You have a nice personality, my friend.
Keep on being you!
As for shells: I am reminded of a physics property.
Suppose we have a conservative potential energy field U(r). That is, at each point r in space, there is a potential energy U(r) associated with that point. If a particle travels from a point r1 to a point r2, the change in kinetic energy of the particle is the difference U(r1)-U(r2). The kinetic energy is 1/2 times the mass m times the square of the speed v. The force is the negative derivative of U. The derivative is the change in U per change in r.
This field is "conservative" since the change in U does not depend on the path between r1 and r2. Short path, long path, winding, looping path, the change in U is the same, which means the change in v is the same.
Suppose you draw an imaginary sphere. Its surface is a "shell" (this is the connection to your post). Now suppose you subdivide the shell into tiny tiles each with area "dA" , and look at a point on one of these tiles. Now, find the component NF of force F that is pointing out of the shell (as in, "coming out of your shell"). The value NF*dA is called the flux of F out of the shell at the point: how much of F is flowing out of the shell. Add up the flux over the entire shell. Then let the size of the tiles shrink to zero. The limit of this sum as dA goes to zero is the total flux out of the shell.
Now, look at the inside of the shell, and divide it into tiny cubes with volume "dV", and look at a point inside a cube. Let DF be the "divergence" of F from this point. The divergence measures how much F is flowing out of the point (if it is a source of flow) or into the point (if it is a sink of the flow, in which case the value is negative). Now, add up DF * dV. Then subdivide into smaller cubes, and take the limit of the sum as dV goes to zero. This is the total divergence of F.
Well, the total flux out of the shell equals the total divergence inside the shell.
So even if you feel that your life is lived on the shell, know that inside the shell is a hidden world of flow, with hidden sources and sinks, interacting. A rich and deep tapestry.
😁
