Breakthrough In Drawing Complex Venn Diagrams: Goes to 11 83
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."
Looks nice, but let's be honest (Score:5, Insightful)
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...
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I wonder if people dabbling in haruspicy see things the same way.
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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.
Re:Looks nice, but let's be honest (Score:4, Interesting)
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.
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beautiful (Score:4, Insightful)
We don't know if it is useless yet (Score:5, Insightful)
Misses the point... (Score:5, Insightful)
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.
Re:Misses the point... (Score:4, Insightful)
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That's more depending on how much drugs you take. Not so much a limitation as a lack of reality disconnect.
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Neither, but if you've got some vodka I've got a thirst that's not of this world.
Re:Misses the point... (Score:5, Interesting)
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.
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Huh, thanks for the info! Learn something new every day. I guess it's drinking time!
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Looks like it's going to be the University of Illinois!
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I don't know... I don't see any drinking courses... https://www.coursera.org/illinois [coursera.org]
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304 Permanent Redirect: https://www.youtube.com/watch?v=i37uttMA6Mc [youtube.com]
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The greatest Tom Cruise movie evar.
(Yeah, I can't believe I just typed that either)
Re:Misses the point... (Score:5, Insightful)
"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.
Re:Misses the point... (Score:5, Insightful)
You've just run head on into the difference between targeted and foundational (or "blue-sky") research. Foundational research almost by definition has no particular application. Why do we care about the Higgs Boson? Why did we care about the electron? Or the neutron? No one had any concrete ideas for applications of any of them at the time - they were just trying to better understand the rules that govern the universe.
Mathematics research is almost all blue-sky, but it's even more fundamental than physics since it the landscape is a construct of rigorous logic built on a foundation of a few of the simplest and most universally accepted rules, and the results apply to anything whose mathematical description can contorted into a compatible format, regardless of the original subject area.
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Sure, the majority of niche mathematical puzzles may never see much application, but by dismissing it as something that "looks neat" I think you risk missing the point. As others have mentioned Venn diagrams get kind of pointless as visual aids with around 4 or 5 groups - the human brain isn't really wired to process it; however, it is an interesting exercise is planar geometry with particular challenges, and it may prove to be something like Penrose Tiles in that respect: silly in it's own right, but with
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Huh, there you go, I did not know that. I mean I still have no clue what real world problems get solved by that kind of math, but I know they do. Somehow.
As a friend of mine put it: "I'm just an advanced maths degree away from understanding why anyone would get an advanced maths degree."
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Heh heh, I've got to remember that line. Having gotten a 4-year math degree sort of by accident I'm still not entirely sure why anyone would want one. My impression is that nobody is crazy enough to get an advanced degree in it unless they're either deeply in love with formal logic or are just too eccentric to fit in anywhere else.
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You out grew it, how sad, a big part of why I go to work is to be able to create things for the shear joy of creation without regard for practicality when I'm not working.
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Actually that sounds much sadder to me, but then I do things I enjoy all the time instead of doing things I hate just to afford to spend some precious little sliver of time with something special. I can't imagine having to spend all that time toiling away just so you can do something you enjoy. Wouldn't you rather have all those hours to do something nice in? Even if it meant you might not afford quite so many gadgets or had to build your non-practical inventions out of second hand stuff instead of brand ne
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we like to at least have some thin veneer of reason behind things...
Because I can should be enough.
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No, it most certainly shouldn't. "Because I can" can never be a blanket explanation. There are a lot of things I _can_ do that would be a complete waste of time, and in addition to that there are a lot of things I can do that would be immoral, illegal, or even borderline suicidal to pursuit. "Because I can" is not enough, never has been, and never should be.
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No wonder you are how you are! You cursed at your mother at 8 years old?
Freak.
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Well, while my mother certainly wouldn't have minded - she as I was of the opinion that swearing is for emphasis and to be reserved for such - no, I wasn't swearing at my mother at age 8. Especially not in English since I never spoke that to her. I did a paraphrased idiomatic translation to express the general level such replies would have had.
So sorry if that left you confused.
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Ah my bad. I failed to consider the lack of quotation marks around the paraphrased text that would have indicated an exact translation rather than an idiomatic one.
Its art (Score:5, Insightful)
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.
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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.
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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.
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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
Of course this is where it all began.. (Score:5, Funny)
(Classic SMBC cartoon)
http://www.smbc-comics.com/index.php?db=comics&id=1917 [smbc-comics.com]
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3D (Score:1)
Can you make one for 4 colors out of 4 spheres?
Certainly not a prime number
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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.)
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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
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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.
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Tell me again how translucency and transparency don't allow you to see through/into something.
Go ahead. Make me laugh more.
--
BMO
Pretty, but limited in usefulness. (Score:2)
3D? (Score:4, Interesting)
IANAM but would 3D help? Since now we have 3D printers one could build a program that would make a disassemblable colored object.
Hallelujah! (Score:2)
Because what the internet needs is more Venn diagrams!
Useless is in the eye of the beholder. (Score:5, Insightful)
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...
Re:Useless is in the eye of the beholder. (Score:5, Funny)
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.
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. 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.
And it's not true - been done before (Score:5, Informative)
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."
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I think it does symmetry: have a look, not at the pictures on the linked page, but the pdfs, which are examples of what he was talking about. But you are quite right it's not simple and my comment should be downvoted, which is my punishment for a knee-jerk reaction. My apologies to Khalegh Mamakani and Frank Ruskey.
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> In 1989 Anthony Edwards
Mother Goose, you pussy!
?
So, where do I get the t-shirt? (Score:2)
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.
been done before? (Score:1)
Thought VennMaster could do it already:
http://www.informatik.uni-ulm.de/ni/staff/HKestler/vennm/doc.html [uni-ulm.de]
Venn diagrams? (Score:2)
Do they have any purpose other than to show some three universally reviled attributes and put a group of criticized people in the middle?
Banana shaped..... (Score:1)
This one goes to 11 (Score:1)
Goes to 11? (Score:2)
7 is enough for Steve Miller. [happyplace.com]
Anyone else with a sudden urge for Spinal Tap (Score:1)