Some physicists imagine a sheet of paper representing ordinary 4-D space-time. The sheet is divided up into irregular regions about 10^-33 centimeters across. Tangent to each of these quantum patches, you then attach, mathematically, some kind of closed topological surface of 'compact manifold' such as a sphere, or a donut, or something with even more 'holes' in it which is called a 'Callabi-Yao' manifold.
What all this means is that if there are more dimensions to space-time than 4, these extra dimensions define 'degrees of freedom' in some additional pieces of space-time at the quantum scale. Every point in our large universe is fashioned from these 10^-33 centimeter quantum patches onto which is 'attached' these compact manifolds with 6 additional dimensions. Particles are characterized by these additional coordinates, and the symmetries we observe among particles and fields, is simply some feature of the geometry of the geometry of these compact manifolds.
Recently, in 1999, physicists have begun to investigate what would happen if these added dimensions were large. With one additional 'big' dimension in superstring theory, gravity would depart from the inverse-square law at scales of 100 million kilometers. With two extra big dimensions (a 5-d space in the large) the departures for gravity would occur at about 1 millimeter. With three extra big dimensions ( a 6-d large space time with a 4-d compact one) the departures for gravity's inverse square law happen at sub-atomic sizes.
Copyright 1997 Dr. Sten Odenwald
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