Basic concepts of abstract spaces, Review of “Identification of some fundamental spatial concepts”, by John D. Nystuen

This article by John D Nystuen is rather short and very straightforward. I do nonetheless acknowledge that not everyone has the leisure, time, or interest to read it and contextualise it. It remains nonetheless a very good gate of entry to the questions and ways of thinking developed by the spatial-analytic school. I summarise here shortly its context and content for people not specialised in geography who would still have an interest in having a look at one debate in this discipline, in this case the debate raised by the spatial-analytic school of geography.

Doors of the Sidi Yehia Mosque, Timbuktu, c. KaTeznik

Doors of the Sidi Yehia Mosque, Timbuktu, c. KaTeznik

As soon as it began emerging as a modern social science geography was confronted to a leading question: that of its object. In the positivist perspective on the definition of science, the answer was straightforwardly to associate any discipline with a specific object: the production and distribution of goods to economy, social facts to sociology, the study of the earth to geology, and so forth. This reasoning has been, as we have seen briefly in the post about the development of the question of social movements in human geography, facing its own limitations as soon as it has been formulated, especially in the Blache/Durkheim controversy and in the Hartshorne/Schaefer controversy. In the first case, the debates regarding which discipline ought to study spatial arrangements, as well as the debate regarding whether geography ought to study non-purely spatial arrangements were linked to a question of object definition. As we have equally seen in the post, for better or worse the debate was temporarily won by Fred Schaefer’s approach according which

Geography […] must pay attention to the spatial arrangement of the phenomena in an area and not so much to the phenomena themselves. Spatial relations are the ones that matter in geography, and no others. Nonspatial relations found among the phenomena in an area are the subject matter of other specialists such as the geologist, anthropologist, or economist. […] For instance, the connections between ideology and political behavior, or the lawful connections between the psychological traits of a population and its economic institutions do not concern the geographer. (Schaefer, 1953)


Defining a basic set of geographic concepts

In other words, as the 1960s began to unfold themselves, the perspective according which geography had to focus on “spatial relations” was getting more and more admitted in the discipline. Nonetheless once the epistemological point is admitted, a lot remains to be done, and to begin with, to define these spatial relations. If Schaefer is rather extensive on the geographic science he does not want, pointing at the historical trend he calls “exceptionalism” and describing it rather lengthily in a well-documented manner, the positive conceptions in his paper are lacking: he explains that the science ought to be divided between theoreticians (systematic geographers) and appliers (regional geographers), organised around predictive mathematical laws, studying a precise object (spatial relations), and with a specific tool (the map). Although he rejects previous concepts as poorly explanatory (and particularly the notion of region), Schaefer does not venture deeper into what spatial relations are, leaving his reader slightly lost[i]. For the reader to be situated, this was before the development of the models which emerged further on in Theoretical Geography (Bunge, 1962), or Explanation in geography (Harvey, 1969). Spatial analysis had been employed either in military action or in an almost spontaneous and “naïve” manner. The generation of geographers following Schaefer have had to conceive their tools from mathematics and geometry. Here is when John D Nystuen comes in. As little information is accessible on his biography, it must simply be said that Nystuen had already authored at least one paper of importance as this one came out (you can find a review of this other paper here, in French). The clarity with which he situates the question makes his paper worth reading as he very eloquently highlights as soon as its formulation what will become a main contradiction of the spatial analytic school, despite not leaving it. Indeed the point of start of the article is the acknowledgement of the danger of tautology in the author’s own perspective:

The definitions of the words we employ to invoke a spatial point of view are tautological. We break the circle of definitions at some point and settle on a group of words which are accepted as undefined.[ii]

The aim of the article is, straightforwardly, to fill in that gap: facing an already-specialised discipline, the author asks himself which common ground can be found. If there is such a thing as a spatial perspective, then it must have some sort of consensual set of concepts, in other words:

The problems found interesting and being investigated in all branches of the discipline are defined using this common set of words – the controversy over the definition of geography notwithstanding. These words describe spatial arrangements and associations of activities and processes in geographical space. We adopt a spatial point of view whether the problem considered is one of physiography, cultural diffusion, economic expansion, or any of the diverse problems found attractive to geographers.

Space as an isotropic plain and three core geographic concepts

In order to maintain that consensual character, the author restricts himself to the largest set possible. Because of that the author also chooses to eliminate entirely the question of the object from his perspective: “In considering a problem in the abstract, one can restrict the properties of the object under study to a bare minimum and allow only simple associations to exist”. From this perspective, the author proposes to conceive an approach of space which would render it strictly equal and indeterminate in all things save one: its very spatiality. By doing so the author aims at emptying a paradox of social sciences, the irreducibility of causes: provided that “In actual life we have only a vague idea of the effect and operation of any single variable because it appears always in conflict with other variables operating at the same time”, the only solution to avoid falling into the type of descriptive geography Nystuen aims at avoiding is a passage into the abstract: “An abstract geography will be an aid in generalization. We may expect essential similarities to emerge from extremely unlike circumstances. More penetrating and critical empirical studies may be planned based on suggestions from theoretical or abstract studies”. This distinction between the abstract, problem-conceiving geographers and the empirical ones was already present in Schaefer’s attempt to attach geography to the model of physics (1953). Here, it serves as a premise for Nystuen to develop his model.

The device used by Nystuen in order to present his set of concepts is a metaphor of space as an entirely neutral container, the “isotropic plain” (sic). The isotropic plain is defined as a flat, ideally unbounded (although this feature is by definition impossible to assert in geography) surface, on which not only all places are the same in all things (save their location), but additionally, movement and orientation from any place to any other place is absolutely equal in terms of the effort it requires. The size, content, or use of this plain is absolutely equal. It can consist in cities, countries, fruit or geographers: the supposition is that every set of spatial relation will have the same type of relation. For the sake of the demonstration the author chooses the image of a mosque in which a priest teaches pupils. Even in such an entirely undefined location the author asserts that things shall not happen randomly in terms of spatiality:

We are interested in those activities and processes which explain how the elements under study are arranged and associated in space. I use the words ‘activities’ and ‘processes’ as synonyms just to emphasise [that] I mean spatial association between groups of people as well as spatial association of all nonhuman elements or the interaction between both these classes of elements.

What this “non-randomness” is will be the set of concepts he will present. To be as general as possible he identifies three of them, the “bare necessities” of a geographic perspective according to him:

  • Directional orientation: The analytic perspective attached itself to spatial relation before all. Therefore a basic assumption is that the points present on this plain are all supposed to be in relation with one another in a certain directional orientation. For instance in this case, all students are supposed to be oriented toward the teacher.
  • Distance: Distance is more, argues the author, than a simple question of scale and unit. Actually he chooses to entirely disregard these issues as problem-bounded. The author supposes two manners in which phenomena can be bounded by distance. The first one is a decreasing relation (the voice of the teacher is expected to be less efficient as the distance with his students increases) and the second one is equally-efficient in a certain perimeter (the jurisdiction of an administration is supposedly equivalent everywhere). Nystuen parts with classical geometry on a second point: the supposed symmetry of distance: it is very possible, even in an isotropic plain, that distance from a point a to a point b were not equivalent (for instance if we are referring to a one-way street system, as the author).
  • Connectiveness: Finally, the author highlights the importance of the relative disposition of each element to the others surrounding it. This is much more important, he argues, than the identification of an adequate measure for distance, or of a scale, for instance. To go back to the question of the mosque, the relative position of students is important not only in relation to the teacher (they may define ranks, more or less packed depending on the advantage of the position regarding the flow of sound which defines their relation with the teacher), but also with one another (depending on the availability of space, affinities, and so forth).

Some essential geographic problems

In the final part of his article the author derives from these three basic concepts a few “legitimate” (according to him) geographic problems which could lead to further enquiry. Before that, he adds another layer of conceptualisation by integrating the distinction between site and situational analyses: certain elements of context, he argues, are attached to the site rather than the spatial situation of the elements under study, without being explicitly spatial. Supposing the translation of his group of student to a park, the author supposes that “A wind blowing, or the orientation of the sun, might shift the orientation of the pupils. The arrangement of rocks or benches would affect the orientation also. All of the geographic elements present inside the mosque are still present, but their effects are modified by the characteristics of the site chosen”. In other words the model proposed by Nystuen is not, as a certain critique would have it, context-blind. It merely relies on a distinction between the effects attached to space and those attached to context. The problems he identifies are nourished by that distinction:

  • Historical tension: For the author the existence of rocks and benches represent the presence of history and historical relations in space, which have “left a trace”. The production of space is already present in the model. This presence of the context can be in some studies the one important point to look at: “In many studies this legacy from the past may be the single most important fact. Existing facilities and institutions will always be not quite suitable for the present because society is always creating new activities which, for greatest efficiency, require new arrangements”.
  • Dimensional tension: In complex systems such as the ones the author sets himself to studying, effects emerge from the layout of elements according to the space they occupy and the distance (physical and/or social) between them. For example, “[On] a national scale, agricultural activities are area-occupying, whereas factories may be thought of as points. A dimensional tension is created by the fact we require association with, and the products of, both farm and factory”. Therefore, the question can arise, in the economic case here, of the distribution of activities in relation to the groups which interact with these activities.
  • Time-space tension: Here it is the realisation of activities within a short time span which creates the problem. For example, events such as road congestions are considered under this category.
  • Scale of observation and unit area: The issue of scale is reintegrated in order to clarify how the abstractions employed in order to map phenomena (say, the choice of points to map the students in the mosque) can become invalid at a different scale (if we want to approach the effect of the place occupied by a certain student on the location of other students, for instance).

Development: a self-critical spatial-analytic model

In summarising his article, the author is deeply conscious of the fact that he has not explored all the possible concepts which could define the “essential toolbox” of analytic geography. He nonetheless manages to show with a very basic consideration how these apparently obvious and basic concepts do interact in spatial analysis to develop more complex problems. This post had for its main goal to present basically the “way of thinking” of spatial-analytic geography without entering the level of detail that can be found in other texts (such as Bunge’s Theoretical Geography).

A small development, based on further considerations found in human geography, tend to show how this article is already aware of the points on which the spatial-analytic school is restricted. Indeed the author does not place a distinction between abstract and contextualised space just for the sake of getting rid of the second. What his development on historical tensions tend to show is how the “purely spatial” approach can very much be associated to a consciousness of place and landscape, two concepts more easily found in humanist or critical geography. In a way, Nystuen offers us a proposal to integrate critiques which were already starting to emerge from the ambition of his own school to “only look at space” into the very principles of the school itself (one could argue, and some have argued, that Nystuen in a way only used the metaphor of the isotropic plain to show how his plain was all but isotropic, since he constantly reaffirms in the text that effects of context emerge inevitably). In a very straightforward manner, he presents a certain perspective on geography which can very much serve as a basis for the reconciliation of abstract and place-based approaches.


Bunge W, Theoretical Geography, Lund: C.W.K. Gleerup, 1966, first edition 1962

Nystuen J D, “Identification of some fundamental spatial concepts”, Papers of the Michigan Academy of Science, Arts, and Letters, n°48, 1963, p. 373 – 384

Harvey D, Explanation in Geography, New York: St Martin’s Press, 1969

[i] This may look like an attack against Schaefer, but I personally believe he was quite clever to proceed in that way. This lack is, indeed, not at all due to the author “forgetting” this point or trying to “hide” it. Schaefer states quite explicitly his restrictions here: “We cannot and need not, as geographers, settle the future of science. But we may wonder what can reasonably be said about the future of geography as a discipline, an organized unit within the intricate division of intellectual labor. This is not strictly a methodological question and depends on many extraneous factors. Yet, it has a theoretical core that is not unrelated to methodology”. In other words, the goal Schaefer set himself to was the definition and formulation of an epistemological perspective on a science, shift included into a restructuration of the relation between sciences and methods.

[ii] To ease my task, all unreferenced quotes in this post are from Nyusten, 1963.

Cite this blog post
Alex Mahoudeau (2016, February 20). Basic concepts of abstract spaces, Review of “Identification of some fundamental spatial concepts”, by John D. Nystuen. The Cobble And The Frame. Retrieved May 21, 2024, from

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