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Watercolour, crayon and Photoshop™
©2014 Charlene Brown
The projection, or shadow, model of four-dimensional geometry first appeared in the 19th century. Mathematicians derived and rendered amazingly complex projections of three-dimensional geometric figures, using basic rules of perspective drawing.
In Shadows of Reality, Tony Robbin suggests that Minkowski had four-dimensional projective geometry in mind when he structured special relativity, and Picasso used the projection model to invent cubism.
It is now possible to computer-generate n-dimensional figures relatively easily. However, I think free-hand renderings are more useful if you’re trying to visualize the concept of multi-dimensionality in order to understand the principles of quantum physics. And they’re certainly more fun.