The Crash Course - Chris Martenson [15]
Now let’s repeat the same experiment, but this time we’ll replace the erasers with two powerful magnets. As you move them together, the first part of the journey will progress in a nice, constant fashion, just like with the erasers. But at a certain point—BANG!—the magnets will suddenly draw themselves together and wreck your deliberately even speed. (Let’s hope your fingers were out of the way.)
We could run this experiment a hundred times, and you would never be able to get your body to achieve the same linear control with the magnets as with the erasers. That is because our brains and bodies are wired to process linear forces, and magnets do not exert constant (or linear) force over distance because their force of attraction increases exponentially as they get closer.
Despite our natural affinity for straight lines and constant forces, we can still achieve a useful understanding of exponential growth and why it is important. That is what we’re going to do in this chapter.
Exponential growth is not unnatural, but the idea of perpetual exponential growth is. We have no models of perpetual exponential growth in the physical world to which we can turn for observation and study. For example, microorganisms in a culture will increase exponentially, but only until an essential nutrient is exhausted, and at that point, the population crashes. Viruses will reproduce and then spread exponentially throughout a population, but they will eventually burn out as their hosts either develop immunity or die off. Nuclear chain reactions caused by neutrons cascading through fissile material are exponential, at least until the resulting explosion forces the material too far apart for the reaction to be sustained.
One thing that we lack here on earth, however, is an example of something growing exponentially forever. Exponential growth is always self-limiting and is usually relatively short in duration. Nothing can grow forever, yet somehow that’s exactly what we expect and require of our economy. But we will explore more about why that’s the case in a bit.
The Concept of Exponential Growth
What do we mean when we say that something is “growing exponentially”?
To begin with, let’s define “growth.” When we say that something is growing, we’re saying that it’s getting larger. Children grow by eating and adding mass, equities grow in price, and the economy grows by producing and consuming more goods. Ponds get deeper, trees grow taller, and profits expand. Within these examples of growth, we can identify two types.
The first type is what we would call “linear growth.” Linear means adding (or subtracting) the same amount each time. The sequence 1, 2, 3, 4, 5, 6, 7 is an example of linear (or arithmetic) growth in which the same number is reliably added to the series at every step. If we add one each time, or five, or forty-two, or even a million, it won’t change the fact that this kind of growth is linear. If the amount being added is constant, then it represents linear growth.
The other type of growth is known as “geometric” or exponential growth, and it is notable for constantly increasing the amount of whatever is being added each time to the series. One example is the sequence 1, 2, 4, 8, 16, 32, 64, in which the last number in the series is multiplied by two (or increased by 100 percent) at every step. The amount that gets added in each period is both dependent upon and a little bit larger than the prior amount. In the sequence example given, we see a case where the growth rate is 100 percent. So 2 becomes 4, and 4 becomes 8, and so on. But it doesn’t have to grow by 100 percent to be exponential; it could be any other constant percentage and it would still fit the definition.
Now let’s take a closer