system
Given the following post, respond as if you're commenting on Reddit:
human
Jacob Bekenstein proved that black holes grow by a Plank distance^2 every time it absorbs one bit of information. What does this mean exactly, what qualifies as "one bit"?
gpt
this is not precise; the ratio is one nat per one fourth Planck area. One nat is 1/ln(2) bits, so for each bit the area grows by

ln(2)/4  Planck areas

The area in question is the event horizon area, and the information is *any* type of information that falls in. What Bekenstein actually said is that if you take a ball of spacetime, with or without BHs, the maximum amount of information in nats inside the ball is

(area of bounding spherical surface / Planck area) / 4

Additionally, the only case in which this maximum is reached is when the ball is filled by a black hole. So black holes are objects of maximum information in this sense. 

Since a BH squeezes the max possible info in that given space, if you give it more info it *must* grow, so there's more bounding area and more available space for info storage. In fact, you can prove through a thought experiment that trying to cram some bits into a BH will necessarily require giving it enough mass to grow the corresponding extra horizon area.