Globe Safety
Frankly, given their extreme gravitational fields and general instability, even 12-inch globes should probably be banned.
Frankly, given their extreme gravitational fields and general instability, even 12-inch globes should probably be banned.
For any given amount of (stationary) mass, a value can be calculated known as the Schwarzschild radius, which denotes the radius of a spherical volume of space. If the mass somehow is compressed into this volume, it becomes so dense that it forms a black hole. The Schwarzschild radius corresponding to the mass of the Earth is about 0.35 inches (roughly 9 mm, or a diameter of 7/10" or 18 mm), meaning that if you could compress the Earth into a ball that small, it would be a black hole. The object at bottom right in the comic, with a triangular warning sign next to it, is a depiction of a black hole.
Globes, in this context, are miniature re-creations of planet Earth, used to show its features without any of the typical problems of a flat map. Randall claims that safety standards are in place to ensure that globes are not manufactured at, below, or even close to the Schwarzschild radius of the Earth which implies that the Schwarzschild radius and black hole formation is less a function of mass, but instead based on the concept of spatial bodies like planets and stars. A scale model of Earth will gain the Schwarzschild radius of the full size Earth because in the XKCD universe Earth-like-things (and presumably representations of other planets and stars) have Schwarzschild radii because that's the way they are.
An alternate interpretation is that any globe of the Earth shares the same mass as the Earth and hence the same Schwarzschild radius. Such a globe might be made by creating a literal 1:1 replica of Earth and then shrinking it without distortion until it has the required size (possibly by removing some of the "empty space" inside atoms). This would, of course, give the most perfect maps; however, for each globe made the Earth's mass would increase by its original amount. In addition it would be impossible to use an Earth-mass globe since something of that density would immediately burrow through the real Earth's crust and proceed to the center of planet.
The title text doubles down on the joke, suggesting that globes up to 12 inches (about 30 centimeters) should be banned, due to their extreme gravitational fields. Again, the implication is that representations of Earth would also gain the actual Earth's gravitational properties or would see those properties as a result of actually having an Earth-like mass.