Three-dimensional space because it is anthropomorphic. At Euclid it is isotropic. And in our sensations – anisotropic. Distinguishable mind: sky-earth, left-right, back and forth. The idea of three-dimensional space is generated in our minds corresponding asymmetry of our body, mind discernible. The idea of the extent of the mind consists of the evaluation of the capabilities of our Hand. If we were weightless balls, then would live without concepts of space.
Question of the dimension of space in mathematics justified, if the concept of dimension makes sense for objects – elements of the space. For those vectors it makes sense, so the vector space can always be identified. Should not be understood literally mathematical terms. Read the rest of this entry »