The Crash Course - Chris Martenson [18]
To illustrate this idea using population, if we started with one million people on the planet and set their growth rate to a relatively tame rate of 1 percent per year (it is actually higher than that), we would find that it would take 694 years for world population to grow from one million to one billion people.
Figure 5.5 Population Growth Example
Note how time “speeds up” by shrinking between each new billion people added to the total population.
But we would reach a world population of 2 billion people after only 100 more years, while the third billion would require just 41 more years. Then 29 years, then 22, and then finally only 18 years, to bring us to a total of 6 billion people. Each additional billion-people mark on our graph took a shorter and shorter amount of time to achieve. The time between each billion shrank each time, meaning that each billion came sooner and sooner, faster and faster. That’s what I mean by speeding up.
Speeding up is a critical feature of exponential growth—things just go faster and faster, especially toward the end.
Making It Real
Using an example loosely adapted from a magnificent paper by Dr. Albert Bartlett,5 let me illustrate the power of compounding for you.
Suppose I had a magic eye dropper and I placed a single drop of water in the middle of your left hand. The magic part is that this drop of water will double in size every minute. At first nothing seems to be happening, but by the end of a minute, that tiny drop is now the size of two tiny drops. After another minute, you now have a little pool of water sitting in your hand that is slightly smaller in diameter than a dime. After six minutes, you have a blob of water that would fill a thimble.
Now imagine that you’re in the largest stadium you’ve ever seen or been in—perhaps Fenway Park, the Astrodome, or Wembley Stadium. Suppose we take our magic eye dropper to that enormous structure, and right at 12:00 pm in the afternoon, we place a magic drop way down in the middle of the field.
To make this even more interesting, suppose that the park is watertight and that you’re handcuffed to one of the very highest bleacher seats. My question to you is this: How long do you have to escape from the handcuffs? When would the park be completely filled? Do you have days? Weeks? Months? Years? How long before the park is overflowing?
The answer is this: You have until exactly 12:50 pm on that same day—just 50 minutes—to figure out how you’re going to escape from your handcuffs. In only 50 minutes, our modest little drop of water has managed to completely fill the stadium. But wait, you say, how can I be sure which stadium you picked? Perhaps the one you picked is 100 percent larger than the one I used to calculate this example (Fenway Park). Wouldn’t that completely change the answer? Yes, it would—by one minute. Every minute, our magic water doubles, so even if your selected stadium happens to be 100 percent larger or 50 percent smaller than the one I used to calculate these answers, the outcome only shifts by a single minute.
Now let me ask you a far more important question: At what time of the day would your stadium still be 97 percent empty space (and how many of you would realize the severity of your predicament)? Take a guess.
The answer is that at 12:45 pm—only five minutes earlier—your park is only 3 percent full of water and 97 percent remains free of water. If at 12:45, you were still handcuffed to your bleacher seat patiently waiting for help to arrive, confident that plenty of time remained because the field was only covered with about 5 feet of water, you would actually have been in a very dire