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. Their meaning is sometimes very far from ordinary. For example, in mathematics space interpreted as logically conceivable structure that serves the environment in which delivery of other structures and forms of these or other structures, as well as the fixed relationship between them.
And so it is not necessary to carry literally mathematical objects in the real world and spend some analogy. Mathematics does not claim to material realization of their constructions. It only gives tools for handling a variety of quite possibly do not exist in reality structures. Other sciences use these tools as the most suitable to describe the real processes.
By the way, since Galileo, physicists believe the object of the science is that the experiment is available, but the variation of characteristics of space and time is not available to we can not even locate them. Therefore, strictly speaking, space and time can not be attributed to physics. Newton knew it, so he absolute mathematical time and absolute mathematical space. His mechanics – a mathematical discipline.
Mathematics, unlike the natural sciences, does not study natural phenomena, as logical constructs, so experiments in mathematics are not the nature of the test, and test hypotheses in terms of logic.
From this it follows that mathematics can play an instrumental role not only in the knowledge of the truth, but also be a guide to the world of illusions, as well as his authority to close out of this world for those who appeared in it.
Here it is appropriate to recall the doggies Pavlov. Remember: Up meat, saliva. Multiple repeat. Conditioned reflex. Now: Up, saliva, and without the meat. Whether dog smarter, it might well impression is that the cause of instrumental way to create meat is the release of her saliva. And modern scholars believe that their math exercises are the real cause of natural processes. And they invented all sorts of dimensions really exist in nature by themselves.
Specific item are spatio-temporal place, but the concept for example, the concept of a chair in general do not have it. But our mind gets no additional spatial dimension – conceptual.