Nat Friedman

Professor Emeritus, Sculptor; Founder and Director of ISAMA
Department of Mathematics, University at Albany
Albany, NY
For me, seeing is what unifies art/math. Moreover, hyperseeing is seeing from multiple viewpoints in a very general sense. For example, one can see knots from the viewpoints of algebra, geometry, combinatorics, topology, and art. In general, one can see mathematics from the viewpoint of art. A sculpture is defined as a form in a position relative to a fixed horizontal plane (base, ground). To hypersee an outdoor sculpture, one walks around it to see overall views and close up detail views from different viewpoints as well as in different light conditions at different times. If two sculptures consist of the same form in different positions, then the sculptures are said to be congruent. Congruent sculptures can look so completely different that one does not realize the sculptures are congruent. This can be the case when the form is a 3D knot. A hypersculpture is a group of congruent sculptures. A hypersculpture is a more complete presentation of the sculptural possibilities of a form. In order to hypersee a form, one presents it as a hypersculture. The author’s hypersculpture Four Right Angles consists of two vertical and three horizontal congruent sculptures and is discussed in an article of the same title in the Spring, 2011 issue of Hyperseeing, . The two vertical sculptures Ascent and Cantilever are shown below. The form consists of four identical angle iron sections welded together. Each section is 5 x 5 x 6 ½ inches and ½ inch thick.
Four Right Angles: Ascent (left) and Cantilever (right)
17 L x 11 H x 7 D inches