1% is Halfway

1% is Halfway

Exponential growth looks nothing like linear.

The world is changing rapidly. The rate of change is itself changing—accelerating rapidly into a future we can scarcely imagine. This can be unnerving, because as humans, we are not very good at understanding exponential growth.

“Absolutely nobody has a gut-feel for what exponential growth is really like. We are just not wired for that sort of intuition. As human beings we are very good at comprehending trends that are linear – like a steady hill, the trend keeps climbing in a straight line.

…Likewise, if we are driving along the road at a fixed speed, we rely on the fact that in two seconds we will have moved twice as far as in one. That is the sort of prediction the human brain is intuitively amazing at. But we are terrible at imagining exponential explosions. When something explodes – not just gunpowder, but the popularity of a new toy, the number of people using the internet, a swineflu epidemic – it is a fundamentally different type of progression: The larger something is, the faster it grows even larger.(Scott-Morgan, 2012)

Peter Diamandis provides a helpful illustration of the massive difference in scale between linear and exponential progression:

“To give you a sense of the difference, if I take thirty linear steps (calling one step a meter) from the front door of my Santa Monica home, I end up thirty meters away. However, if I take thirty exponential steps (one, two, four, eight, sixteen, thirty-two, and so on), I end up a billion meters away, or, effectively lapping the globe twenty-six times.” (Diamandis & Kotler, 2012)

Ray Kurzweil gives another example that shows how rapidly exponential change can creep up on those who are unprepared for it:

“Exponential growth is deceptive. It starts out almost imperceptibly and then explodes with unexpected fury— unexpected, that is, if one does not take care to follow its trajectory. Consider this parable: a lake owner wants to stay at home to tend to the lake’s fish and make certain that the lake itself will not become covered with lily pads, which are said to double their number every few days. Month after month, he patiently waits, yet only tiny patches of lily pads can be discerned, and they don’t seem to be expanding in any noticeable way. With the lily pads covering less than 1 percent of the lake, the owner figures that it’s safe to take a vacation and leaves with his family. When he returns a few weeks later, he’s shocked to discover that the entire lake has become covered with the pads, and his fish have perished. By doubling their number every few days, the last seven doublings were sufficient to extend the pads’ coverage to the entire lake. (Seven doublings extended their reach 128-fold.) This is the nature of exponential growth. (Kurzweil, 2005)

One of the clearest indicators of how difficult it is for us to grasp exponential growth is this: In exponential systems, 1% is halfway. This is illustrated in Kurzweil’s lily pad example above and in the table and chart below:

GenerationPercent Complete

1% is Halfway

Why are we so bad at understanding exponential growth and its implications? Peter Diamandis suggests that it has to do with our predominantly local frame of reference:

“The issue, then, is that we are interpreting a global world with a system built for local landscapes. And because we’ve never seen it before, exponential change makes even less sense. …The disconnect between the local and linear wiring of our brain and the global and exponential reality of our world is creating what I call a “disruptive convergence.” Technologies are exploding and conjoining like never before, and our brains can’t easily anticipate such rapid transformation.” (Diamandis & Kotler, 2012)

So what? What does it matter if we tend to be lacking in our default ability to understand exponential growth?

First, it makes prediction of exponential trends very difficult. Not only does accurate prediction require recognizing the linear nature, but an accurate prediction may not seem believable to others:

“…it is only linear predictions of the future that feel intuitively believable to their readers. Most people… simply cannot handle exponential.” (Scott-Morgan, 2012)

A related problem is that early stages of exponential growth look suspiciously like very shallow linear growth:

1% is Halfway

Executives who do not recognize an exponential growth pattern and the vastly greater outcome that will occur in the last 2-3 generations of growth may attempt to correct the perceived shallow rate of linear growth. In so doing, they may increase production at the expense of investing in production capacity.

1% is Halfway

Their good intent may doom the outcome, if they find they are unable to sustain an accelerated rate of linear growth and they achieve neither the exponential outcome (for lack of building exponential capacity) nor the linear outcome (for lack of production capacity).

The Solution

There are three key aspects of achieving the desired outcome in an exponential system.

  1. Be sure it is exponential – Sometimes shallow linear growth is just that, and not the precursor to a “hockey stick-shaped” upturn at the end. Sometimes, the exponential growth pattern is possible but needs to be encouraged. This may require investing resources to build the capacity of a larger network working toward a common objective. This kind of intangible work and resource allocation can be risky, especially if investors and boards do not understand the need to build immense capacity in the network in order to achieve the massive win in the end.
  2. Be disciplined – The lure of better numbers in the short term can be very strong. Producing more in the short term needs to be balanced against building capacity for an exponential finish—and both may not be possible.
  3. Stay the course – The only way to get to the exponential finish is to persevere to the end, past the tipping point. This requires leadership and unwavering confidence that the end is not only achievable but inevitable.


  1. Diamandis, P. H., & Kotler, S. (2012). Abundance: The Future Is Better Than You Think (Reprint edition). Free Press.
  2. Kurzweil, R. (2005). The Singularity Is Near: When Humans Transcend Biology. Penguin Publishing Group.
  3. Scott-Morgan, D. P. B. (2012). The Reality of our Global Future: How five unstoppable High-Tech trends will dominate our lives and transform our world.