Exponential growth means something doubles in each period, whether that period is a year, a decade, or a generation. The key feature is that growth compounds: each step is built on the step before, so a process that doubles five times doesn't produce five times the original, it produces thirty-two times the original. A process that doubles ten times produces a thousandfold increase. The doubling is always the same; what changes is how much is being doubled.
The problem with exponential growth is that human intuition was not built for it. We understand addition: ten more of something each year. We understand multiplication poorly, especially when compounding is involved. The famous illustration is a chessboard: put one grain of rice on the first square, two on the second, four on the third. On square thirty-two you have given roughly four billion grains. The second half of the board requires more rice than has ever been harvested in human history. The game looks trivial for the first twenty squares, and then it becomes impossible.
Computing power has followed an exponential curve since the 1930s, compounding at roughly 50% per year in price-performance terms across relays, vacuum tubes, transistors, and modern chips. This single persistent curve is why AI researchers who tracked it were able to predict, decades in advance, that something qualitatively new would eventually emerge. They didn't know what form it would take. They knew the power would be there when it was needed, because the compounding had never stopped.
For a reader without a technical background, exponential growth is best understood through the feeling it produces: a long period of apparent quiet followed by sudden, overwhelming change. The internet looked like an academic curiosity until it didn't. Smartphones looked like expensive toys until they weren't. The question to hold when reading about AI is not where are we today, but how many doublings are left. At the early stages of an exponential curve, even sophisticated observers consistently underestimate what is coming.
The flip side is that exponential growth eventually hits physical limits, resource constraints, or diminishing returns — it cannot continue indefinitely in any real system. The curve is not a promise, it is a pattern. Understanding it is the difference between being surprised by the present and being ready for it.
