Space and Spatial Cognition

A Multidisciplinary Perspective

Michel Denis

• Publisher: Routledge
• Year: 2017
• eBook ISBN: 9781351596176
• Topic: Psicología
• Subtopic: Psicología cognitiva y cognición

All living creatures inscribe their activity in space. Human beings acquire knowledge of this space by traversing it, listening to verbal descriptions, and looking at maps, atlases, and digital media. We memorize routes, compare distances mentally, and retrieve our starting place after a long journey. Space and Spatial Cognition provides an up-to-date introduction to the elements of human navigation and the mental representation of our environment.

This book explores the mental capacities which enable us to create shortcuts, imagine new pathways, and thus demonstrate our adaptation to the environment. Using a multidisciplinary approach which draws on psychology, neuroscience, geography, architecture and the visual arts, the author presents answers to a number of questions. Which mental capacities do people mobilize when confronted with space? Which brain functions do they implement? How do digital technologies extend these capacities? By presenting space at the crossroads of a number of disciplines, this volume reveals how each of them enhances our understanding of human behaviour in space.

Space and Spatial Cognition provides a unique insight into all facets of spatial cognition, including spatial behaviour, language, and future technologies. It will be the ideal companion for all students and researchers in the field.

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PART I

Space as object of knowledge and object of practice

Humans experienced space long before producing any discourse about it and, a fortiori, before building any scientific discourse. For most living creatures equipped with a nervous system, the environment is apprehended by perceptual experience and locomotion. It provides a frame in which actions are inscribed and motor programs set up, to progressively become refined. Since probably quite early in phylogeny, the environment has been internalized in the form of representations, which offer a substratum for implementation of action. At a more advanced stage in the evolution of the nervous system, the environment and the actions taking place within it became a subject for communication between individuals. For a given individual, the capacity to undertake procedures intended to transfer to a congener’s mind his/her own internal representation of an environment – to serve a specific behavioral episode – undoubtedly marks a crucial stage in evolution. For the human species, it is correlated with the capacity to generate discourse about space, build a conceptual representation of it, apply measurement onto it, and draw laws and principles. Lastly, when it comes into play, scientific thinking brings with it a set of instruments – both intellectual and technical – that make it possible to grant space the status of an object of science.

To start with, how can we characterize this object? Space imposes itself on anyone as an intuitive reality which provides a context for a variety of sensory and locomotor experiences. It nevertheless remains an abstract concept. Speaking of physical entities endowed with spatial extension is not an insignificant task. It consists of not only describing the ingredients that inhabit spaces open to our experience, but also accounting for the principles that regulate a spatialized world. It is a fact that empirical sciences that contribute to substantiating the concept of “spatial cognition” do not deal so much with space properly speaking, but rather with people’s behavior within that space and the knowledge they build of it. They primarily take space as a venue for action. This approach is biased towards behavior and representations, and is used by scientists as an angle of attack in uncovering the properties of the object “space.” It will be amply illustrated in this book. But beyond its full validity, this empirical approach does not exempt scientists from an intellectual effort to figure out the concept itself, in particular through the philosophical reflection that space has elicited throughout centuries. We will also have to consider the contribution from disciplines whose proper object is space, such as geography and cartography, but also sciences of the Earth and of the Universe. Lastly, we will examine the disciplines that develop space-related practices such as architecture and the visual arts.

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Only later will we dedicate ourselves, in Part II and afterwards, to what ordinary people (neither scientists nor practitioners) know about space and how they display their knowledge through navigational performance, spatial reasoning, and spatial discourse.

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1

PHILOSOPHICAL APPROACHES TO SPACE

The concept of space attracts everyone’s intuition. A review of the philosophical approaches to this notion reveals, however, a variety of points of view. Interestingly, it will appear that a pronounced tendency has developed, which consists of taking the human into account in delineating the concept of space. Also, we will see that Euclidean geometry is grounded in a geometric intuition shared by all, and even considered by some theoreticians as universal.

From absolute to relative space

We owe to Newton the formulation of an absolute conception of space. For the author of Principia Mathematica, space is a reality in itself. It exists as a permanent entity, independently of the matter that it contains, and even if it does not contain any matter. This radical conception is related to Newton’s commitment to the idea of an immanent world. It was vigorously disputed by Leibniz, his contemporary. This philosophical dissent added to other controversies which brought the two philosophers into conflict (on the theory of gravitation or the paternity of the discovery of infinitesimal calculus). Contrary to Newton, Leibniz argued for space as being essentially relative (in fact, a property that space shares with time). For him, there is no space without matter, and space can only be conceived and seized by our mind because there are objects filling it. Populated with objects of the physical world, space is to be understood as the collection of spatial relations among these objects. These relations are expressed in terms of distances and directions. In sum, the author of the New Essays on Human Understanding subscribes to the notion of a discretization of space, at the expense of the intuitive postulate of its continuity. For him, space is an abstract reality, for which he proposes a vivid metaphor: space is to be conceived as the relationships between members of a family. All the concerned people are related to one another, but their relationships cannot be conceived independently of the existence of these people.

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One century later, Kant’s metaphysics would support the idea that although space and time can be apprehended as objective realities of the world, both are unanalyzable intuitions, inaccessible to rational reasoning, and providing to the mind the organizing frame of every human experience. But if the intuition of time has its origin within the individual, the intuition of space is engendered by the external world. It remains that Kant’s space, contrary to the view promoted by Leibniz, is homogeneous and continuous.

At the beginning of the twentieth century, Bergson contributed more than anyone to the reflection on time, which durably prevailed in philosophical thinking, while pointing out also the cross-links between the concepts of time and space, in particular in the passage of his Time and Free Will: Essay on the Immediate Data of Consciousness (1910) where he analyzed the spatial counterparts (the course of the hands of a clock) of temporal events (the time elapsed during that course). It is in this context that Bergson introduced the famous formula by which he characterizes time as “the ghost of space” (p. 99).

The notion of the continuity of space was still present in the views promoted by Franz Brentano while he was drawing the first outlines of his phenomenological approach.¹ Brentano did not postulate any radical opposition between the outer world and the psychological world. Both are associated by a relation of “intentionality,” which means that thought cannot be dissociated from the objects to which it applies, and that perception is always perception of something. Therefore, psychic phenomena are essentially characterized in terms of their relation to an object. This is the essence of every mental act to be relational in nature. Brentano is probably the first thinker to have noticed that the various philosophical conceptions of space were dependent on the meaning attached to the terms that refer to space. For instance, the ancient Greeks did not have at their disposal any term equivalent to what we call “space.” The Greek word “topos” corresponds more precisely to our notion of “place,” with the possibility for a specific object to be attached to this place. This terminological determination is probably related to Aristotle’s conception of space as non-infinite, but instead bounded by the heavenly sphere. On his part, Brentano promoted the idea that space, like time, does not exist by itself. Both can only be conceived in terms of the intentional relations in which they are involved. In this sense, Brentano’s approach is consistent with Leibniz’s “relative” conception of space (see Kavanaugh, 2008).

Poincaré, space, and geometry

In the early years of the twentieth century, the most advanced approach to the concept of space was proposed by Henri Poincaré, who aptly articulated his philosophical views to a deep reflection on geometry. The most remarkable facet of Poincaré’s thought was to take into account the individual’s body to circumscribe the concept of space. In Science and Hypothesis (1905, first published in French in 1902), Poincaré questioned the notion that the space in which our images of external objects are displayed would be the same as the notion of space for geometers and would have the very same properties. He recalled the essential properties of “geometrical space”: it is continuous; it is infinite; it has three dimensions; it is homogeneous; and it is isotropic.

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Poincaré developed an analysis intended to demonstrate that this set of characteristics is not systematically found in what he calls “representative space.” First, if the visual images formed on the retina can be considered as continuous, they in fact possess only two dimensions, which distinguishes “purely visual space” from geometrical space. Second, all the points on the retina do not play the same role, which casts doubt on the idea that visual space would be homogeneous. Third, if sight enables people to estimate distances and therefore to perceive the third dimension, this perception might well be restricted to the impressions associated with the effort of accommodation and ocular convergence. These muscular sensations are distinct from the visual sensations that convey to the individual the knowledge of the first two dimensions. Thus, the third dimension cannot be considered as playing the same role as the other two, so that visual space can hardly be viewed as isotropic.² Lastly, the tactile experience and the muscular sensations linked to movements also contribute to engender our notion of space, while remaining remote from the notion of geometrical space.

Thus, for Poincaré, “representative space in its triple form – visual, tactile, and motor – differs essentially from geometrical space. It is neither homogeneous nor isotropic; we cannot even say that it is of three dimensions” (p. 56). The consequence that Poincaré draws from this analysis is that “representative space is only an image of geometrical space, an image deformed by a kind of perspective, and we can only represent to ourselves objects by making them obey the laws of this perspective” (p. 57). The innovative view introduced by Poincaré is that when we localize an object in a given point of space, “it simply means that we represent to ourselves the movements that must take place to reach that object” (p. 57). To represent to ourselves these movements means to represent to ourselves the muscular sensations that accompany them, but these sensations have obviously no geometrical character and do not imply the pre-existence of the notion of space.

The text on the relativity of space, first published in 1906 in L’Année Psychologique, then in Science and Method (1914), opens with a strong statement: “It is impossible to picture empty space” (p. 93). Poincaré rejects the concept of absolute space and maintains the principle of relativity of space, following on Leibniz’s theory. He casts doubt on the idea that one would claim to “know” the distance between two points. According to him, any reference to “absolute space” is meaningless. There can be no question of absolute magnitude, but of the ratio of that magnitude to the instrument used to measure it (a meter, the path traversed by light, etc.). The notion of a “direct intuition of space” (intuition of distance, of direction, of a straight line) is illusory. If people ultimately succeed in “building up” a sense of space, it is thanks to an instrument that they use naturally, namely, their own body. “It is in reference to our own body that we locate exterior objects [. . .]. It is our body that serves us, so to speak, as a system of axes of co-ordinates” (p. 100). This approach applies to “restricted space” (nowadays, one would refer to “pericorporeal space”) as well as “extended space” (the wider space accessed when one moves). In this space, points are defined by the succession of movements to be made in order to reach them, starting from the initial position of our body. Poincaré acknowledges that it is possible to translate our physics into the language of a geometry of more or less three dimensions, but points that “the language of three dimensions seems the best suited to the description of our world” (p. 113). If the contrast between the roughness of a “primitive geometry” and “the infinite precision of the geometry of geometricians” is well recognized, it remains true that “the latter is the child of the former” (pp. 114–115). But, of course, “it required to be fertilised by the faculty we have of constructing mathematical concepts, such, for instance, as that of the group” (p. 115). Therefore, geometry, which is not an experimental science, is nevertheless connected to experience. If we have created the space that geometry studies, it is by adapting it to the world in which we live.

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In the historical context where Euclidean geometry was confronted with the “other” geometries (hyperbolic, elliptic, etc.), the question of the nature of real space was hotly debated. Poincaré’s position consisted of proposing that the choice of a geometry to describe space is finally a matter of convention. Euclidean geometry is certainly “simpler” than a non-Euclidean one, which explains that it is preferred when we have to account for the geometry of our surrounding world. Simplicity and efficiency appear to be plausible criteria for the selection of a geometrical system at the expense of another. Here we realize the break endorsed by the author of Science and Method: intuition is recognized as contributing to the foundation of mathematics, including geometry. The human mind easily accesses the notion of continuity, in particular when it applies to the domain of space. Therefore, there is an intuitive grounding of geometry, and it is on this intuition that the mathematical construction of the discipline relies.

This idea is therefore the opposite to that of a geometrical space governed by universal logic rules, independent of humans. For instance, for Frege, these axioms can only be expressed in a highly abstract language and their objectivity is the very condition of the foundations of mathematics. But this position simply neglects that it is the human, as a living being in the world, who constructs mathematical concepts, and not any other thinking and acting entity. Geometry, initially the science of figures, then becoming the science of space, tended to become, thanks to Poincaré, the science of movement in space. This approach prefigured a broader, more recent view of science which takes into account the relation of the human to the world and the knowledge that the human constructs of it. For instance, as regards geometry, the exchanges with the experimental disciplines dedicated to the study of movement (gesture, locomotion) and spatial knowledge establish new connections between “mathematical geometry” and the “geometry of the sensible world” (see Longo, 2003). In these conditions,

our practice of the invariance of objects of the world [. . .] allows us to build o...

Table of contents

• Cover Page
• Space and Spatial Cognition
• Praise
• Title
• Copyright
• Contents
• List of Figures
• Foreword Space and Spatial Knowledge
• Part I Space as Object of Knowledge and Object of Practice
• Part II Spatial Behavior and Spatial Representations
• Part III Brain and Sensorimotor Systems: Functions and Dysfunctions
• Part IV Space and Language
• Part V Computation and Technologies
• Epilogue Spatial Thinking
• Bibliography
• Index of Names
• Index of Terms