Exponential Growth

The lily pad doubles in size every day. On day 30, it covers the entire pond. On what day did it cover half the pond? Day 29. For most of the month, the lily pad was negligible. Then, suddenly, it overwhelmed everything. This is the nature of exponential growth: slow, slow, slow, then all at once.

Human intuition is linear. We expect steady, proportional change — walk twice as long, go twice as far. But exponential processes don’t work that way. Compound interest, viral spread, population growth, technological improvement: these double, then double again, then double again. The early phase looks harmless; the late phase is vertical.

The mathematics are simple: a quantity that grows by a fixed percentage in each period doubles in a predictable time. The Rule of 72: divide 72 by the growth rate to get the doubling time. 7% annual growth doubles in about 10 years. 10% doubles in 7 years. Over enough doublings, any positive growth rate produces astronomical numbers.

This is why pandemics explode suddenly, why tech giants emerged from garages, why feedback loops can spiral beyond control. By the time an exponential trend is obvious, it’s often too late to change course. The time to act was earlier, when the numbers looked small and the threat seemed abstract.

Exponential growth cannot continue forever. Physical limits exist: carrying capacity, resource depletion, market saturation. Every S-curve starts exponential and ends in a plateau. The question is always where the inflection point lies — and how much damage occurs before the system hits its ceiling.

The implications for judgment: distrust your intuitions about compounding. The future will contain more of what’s currently doubling than your linear mind expects. And the past contained less — the present is the accumulated result of many doublings that once seemed negligible. Time and growth are conspiring against your ability to see clearly.