Tuesday, August 1, 2017

Birthday: "We endeavour to employ only symmetrical figures, such as should not only be an aid to reasoning, through the sense of sight, but should also be to some extent elegant in themselves.”

John Venn (1834-1923)
Mathematician, author

A son of the vicarage, John Venn was a Yorkshireman who earned a place a Gonville & Caius College, Cambridge, in 1853. He read maths, graduated in 1857, and was elected a fellow of the college.

Venn took Anglican orders in 1859 and served several parishes before returning to his college as a lecturer in 1862. He stayed there for the rest of his life.

His intellectual interests were wide, ranging across set theory, probability, logistics, statistics, and the origins of what we now know as computer science. In 1880, he published a paper, 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.

His concept, which he called Eulerian Circles- after the work of the 18C German Leonard Euler- went further. His work has been called

a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S. Thus, for example, the set of all elements that are members of both sets S and T, S ∩ T, is represented visually by the area of overlap of the regions S and T. In Venn diagrams the curves are overlapped in every possible way, showing all possible relations between the sets. They are thus a special case of Euler diagrams, which do not necessarily show all relations.

Venn’s idea caught on, and by 1918 references to Venn Diagrams began appearing in texts on logic. It made its way into popular culture after its incorporation into New Math pedagogy in the 1960s.

A thoroughly modern Victorian man, Venn was also an inventor. One of his devices, a mechanical cricket bowler, won fame when a New Zealand team visiting Cambridge took it on, and the machine bowled out the Kiwis’ top player four times running.

In 1883, finding the Anglican faith no longer fit into a Venn Diagram with mathematical proof, resigned his ordination. He was elected president of Gonville & Caius in 1902 and held the post until his death. Blessed by a happy union that produced another mathematician, Venn became an ardent supporter of women’s suffrage in the early 20C and was a champion rose gardener.

A chapel window at Gonville & Caius is one of a number of monuments to John Venn, who died short of his ninetieth birthday in 1923.

Venn also left as part of his legacy an inexhaustible starting point for cartoonists.

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