Do Extra Dimensions Really Matter Before String Theory?

[tnadys]

This may be a stupid question, but I have been curious about it for awhile. Before string theory, extra dimensions seem not to be taken seriously. But if gravity warps space doesn't it need another dimension to warp into? I saw Brian Green on TV and I thought he suggested that you don't, but he didn't explain why.

 

[MeJennifer]

But if gravity warps space doesn't it need another dimension to warp into?

Mathematically it is not necessary to introduce extra dimensions because a hyperplane (which is just a multi-dimensional plane) can be intrinsically, as opposed to extrinsically curved.