The Crash Course, Revised Edition

CHAPTER 5Dangerous Exponentials

Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it.

—Albert Einstein

In this book, we will explore a few key concepts to help you gain a better understanding of what lies ahead. None of them is more important than exponential growth. Exponential growth holds the honorary position as the “fourth E” in this story alongside the economy, energy, and the environment.

Understanding the ways in which our lives are shaped by exponential growth is foundational. Once you see it, you'll see it everywhere. Want to be able to foresee the future and anticipate what's happening right now? Then you'll want to spend some time on exponential growth.

So what are we talking about, exactly? When a government official comes on the television and says our highest priority is “returning the economy to a path of growth,” what they are really saying is that our top priority is returning the economy to a path of exponential growth.

That's because anything growing by some percentage over time is growing exponentially. Even something as seemingly tame as “1% per decade” is still a measure of exponential growth because it's a percentage of growth over time. This is because any future growth is itself based off of all past growth. That is, the growth compounds upon itself.

Examples of exponential growth in our lives extend well beyond the economy. We are literally surrounded by examples of exponential growth. The ...