It only took a few years for the most successful internet-based companies like Google or Facebook to reach the summit of economic power. These companies have revolutionized how people interact with information, growing larger and larger every year. In 2022 three of the top 10 companies by market capitalization were initially born with the internet boom: Alphabet (Google), Amazon and Meta (Facebook). New companies such as Uber or Airbnb have penetrated markets as new entrants, quickly disrupting older businesses. The speed at which they grew illustrates the impact of the knowledge economy on how we conduct our lives and the acceleration of societal change we face. Is there some limit to the change we can expect in the future, or should we anticipate seeing relenting disruption forever?
When you drive your car and step on the gas pedal, the speed increases until, eventually, the engine cannot keep up delivering more power. Assuming that you do not crash or are pulled over by a policeman, you reach a maximum speed you cannot exceed further. On the contrary, some phenomena around us appear to grow forever, or at least for a sufficiently long time that one cannot control them anymore. We call this behaviour exponential.
Unfortunately, most of us are not well prepared to understand and deal with exponential phenomena. Our understanding of the world is often based on a mechanical perspective, where exponential phenomena are very limited. A mechanism, like the car engine mentioned before, usually can sustain acceleration only for a limited time before some limiting factor kicks in. On the other hand, a complex system consisting of a web of feedback loops interacting with each other can display a behaviour that is not easily predictable. In particular, exponential behaviour can arise when a reinforcing feedback loop is not balanced by a corresponding limiting factor.
An old story illustrates how easily one can get fooled by something presenting an exponential pattern. Once upon a time, a sovereign longing for distraction launched a contest to invent the most entertaining game. A wise person introduced the game of chess and captivated everyone through eloquence and wit. By explaining the rules and strategies in a way everyone could understand, she triumphed in the competition. The king was so enthusiastic about this new game that he allowed the winner to name her prize. The sage simply asked for rice: one grain for the first square of the chessboard, two grains for the second, four for the third, and so on, doubling the grains for each of the 64 slots. The king thought the request was ridiculously modest at first until he realized that all the kingdom's rice would not be enough to satisfy it. He realized that he would have to ask for more rice, which would cause the people to riot and overthrow him. The story does not end well for the sage, but that is not the point.
Phenomena that display exponential behaviour can be tricky to control. At each step, daily, weekly or yearly, some value grows proportionally to the value of the previous step. One may initially be relaxed, under the impression that the situation is under control and there is still time to take more drastic actions should the need arise. Unfortunately, mitigating measures take time before achieving an impact, and the phenomenon may get out of hand.
A quiz illustrates the power of exponential behaviour. Consider a pond where a lily pad grows, doubling its size daily. If the lily pad takes an entire month, say September, to cover half of the pond, when will it cover the whole pond? It is trivial, but still oddly surprising, to realize that the pond will be fully covered on October first.
The COVID pandemic is a typical example of exponential behaviour, with infections initially growing at an apparently controllable rate but suddenly overwhelming national health systems. Like the ancient king, many politicians in power couldn't grasp the implication of an exponential event and mostly failed to take the emergency seriously and decide promptly on the necessary measures. Reacting just a few weeks sooner would not have stopped the pandemic, but it could possibly have saved thousands of lives. Eventually, in a finite environment, exponential trends always encounter a limiting factor. Even the most contagious virus stops growing once a significant fraction of the population is infected.