I aim to make this blog more readable for people who haven’t been studying advanced math for the last 8 years, so before I start, I will give a brief calculus lesson to those who just roll their eyes back at it.  Hopefully you know what a function is.  If you don’t, look it up on Wikipedia.

The derivative of a function measures the rate of change at a given point.  If you go 0-60mph in 3 seconds, the rate of change of your speed for that interval was 20mph per second.

The integral of a function is the opposite.  It takes the rate of change and performs the reverse operation to get the total change.  If you know you started at 0mph and accelerated at 20mph per second, you know that after 3 seconds you will be going 60mph.

Obviously there are many other applications, but that’s the basic idea.  I also chose that one because it’s a nice metaphor for explaining both the computational method involved in measuring production without the use of money, as well as a major problem with the modern economy.

Frequently you will hear figures like “We are using 1.2 Earths worth of resources every year,” which doesn’t sound like it’s possible.  What is meant by this is not that we are using the entire supply of Earth’s resources plus one-fifth of another Earth, but rather the rate we are using them is 1.2 times faster than the Earth can supply.  It still may not sound possible or intuitive, so think of it this way:

If you are on a one-lane road, a mile behind a car going 55mph, you can go 66mph, which is 1.2 times faster than the car in front of you.  You will not hit this car even if you don’t slow down, at least for 5 minutes.  In less than 30 more seconds, though, you’re going to rear-end that car.  We are treating Earth the same way.  We can use 1.2 Earths worth of resources, until we can’t anymore.  Pencils down, that’s the end of the brief lesson.  If you found this useful, check back occasionally, I’ll add some introduction to statistics, combinatorics, and graph theory.