Eli5: Why are exponents so common in scientific formulas? Why is it so common that numbers in nature are multiplied by themselves?
In: Mathematics
One big reason is that we live in three-dimensional space. When it comes to things like how forces act over distances, such as gravity, you can think of the total “force” being the same at every distance (ie, if you add all of the infinite force vectors at a given distance from a gravitational source, the sum total will be the same regardless of the distance). Since the strength at any distance is essentially proportional to the surface area of a sphere of that radius, the strength must decrease by the square of the distance. Similarly, any other effect or force in 3-dimensional space that has a single point of origin and acts in any direction will also decrease by the square of the distance.
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