our earliest lesson in spatial perception-these positional signs receive a new significance from the active and passive touches that accompany them, just as they impart to these last a significance they could never have alone.

Tactual Perception of Space.

$4. It is only in the resulting complex that we have the presentations of actual position and of spatial relation. For space, though conceived as a coexistent continuum, excludes the notion of omnipresence or ubiquity: two positions la and l, must coexist, but they are not strictly distinct positions so long as we conceive ourselves present in the same sense in both. But, if Fa and F, are, e.g. two impressions produced by compass points touching two different spots as la and l on the hand or arm, and we place a finger upon la and move it to l, experiencing thereby the series P1, P2, P3, P4, this series constitutes la and la into positions and also invests Fa and F, with a relation not of mere distinctness as Tóжо but of definite distance. The resulting complex perhaps admits of symbolization as follows: FaFoFo FaFe FFFnFx · ·

d

Tttt

Here the first line represents a portion of the tactual continuum, Fa and F, being distinct 'feels,' if we may so say, or passive touches presented along with the fainter sensations of the continuum as a whole, which the general 'body-sense' involves; T stands for the active touch of the exploring finger and P1 for the corresponding kinaesthetic sensation regarded as 'positional sign'; the rest of the succession, as not actually present at this stage but capable of revival from past explorations, is symbolized by ttt and p2p3ps.

When the series of movements is accompanied by active touches without passive there arises the distinction between one's own body and foreign bodies. When the initial movement of a series is accompanied by both active and passive touches, the final movement by active touches only, and the intermediate movements are unaccompanied by either, we get the further presentation of empty space lying between us and them-but not until, by frequent experience of contacts along with those

intermediate movements, we have come to know all movement not merely as a succession but as a change of position. Thus active touches come at length to be 'projected,' passive touches alone being 'localised' in the stricter sense. But in actual fact, of course, the localisation of one impression is not perfected before that of another is begun. We must take care lest our necessarily meagre exposition give rise to the mistaken notion that localising an impression consists wholly and solely in performing or imaging the particular movements necessary to add active touches to a group of passive impressions. That this cannot suffice is evident; for a single position out of relation to all other positions would be a contradiction. Localisation, then, though it depends on many special experiences of the kind described, is not like an artificial product which is completed a part at a time. It is essentially a growth, and such that its several constituents advance together in definiteness and interconnexion. So far has this development now advanced that we do not even imagine the special movements which the localisation of an impression implies; that is to say, they are no longer distinctly represented as they would be if we definitely intended to make them: the past experiences are 'retained,' but too much 'complicated' in the mere perception to be appropriately spoken of as remembered or imaged.

À propos of this almost instinctive character of even our earliest spatial percepts it will be appropriate to animadvert on another misleading implication in the current use of such terms as 'localisation,' 'projection,' 'bodily reference,' 'spatial reference' and the like. The implication is that the body as extended, or more generally that external space, is in some sort presented or supposed apart from the localisation, projection or reference of impressions to such space. That it may be possible to put a book in its place on a shelf there must be (1) the book, and (2), distinct and apart from it, the place on the shelf, and (3) a ticket or mark on the book indicating this place'. But in the

1 It was in this sense that Lotze used the term 'local sign.' But this is just the meaning we have to avoid and the use of the term sign is so far misleading. "Topical factor' would be a safer term, if we could begin framing our terminology afresh. Anyhow it must be borne in mind that 'local sign' is used proleptically not indicatively. It is not meant to refer to a clue by means of which sensations can be localised in our percept of space' (Lotze, Metaphysik, § 279). It is our name for one of the factors whereby that percept is obtained. This, of course, applies also to the term 'positional sign.'

153 evolution of our spatial experience impressions and positions are not thus presented apart. We can have, or at least we can suppose, an impression which is recognised without being localised as has been already said. But if it is localised this means that a more complex presentation is formed by the synthesis of new elements, not that a second distinct object is presented and then some indescribable connexion established between the impression and it, still less that the impression is referred to something not strictly presented at all. The truth is that the body as extended is from the psychological point of view not perceived apart from localised impressions. In like manner impressions projected (or the absence of projected impressions) will constitute all that is perceived as the occupied (or unoccupied) space beyond. It is not till a much later stage, after many varying experiences of different impressions similarly localised or projected, that even the mere materials are present for the formation of such an abstract concept of space as 'spatial reference' implies1. Psychologists, being themselves at this later stage, are apt to commit the oversight of introducing it into the earlier stage, the genesis of which they are seeking to ascertain.

Visual Perception of Space.

§ 5. To ascertain the genesis of the tactual perception of space is all that we have yet attempted. The visual perception -so far as it is metrical-presupposes this; as the common names for linear magnitudes, hand, foot, ell, step, &c., at once suggest. It is only by reference to tangible or 'real' magnitude, that, as Berkeley shewed long ago, the various visual or 'apparent' magnitudes of an object have any sense or meaning: "otherwise there can be nothing steady and free from ambiguity spoken of it?" "But, as has been often remarked, this is true, though to a less degree, of tangible as well as of visible objects": such is the comment on this passage of Berkeley's editor, Dr Campbell Fraser. There is a certain relativity besetting our tactual as well as our visual perception of magnitude, it is true; but it is not true that the difference between the two is one of degree; it is rather a difference of kind. For in vision the apparent size of

1 Cf. on this point Poincaré, La Science et l'Hypothèse, pp. 74, 75.

2 Cf. Essay towards a New Theory of Vision, §§ 55-61.

an object is relative to its distance from the eye; in touch, which -necessarily implying contact-excludes distance, it is relative to the part touched or touching: compare, e.g. a corn-plaster applied to the back and then to the thumb or a dental cavity explored by the tongue and afterwards by the finger-tip. But for the parts severally, Berkeley's assertion holds: for each any given object has a constant determinate magnitude, though such magnitudes differ widely inter se. For the eye, on the other hand, any given magnitude may appear as that of an object that is really either very large or very small, if the object be sufficiently distant in the one case and sufficiently near in the other. But "distance of itself, and immediately cannot be seen. For distance, being a line directed endwise to the eye, it projects only one point on the fund of the eye-which point remains invariably the same, whether the distance be longer or shorter." That is to say, till we know the distance we cannot judge the size: distance is in the last resort entirely a tangible or locomotor magnitude. If, then, visual magnitude can only be interpreted by means of tangible magnitude, and if the tangible magnitudes of an object differ widely from each other according to the parts exploring or affected, what determines which is to be the standard? Nothing but convenience: experience very soon singles out and perfects the best, that for which the local signs of passive touch and the positional signs of active touch are in themselves the most finely graduated and together the most easily combined. That one is the hand. The most mobile parts have the keenest 'spatial sense' and the least mobile the bluntest of all, as Vierordt has shewn. In these facts we have, by the way, further confirmation of the mutual co-operation of the two factors, extensity and motility, in producing and perfecting our tactual perception of space.

But though Berkeley was right in his contention that ocular perception cannot be the primary source of (metrical) geometry,

1 Berkeley, op. cit. § 2. In the last clause Berkeley went too fast, as he might have learnt if it had occurred to him to put his a priori statement to the test of experiment (cf. below, p. 160).

2 For "the space inside the mouth, which is so intimately known and accurately measured by its inhabitant the tongue, can hardly be said to have its internal directions and dimensions known in any exact relation to those of the larger world outside. It forms almost a little world by itself." W. James, Psychology, ii. 181. 3 Physiologie des Menschen, 5te Auf. 1877, pp. 342-9.

155 he nevertheless overlooked what Reid afterwards made clear, viz. that it does give rise to a geometry altogether independent of 'tactual perception'; such is the 'geometry of visibles,' as Reid called it, projective geometry as we now say. It would be strange if it were not so, since to the eye pertains an extensity and motility peculiar to it, which are most minutely differentiated inter se and most intimately correlated together. The differentiation into local signs of the retinal extensity is but a further stage in the development which began in the differentiation within the general dermal sensibility of a specific light sense. It seems to consist in an increased specialisation of the more central portions of the retina as compared with the rest. The most central portion which answers to the functioning of what, from its colour, is called 'the yellow spot,' is trichromatic under conditions (as to amount of light, size of object, &c.), such that its marginal zones are only dichromatic, and the peripheral zone only monochromatic. Also-and still more important-along with this comparative lack of sensory differentiation, there is a marked diminution in exact definition as we pass from centre to periphery thus, the ace of diamonds, say, which in the first case is distinct both in shape and colour becomes in the last only a colourless blur and is soon lost to sight altogether if it remains at rest. Again, as with touch, the question arises: which of these conflicting deliverances are we to prefer? And again we may answer that practice selects and perfects that which works best. The yellow spot, or rather a central hollow within this, called the fovea centralis, thus comes to be the finger of the eye, if we may so say. And surely we may; for though there is not much resemblance between a dimple and a finger, still the functions of the finger in active touch and that of the fovea centralis in active vision are practically identical. The whole extensity of the field of sight, the somatic field as it should be called to distinguish it from its objective projection, is simultaneously presented and its content passively received, but what we actively fixate and look at the contour or the motion of the object, for example -forms a successive series and each item of it is brought in turn. by the movements of the eye to occupy the yellow spot. The

1 Cf. the German Sehen and Blicken, Fühlen and Tasten.

2 These movements as 'positional signs' again, as in the tactual perception of space, are not objective movements already implying space, but the serial kinaesthetic