We think there are only 4, but physicists searching for a theory that describes all of the forces in nature seem to need at least 6 more dimensions to do the math they are using. There are currently no experiments that show the universe has more than the usual 4 dimensions ( 3 of space and 1 of time).
Since 1998, physicists have investigated whether there could be additional large dimensions to the world beyond the 3-space ones. In string theory, the size of these extra dimensions decreases the more you add. One extra one appears as a change in gravity at 100 million kilometers. Two extra ones, and the changes occur at about 1 millimeter. Three extra ones cause gravity to change at atomic dimensions. So far, we can easily say we do not have a universe with 4 space dimensions, and in 5 years we will know if we live in a 5-space universe or not once the experiments are perfected.
Copyright 1997 Dr. Sten Odenwald
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