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Projective geometry
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.
