[aaaaaaaaaab]

That wasn’t the issue with their analogy.

The issue was that the holographic principle states that the boundary completely determines what’s inside a volume, as opposed to Gauss’s law which only talks about the total amount of charge.

[avmich]

You're right, Gauss law only talks about magnitude, not distribution. I chose this example because it's simpler than explaining reversal of wave fronts, so the formula FF = Q / epsilon_0 is shorter. Note I mentioned "what those properties are is another matter".

The choice of analogy is less precise but hopefully easier to understand. The idea is just that there could be relationship between boundary conditions and internal conditions.