We take it for granted we live in the three-dimensional space, but we do not perceive the three dimensions directly. Why do we consider the space to be 3D?
1. Is the space really 3D?
The most reliable sense for us is that of sight. The visual data are, however, not three- but two-dimensional. For example, when you see a cube diagonally, it looks like a hexagon and right angles at corners of the cube seem to be those of 60 or 120 degrees. This means that the three-dimensional object is projected to the two-dimensional retinal visual field. How do we perceive the two-dimensional retina image to be three-dimensional, then?
Psychologists insist the retinal image should have some three-dimensional features in itself, for example, the contrast between light and shade, retinal size, gradient of texture density, overlapping, linear or aerial perspective and so on. But these are tricks the animation movies use to make two-dimensional pictures seem three-dimensional. So, we cannot rely on these.
How about other devices, such as lens accommodation, binocular parallax and convergence? When an eye looks far ahead, the suspensory ligament pulls lens thin, which makes their refractive index lower and the focal distance long. So, even a single eye can distinguish between near and far. Moreover, fusing the binocular disparity produces the stereoscopic effect. At the same time, we can judge the distance to objects by the convergence angle. If you equate the convergence angle with 2a and the distance between two eyes with 2d, then the distance to the object you look in the face is "dcota".
Of course, we do not make such a trigonometric calculation or refer to optics in recognizing three dimensions. Our space perception is more intuitive and primitive. How did we get to know primitively we are looking far ahead when the lenses of eyes become thin or the convergence angle becomes narrow?
2. The association with the tactile experience
Most of modern philosophers thought that, in order to perceive the three-dimensional space, the visual experience was inadequate and had to be associated with the tactile experience. They thought it was because the visual experience was not associated with the tactile experience that an operation to give a blind adult sight did not enable him or her to arrange retinal images in the three-dimensional space, though the images are physically the same as those presented to the normal.
How are the visual data meaningfully associated with the tactile data? To elucidate this problem, I would like to distinguish the active from the passive sense. The active sense corresponds to kinesthesia. This jargon of phenomenology is composed of two Greek words, kinesis (movement) and aesthesia (sense). But I want to call kinesthesia the active sense for the sake of contrast.
You might think, " My hand moving at 30 km/h hitting a car in the front and the car running at 30 km/h hitting me in the hand give the same amount of physical impetus. So, it is not significant to distinguish the active from the passive sense." But the active sense is qualitatively different from the passive sense in that the former is based on free will. Thanks to the body movement of your own will, you can associate senses with each other through the process of experiment. If you are given sense data externally and accidentally, you cannot associate senses meaningfully.
3. The active sense makes the space 3D.
The most primitive and primary way to affirm that two-dimensional visual data are three-dimensional is to stretch out your arm vertically through the visual plane.
You extend your arm of your free will, until the resistance of the object restricts your freedom. If nothing restricted your freedom or you had no freedom, you could not perceive three dimensions. It is not until you associate the active sense of stretching out your arm with the passive sense of my hand feeling resistance that I know the distance to the visual object. Babies will stretch their arms to grab whatever they find and it must be practice to affirm three dimensions of visual data.
The accommodation and convergence of eyes is also a sort of body movement and has the same dialectical structure. In addition, the motion parallax contributes to visual perception of space.
Both active and passive senses are necessary to perceive three dimensions. We reflectively perceive the active sense of our bodies that move three-dimensionally through the medium of passive sense that changes according to the movement and thus recognize the three dimensions of space.