Child's Conception of Space

Selected Works vol 4

Jean Piaget

• Publisher: Routledge
• Year: 2013
• eBook ISBN: 9781136220791
• Topic: Medicine
• Subtopic: Health Care Delivery

First published in 1997. This Volume 4 of Jean Piaget's selected works and explores the study of the concept of space, or rather, of the innumerable ideas involved in the concept of space, which Piaget sees is for many reasons an indispensable part of child psychology.

PART ONE

TOPOLOGICAL SPACE

Chapter One

PERCEPTUAL SPACE, REPRESENTATIONAL SPACE,
AND THE HAPTIC PERCEPTION OF SHAPE¹

THE chief obstacle to any developmental study of the psychology of space derives from the circumstance that the evolution of spatial relations proceeds at two different levels. It is a process which takes place at the perceptual level and at the level of thought or imagination.

The commonsense approach to the problem, which is also that adopted by many mathematicians, assumes that the idea of space develops under the influence of motor and perceptual mechanisms; and so far as it goes this is quite correct. But this view goes on to assume that representational images and geometrical ideas are no more than a mere copy of existing sensori-motor constructs. This, however, oversimplifies and completely misrepresents the facts.

Kant considered space an a priori structure of ‘sensibility’, the function of thought being merely to submit the data of space perception to a process of logical deduction capable of analysing them indefinitely without ever exhausting their content. Poincaré too, ascribed the formation of spatial concepts to sensory impressions, endeavouring to apply his theories on the group of displacements to the interplay of actual sensations, as if sensori-motor space furnished the basis for geometrical thought whilst the intellect elaborated this previously prepared material.

Now it is perfectly true that such a sensori-motor space begins to evolve right from the child's birth, and together with perception and motor activity it undergoes considerable development up until the appearance of speech and symbolic images, i.e., the symbolic functions in general. This sensori-motor space is superimposed upon various pre-existing spaces such as the postural, etc., though it is by no means a simple reflection or repetition of them. On the contrary, it has its own course of development which can be traced fairly easily, and in addition, the spatial organization of sensori-motor behaviour results in new mental constructs, complete with their own laws.²

At this juncture, however, there appears a rather curious phenomenon which tends to complicate the task of analysis. Though in a sense profiting from the achievements of perception and motor activity (which at their own level provide experience of straight lines, angles, circles, squares, projective systems and so on), representational thought or imagination at first appears to ignore metric and perspective relationships, proportions, etc. Consequently, it is forced to reconstruct space from the most primitive notions such as the topological relationships of proximity, separation, order, enclosure, etc., applying them to the metric and projective figures yielded by perception at a level higher than that of these primitive relationships themselves.

Through failing to observe the discrepancy between the form of these initial relationships and the perceptual content to which they refer, outwardly at a more advanced stage, one tends to reduce everything to one common level and imagine that geometrical concepts are based directly on sense data.

Moreover, during the development of representational space, representational activity is, in a manner of speaking, reflected or projected back on to perceptual activity. Thus, beginning with the stage at which representation can arrange all spatial figures in co-ordinate systems (in line with the vertical-horizontal axes derived from physical experience but developed geometrically), perception itself begins to locate the partial configurations it has achieved within such systems, whereas formerly it was content with a far more limited degree of structurization.

Knowing nothing of the stages which led up to this transformation, the adult assumes that perception involves co-ordinate systems or vertical-horizontal relations right from the outset, when in fact such systems are extremely complicated and are only fully developed by the age of 8 or 9. And such an illusion naturally tends to reinforce the misconception mentioned earlier, regarding the way perception is related to representation, a misconception which has influenced current explanations of geometrical concepts.

So deep-rooted is this misconception that we offer no apology for the length of this first volume in trying to eradicate it. In the present chapter we will merely outline the problem. In the first part we shall try to give a very brief summary of the facts relating to sensori-motor and perceptual space. In the second part we shall introduce the study of representational space by examining some of the very simplest sensed spatial notions constituting an image, namely, those relating to the shape of objects. In neurology and experimental psychology, tactile recognition of solids (relative to unseen objects) is often called ‘haptic perception’. This term, which has become general, is nevertheless incorrect; for these so-called perceptions go far beyond the limits of the purely perceptual and usually presuppose the translation of tactile perceptions and movements into visual images. But quite apart from the question of terminology, it is precisely this mixed character which pertains to the facts of ‘haptics’ that will interest us here. For it gives us the opportunity of observing in the raw the actual process of development from the perception of shapes to their representation, in children between the ages of 2–7 years. Taken together with the study of drawing, which marks the transition from visual perception to ideo-motor representation, the study of ‘haptics’ provides a very natural introduction to the study of representational space.

SECTION I—PERCEPTUAL OR SENSORI-MOTOR SPACE

The subject of the present work is not the development of space in general, but only that of representational space, and therefore the analysis of perceptual space goes beyond our set limits. But since the perceptual sensori-motor structures, or frames of reference, constitute both the point of departure and the foundation of the entire representational construction of space, it is as well to start by going over what is at present known on this subject. We will be very brief as regards sensori-motor space, since we have elsewhere endeavoured to trace its origin (C.R. Chs. I and II) during the first eighteen months of life, and it is this earlier outline that we shall refer to here.

§1. Spatial perception prior to representation

According to currently accepted explanations of the perceptual process, every perceptual ‘field’, from the most elementary to the most highly developed, is organized in accordance with the same types of ‘structure’. This organization is supposed to be of a geometrical character right from the start, quite apart from the effects of the laws of ‘good gestalt’, and to involve the immediate formation of perceptual constancies of shape and size. This would mean that at any age a baby could recognize the shape of an object independent of perspective, and its size apart from its distance. Thus there would be from the very outset a perception of relationships at once spatial and metric. If this hypothesis were correct it would only be necessary to call to mind the laws of spatial configurations in order to describe perceptual space.

But we have already shown in the work referred to above that the constancy of the shape of objects is far from being complete at the outset, since at 7 or 8 months a child has no idea of the permanence of objects, and does not dream of reversing a feeding bottle presented to him wrong way round (C.R. pp. 128–9). Since then we have shown, together with Lambercier, that as regards size constancy, great differences still persist between an 8-year-old child and an adult,¹ whilst Brunswik and Cruikshank² have demonstrated its absence during the first six months of existence. It is thus by no means absurd to suppose that perceptual relationships of a projective order (perspective) and of a metric order (estimation of size at varying distance) should appear later than these more elementary spatial relationships whose nature has first to be defined. It is also quite obvious that the perception of space involves a gradual construction and certainly does not exist ready made at the outset of mental development.

What does this construction consist of? We shall try to sketch its main outlines during the three periods of sensori-motor development, from birth to the commencement of representation. The first period consists of two stages, that of the pure reflexes, and that of the acquisition of primary habits. The second period is also marked by two stages; namely, the stage of ‘secondary circular reactions’ (beginning of manipulation of objects, about 4–5 months), and that of the first fully intelligent behaviour, i.e., extending to the end of the first year. Finally, the third period covering the stage of ‘tertiary circular reactions’ (beginning of experimentation) and the first ‘internalized co-ordinations’ (rapid comprehension of novel situations).¹

First period. The first two stages of development are marked by an absence of co-ordination between the various sensory spaces, and in particular by lack of co-ordination between vision and grasping—visual and tactile-kinaesthetic space are not yet related to one another as a whole. Thus it is hardly surprising that at this level there exists as yet neither permanence of solid objects, nor perceptual constancy of shape and size. (Cf. C.R. Ch. I.)

It is therefore necessary, difficult as the task may seem, to try to reconstruct the spatial relations which arise in primitive or rudimentary perception (e.g., in the exercise of the reflexes of sucking, touching, seeing patches of light, etc., and the earliest habits superimposed on these reflexes). But since these initial perceptions fail to attain constancy of size and shape, what sort of relations go to make up such a space?

1. The most elementary spatial relationship which can be grasped by perception would seem to be that of ‘proximity’, corresponding to the simplest type of perceptual structurization, namely, the ‘nearby-ness’ of elements belonging to the same perceptual field. Following the work of the Gestalt School, it is well known that the primary factor in the organization of structures is undoubtedly the proximity of structural elements. However, it should be noted that this relationship alters as the child grows older. The younger the child, the greater the importance of proximity as compared with other factors of organization (resemblance, symmetry, etc.). Conversely, as the child develops so this ascendancy is lost, and the elements which make up the perceptual whole can be brought into relation with one another over greater and greater distances.¹

2. A second elementary spatial relationship is that of separation. Two neighbouring elements may be partly blended and confused. To introduce between them the relationship of separation has the effect of dissociating, or at least of providing the means of dissociating them. But once again, such a spatial relation corresponds to a very primitive function; one involved in the segregation of units, or in a general way, the analysis of elements making up a global or syncretic whole. In a syncretic perception, such as that experienced by a baby when it sees some object leaning against the wall, appearing as a patch scarcely distinct from its surroundings, there is proximity without clear separation. The more analytic perception becomes, the more marked is the relationship of separation. Since the child tends more and more to analyse objects as he grows older, this relationship too undergoes development. But it should not be concluded that the evolution of ‘separation’ and ‘proximity’ pursue divergent paths, so that the importance of ‘separation’ simply increases with age, while that of ‘proximity’ declines. On the contrary, just as his progress in analysis enables the child to establish ever more numerous’ separations’ between elements as yet undifferentiated, so they lead him, in constructing perceived figures, to take account of different degrees of ‘proximity’ operating over larger areas, instead of being confined to the relation of immediate proximity.

3. A third essential relationship is established when two neighbouring though separate elements are ranged one before another. This is the relation of order (or spatial succession). It undoubtedly appears very early on in the child's life, not merely when the baby's gaze or touch passes over a series of elements ranged in some fixed order (such as the rungs of his cot), but also when a series of habitual movements is guided by perception according to organized points of reference. For example, the sight of a door opening, a figure appearing, and certain movements indicative of a forthcoming meal, form a series of perceptions organized in space and time, intimately related to the sucking habits. Inasmuch as the relations of order appear very early it is hardly necessary to point out that they are capable of considerable development, in terms of the growing complexities of wholes. In the perceptual realm there is one relation in particular, of which order constitutes a fundamental part. This is the relation of symmetry, represented in the simplest case by the double order . . . CBA/ABC . . . , whose role is well known in the construction of ‘good configurations’, or familiar ‘empirical’ forms such as a face.

4. A fourth spatial relationship present in elementary perception is that of enclosure (or surrounding). In an organized series ABC, the element B is perceived as being ‘between’ A and C which form an enclosure along one dimension. On a surface one element may be perceived as surrounded by others; such as the nose framed by the rest of the face. In three dimensions enclosure takes the form of the relation of ‘insideness’, as in the case of an object in a closed box. But it is clear that although the relationship of ‘enclosure’ is originally a perceptual given, no sooner do the factors of ‘proximity’, ‘separation’ and various types of ‘order’ become organized, than ‘enclosure’ undergoes a complex process of evolution, particularly as regards three dimensions. Thus the partial disappearance of an object behind a screen results, not in a true perception of what in fact takes place, but rather in the perception of something like the re-absorption of the object within the screen. Again, still about the age of one year, when the child attempts to replace a ring which encircles a stick, he contents himself with pushing it against the stick as if encirclement could be brought about simply by contact and did not involve the act of passing the ring over the stick.¹

5. Lastly, it is obvious that in the case of lines and surfaces there is right from the start a relationship of continuity. But it is a question of knowing in precisely what sense the whole of the perceptual field constitutes a continuous spatial field. For quite apart from the fact that the various initial qualitative spaces (such as the buccal, tactile, visual, etc.) are not for a long time co-ordinated among themselves, it has not been shown in any particular field, such as the visual, that perceptual continuity retains the same character at all levels of development. Poincaré linked empirical continuity with the following formula: in a series ABCDE etc., in which the adjacent elements are confused or perceived without being distinguished (thus A=B; B=C etc.), but where A and C or B and D are distinguished (thus A C; B D etc.), the subject has an impression of continuity throughout the process. Köhler describes in a similar way the differential thresholds occurring under Weber's Law. Thus we may say that the perception of continuities is modified in terms of the increasing fineness of the thresholds of sensitivity, and consequently by the evolution of the relationships of proximity and separation.

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Table of contents

• Cover Page
• Half Title page
• Title Page
• Copyright Page
• Contents
• Preface
• Translators' Notes
• Summary
• Part One Topological Space
• Part Two Projective Space
• Part Three The Transition from Projective to Euclidean Space
• Index