There is a colorful story from ancient India about the origins of chess. The inventor of the game brought it to a king who, impressed, offered him a reward of his choosing. The man asked for a single grain of rice for the first square of the chessboard, two for the second, four for the third, and so on, for all 64 squares on the board. The king agreed, thinking this was a modest request. However, he soon realized he had unknowingly agreed to provide the man with more than all the rice that had ever been produced throughout history. Doubling the amount of rice 63 times would amount to more than 18 quintillion grains, or 18 million million million grains of rice.
The ancient king serves as a reminder of the often-underappreciated nature of exponential growth. It’s a concept that has captivated mathematicians, scientists, and futurists for centuries, and it lies at the heart of understanding the accelerating pace of change in the world today. If you aren’t paying attention to the dynamics of exponential growth, you risk underestimating consequences, failing to adapt, and missing critical opportunities. As Albert Einstein is rumored to have said, “Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.”
As we recently discussed, Stuart Kauffman’s ‘Adjacent Possible’ theory offers a compelling framework for understanding the process of innovation. Kauffman shows that at any given time, there exists a defined set of potential advancements, and these breakthroughs typically arise from the recombination of existing knowledge and technologies. Invention of the bow led to the bow and arrow, allowing early hunters to target prey from longer distances.
We often see this principle manifest in the business world. Airbnb blended peer-to-peer sharing with the established infrastructure of residential properties. Uber capitalized on the integration of on-demand services with GPS technology. These companies, and others like them, have defied traditional linear growth models, achieving multibillion-dollar valuations in short timeframes. Their success stems from their adept utilization of technology and innovation to achieve rapid scaling and global reach. The synonym for exponential growth in this context is “unicorn.”
Consider the contrast between a software company and a barbershop. The barbershop’s growth is inherently constrained by its physical capacity, the number of customers it can get into its chairs, and the number of barbers it can employ. Conversely, a software company’s application has the potential to serve millions, or even billions, of users with minimal incremental cost. This distinction captures the core essence of a business that has a linear business model and one that has a superlinear business model.
As Kauffman’s formula illustrates, the pace of change is directly proportional to the number of possible combinations. Humanity accumulates more knowledge and inventions over time—more ideas, concepts, patents, widgets, and so on—and the potential for new combinations explodes, leading to an accelerating rate of innovation. Exponential growth begets exponential growth.
Kauffman observed, “My father was born in 1903. That’s the year we created the airplane. My son was born in 1969. That was the year we landed on the moon. In 66 years, we got from before flight to our feet on the moon.”
Chances are, you’re reading these words on a device that has more computing power than the world’s most powerful computer 25 years ago.
Kauffman’s specific equation says the entire set of what is possible today is equal to everything that’s available today plus all the possible combinations of what’s available today. If we moved “everything that’s available today” from the right side of the equation to the left side, this expression denotes the pace of change: what’s possible today minus what’s available today. The pace of change, therefore, is equal to all possible combinations of what’s available today.
If we were to plot human ingenuity on a graph with the time scale on the horizontal axis and information on the vertical axis, we would see something that looked like a flat line for thousands of years with imperceptibly slow growth, changing to a steeper upward slope beginning around the time of the Industrial Revolution, and suddenly shooting up to a nearly vertical line today.
The same line plots the world’s GDP. Looking back thousands of years, the global economy remained more or less flat for centuries with only slight variations resulting from war, famine, or technological breakthroughs. Then there began a dramatic rise around the time of the Industrial Revolution and subsequent technological innovations. Today, it grows by amounts that would have been unimaginable to our ancestors.
Kauffman wasn’t the first person to analyze these ideas. Far from it. In the late eighteenth century, the wise Reverend Thomas Robert Malthus observed that resources like the food supply grew linearly (two, three, four…) while the human population grew exponentially (two, four, eight…). This mismatch, he predicted, would eventually lead to scarcity, hardship, social unrest, and population decline. The dilemma became known as the Malthusian Trap.
However, Malthus failed to anticipate the transformative power of the Industrial Revolution. Technological advancements in agriculture and manufacturing dramatically increased productivity, effectively addressing the supply side of the equation. In other words, human innovation sidestepped the Malthusian Trap by beginning to produce resources at a superlinear scale.
Back in the 70s and early 80s, another explorer of exponential growth, Buckminster Fuller, coined the term “Knowledge Doubling Curve,” which, as the name implies, observes that it takes shorter and shorter amounts of time for knowledge to double. Fuller noted that in recent centuries until around 1900, human knowledge doubled roughly every 100 years. By the mid-20th century, however, the rate had significantly increased. By 1945, it was doubling every 25 years, and by 1982 when Fuller published his book Critical Path, he estimated it was doubling every 12 to 13 months.
Building on Fuller’s work, Ray Kurzweil, computer scientist, author, and inventor, references the Law of Accelerating Returns, which points to the explosion of things like the number of scientific publications, the growth of the internet and digital storage, the computational capacity of AI systems, and the expansion of databases and human-created content, and describes how information technology and knowledge are progressing at an ever-increasing rate.
Kurzweil extrapolated to the natural conclusion: doubling time would become so short that human advancements would essentially balloon ever larger at every moment.
Let that sink in for a moment.
From the time you begin reading this sentence to the time you finish, the entire stock of human information would double.
Kurzweil called this the Singularity (with a capital “S”) in his book The Singularity Is Near. The natural implications would be a world where humans and technology merge, and people could essentially live as long as they wanted to live with the help of nanobots, biotechnology, regenerative processes, and AI. “People will soon have the choice to live as long as they want to live,” Kurzweil alleges.
If you’re thinking this all sounds like a Netflix sci-fi series, you’re not alone. There are lots of entertaining movies about time travel, introducing future technology to the present or present technology to the past. The Terminator and Terminator 2 (cyborgs from the future looking for present-day John Connor), Minority Report (where cops can see crimes committed in the future and use that information to apprehend criminals before they act), and Back to the Future (where a teenage Marty McFly uses a time-traveling DeLorean to encounter his parents when they were teenagers) are some examples.
So what’s the lesson? I think there are two important lessons, both relating back to the king and the chessboard. First, don’t be caught off guard by exponential growth. It has the power to change a situation from utterly insignificant to monumentally significant. If you’re like most people, your mind tends to think linearly, which means you’re probably not accustomed to spotting runaway growth as it’s happening.
This can be dangerous. As Mike Campbell said in Hemingway’s The Sun Also Rises when asked how he went bankrupt: “Two ways. Gradually and then suddenly.”
Don’t allow yourself to be like the victim in the slasher movie who scans the rain-soaked night for the predator, notices just a faint movement in the distance, and then suddenly screams as a flash of lightning reveals the predator is right here. Exponential growth causes big things to appear out of nowhere.
Second, don’t underestimate the pace of change. Kurzweil points out that when people estimate how long it will take to achieve a certain milestone, they usually benchmark the time to today’s pace of advancement. But that is a mistake. Extrapolating forward at today’s pace causes people to overestimate the time it will take to achieve the milestone. The pace of advancement is not constant. Rather, the pace accelerates. Beware of the pitfalls of overestimation. As that warning on the car mirror says, “Objects are closer than they appear.”
In a world of exponential change, adaptability is crucial. Individuals and organizations must be able to learn and adapt quickly to stay ahead of change. And this means shifting our mindset from linear to superlinear thinking. Just as Apple Computer’s old slogan was “Think Different,” the takeaway from this lesson is “Think Exponential.”