Imagine taking a simple sheet of paper and folding it in half. Then, fold it in half again and repeat the process, folding it again and again. Now, pause for a moment and guess how thick the paper would be after 50 folds. Keep your guests in mind as we delve into the fascinating concept of exponential growth. Additionally, we’ll explore a thought experiment involving two options for daily monetary rewards. Get ready to challenge your intuition and uncover the surprising implications of exponential growth.
Unfolding Exponential Growth
Exponential growth, at its core, refers to a process where the quantity increases at a rate proportional to its current value. In simpler terms, this means that the more you have, the faster it grows; unlike linear growth, where something increases by a fixed amount, exponential growth doubles, triples, or increases by some fixed percentage at regular intervals.
To better understand this, let’s revisit the paper folding exercise. Most people imagine that a sheet of paper, even after being folded several times, would result in a small stack. However, due to the doubling nature of the folds, the outcome is far more dramatic. After 50 folds, the thickness of the paper would exceed 60 million miles, which is approximately the distance between Earth and the Sun. Initially, the folds barely change the thickness, but as the process continues, the paper’s thickness multiplies exponentially. What began as a thin sheet of paper turns into a massive stack in a shockingly short period of time. This example serves to show just how powerful exponential growth can be. The early stages may feel insignificant, but once the process hits critical mass, it escalates into something vast and far-reaching.
Exponential growth appears in many areas of our lives, from the growth of digital data and technology to financial investments and even disease outbreaks. Understanding this concept is crucial, especially in an age where technological advancements are largely driven by exponential growth, and its effects are not always immediately visible. This type of growth is often counterintuitive and difficult to predict, which is why it can take people by surprise when its impact becomes apparent.
The Dilemma of Growth
The idea of exponential growth often poses a dilemma when presented in practical scenarios. Consider the two choices offered: $1,000 per day for 30 days or doubling an initial amount of money starting with just one cent. On the surface, the first option looks overwhelmingly better. A consistent $1,000 per day results in $30,000 after 30 days. However, the second option, though starting small, has a far more substantial payoff. By the end of the month, the compounded effect of doubling the amount each day results in over $5 million.
This stark difference showcases the power of exponential growth, even when the initial stages seem underwhelming. On day one, receiving just one cent seems insignificant, and the progression from 1 cent to 2, to 4, to 8 cents doesn’t seem like much. But by the time you reach day 30, the cumulative total has skyrocketed into millions. The point is that exponential growth is often deceptive. It doesn’t feel impactful at first, but as time progresses, the gains become extraordinary.
This dilemma also highlights how people tend to underestimate the power of compounding. The first few days of exponential growth don’t show much improvement, but this slow start is part of the process. As a result, many people might gravitate toward the more tangible, immediate rewards of a linear payout without realizing the long-term power of exponential growth.
Why Exponential Growth Is So Hard to Grasp
Human intuition is rooted in the understanding of linear growth. Throughout much of history, our ancestors lived in a world where doubling or halving things was often based on simple actions. If you gathered twice as much food, you could feed yourself for twice as long. If you worked harder, you would earn more in direct proportion to the effort put in. This cause-and-effect relationship was the basis of survival and social organization for thousands of years.
However, exponential growth was rarely encountered in early human life. It wasn’t something that nature presented frequently, and its scale wasn’t as pronounced even when it did. For instance, while a forest might grow slowly over time, it doesn’t exponentially increase in size until it reaches a critical mass. This lack of exposure to exponential growth in our evolutionary history means that we are ill-equipped to understand how quickly things can multiply.
Today, however, exponential growth has become a fundamental characteristic of the modern world. The digital revolution, for instance, operates entirely on exponential principles. With each new technological breakthrough, the speed of innovation accelerates, compounding the effects of past discoveries. The growth of the internet or social media platforms is another prime example. The number of users and the amount of content on these platforms don’t just grow linearly; they multiply exponentially, meaning that one new user can connect with millions of others, creating a network effect. This dynamic can feel unsettling because it defies our usual experience of growth. We are accustomed to seeing slow, steady progress, but exponential growth introduces a rapid acceleration that can sometimes be difficult to grasp until it’s too late.
Moreover, the psychological distance between a modest beginning and an overwhelming result is part of what makes exponential growth so hard to conceptualize. People often fail to recognize that small changes can have outsized effects over time, which is why exponential growth seems so alien. This misunderstanding can lead to complacency or misjudgment, as people may not appreciate how quickly a seemingly small percentage can expand into something huge.
The Inflation Trap
Inflation is a perfect example of how exponential growth can quietly eat away at the value of money. When inflation rates are presented as a percentage—say, 5% per year—it might seem manageable. After all, 5% is relatively small. However, when we apply the formula for doubling time—70 divided by the inflation rate—we realize that the value of money will halve in 14 years. This calculation is staggering. For anyone holding cash, savings, or relying on fixed incomes, the consequences of inflation can be devastating.
Over time, inflation erodes purchasing power. The impact may not be immediately noticeable, but as the years progress, the cost of living rises steadily, and the value of savings decreases. For example, in 14 years, something that costs $1 today will cost $2, and in 28 years, it will cost $4. The effect is cumulative and accelerates over time. As prices rise, people are forced to spend more to maintain the same standard of living, all the while their savings lose value. Inflation can sneak up on people because its effects are spread out over many years, but understanding the mathematics of exponential growth helps illustrate just how insidious inflation can be.
The same logic applies to other forms of economic growth, such as rising healthcare costs or housing prices. In the face of exponential growth, even modest percentage increases can result in substantial economic shifts. Acknowledging the reality of exponential inflation is crucial to planning for the future for individuals and governments alike. The compounding nature of inflation requires proactive measures, such as investing or adjusting wages, to mitigate its effects.
Changing the Narrative
Exponential growth doesn’t only apply to finances and economics; it also plays a significant role in shaping narratives and public perception. Take, for instance, a statistic like the number of dog registrations in a city increasing by 10% annually. The impact seems trivial if presented as a simple percentage increase—“Dog registrations rising by 10%”—. People may barely notice such a statistic, and the attention it garners will be minimal. However, when framed in terms of exponential growth—“Twice as many dogs in 7 years”—the story becomes far more compelling and urgent.
By emphasizing the doubling time of an increase, we can make the significance of seemingly small changes much clearer. The key to understanding exponential growth is recognizing how small, incremental changes accumulate over time. As with financial growth or population increases, small percentages can lead to massive results if they compound over a long enough period. This shift in framing transforms the statistic from an inconsequential detail into something that demands attention.
Journalists and media outlets can harness this insight to communicate the true importance of exponential growth in various domains, from technological advancements to societal trends. It’s not just about presenting numbers; it’s about telling a story that accurately reflects the potential impact of those numbers. Understanding the mechanics of exponential growth can enhance how we report on important issues, helping people grasp the true scope of challenges or opportunities ahead.
The Limits of Exponential Growth
While exponential growth can seem boundless, it’s essential to recognize that it is not infinite. All systems that grow exponentially eventually hit a ceiling, a limit imposed by physical, environmental, or resource constraints. For instance, in the case of bacteria like Escherichia coli, which divides rapidly under favorable conditions, the growth will continue only until it exhausts available resources such as nutrients and space. As the bacterium consumes oxygen and sugar at an increasing rate, the environment becomes inhospitable, and growth slows or halts altogether.
This natural cutoff point is critical to understanding exponential growth. Getting caught up in the excitement of rapidly growing numbers is easy, but recognizing that growth is finite can help us better anticipate and manage its eventual decline. Whether in business, technology, or nature, growth doesn’t go on forever. At some point, every system will experience limitations, and planning for these eventualities is important.
Moreover, many human systems also face these limitations. Technological advancements, for example, may experience diminishing returns after a certain point. For businesses, rapid growth may eventually hit a plateau where further expansion becomes unsustainable. Recognizing these limits can help individuals, businesses, and governments prepare for the future, ensuring that growth is managed and sustainable.
The Persian Tale of Exponential Growth
The ancient Persian tale about the wise courtier and the chessboard is a classic illustration of exponential growth’s power to astonish. The courtier’s seemingly modest request—to place one grain of rice on the first square of the chessboard, then double it for each subsequent square—initially seems small and manageable. The king, underestimating the power of exponential growth, readily agrees. However, as his servants begin placing the rice, the amount quickly spirals out of control. The total rice grains required by the chessboard’s end far exceed the kingdom’s rice supply. The amount would be so vast it would surpass the total rice production of the entire Earth.
This tale encapsulates that exponential growth can start small but quickly become unmanageable. The early stages are inconspicuous, but the results can overwhelm any expectations. When faced with exponential growth, we often underestimate its potential until it’s too late. This ancient story is a powerful reminder of the need to anticipate and manage growth before it becomes too overwhelming.
The Lesson: Trusting Exponential Growth
The primary lesson from these examples is that our natural intuitions often fail when understanding exponential growth. Linear growth feels natural because it aligns with our daily experiences, but exponential growth defies our expectations. To truly understand the scope of exponential growth, we must rely on mathematical tools like calculators or the “doubling time” formula.
In a world where technological advancements, economic trends, and even social phenomena are driven by exponential growth, developing a better understanding of how this growth operates is essential. By embracing exponential growth in all its complexity, we can make more informed decisions, anticipate challenges, and capitalize on opportunities. Trusting the math, rather than our instincts, allows us to see the world more clearly and prepare for rapid changes.
Conclusion
The enigmatic nature of exponential growth challenges our intuition, which is more accustomed to linear growth patterns. By unraveling the astonishing thickness of a folded sheet of paper and exploring thought experiments involving monetary rewards, we have gained insight into the power of exponential growth. Understanding exponential growth allows us to make more informed decisions, communicate effectively, and perceive the world through a new lens. So, the next time you encounter exponential growth, trust calculators and embrace the magic number 70 to navigate the intriguing complexities of this fascinating phenomenon.
This article is part of The Art of Thinking Clearly Series based on Rolf Dobelli’s book.