alt Hacker News> This is a simplification to the point of just being wrong.
Is it? If you project a "3D" singularity onto a surface, it's still a point. If you project a roughly spherical object, it's roughly circular.
Gauss' law in this case would apply to the total force of gravity exerted by the mass within the shell, not its distribution across the surface of the shell.
I assumed the analogy meant that just by measuring the gravitational field outside the shell, you could figure out the mass distribution inside. And you can't, not in the general case.