NUMBER-FORMS.

Persons who are imaginative almost invariably think of numerals in some form of visual imagery.  If the idea of six occurs to them, the word “six” does not sound in their mental ear, but the figure 6 in a written or printed form rises before their mental eye.  The clearness of the images of numerals, and the number of them that can be mentally viewed at the same time, differs greatly in different persons.  The most common case is to see only two or three figures at once, and in a position too vague to admit of definition.  There are a few persons in whom the visualising faculty is so low that they can mentally see neither numerals nor anything else; and again there are a few in whom it is so high as to give rise to hallucinations.  Those who are able to visualise a numeral with a distinctness comparable to reality, and to behold it as if it were before their eyes, and not in some sort of dreamland, will define the direction in which it seems to lie, and the distance at which it appears to be.  If they were looking at a ship on the horizon at the moment that the figure 6 happened to present itself to their minds, they could say whether the image lay to the left or right of the ship, and whether it was above or below the line of the horizon; they could always point to a definite spot in space, and say with more or less precision that that was the direction in which the image of the figure they were thinking of, first appeared.

Now the strange psychological fact to which I desire to draw attention, is that among persons who visualise figures clearly there are many who notice that the image of the same figure invariably makes its first appearance in the same direction, and at the same distance.  Such a person would always see the figure when it first appeared to him at (we may suppose) one point of the compass to the left of the line between his eye and the ship, at the level of the horizon, and at twenty feet distance.  Again, we may suppose that he would see the figure 7 invariably half a point to the left of the ship, at an altitude equal to the sun’s diameter above the horizon, and at thirty feet distance; similarly for all the other figures.  Consequently, when he thinks of the series of numerals 1, 2, 3, 4, etc., they show themselves in a definite pattern that always occupies an identical position in his field of view with respect to the direction in which he is looking.

Those who do not see figures with the same objectivity, use nevertheless the same expressions with reference to their mental field of view.  They can draw what they see in a manner fairly satisfactory to themselves, but they do not locate it so strictly in reference to their axis of sight and to the horizontal plane that passes through it.  It is with them as in dreams, the imagery is before and around, but the eyes during sleep are turned inwards and upwards.