Exponential Change

Exponential vs Linear Rates of Change

Linear growth is growth that happens at a constant, and easily predictable rate—like someone aging: it just goes up by one year, every year. By contrast, exponential growth is growth that happens cumulatively at a faster and faster rate over time—like bacteria multiplying in a petri dish or population growth; the growth rate isn’t constant, but instead accelerates.

Human beings usually have an easier time understand linear growth or progress. But when we look closely at change plotted over time, we can learn to recognize exponential growth patterns all around us. This is important because, whether or not we recognize the exponential growth patterns, we are subject to their effects and consequences.

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The truth-is-stranger-than-fiction factor keeps getting jacked up on us on a fairly regular, maybe even exponential, basis. I think that’s something peculiar to our time. I don’t think our grandparents had to live with that.

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William Gibson

Most technological development today follows an exponential growth curve. The power of our tools and our technologies is increasing not at a steady, constant, linear rate, but at a rapidly accelerating rate. For example: if computer processing and computer power progressed linearly for the last 60 years, the same processing power that handled calculations sending astronauts to the moon would today occupy roughly ten square feet. Instead, that processing power today fits into a tiny microchip inside a hand-held smartphone—tens of thousands of times smaller than our linear predictions would have anticipated.

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So that means that the twentieth century wasn’t a hundred years of change at today’s rate of change, because we’ve been speeding up. It was actually twenty years of change at today’s rate of change. Exponential change is quite explosive, so in the next century we’ll make about twenty thousand years of change at today’s rate of progress—about a thousand times greater than the twentieth century, and that century was no slouch for change.

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Ray Kurzweil

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The Singularity Is Near

In fact, this exponential trend of computer processors getting smaller was observed by Gordon Moore in the 1960s, and has been coined Moore’s Law. Moore’s Law has reliably predicted this exponential trend for more than half a century. Projecting still into the future, we could predict that in twenty years we will have the computing power of a smartphone in something the size of a single human cell.

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Moore’s Law is really a thing about human activity, it’s about vision, it’s about what you’re allowed to believe. Because people are really limited by their beliefs, they limit themselves by what they allow themselves to believe about what is possible.

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Caltech Engineering Professor Carver Mead

We don’t know how far this trend will go, but the practical impact of what Moore’s Law describes on society in the past 50 years is almost impossible to overstate. Recognizing and understanding the difference between linear and exponential progress is absolutely essential in preparing for the future.

Questions for Discussion

• What is the difference between linear and exponential growth curves?
• How has society been impacted by Moore’s Law in the last 50 years?
• When we consider technological growth in exponential terms, what opportunities and risks do you see on the horizon?
• What are some of the potential risks from failing to understand technological growth in exponential terms? What are the potential benefits of properly understanding it?
• Does recognizing the exponential character of technological development make you more hopeful or more nervous about the future?

Advance to Primer 5