Today I was struck anew by a passage in H.H. Price's classic book Perception (1932). After endorsing the idea that outside the "zone of perfect stereoscopic vision" (about six inches to a few feet, in his estimation), things look smaller the farther away they are (maybe I'll discuss that issue next week!), Price goes on to say:
And if we come inside the zone of perfect stereoscopic vision [i.e., closer than about six inches] (a region too little explored by philosophers) we find that there is indeed a correlation between depth and sensible size, but it is the other way about; the smaller the depth, the smaller the size. Thus if I bring a match-box up to the end of my nose, the top surface is manifested by a trapeziform expanse having its longer side at a greater depth than its shorter one: the box has rather the appearance of a wedge, whose 'thin end' is directed towards me.A surprising claim, and not one I recall reading elsewhere! I'd be interested to hear if the readers of this blog share Price's sense of this.
Suppose we call "visual arc subtended" the amount of the visual field some object occupies, defined geometrically by how much surface area the object would occupy if projected onto a sphere centered at the eye. As an object approaches the bridge of my nose, the visual arc subtended increases dramatically as it moves from about twelve to six inches; but in the last two inches or so, there's not much increase.
I don't think that can be Price's point, though: First, there's a simple geometrical explanation for the fact about visual arc. Within the last two inches, bringing the object closer to my nose does not actually bring it much closer to either eye. If I instead bring the object close to the pupil of my dominant eye, there is no slowdown in the increase in visual arc subtended. And second, Price emphatically does not think that apparent size changes when objects move around within the zone of perfect stereoscopic vision -- such as from twelve to six inches -- though the visual arc subtended obviously does increase. So what Price is after here is not, I think, a matter of visual arc.
Is there some other sense, then, in which the nearer end of the matchbox almost touching my nose looks smaller than the farther end? I can almost feel the pull of that....