Kurt Lewin’s Field Theory: a review and Re-evaluation

Mapping the field: the challenge of rigour

Having established the importance of the life space to an individual’s and group’s behaviour, Lewin was left with the puzzle of how to map the life space. One of the criticisms gestaltians faced was that, in con- trast to behaviourists and structuralists, their work was too qualitative. Inspired by Cassirer’s phil- osophy of science, and field theory in physics, Lewin (1940a) believed his psychological field must be based on mathematical concepts and laws. In order to achieve this, he was drawn towards topology:

The youngest discipline of geometry called ‘topol- ogy’ is an excellent tool with which to determine the pattern of the life-space of an individual, and to determine within this life-space the relative posi- tions which the different regions of activity or persons, or groups of persons bear to each other. (Lewin 1939a, p. 8)

Topology is a major area of mathematics developed by physicists and mathematicians and is concerned with mapping out the geometrical properties and spatial relations of objects such as circles and spheres. Topologists are concerned with the way in which the constituent parts of a space or field are interrelated or arranged and how they change when the forces around them are increased or decreased (Mendelson 1990).

Figure 2 shows a simple example of how Lewin used topology to map out an individual’s life space. Within the field of forces that make up the individual’s life space, P is the individual, O represents their current situation or behaviour, and G is the goal that they wish to achieve or the change that they wish to





Figure 2. Life space with person and goal
make. The dotted line represents the shortest path between where they are in their life space and where they want to be. The sectors immediately above, below and behind O represent the forces for change, and those between O and G represent the forces resisting change. The other forces in the field will also exert an influence on the change the person wishes to make and will also be affected by the change.
Topology provided Lewin (1929, p. 125) with a valuable method of creating a visual representation of the forces that impinge on an individual or group and the interconnections between these, allowing the individual to be represented

1. 
   as a total person with a certain structure
   
2. 
   as a relative unity within a psychological envir- onment of particular topology and particular field forces.
   

This is why Lewin also referred to field theory as topological psychology. However, as Wheeler (2008,

p. 1640) observed, Lewin later invented ‘hodology’ (from the Greek word ‘hodos’ meaning path) to over- come what he saw as the shortcomings of topology. For Lewin, the main shortcomings were that topology provided only a static picture of behaviour, and it did not allow for the measurement of forces. Lewin believed that ‘the concrete person in the concrete situation can be represented mathematically’ (Hall and Lindzey 1978, p. 386). Though familiar with the formal mathematical systems of his day, he rejected these as unsuitable to his needs and so developed his own – hodology (Kadar and Shaw 2000). As Lewin commented:

The topological space is too ‘general’ for repre- senting those dynamical psychological problems which include the concept of direction, distance, or force. They can be treated with a somewhat morespecific geometry, which I have called ‘hodological space’. This space permits us to speak in a math- ematically precise manner of equality and differ- ences of direction, and of changes in distance, without pre-supposing the ‘measuring’ of angles, directions, and distances, which is usually not pos- sible in a sociopsychological field. Lewin (1939b, pp. 890–891)

Hodology allowed Lewin to ‘plot possible paths from one region to another in a topological diagram’ and to develop important theoretical constructs such as ‘region, locomotion, barrier, valence, goal, force, field of force, and gradient of force field’ (Wheeler 2008, p. 1640). Lewin’s new hodological geometry not only allowed him to use mathematics to represent the forces in a group’s life space, but also to measure them and their effect on each other. This meant that he could understand the forces that brought about a group’s current behaviour and also establish which forces would need to be increased or decreased and by how much, to change that to a more desired behaviour (Lewin 1938, 1939a,b).

Therefore, Lewin’s field theory relied on topology to create a static picture of a group’s current behav- iour and the mathematics of hodology to turn this into a dynamic model that could be used to change behaviour. He was inconsistent in his use of termi- nology, and tended more often than not to use the term ‘topology’ when also discussing hodology, as did his followers (Cartwright 1952a; Marrow 1969). To try to avoid confusion, we use the term ‘topology’ when referring to conventional topology and the term ‘Lewinian topology’ when referring to the mathematical-hodological variant. Though he saw Lewinian topology as a major step forward for field theory, as the following section shows, the result of Lewin’s foray into mathematics was to undermine rather than support field theory.