We all remember venn diagrams from junior high school, they were used as examples for teaching sets. But once you’re familiar with the basic idea of set intersection and set union, drawing those diagrams doesn’t seem to help much. I’ve yet to see a venn diagram that showed anything which wasn’t already intuitive from an ordinary english-level description.
Aside from a teaching tool in junior high, are venn diagrams actually used by any professional mathmaticians, engineers, etc?
at a glance you can see a relationship that might take many words. also the diagram provides its own memory of the relationships; to express in words would take rereading and brain memory on your part.
there are useful and used in a number of fields both social and technical.
The two-set diagrams are too simplistic to be much use, I agree, but 3-set diagrams are convenient. It is easier to show a labeled diagram than explain 7 different relationships verbally, and they are pretty much universally understood.
Asking if there is any practical applications of Venn diagrams is like asking if there is any practical applications of the “+” sign for addition. Yeah, you don’t really need the “+” sign, you can write/say “plus” or some such, but people heavily use it.
Here’s a page I linked to recently on the Dope to explain some stuff about the complexity of some problems.
They’re all over the place.
I remember once leading a discussion in front of some very top people in our field, I had to resort to a simple Venn diagram to get a point across. Well, try to. Most of the room still didn’t get it. But it helped. (Hey, if I just showed you an example of something in set A that is not in set B, then stop believing that set B contains set A, okay?)
You can design T-shirts and make a political statement:
Some people understand an image better than the same information in words.
Here’s a non-technical area where I found it helpful: to show the pieces of Great Britain:
They supply the addictive element to graphjam.
I think that is an Euler diagram.
I think they can be kind of useful when area is used to indicate the size of the overlap and each group. I encounter that a lot in genomic experiments, it’s a good quick way to compare two or three datasets. Here’s the first example that came up on GIS.
Well that is self-explanatory.:rolleyes:
I am open to being corrected, but I believe that Venn diagrams are a subset of Euler diagrams, and the one Arjuna34 linked to is an Euler but not a Venn.
Venn diagrams are meant to show fairly simple relationships, so there’s not going to be any hard science that really relies on one, but they are still useful.
Look at the first one on the wiki page that shows the intersections of the Greek, Latin and Russian alphabets. It quickly condenses information into an easy reference that would otherwise take columns and lists and headaches to achieve and use. But, aside from showing the relationship, the Venn diagram could have been used to discover it too. Whoever did the original research could have started with a diagram then filled in the letters as they classified them.
In terms of expressibility, it is the other way around; everything a Euler diagram can say, a Venn diagram can, but there are some things a Venn diagram can say that a Euler diagram cannot. Note that the way Euler and Venn diagrams represent is different, and it is the reason we are getting some examples that are not Venn diagrams. A Venn diagram shows all possible intersections between sets, and once we get up to 4 sets, the diagrams become complicated. Check out the wiki link in Fubaya’s post above for examples.
I am a teacher and I will occasionally use Venn diagrams to illustrate relationships, but good lord–my principal and department head seem to think they are the only way to teach and must be used practically every day. I think they must have attended a workshop that focused on Venn diagrams and concept maps and now they think that is the only way anything can be learned. So once a year I’ll have my students make Venn diagrams and we tape them up to the wall in the hallway so my administrators can feel validated in their leadership. Great work, boss!