Equations like E=mc^2 and stuff like how the force og gravity becomes 1/4 as strong when the distance between the objects dobles. Similarly with braking distance with cars, double the speed and the braking distance quadruples. These all seem to fit so well.
Have we made math to fit so nicely with physics? Am I thinking of all this wrong? Since I feel it like it would be to big of a coincidense that we can so easily use equations to predic physics. What is actually the reason for this?
In: Mathematics
Assuming something can be quantified and is related to another thing in a non random then it should be describable by math. As long the number of things you are trying to describe remains small it make sense to me that the relations aren’t terribly complicated.
Complexity shows up when you try to add more variable. For instance with your breaking example the relationship is simple as long as you are only dealing with breaking force and speed. But in reality as the car slows down the air resistance will also drop, slightly increasing the breaking distance. A lot of commonly given physics examples are chosen because the effects of the other variables is small, but there are lots of places where they aren’t.
It’s probably also worth noting that some relationships between units are simple because they are defined that way. And then we assign a meaning to the bigness of that number. For instance F=ma requires an ugly constant to be made to work if you are working in non SI units.
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