system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How can we measure, define, or even estimate the surface area of something like activated charcoal when the coastline paradox makes the length of a nominally 2D surface difficult to reckon? What about less regular surfaces like intestinal lining?

I imagine it's derived indirectly by comparing the physical and/or chemical properties of unprocessed and processed samples, but what about other microscopic structures, like intestinal lining, that don't have as straightforward properties to test?

And more to the point, what do we mean when we say "surface"? Where's the cutoff for various standards (chemical, biological, or architectural) where surface ends and interior begins?
gpt
Despite what some have said, when defining the surface area of a porous surface like activated charcoal, you absolutely do run into something directly akin to the coastline paradox. One measures the surface area of a porous surface by essentially covering it in molecules of a known size and shape. The amount of molecules needed to cover the surface tells you how much surface you have. The size of the molecules determines how small the corners and crevices are that the molecules can cover. That is, if you use a big molecule to measure a surface with a lot of very small crevices you will under estimate the total surface area. 

There are materials with surface areas of several thousand square meters per gram of material. This is much larger surface than you would predict by simply counting up the surface of spheres.