If you scale the radius of a sphere by one unit then you indeed get an order of magnitude increase in volume (bits of info), but that's not the correct model! We don't increase by on unit! RAM isn't a one unit increase in radius! It's an order of magnitude increase! If you increase the radius by an order of magnitude you get a 3 fold order of magnitude increase in memory. So you jump up in latency by one order of magnitude and you get 3 orders of magnitude of memory in return.
You're totally missing his argument. If you scale RAM cubicly at any positive density, as you are suggesting, eventually you will achieve the matter density sufficient for your RAM to gravitationally collapse into a black hole.
If the density of your RAM is d, then the volume that a mass of M RAM takes up is M/d. If it's arranged in a sphere, the radius is ((3M)/(4dpi))^(1/3). Notice how this radius is a constant times the cube root of M.
Whereas the Schwarzschild radius scales proportionally to mass.
Thus, if you put enough mass of constant postive density together (no matter how small that density is) eventually you get a black hole.
N.B. - The author's argument is a little more subtle because he's talking about information density via the Berkenstein Bound, and he gets a square root instead of a cube root. But the argument is the same flavor.
You clearly did not understand the linked article at all. He is referring to theoretical results on the information density of a black hole, which indeed collapses to area. In practice, the reason RAM doesn't appear to increase by three orders of magnitude is not that (it's that we don't actually build RAM in a sphere) but his point is that whether you are looking at theory or practice the square root is the correct model.
If you scale the radius of a sphere by one unit then you indeed get an order of magnitude increase in volume (bits of info), but that's not the correct model! We don't increase by on unit! RAM isn't a one unit increase in radius! It's an order of magnitude increase! If you increase the radius by an order of magnitude you get a 3 fold order of magnitude increase in memory. So you jump up in latency by one order of magnitude and you get 3 orders of magnitude of memory in return.
His analysis and math are wrong.