than effectiveness
  • A suitable tool would need to be understandable and accessible, yet complex enough to be practically effective
  • A successful tool would encourage the user to achieve a sophisticated and effective level of self-reflexivity
  • This tool will be offered to United Nations when it is sufficiently developed

Tool Process


  • Four (rather than any other number) has been chosen because tetrahedral logic has auspicious properties

The Players - the nodes, or vertices of the tetrahedron

  • It is also handy because it can be used as a four-dimensional fractal ethics that reconciles the needs of:
    • a) ME - (could signify one's role as a designer, creative agent, manager or worker)
    • b) PROPOSITION - (could signify work done, a service, a design or an idea)
    • c) CLIENT - (could signify a stakeholder, recipient or customer)
    • d) CONTEXT - (e.g. could signify the locality, constraints, or natural environment, etc.)

Tool Example


  • John Ruskin's notion of craft as a whole system can easily be mapped using this tool
  • In the above illustration, the relations between the four players/agents are represented by the 6 edges:

The Relations - the edges of the tetrahedron

    • 1) The employer's relationship with/experience of the community and Nature
    • 2) The craftsman's relationship with/experience of the community and Nature
    • 3) The craftsman's experience of the act of working
    • 4) The employer's experience of the work itself
    • 5) The relationship between the work carried out and the community and environment
    • 6) The employer's relationship with the craftsman


  • Much of the (tetrahedron's topology) history is explained in the tetrahedral logic tool
  • Rudolph Laban used the tetrahedron as a body-oriented constant within his Labanotation method of 1928
  • Wood (1995) critique of academic rigour
  • Wood (2000) notion of mapping relations in a space-time continuum
  • Wood (2005) emphasis on ethical issues that would emerge from a less deontological, linear


    • Wood, J., (1995), "The idea of academic rigour in 4-D space": paper delivered at the "4-D Dynamics" conference, Design Research Society, De Montfort University, Leicester, UK, (September 1995),
    • Wood, J., (2000),"2-D Writing in a 4-D World", paper given at the "New Kinds of Writing in the Academy; ESAP in the Humanities" Conference, Goldsmiths College, 26 February, 2000
    • Wood, J., (2005) ‘The Tetrahedron Can Encourage Designers To Formalise More Responsible Strategies’, for the ‘Journal of Art, Design & Communication’, Volume 3 Issue 3, Editor, Linda Drew, UK, ISSN: 1474-273X, pp. 175-192

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