Why Can We Ignore the Shape of the Universe? (Gauss's Law)

Why Can We Ignore the Shape of the Universe? (Gauss's Law)

What if I told you the secret to the universe's shape starts with a fishing net? Imagine a steady river flowing. If you dunk a circular net into the current, water rushes through it. Make the net bigger, or the river faster, and you catch more water.

Now, swap the water for an invisible electric field, and the net for a mathematical surface. Physicists call the total amount of field piercing this surface 'Electric Flux'. It's just a fancy word for flow.

But here's the strange part. What happens if you take that net, and stitch it completely closed into a sphere, trapping a spring of water inside? That weird thought experiment is Gauss's Law.