In this lecture author and professor at the University of Texas, Dr. Linda Dalrymple Henderson, discusses the subject of her book 'The Fourth Dimension and Non-Euclidian Geometry', pictured below. In it, she traces a parallel development between developments in geometry and modern art.
Non-euclidian geometry required a shift in how we perceive and understand the space we live in, from assumptions based on immediate perception and human experience to concepts which are no longer derived from human experience and intuition. You can draw two parallel lines on a piece of paper and they will never meet, but draw those two lines across the surface of the spherical Earth and they will curve and meet. Henderson argues that this development, with the possibility of a spatial fourth dimension "encouraged radical innovation by a variety of early twentieth-century artists, ranging from French Cubists, Italian Futurists, and Marcel Duchamp, to Max Weber, Kazimir Malevich, and the artists of De Stijl and Surrealism."
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