Exponential change


  • Distinguish between linear and exponential rates of change.
  • Appreciate that the rate of technological progress is following an exponential curve.


Humans usually think in terms of linear growth, but technological development is following an exponential curve. In order to prepare for the future, we need to learn to recognize exponential growth.

Exponential vs Linear Rates of Change

Linear growth Growth that happens at a steady rate. E.g. the rate of aging, or a piggy bank that gets $1 each week. is growth that happens at a constant rate — like someone’s age — it just goes up by one year, every year. By contrast, exponential growth Growth that happens at a faster and faster rate; the later in time, the greater the change (or growth). E.g., bacteria multiplying in a petri dish, or the spreading of a viral video. is growth that happens at a faster and faster rate — like bacteria multiplying in a petri dish — the growth rate isn’t constant, but gets faster as time passes.

Humans usually perceive growth as linear. But when we look at change plotted over time, we can recognize trends of exponential growth. Whether or not we recognize the trends, we are still subject to their consequences.

Technological development is following an exponential curve The graph of an exponential rate of growth.. This means that the power of our tools and technology is increasing not at a steady, fixed rate, but at an accelerating rate. For example, if computers progressed linearly from the 1960s, the same processing power that handled calculations to send astronauts to the moon and back then would today roughly occupy 10 square feet. Instead, that processing power today fits inside the microchip in a smartphone — 10,000x smaller than our linear predictions.

In fact, a trend of computer processors getting smaller was observed by Gordon Moore in the 1960s, and has been coined Moore’s Law A trend in computing first discovered by Gordon Moore in which the complexity of computing circuitry doubles roughly every 1.5 years. This term has been abstracted to refer to many different types of increases in computing complexity. This has been observed in areas such as storage capacity, rates of computation, and energy efficiency.. Moore’s Law has been reliable for at least the last 50 years. Using the trend to project into the future, we could predict that in twenty years we will have the computing power of a smartphone in the size of a human cell.

Nobody knows how far this trend will go, but society has been repeatedly impacted by Moore’s Law over the last 50 years. Understanding the difference between linear and exponential progress is critical in preparing for the future, and should prompt a thoughtful, considered response.

Discussion Questions

  • In what ways has society been impacted by Moore’s Law in the last 50 years?
  • What opportunities and threats do you see in light of exponential trends in technology?
  • What are some risks/rewards in seeing/not seeing exponential progress in technology?

Call to Action

Write down your views on what would be a thoughtful response to the trends in technological progress. Learn about a group or individual who has a thoughtful response to the trends of technological progress.

Resources for further study/engagement: