**WARNING: THIS POST IS ABOUT A RECENT EPISODE OF SOUTH PARK. AS SUCH, IT IS MORE OR LESS A DISCOURSE ON THE MATHEMATICS OF THE MALE GENITALIA. IF YOU DON’T WANT TO READ ABOUT THAT, LEAVE NOW.**

I love South Park and I love math. So I was pretty stoked when I saw the new episode entitled “T.M.I.” last month. Quick synopsis: Those goofballs in Colorado declare that the size of a man’s–ahem–member can not be adequately described using just one number (length), and so Randy Marsh introduces an equation (video here) for adjusted length, or T.M.I:

Now, this equation should set off some alarms for any math dork because when you look at the units, *it makes no sense.*In the numerator, we have (Lxd), which gets you units of length squared. We also have the term W/G, weight over girth, which gets you units of weight per unit length. And then you add length squared to weight per unit length? That makes no sense! And don’t get me started on the fact that they were using kilograms as their unit of “weight!” (Kilograms are mass, not weight) AND they mixed imperial units (inches) with metric units (kilograms)!

Ignoring the unit fiasco, let’s look at what this equation actually says. I think for the sake of the discussion, it would be easier to rewrite it like this:

The first thing I notice here is that the T.M.I. increases with the product of length and diameter. This makes sense- a girthy wang can make up for shortcomings in the length department, so it’s important to consider both. In the second term, we have weight divided by girth- a sort of quasi-density measurement. This term would tell us how much the section under an arc of a given length would weigh. So we see that a higher density leads to an increased T.M.I. So far the equation kind of makes sense if you ignore the units. But then we come to the troubling part: dividing by the angle. The cartoon fails to describe just what it means by “angle of the tip.”

But all this is minor compared to the epic math fail that comes later in the episode (video here). The doctor says that when somebody is “consistently angry, or always finding new reasons to be angry, it means they have a very very very very small dick.” This statement implies that there is a negative correlation between penis size and anger. And he writes the following equation on the board:

where L=length, W=width, and M=mass. The equation shows a positive correlation between penis size and anger,directly contradicting what he says *while referring to the equation*. Like the Chewbacca Defense, it makes no sense.

Overall I was disappointed by the nonsensical pseudo-math in the episode. The equations they use are clearly just slapped together, designed only to sound complicated and get a cheap laugh. I get pretty stoked when cartoons put thought in to their math jokes- like the Simpsons’ gag about Fermat’s Last Theorem or the Futurama episode that introduced an original theorem.

It’s not all doom and gloom, though. South Park did seem to accurately use the term “yaw.” (In the interest of not having to draw diagrams, I’ll just leave it at that.) And in the end, it was a pretty good episode, with the South Park guys doing what they do best. They used the town of South Park as an allegorical microcosm of an issue that’s going on in the world, and took the ideology behind the issue to its logical extreme–with hilarious results. So I can forgive them for their sloppy math.