3 ms·
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 su
by zeroer 10y ago
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.
https://en.wikipedia.org/wiki/Schwarzschild_radius https://en.wikipedia.org/wiki/Schwarzschild_radius
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.