Copyright: dariaren

However, growth may be exponential for a while, but not indefinitely. There are many real-world examples of growth that start exponentially: the size of the human population, the number of telephones, the number of motorized vehicles, the number of McDonalds restaurants (Gus Lubin, 23 charts on the amazing history of human progress. Business Insider, 28^{th} March 2011).

Because the physical world is finite, growth must stop sometime. The slope of these growth curves will eventually become zero or negative. Each of them will land on a plateau or collapse. So whenever you see a J-curve pointing to the ceiling, ask yourself what happens further to the right (Raworth, 2018).

But even if there cannot be indefinite exponential growth in the physical world, perhaps exponential growth in the virtual world is possible? In the symbolic world of mathematics, compound interest at a fixed rate makes capital grow exponentially. In the virtual world of the digital economy, the volume of data created, copied, and consumed worldwide grows exponentially. Maybe we can all become rich exponentially?

But even here, there are limits to growth. The number of physical servers on which data is stored cannot grow exponentially forever. And the size of the number that represents the amount of exponentially growing capital cannot grow indefinitely — at least if we want to be able to write the number on some physical medium.