Slashdot Mirror
Breakthrough In Drawing Complex Venn Diagrams: Goes to 11
00_NOP writes "Venn diagrams are all the rage in this election year, but drawing comprehensible diagrams for anything more than 3 sets has proved to be very difficult. Until the breakthrough just announced by Khalegh Mamakani and Frank Ruskey of the University of Victoria in Canada, nobody had managed to draw a simple (no more than two lines crossing), symmetric Venn diagram for more than 7 sets (only primes will work). Now they have pushed that on to 11. And it's pretty too."
Visually, you don't really get fast useful information out of it, it's too hard to map a certain part of it to exactly which 11 regions it contains...
(Classic SMBC cartoon)
http://www.smbc-comics.com/index.php?db=comics&id=1917
I agree that the 11-Venn is fairly useless as a PowerPoint slide, but Slash Dotters of all people should understand that pure mathematics often leads to applied mathematics. For example, suppose this new finding leads to improved approaches to signal multiplexing, so that you can have billions more 8G cell phones and thousands more channels of nothing-to-watch on cable and satellite TV. Or perhaps it will lead to more advanced neural networks, so that we can get Cyberdyne Systems and SkyNet up and running. Or maybe it will even lead to advances in political science that give rise to governments that are actually capable of serving the people they govern. One just never knows...
In 1989 Anthony Edwards figured out how to make Venn diagrams of arbitrary size: http://www.qandr.org/quentin/software/venn
"Dr Edwards came up with an ingenious solution based on segmenting the surface of a sphere, beginning with the equator and the 0 and the +/- 90-degree meridians. It can be extended to an arbitrary number of sets by creating wobbly lines that cross the equator - starting with the pattern of stitching found on a tennis ball. You can unwrap the sphere back onto a plane and the sets still work."
Venn diagrams do not show proportion (what I assume you mean by amounts)!
If you draw a Venn diagram with a tiny little overlap, or a huge overlap, in order to make some point, [b]you are doing it wrong[/b].
Now it's one thing to do this for comedic effect, but I see this all the time when people are trying to be serious and it makes me stabby.
Venn diagrams are a way of visualizing overlaps in sets; the ONLY thing that matters is what region an element is placed, not how big that region is.
A Venn diagram is a precise tool which displays particular information with no ambiguity, and trying to shoehorn proportions into it just makes it muddy. Plus, humans are fucking terrible at telling how much larger one roughly circular area is than another; make those areas slightly different shapes, and it's even less helpful.
Many seemingly pointless exercises in math lead to surprising breakthroughs. Graph partitioning is a very active area of research. Imagine creating an index on a ultra large database with pairwise "and" condition on many pairs of fields. Then finding multiple "and" or "or" condition based records within minimal traversing and merging of the index files. Who knows it might actually lead to dramatic speed ups of queries in large data bases.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
"Simple Venn diagrams" are mathematical objects with certain properties. Constructing such an 11-Venn is an impressive feat and adds significantly to the body of mathematical knowledge surrounding these objects. This is an example of mathematical research.
Taking an idea, extending it, and applying it to other things is what mathematicians do. They are not struggling to understand the purpose of the original definition; instead they are leaving those of you who do not have such capacity for abstract thinking behind. In this case, you are missing the point.