All's not fair Venn you're a girl.
by Dr Gavin Hitchcock
About 15 years after John Venn (of Cambridge) introduced his Venn diagrams to the world, in a book called Symbolic Logic, another book of the same name appeared in 1896, from a mathematician (in Oxford, of course) in which he advocated a more democratic picture. The author was Lewis Carroll, the creator of Alice in Wonderland, although his mathematical books were written under his real name, Charles Dodgson. He wrote:
"My method of diagrams resembles Mr. Venn's, in having separate Compartments assigned to the various Classes, and in marking these Compartments as occupied or empty; but it differs from his Method, in assigning a closed area to the Universe of Discourse, so that the Class which, under Mr. Venn's liberal sway, has been ranging through Infinite Space, is suddenly dismayed to find itself cabin'd, cribb'd confined, in a limited Cell like any other Class!"
In this early display of concern for Aggregate
Egalitarianism, Ensemble Equity or
Minority Set Rights, Mr Carroll refused to discriminate against
points either IN or OUT of any set - even if we must discriminate
between them. He recognized that to be a GIRL means far
more than just to be an UN-BOY, and that we sin against one or other of
the Genders when we cabin, crib or confine one inside a limited Cell,
leaving the other to range freely through Infinite Space.
Suppose you are interested in who's who in your school with regard to the
following four logical alternatives:
Mr Carroll's fair, equal and just (and symmetrical) representation of the Classes is given below the unfair pictures:
Problem If you object and point out that our sense of justice to the IN's and the OUT's has not been extended to the third and subsequent set(s), then all we need to do is to look at a tennis ball, on which the first three sets are mutually perpendicular great circles and the 4th set and its complement are already displayed in a manner acceptable to the any Equal-Opportunities Commission. Alas, for equality after that we shall have to enter higher and unvisualisable dimensions.
Lewis Carroll did not guess how he could have developed this for more than four sets, although he came very close! We had to wait another century for the brilliant but simple strategy revealed in the article following this one....
File translated from TEX by TTH, version 1.50.
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