Why can mathematics and physics simulate natural phenomena so closely in thought experiments, calculations and computer programs?
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Mathematics and Physics were built based on what we observed in nature.
If I have 🍎, then put another 🍎 next to it, I now have 🍎🍎. We needed a name for this, so we called the number of apples “2” and called the process of adding more apples “addition.” Nature came first, and then we wrote rules to fit our observations.
Physics was the same way. We threw a rock and realized that if we put the same amount of “oomph,” into the throw and aimed at the same spot, the rock always landed in the same place. We then realized that by measuring the speed and angle, we could use math to predict where it would land and again wrote rules to match these observations.
Both of these situations involve writing rules to match our observations about nature. We know we’re correct (or at least correct enough) when we can take those rules and use them to predict things outside of our testing scenarios.
A great example of this are black holes. We saw stars moving in strange ways, and since we could estimate the mass of the stars, we could make an educated guess that there was a very large “invisible,” object exerting force on the stars. By doing more math, we realized an object might exist that was so massive that not even light could escape it’s gravity, and that might be our “invisible,” object. We built a massive telescope the size of the planet, pointed it where we thought one of these things might be, and bingo, [a black hole](https://www.nasa.gov/sites/default/files/styles/full_width/public/thumbnails/image/20190410-78m-4000×2330.jpg?itok=SGK55kJs), confirming our guess was correct. If it wasn’t, we’d need to go back and re-adjust until we could reliably figure out what was causing those stars to move.
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