Hodological space (from the Greek word hodos, which means "way") refers to the space of possible movement. Unlike the straight line, this space involves the so-called "preferred paths", which serve as a compromise of different domains that include shortest distance, security, minimal work, and maximum experience.
The German psychologist Kurt Lewin first introduced this concept in the early part of the 20th century. It emerged in his attempt to use mathematical concepts to deal with psychological problems. At the time, topology was a new field, "To some degree it is possible to give a general mathematical solution using a kind of space which is defined through the possible paths between points, and which one may call 'hodological space.'
According to Gilles Deleuze, the hodological space concretely holds the sensory-motor schema as the field of forces, oppositions, and tensions are resolved according to their goals. Otto Friedrich Bollnow further refined Lewin's notion and described the hodological space as not something that is homogenous nor predetermined since it is extemporaneously expressed as we move through space.
A penetrable space can be perceived in two different ways: navigable and navigated. The navigated perception is realized by the hodological space while the former by ambient space. According to this conceptualization, we do not move within a hodological space but that it is created once we move through an ambient space. The space is interpreted as "lived" and is distinguished from the Euclidean space, which is considered "represented". It is, thus, analogous to "seeing an object and making the hodological leap from this actuality to its virtual potentiality of the past in forming the sensory-motor connection."
Hodological space is articulated by a nonquantitative, mathematical analysis that does not necessarily involve the consideration of distance. Here, the distance of points A and B in terms of such space may be different from the distance from B to A.
Hodological space is described as more general than the space of Euclid and Riemann [see metric space], but not as general as topological space, in which it is not possible to define distances or directions." It is noted that Lewin's conceptualization was more mental rather than a physical typology. According to Gilles Deleuze, the hodological space concretely holds the sensory-motor schema as the field of forces, oppositions, and tensions are resolved according to their goals.
Hodological space can be applied to different fields. For example, in the fields of literature and film, it typifies a narration or a speech that is referred to as "economical" allowing for the simplest route or an appropriate detour. According to Deleuze, hodological space addresses the issue of overlapping perspectives so that a given object can be effectively grasped.
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