A Lesson In Venn Diagrams… And Who Gets Paid To Touch Your Junk

from the deconstructing-a-joke dept

Recently on Reddit, a link to a “Venn diagram” about “people paid to touch your junk” got pretty popular (even though it was apparently a repeat post of one that didn’t get nearly as popular. You can see it here:

The image then got plenty of attention with links from a variety of much bigger sites that I’m not going to mention, and it seemed to get a good chuckle out of folks who have been following the whole TSA/junk touching situation.

Well, that is unless you actually understand what a Venn diagram is supposed to show. Those people were somewhat horrified.

Rich Skrenta points us to an absolutely hilarious deconstruction of the problems with this graphic and how it’s not actually an accurate Venn diagram at all written by Andrew Plotkin. As he notes, the overlapping parts of circles on a Venn diagram are supposed to include both sets. In other words, if those three original sets formed a Venn diagram like the one above, the real categorization would be as following:

You have to imagine that the set of “airport-guarding hookers with medical degrees,” is somewhat small. Or non-existent in all likelihood. So if we were to draw the chart above to scale, there likely would be almost no overlap between any of the three circles.

As Plotkin then points out, what the original creator of the diagram meant for the diagram to show, is that all three of those professions are paid to touch your junk — and thus a more accurate — but not at all funny nor understandable, version of the Venn diagram would be the following:

I might quibble with that one a bit, seeing as not all TSA agents or doctors are necessarily paid to touch your junk (and I guess there could be a tiny subset of prostitutes who aren’t either, but I can’t imagine that’s a very large number), but still, the overall point is there. Though, um, it’s not funny. Or really all that understandable.

So, if you wanted to create a Venn diagram that actually makes the same point (sorta) and does it without being the mess above, what would you do? Well, Plotkin comes to the rescue again with the following:

Plotkin then goes on to do a few more diagrams and teach folks a bit about how Venn diagrams are supposed to work — which is totally worth checking out as well.

They say that if you have to deconstruct a joke, you’ve probably ruined it, but if that joke contains a Venn diagram, and that Venn diagram is wrong, but still becomes popular with people claiming it’s an accurate Venn diagram, suddenly that deconstruction can be a lot funnier than the original. Kudos to Plotkin for breaking it down…

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Comments on “A Lesson In Venn Diagrams… And Who Gets Paid To Touch Your Junk”

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Jose_X (profile) says:


Except that the original diagram was essentially correct.

Venn Diagrams cover sets of things, but a thing can be a “property of a thing” as well.

In other words, each circle doesn’t have to refer to people.

For example, the three circles can each have elements that represent, respectively, “properties of prostitutes”, “properties of doctors”, and “properties of TSA agents”.

And then we’d label these using short-hand: “prostitutes”, “doctors”, and “tsa agents” rather than using the more accurate longer text.

This is why most people will see the original diagram and understand what is being described, because in fact it is a correct association but with the figure labeled a bit tersely.

Also, the universe set (that name that appears on the lower right corner of the surrounding box) would more accurately be labeled “properties of people”.

Note, by “properties” I mean “characteristics” or “features” and not “items owned”. See definition 4 here http://www.thefreedictionary.com/property


Jose_X (profile) says:

Wrong again

See the other comments about replacing the simplified set name “X” with “Characteristics of X”

Then, Michael’s comment will make sense since there is more than simply 1 item in each of the overlapping regions. Eg, another characteristic of all 3 professions is that they “are practiced by people who almost always have two arms and two legs”, yet that characteristic is not represented.

Of course, we can fix that as well by replacing “X” with “Representative Characteristics of X”.

[I think a similar disease to what led that other group to want to correct the first diagram explains why I keep posting this “correction of correction” over and over on this thread.]

Bradley Slavik says:

Clarification on Jose X

The author is wrong. The diagram can be fixed simply by renaming the big circles like categories from the $25,000 pyramid game show. For instance, the circle named “Doctors” should say “things a doctor gets paid to do”, the circle marked prostitutes could be labeled “things a prostitute does”, and the circle marked TSA agents should be labeled “things a TSA agent get paid to do”. Then everything else is fine. But who is that pedantic? It was pretty clear to most readers that the joke was about common activities, not looking for people who work multiple jobs. I almost feel like declaring this an example of “Political Correct” mathematical snobbery. My Venn diagrams are superior to yours, so nyah! Grow up.

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