Heres a question I've been trying to get answered. Science
is up to the 4th dimension but what is the theory behind others, is there
a 5th or a 6th? And how many are there supposed to be?
There is a book by Micio Kau called "Hyperspace" that discusses this topic
at length. It is intended for non-scientists and is very readable. I have
found it very enjoyable.
I could tell you what he said but it's not my area of expertise and I
wouldn't want to give away the ending ;)
...Sorry, I couldn't resist.
I suggest you read Hyperspace by Michio Kaku where he discusses the "ultimate"
ten dimensions of space.
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Update: June 2012