2013-08-02
Explanation
This comic is a math and anatomy joke presented on a yellow sticky note. It sets up the problem with two measurements: L = average leg length = 0.9 m, and l = average erection length = 0.15 m (for males in the USA). The comic then uses the cross product formula from linear algebra to calculate the angle between a man's legs.
The mathematical derivation goes as follows: the cross product of two leg vectors L1 and L2 yields a vector whose magnitude equals L squared times the sine of the angle theta between the legs. Setting this equal to l (the erection length) times a unit normal vector, the comic solves for theta using the inverse sine function: sin^-1(0.15 / 0.9^2) is approximately 10 degrees. The caption at the bottom reads: "Fact: If they're 10 degrees apart, the cross product of your legs is your penis."
The joke is a classic SMBC-style absurd application of real mathematics to a juvenile subject. The cross product is a legitimate vector operation used extensively in physics and engineering, but applying it to human anatomy in this way is deliberately ridiculous. The humor comes from the contrast between the formal mathematical presentation and the crude punchline. It also plays on the double meaning of "cross product" -- it is both a mathematical operation and, in this context, something that literally "crosses" between the legs.
The votey shows a woman looking unimpressed and saying, "Meh. This implies your penis is normal," delivering a deadpan burn that deflates the mathematical showmanship by pointing out that the calculation only works if one assumes perfectly average measurements.