Okay, we were watching a show about parallel universes last night - like if they exist, how they exist, etc... and I was getting really sick of the dumb-ed down examples, but I actually was originally going into college to study aerospace engineering. And yet, I graduated in anthropology (studying ANCIENT cultures). Math isn't always my friend.
Anyway, I do believe that there are other dimensions (I won't necessarily say 'parallel'). But, I think we're like Darwin defining evolution. We got the basic world-shattering premise right, but we've got the mechanisms totally wrong. The giraffe example: Darwin wrote that because the giraffe needed to eat the tall leaves that the generations of giraffes grew longer necks. Now, we know that mutations in the genetic code allow for survival of the most well adapted - i.e., the giraffe's with longer necks got to eat more food than those without, so the taller giraffes got to have the babies. I think we're like that with other demensions. We know they're there (in all probablity), but we lack the tools for observation and exploration to really define how they work.