Richer Ramblings here presents a rather attractive Venn diagram showing the possible combinations of eleven distinct sets. It’s a neat picture and one of the things that people who insist mathematics can be artistic are thinking of when they say it.

Venn diagrams are fairly good ways to visualize data, particularly the ways in which things can be parts of one or more sets simultaneously (or maybe part of no set). I find them most useful, in teaching, in doing probability questions, because so many questions about how probable something is amount to “how many ways can a described outcome happen”, and a nice, clean diagram can show just which outcomes fit which description. (“Coin comes up heads

andthe first child is a girl; coin comes up headsandthe second child is a girl; coin comes up tailsandthe die roll is a prime number”, etc).For that, though, I find their use kind of limited: if there are too many things happening (coin, child’s gender, die being rolled, goat behind door number two) the problem becomes one students’ eyes glaze over rather than try solving and I lose the thread of the question too. Worse, if there are too many possibilities, the number of lumpy circles I need to draw becomes smaller than the number of lumpy circles I can draw.

This picture does pretty completely away with the lumpy circles and goes in for much more involved curves. Some of the details are kind of small, but, this covers — at least if it was done correctly and I admit not testing — all the different ways that something can belong or not belong to eleven distinct sets simultaneously.

Thinking about the number of different subsets and shades that are needed — go on, how many are needed to give every distinct combination its own color (which isn’t what’s done here)? — makes me appreciate how choroplethy isn’t my thing.

Venn diagrams are cool, and extremely varied.

“*If you think Venn diagrams are just a bunch of interlocking circles, think again. Pushing this iconic branch of mathematics to its limits reveals just how varied – and beautiful – these diagrams can be. This gallery showcases some of the wilder possibilities, including the most recent breakthrough in Venn geometry – the first simple, symmetric diagram to encompass a whopping 11 sets.*” (New Scientist)

The picture above is the said first simple, symmetric diagram to encompass 11 sets, and yes, it is beautiful. “*One of the sets is outlined in white, and the colours correspond to the number of overlapping sets. The team called their creation Newroz, Kurdish for “the new day”. The name also sounds like “new rose” in English, reflecting the diagram’s flowery appearance.*“

Amazing stuff. Onwards!