Constraints of Copying versus Processing of Information

I find it interesting that copying of information is best done in a low number of dimensions (think DNA), while processing of information is best done in a high number of dimensions (think 3D brain).

It has been shown, however, that any kind of information processing can be theoretically accomplished by a purely local, one-dimensional scheme, in the form of a cellular automata. That being said, the difficulty of actually writing programs in a medium like this is tremendous; it is possible, but not at all practical. The reason for this is that it is difficult to shuttle information around without the signals bumping into and disrupting eachother. There just isn't enough room for everything to happen easily. Another example: it is possible to make logical circuits in the 2D environment of Langton's Game Of Life, but it is difficult as heck (I had a friend who actually did this for fun... yikes!)

So it is interesting (and not suprising) that nature has optimized both of these mechanisms, choosing a 1-dimensional copying scheme (DNA/RNA), and a 3-dimensional processing scheme (brain); 1 and 3 being the respective minimum and maximum dimensionalities allowed in our particular universe.

But what if our universe were > 3 dimensions? Would nature have made use of the extra dimensions to develop even more routes of connectivity than are possible/convenient in 3 dimensions? Would this have led to very different (better?) styles of information processing?