hey-2
Explanation
This comic uses a crude pickup line to make a joke about the Coastline Paradox applied to surfaces and human anatomy.
A man suggestively opens his shirt and says: "Hey babe, guess who's packing infinite area over a finite volume?" The woman stares at him with visible discomfort. The caption reads: "Did you know the Coastline Paradox can be extended to surfaces?"
The Coastline Paradox is a well-known concept in fractal geometry, originally discussed by mathematician Benoit Mandelbrot. It observes that the measured length of a coastline depends on the scale of measurement: as you measure with smaller and smaller rulers, the coastline length increases without bound because you capture more and more fine detail in the irregular shape. In the limit, a coastline can be considered to have infinite length while enclosing a finite area.
The comic extends this idea from lines (coastlines) to surfaces, suggesting that a sufficiently wrinkly or fractal surface could have infinite surface area while enclosing a finite volume. The man's pickup line boasts about having "infinite area over a finite volume," which is both a genuine mathematical observation about fractal surfaces and a deeply unsexy way to describe one's own skin (which is indeed highly wrinkled and folded at microscopic scales). The humor lies in the collision between the suggestive framing of a pickup line and the deeply nerdy mathematical concept being referenced, plus the implicit joke that describing your body in terms of fractal geometry is the opposite of attractive.