Black holes behave in a way that seems to defy common sense. For ordinary objects, entropy — a measure of how much hidden information something contains — grows with volume. A bigger box can hide more disorder inside it. But black holes break this rule completely. Their entropy grows with surface area, not volume.
In the 1970s, Jacob Bekenstein and Stephen Hawking discovered the precise formula. The entropy of a black hole is proportional to the area of its horizon, measured in Planck units, and — most mysteriously — multiplied by exactly one quarter. Physicists have confirmed this result many times using very different methods. What’s been missing is a simple explanation of why that fraction is exactly one quarter, rather than some other number.
This paper offers a structural answer. The key idea is that a black hole horizon acts like a filter on information. Inside the black hole, space may have many microscopic degrees of freedom. But once you look only at what an outside observer can access, most of those degrees of freedom stop mattering. Some are hidden behind the horizon, some are locked by the special geometry of a light-like surface, some are duplicated across neighboring regions, and some are just different labels for the same physical state.
After all of that filtering, something striking happens: each small patch of the horizon is left with just one independent yes-or-no choice. Not one per Planck area, but one per four Planck areas. Neighboring patches share constraints, so they can’t make independent choices until you move two steps away. That sets a natural “pixel size” on the horizon: a square two Planck lengths on a side.
Once you see this, the famous “1/4” stops being mysterious. The entropy of a black hole is simply counting how many of these independent horizon patches fit on its surface. One binary choice per four Planck areas gives exactly the Bekenstein–Hawking result. No tuning, no special parameters, and no appeal to hidden interior microstates is required — just careful accounting of what information survives at a boundary.
What makes this especially interesting is that the rules used in the paper weren’t invented to explain black holes. They come from earlier work on how discrete pieces of space can fit together consistently at all. When those same rules are applied to a horizon, the black hole entropy formula falls out automatically. That suggests the “1/4” is not an accident of a particular theory, but a reflection of how boundaries, information, and geometry fit together at the most fundamental level.