A New Address Or A Higher Density?

I've had this same thought myself.  It makes sense to me intuitively that if these other dimensions do exist, that the way in which any one of them might nexus with our own dimension would be in such a seemingly strange manner.

As a kid I read a book called "A Wrinkle in Time" by Madeleine L'Engle.  It dealt with interdimensional travel and individuality versus Borg-type collective conscousness.  Pretty deep for a kid's book, now that I think about it.  In this story, one of the old adept-type women explains how higher dimensions intersect with our 3D universe by drawing an analogy of a three-dimensional object moving through a 2D space (a geometric plane).  Take the surface of a pool of water as an example of a 2D plane, and now slowly lower an object, say a pair of scissors, into the water.  The shape of the object on the 2D plane itself will continue to change as the object moves through that plane in 3 dimensions.  A 2D creature living of that plane would observe an object seeming to change shape and form with no apparent rhyme or reason.  But that appearance would be due only to the 2D creature's lack of understanding of the higher 3rd dimension, not because the object was violating any physical laws. 

Similarly, it seems to me that higher-dimensional objects moving through our space would manifest in strange changes to physical reality, or to spacetime itself.  Time itself probably IS the fourth dimension in some sense or another, after all.