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."

Comments

Looks nice, but let's be honest

[Lord Lode]

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:Looks nice, but let's be honest

[Anonymous Coward]

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

Re:Looks nice, but let's be honest

[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.

Re:Looks nice, but let's be honest

[Impy the Impiuos Imp]

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, 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.

Re:Looks nice, but let's be honest

[jmerlin]

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

[gsgriffin]

But useless

Misses the point...

[Havenwar]

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...

[gmuslera]

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.

Re:Misses the point...

[Asmor]

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.

Re:Misses the point...

[Anonymous Coward]

"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...

[Immerman]

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.

Its art

[nurb432]

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.

Re:Its art

[guttentag]

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:Its art

[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 certainly makes the task of identifying the flaws in the arguments easier, it also implies that attempts to point out those errors will fall upon uncomprehending ears. There is a point at which an argument cannot be further simplified without destroying the content of the argument. At some point, certain arguments can no longer reach people due to the nature of their complexity. At that point, the argument itself must be abandoned and instead one must first correct the ability to think before returning to the task of correcting the understanding of a particular point.

I run into this all the time. I find that I am more often correcting people on basic definitions and destroying bromides(propositions held without justification, accepted without thought) in their minds. I cannot even get to the meat of the subject because I have to deal with faulty reasoning methodologies first. I cannot speak on economics until I've gone back to deal with misunderstandings of epistemology, explaining the error in misusing the natural scientific method to justify some policy for effects it supposedly has by virtue of the fact that conditions were of some state while said policy was in effect(ignoring any attempt to control all the other countless variables that were also operating at the time). I cannot speak on philosophy and ethics until I've first dealt with misunderstandings of appeals to incidental and limited effect, where the outcome is subjectively valued differently by different actors and begs the question of any objective standard, while trying to point out when and where objectivity does exist in the universally preferable behaviors of men.

Going back to this level of reasoning before returning to the actual point would be a dream for me. More often, I must define the most basic of terms like statism, the initiation of violence, and so on. Just trying to get people to stop calling random politicians a socialist or whatever other ideology is tough enough. I can talk about the central violent control of the means of production within a geographical region all I want, but some people cannot see the economic fascism at all. I can point out that even the closest thing to it(like North Korea) still uses money and has markets but still many think the northern European so called social democracies(which have far more voluntary market exchange between peaceful individuals) are anything close to socialism. I can point out the degree of self ownership such places foster is comparable to the US and yet I see unending claims that America is capitalist while much of Europe is not. I can point to the degree of fascistic controls dominating the markets in the US only to be met with blank stares. It is entirely frustrating. The ability to think critically on these topics is absent in a large number of people. I do not think it is complete however. I suspect these blatant gaps in reasoning are exclusive to certain contentious and traumatic thoughts and experiences. Many wonderfully smart people exhibit these problems. It isn't an issue of a persons overall ability to think. This suggests that the next level down we must go to address this sort of inflicted thoughtlessness is in the realm of the psychological. One cannot reason a person out of a position they reached by means other than reason. If a man is indoctrinated, one cannot expect him to be rational about the subject. One must address the source of his ailment, not the symptom. So, my final long winded and off topic point is that to deal with the problem of stupidity in voters, you must deal with their mental blocks first, then show them how to reason, then explain the actual subject at hand. No small task at all...

Of course this is where it all began..

[wisebabo]

(Classic SMBC cartoon)

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

3D?

[mattr]

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

Useless is in the eye of the beholder.

[Anonymous Coward]

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.

[guttentag]

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.

And it's not true - been done before

[Bozovision]

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."

We don't know if it is useless yet

[140Mandak262Jamuna]

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.

Re:Not been done before

[Bozovision]

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.