What does exponential mean? A simple explanation

The graph illustrates how exponential growth (green)
surpasses both linear (red) and cubic (blue) growth.

  Exponential growth

  Linear growth

  Cubic growth

So what does exponential mean? It's one thing to learn what it means on a technical level, it's something else to understand its significance, and the ramifications of exponential growth - especially with regard to human activity. Watch the video below:

See the complete video here:

Why Cities Grow, Corporations Die, and Life Gets Faster

The entire video is fantastic and I highly recommend watching it all, but I decided to upload this bit in particular because it's one of the simplest, shortest and best explanations of exponential growth I've ever heard. I think he's right that few people really understand what it means, which is tragic.

Here's the video description:

Scaling up always creates new problems. Cities can innovate faster than the problems indefinitely, while corporations cannot. Every week a million people are being urbanised all around the world. It's the problem and also the solution. Creativity and wealth comes via cities.

These revolutionary findings come from Geoffrey West's examination of vast quantities of data on the metabolic/economic behavior of organisms and organizations. A theoretical physicist, West was president of Santa Fe Institute from 2005 to 2009 and founded the high energy physics group at Los Alamos National Laboratory.

Is there a grand unifying theory of sustainability that can be applied to our cities? Are we sustainable? Are their measurable predictive laws of life? West and his team have tried to find the science of cities. Our future may depend on it. 

He's speaking to the Long Now Foundation, then is interviewed by its founder Stewart Brand. 

Geoffrey West is a physicist. He was born in a rural town in western England in 1940 and moved to London when he was 13. He received a bachelor's degree in physics from Cambridge and pursued graduate studies in California at Stanford. West eventually became a Stanford faculty member before he joined the particle theory group at New Mexico's Los Alamos National Laboratory. After Los Alamos, he became president of the Santa Fe Institute, where he works on biological issues around power laws in biology, or allometric law. He has since been honored as one of Time magazine's "Time 100" most influential people. 

Stewart Brand is an American writer, best known as editor of the "Whole Earth Catalogue". He founded a number of organizations including The WELL, the Global Business Network, and the Long Now Foundation. He is the author of several books, most recently "Whole Earth Discipline: An Eco-Pragmatist Manifesto".

 Here is the same explanation by someone else, but a bit longer and with a few more details: