system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How is information inferred from mathematical formulas?
gpt
Let's use gravity in space as an example.

We know (based on experiments on Earth) how gravity works. You release a ball, it falls towards the Earth. We also know that the larger the planet is, the more force gravity pulls with. This is why you can jump higher on the Moon.

These forces determine how planets orbit. It's the reason we orbit around the Sun; the Sun is massive, so it pulls on the Earth. We've seen this sort of behavior with a lot of planets, so we know exactly how orbits are supposed to look.

Now, let's say we see an orbit that makes no sense. Based on our understanding of gravity and all of the planets in the proximity of the new planet, we know what the orbit should look like. However, it looks entirely different!

There are a few possible explanations. One is that our equations for gravity are wrong. We may have misunderstood how things worked, and need to adjust the equations. A second explanation, however, is that there is an unknown object out there. This could be introducing different forces of gravity that would affect the orbit of our new object. Based on our equations, we could try to figure out where that new object should be based on how the orbit looks.