In his acclaimed book on the philosophy of space and time รฐ0ล\ H[ Reichenbach wrote\ around 0816\ the following passage which we think is an excellent introduction to the basic idea behind the work to be discussed here[ Reichenbach wrote {{Another case would arise if space were four "or more# dimensional in its smallest elements[ This situation would correspond to the case of thin layer of grains of sand which\ although each is three!dimensional if taken individually\ taken as a whole forms essentially a two dimensional space[ Similarly\ atoms which individually are higher!dimensional could cluster into three dimensional structure[ In such a world\ a macroscopic structure would have only the three degrees of freedom of the three dimensions of space\ while an atom would have many more degrees of freedom[ Since perception in such a world would not be noticably di}erent from those of our ordinary world and conversely it is in principle possible to infer from our ordinary experiences\ the higher dimensional character of the microscopic world[ Incidently\ it is not impossible that quantum mechanics will lead to such result[||