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Math Science

Breakthrough In Drawing Complex Venn Diagrams: Goes to 11 83

Posted by timothy
from the next-week-better-shopping-lists dept.
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."
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Breakthrough In Drawing Complex Venn Diagrams: Goes to 11

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  • by Lord Lode (1290856) on Sunday August 12, 2012 @09:06AM (#40963937)

    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...

    • Re: (Score:2, Funny)

      by Anonymous Coward

      I wonder if people dabbling in haruspicy see things the same way.

    • Re: (Score:2, Insightful)

      by Anonymous Coward

      I hope yours is just a snide remark, but, just so no one is confused, the mathematicians who did this were definitely NOT trying to display information graphically. Their may be (useful) implications of this research, but there was never an intent that it be for some kind of typography.

    • by Impy the Impiuos Imp (442658) on Sunday August 12, 2012 @11:32AM (#40964661) Journal

      This. They just found a clever way to jam too much information onscreen at once.

      Of course it's pretty -- Spirograph drawings are!

      This reminds me vaguely of Chernoff Faces [wikipedia.org], which were an attempt to give people viewing 4D or higher data a "feel" for it, since you can't really visualize 4D drawings. It takes advantage of brain circuitry for recognizing faces using many different little hard-wired things, like eye position, mouth width, and so on.

    • by jmerlin (1010641)
      What I find interesting is that if colored slightly differently and used jagged edges instead of curves, it would resemble the BP logo. BP paid $210,000,000 for their logo. Heh.
  • beautiful (Score:4, Insightful)

    by gsgriffin (1195771) on Sunday August 12, 2012 @09:14AM (#40963965)
    But useless
    • by 140Mandak262Jamuna (970587) on Sunday August 12, 2012 @11:19AM (#40964605) Journal
      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.
  • by Havenwar (867124) on Sunday August 12, 2012 @09:20AM (#40964001)

    The entire point of a venn diagram is a quick overview to easily be able to get an understanding about how things overlap, in what amounts and what areas. The diagrams on the linked page might be pretty, but they are in no way useful, and I doubt anyone would get more information out of it than reading the datalist it was compiled from.

    • by gmuslera (3436) on Sunday August 12, 2012 @09:34AM (#40964081) Homepage Journal
      There is the limitation of the media and the limitation of the receiver. With the appropiate culture, you could see blondes, brunettes and redheads in falling letters.
      • by Havenwar (867124)

        That's more depending on how much drugs you take. Not so much a limitation as a lack of reality disconnect.

    • by Asmor (775910) on Sunday August 12, 2012 @11:14AM (#40964547) Homepage

      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.

    • by Anonymous Coward on Sunday August 12, 2012 @12:20PM (#40965025)

      "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.

  • Its art (Score:5, Insightful)

    by nurb432 (527695) on Sunday August 12, 2012 @09:23AM (#40964013) Homepage Journal

    At that level its just a shiny object with no substance.

    But then again, with what goes on in the political world these days perhaps it's appropriate.

    • by guttentag (313541)

      At that level its just a shiny object with no substance.

      Which means there will be a function built into the next version of Flash to allow people to quickly build these. That way Flash can stay at the forefront of the SONS (Shiny Object No Substance) niche market.

    • by guttentag (313541)

      At that level its just a shiny object with no substance.

      But then again, with what goes on in the political world these days perhaps it's appropriate.

      Actually, what we have here is a perfect model of the beltway (the highway that surrounds Washington DC). A giant traffic jam of conflicting yet semi-exclusively intersecting interests with a whole lot of nothing going on in the middle as a result.

    • Re: (Score:2, Insightful)

      by Anonymous Coward

      Interestingly, these more complex venn diagrams are going in the opposite direction that politics keeps moving in maturing democracies. Voters may prefer only a 2 set diagram this coming election: http://www.yourdictionary.com/library/presart1.html

      The ability for complex thought is certainly not determined by reading level, but it is a good warning indicator. Politicians are steadily creating ever simpler arguments to appeal to those who are willing to give them sanction for their actions. While it certainl

  • by wisebabo (638845) on Sunday August 12, 2012 @09:29AM (#40964057) Journal

    (Classic SMBC cartoon)

    http://www.smbc-comics.com/index.php?db=comics&id=1917 [smbc-comics.com]

  • by meekg (30651)

    Can you make one for 4 colors out of 4 spheres?
    Certainly not a prime number

    • Can you see the internals of your four spheres?

      In that sense, 4 categories would lead to 15 regions total. But as we can't really see in 3 dimensions - we can't see the inside and outside at the same time, we only see in stereo - this is not an improvement. (A computer could, in a theoretical sense, represent a large number of categories in any number of dimensions. It just can't present the results to you in more than stereo 2D.)

      • by bmo (77928)

        But as we can't really see in 3 dimensions - we can't see the inside and outside at the same time,

        Sure we can. It's called transparency and translucency and computers are pretty good at simulating this as 2D projection on a flat screen. If you were to do it in meatspace, you could use a translucent coloured glass or plastic.

        There is no reason why you can't use spheres.

        --
        BMO

        • The person below with the 3D printer where you could actually disassemble the pieces might be onto something, but with too many colors transparency in a strictly solid model isn't enough to help.

          • by bmo (77928)

            Tell me again how translucency and transparency don't allow you to see through/into something.

            Go ahead. Make me laugh more.

            --
            BMO

  • Nice and shiny. But as others have observed, it doesn't actually do much for visualizing the relationships. Up to about six sets really is my personal limit for visualizing these things at a glance. and I use a Karnaugh map [wikipedia.org] for that.
  • 3D? (Score:4, Interesting)

    by mattr (78516) <mattr&telebody,com> on Sunday August 12, 2012 @10:07AM (#40964221) Homepage Journal

    IANAM but would 3D help? Since now we have 3D printers one could build a program that would make a disassemblable colored object.

  • Because what the internet needs is more Venn diagrams!

  • by Anonymous Coward on Sunday August 12, 2012 @10:30AM (#40964305)

    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...

    • by guttentag (313541) on Sunday August 12, 2012 @10:42AM (#40964351) Journal

      I agree that the 11-Venn is fairly useless as a PowerPoint slide...

      Are you inferring
      -(next slide)-
      that there are things which
      -(next slide)-
      are not
      -(next slide)-
      fairly useless as PowerPoint slides?
      -(next slide)-
      Many have claimed to invent such a thing, but none have succeeded.

    • by makomk (752139)

      . 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.

      Of course, most /.ers have probably come across the ideas of channel capacity and Shannon information, which kind of put a dampener on that possibility.

  • by Bozovision (107228) on Sunday August 12, 2012 @10:35AM (#40964321) Homepage

    In 1989 Anthony Edwards figured out how to make Venn diagrams of arbitrary size: http://www.qandr.org/quentin/software/venn [qandr.org]

    "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."

    • by Mana Mana (16072)

      > In 1989 Anthony Edwards

      Mother Goose, you pussy!

      ?

  • As others have said, I'm not sure that 11-Venn is useful for most people's comprehension, but I'd love to have it on a t-shirt. Mathematicians come up with some awesome abstract art, sometimes.

  • Thought VennMaster could do it already:
    http://www.informatik.uni-ulm.de/ni/staff/HKestler/vennm/doc.html [uni-ulm.de]

  • Do they have any purpose other than to show some three universally reviled attributes and put a group of criticized people in the middle?

  • But can they do a BANANA shaped venn? http://boingboing.net/2012/07/12/just-look-at-that-banana-genom.html [boingboing.net]
  • It's one louder

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