Techniques for visualising $n$ dimension spaces

When somebody says "high-dimensional space is hard to visualize", they are thinking of visualizing with the eyes. But mathematicians visualize with the brain!

I highly recommend the AMS article The World of Blind Mathematicians. Who could be better at visualizing things they can't see?

I'm looking at model for navigating data using a computer screen (so 2 dimensions). Add a third dimension (think zoom in zoom out). Ok so what about n dimensions, what techniques could help me navigate them while confining my self o the 3d world of the computer model.

There is a very large body of published work (both theoretical and applied) on multidimensional data visualization (also called multivariate or $n$-dimensional). Try a web search with these terms! Some example titles:

• Visualization of Multi-variate Scientific Data (Bürger & Hauser)
• A Taxonomy of Glyph Placement Strategies for Multidimensional Data Visualization (Ward)
• Handbook of Data Visualization (Chen, Härdle & Unwin)

and so on. Ward's paper (p. 10) offers some advice when viewing N-dimensional data with a 2-dimensional display, re selecting from the N(N − 1)/2 possible orthogonal views in the N-dimensional space (not including rotational variations).

Check out http://en.wikipedia.org/wiki/Parallel_coordinates if your data is discrete, it maybe very useful. If it is not, there are extensions but they are not always insightful.