discussion I have given for sight.
But apart from the data of sight and touch, there are other sensations which contribute as much and more than they to the genesis of the notion of space. These are known to every one; they accompany all our movements, and are usually called muscular sensations.
The corresponding frame constitutes what may be called motor space.
Each muscle gives rise to a special sensation capable of augmenting or of diminishing, so that the totality of our muscular sensations will depend upon as many variables as we have muscles. From this point of view, motor space would have as many dimensions as we have muscles.
I know it will be said that if the muscular sensations contribute to form the notion of space, it is because we have the sense of the direction of each movement and that it makes an integrant part of the sensation. If this were so, if a muscular sensation could not arise except accompanied by this geometric sense of direction, geometric space would indeed be a form imposed upon our sensibility.
But I perceive nothing at all of this when I analyze my sensations.
What I do see is that the sensations which correspond to movements in the same direction are connected in my mind by a mere association of ideas. It is to this association that what we call 'the sense of direction' is reducible. This feeling therefore can not be found in a single sensation.
This association is extremely complex, for the contraction of the same muscle may correspond, according to the position of the limbs, to movements of very different direction.
Besides, it is evidently acquired; it is, like all associations of ideas, the result of a habit; this habit itself results from very numerous experiences; without any doubt, if the education of our senses had been accomplished in a different environment, where we should have been subjected to different impressions, contrary habits would have arisen and our muscular sensations would have been associated according to other laws.
Characteristics of Perceptual Space.—Thus perceptual space, under its triple form, visual, tactile and motor, is essentially different from geometric space.
It is neither homogeneous, nor isotropic; one can not even say that it has three dimensions.
It is often said that we 'project' into geometric space the objects of our external perception; that we 'localize' them.
Has this a meaning, and if so what?
Does it mean that we represent to ourselves external objects in geometric space?
Our representations are only the reproduction of our sensations; they can therefore be ranged only in the same frame as these, that is to say, in perceptual space.
It is as impossible for us to represent to ourselves external bodies in geometric space, as it is for a painter to paint on a plane canvas objects with their three dimensions.
Perceptual space is only an image of geometric space, an image altered in shape by a sort of perspective, and we can represent to ourselves objects only by bringing them under the laws of this perspective.
Therefore we do not represent to ourselves external bodies in geometric space, but we reason on these bodies as if they were situated in geometric space.
When it is said then that we 'localize' such and such an object at such and such a point of space, what does it mean?
It simply means that we represent to ourselves the movements it would be necessary to make to reach that object; and one may not say that to represent to oneself these movements, it is necessary to project the movements themselves in space and that the notion of space must, consequently, pre-exist.
When I say that we represent to ourselves these movements, I mean only that we represent to ourselves the muscular sensations which accompany them and which have no geometric character whatever, which consequently do not at all imply the preexistence of the notion of space.
Change of State and Change of Position.—But, it will be said, if the idea of geometric space is not imposed upon our mind, and if, on the other hand, none of our sensations can furnish it, how could it have come into existence?
This is what we have now to examine, and it will take some time, but I can summarize in a few words the attempt at explanation that I am about to develop.
None of our sensations, isolated, could have conducted us to the idea of space; we are led to it only in studying the laws, according to which these sensations succeed each other.
We see first that our impressions are subject to change; but among the changes we ascertain we are soon led to make a distinction.
At one time we say that the objects which cause these impressions have changed state, at another time that they have changed position, that they have only been displaced.
Whether an object changes its state or merely its position, this is always translated for us in the same manner: by a modification in an aggregate of impressions.
How then could we have been led to distinguish between the two? It is easy to account for. If there has only been a change of position, we can restore the primitive aggregate of impressions by making movements which replace us opposite the mobile object in the same relative situation. We thus correct the modification that happened and we reestablish the initial state by an inverse modification.
If it is a question of sight, for example, and if an object changes its place before our eye, we can 'follow it with the eye' and maintain its image on the same point of the retina by appropriate movements of the eyeball.
These movements we are conscious of because they are voluntary and because they are accompanied by muscular sensations, but that does not mean that we represent them to ourselves in geometric space.
So what characterizes change of position, what distinguishes it from change of state, is that it can always be corrected in this way.
It may therefore happen that we pass from the totality of impressions A to the totality B in two different ways:
1º Involuntarily and without experiencing muscular sensations; this happens when it is the object which changes place;
2º Voluntarily and with muscular sensations; this happens when the object is motionless, but we move so that the object has relative motion with reference to us.
If this be so, the passage from the totality A to the totality B is only a change of position.
It follows from this that sight and touch could not have given us the notion of space without the aid of the 'muscular sense.'
Not only could this notion not be derived from a single sensation or even from a series of sensations, but what is more, an immobile being could never have acquired it, since, not being able to correct by his movements the effects of the changes of position of exterior objects, he would have had no reason whatever to distinguish them from changes of state. Just as little could he have acquired it if his motions had not been voluntary or were unaccompanied by any sensations.
Conditions of Compensation.—How is a like compensation possible, of such sort that two changes, otherwise independent of each other, reciprocally correct each other?
