Amalia Pica makes sculptures, installations, performances, and drawings that address a correspondingly broad array of themes. She favors found objects and commonplace materials to create her pieces, whose concerns range from language and communication, to history and politics, or to the ways in which our childhood experiences shape our adult imaginations.
As a primary school student in Argentina, Pica was taught set theory as expressed in Venn diagrams, though, as she notes, only a few years before she would not have been. She recalls that the ban of set theory by Argentina’s dictatorship in the 1970s occurred just as group assembly was also deemed subversive. Pica speculates that set theory was prohibited because it was seen as the mathematical expression of a gathering. With this work, she literally shines a light on the absurdity of the injunction. A caption on the wall provides historical context for the work.
Pica's interest in the relationship between text and image is evident in Venn Diagrams (under the Spotlight), which consists of two colored circles of light cast from theater spotlights to form a Venn diagram. The Argentine government banned this diagram from being taught in classrooms in the 1970s, as it was thought to be an incendiary model of social collaboration. "The two circles of light are nothing but forms until the caption situates them historically, cluing you to their perception as subversive in the context of Argentine dictatorship in the 1970s. I’m interested in the ideas that we project onto images and objects: how they resist as much as accommodate them."
https://en.wikipedia.org/wiki/Amalia_Pica
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram uses simple closed curves on a plane to represent sets. The curves are often circles or ellipses.
History
Venn diagrams were introduced in 1880 by John Venn in a paper entitled "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings" in the Philosophical Magazine and Journal of Science, about the different ways to represent propositions by diagrams. The use of these types of diagrams in formal logic, according to Frank Ruskey and Mark Weston, predates Venn but are "rightly associated" with him as he "comprehensively surveyed and formalized their usage, and was the first to generalize them".
Diagrams of overlapping circles representing unions and intersections, such as Borromean rings, were already in frequent use in the Middle Ages. However, the extent to which these types of diagrams can be considered precursors to Venn diagrams is disputed. Euler diagrams, which are similar to Venn diagrams but do not necessarily contain all possible unions and intersections, were named after the mathematician Leonhard Euler in the 18th century. However, these diagrams, which are considered the precursors of Venn diagrams, can also be clearly traced back to the 16th century. Pioneers in this tradition of Euler diagrams included Erhard Weigel (1625–1699) and his students Johann Christoph Sturm (1635-1703) and Gottfried Wilhelm Leibniz (1646–1716). Christian Weise (1642–1708) is also worth mentioning, whose student Johann Christian Lange worked intensively on these diagrams. Euler further developed these diagrams, and Immanuel Kant (1724–1804) and his students popularized them in the 19th century.
Venn did not use the term "Venn diagram" and referred to the concept as "Eulerian Circles". He became acquainted with Euler diagrams in 1862 and wrote that Venn diagrams did not occur to him "till much later", while attempting to adapt Euler diagrams to Boolean logic. In the opening sentence of his 1880 article Venn wrote that Euler diagrams were the only diagrammatic representation of logic to gain "any general acceptance".
Venn viewed his diagrams as a pedagogical tool, analogous to verification of physical concepts through experiment. As an example of their applications, he noted that a three-set diagram could show the syllogism: 'All A is some B. No B is any C. Hence, no A is any C.'
Charles L. Dodgson (Lewis Carroll) includes "Venn's Method of Diagrams" as well as "Euler's Method of Diagrams" in an "Appendix, Addressed to Teachers" of his book Symbolic Logic (4th edition published in 1896). The term "Venn diagram" was later used by Clarence Irving Lewis in 1918, in his book A Survey of Symbolic Logic.
In the 20th century, Venn diagrams were further developed. David Wilson Henderson showed, in 1963, that the existence of an n-Venn diagram with n-fold rotational symmetry implied that n was a prime number. He also showed that such symmetric Venn diagrams exist when n is five or seven. In 2002, Peter Hamburger found symmetric Venn diagrams for n = 11 and in 2003, Griggs, Killian, and Savage showed that symmetric Venn diagrams exist for all other primes. These combined results show that rotationally symmetric Venn diagrams exist, if and only if n is a prime number.
Venn diagrams and Euler diagrams were incorporated as part of instruction in set theory, as part of the new math movement in the 1960s. Since then, they have also been adopted in the curriculum of other fields such as reading. With the work of Sun-Joo Shin, Venn diagrams have been recognized as a logical system equivalent to symbolic logic. Similar methods were then adopted in mathematics and subsequently in computer science.
