space might have more than three dimensions; we don't know.  edwin abbott wrote a very famous book called "flatland" about people who were confined to life in a two-dimemsional world, and what it was like to live there.  it was part geometry, part philosophy about the nature of the universe, and part statement about the social behavior of humans.  it's excellent and you can read the whole thing online at the link below.
Why Space has exactly three dimensions and not more or less ?