The integral matters

Imagine you're in a situation where you try to estimate how much you can help other people.

But you come to a point where you don't know if it is efficient enough what you do because you think that you only can help a certain number of people at the same time.

Sometimes this bothered me. Trying to understand how I can maximize the number of people I can help simultaneously. But then Elon Musk let me realize that I forgot about the second axis in that function.

He once said that it's not about how many people you help. It's more about the calculation of the integral of help you provide. So, the second axis is how much help you provide, the amount so to speak.

A integral in math descibes the sum of an area under a curve of a function.

Let's say you help a few people a lot. The integral could possibly look something like figure A, when N is the number of people and H the amount of help you provide.

Or the other way around when you provide little help to many people. Then you spread out the equivalent amount of help, just differently distributed like in figure B.

This boiled down to me in a simple sentence: It doesn't matter if you help many people a little or one person a lot. It all comes down to the integral, the volume of help you try to give.