Adam Brown

And in fact, black holes maximize that.

Black holes store that amount of information in a given area.

But specifically area meaning surface area.

Meaning surface area, exactly.

So the reason that that's such a wild answer, and an answer that's led to all sorts of thought experiments to do with quantum gravity ever since then, is that you might naively think that the amount of information you can store in a region is given not by its surface area, but by its volume.

So if I have a hard drive and I take another hard drive and another hard drive and another hard drive and I keep piling them up, the amount of information I can store on those hard drives scales like the number of those hard drives.

And that means it scales like the volume of the region in which I'm storing the hard drives.

Everything we know about classic thermodynamics

tells us that the amount of information should scale like the volume.

Everything we know about non-gravitational physics tends to tell us to point in the direction of the amount of information you can store

goes like the volume.

And yet, this is like the most surprising fact that is incredibly generative, is that once you add gravity to the picture, once you combine quantum mechanics and gravity, the amount of information you can store in a given region, a given sphere, goes like the surface area of that region, not like the volume in that region.

And you might think that that's...

you might think that that possibly be right.

And you might give the following argument.

Okay, so there's some region, and I'm just gonna keep adding more and more hard drives to that region.

And as I make that region bigger and bigger and bigger,

the amount of information on those hard drives scales like the number of those hard drives, which goes like the radius of that region cubed.

And the thing about the radius of the region cubed is it grows faster at large radius than the radius of that region squared.

So I just told you that the amount of information you can store in a region