Eli5: Why are exponents so common in scientific formulas? Why is it so common that numbers in nature are multiplied by themselves?
In: Mathematics
It’s because of how we measure units of stuff.
We represent terms with multiplication & division because it makes it so that we can make our units proportional to each other. If you hit something twice as hard as before, you’re either hitting it twice as fast, or making your fist twice as heavy (or a combination of the two). We also like to base our new units on preexisting ones, and that means as things get more complex, the same types of value start to get mixed in multiple times. Since repeated multiplication is exponentiation, we get exponents.
For example: Acceleration is m/s² because, it’s your increase/decrease in velocity over time. Since velocity is measured in meters per second, 1 unit of velocity per second = 1 meter per second, per second = 1m/s².
Then it just snow balls.
Force = Mass by Acceleration, so 1 newton of force is 1 Kilogram-Meter per Second per Second (kgm/s^(2))
Work is Force by Distance, so 1 joule = 1 Meter-Kilogram-Meter per Second per Second (kgm^(2)/s^(2))
Power is Work over Time, so 1 watt = 1 Kilogram-Meter-Squared per Sec per Sec per Sec (kgm^(2)/s^(3))
etc. etc. etc.
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