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Humans are famously bad at predicting the impact of exponential growth. The problem is demonstrated by the following question, often posed to unsuspecting students.

A colony of bacteria grows in a petri dish and doubles in size each day. It fills the dish on the 100th day, triggering a population crash. On what day is the petri dish half full?

The answer is on the 99th day, a result that is mathematically trivial and yet still has the power to surprise. The truth is that humans just haven’t evolved to think intuitively about exponential change.

This difficulty has important implications for our environment and how we should use the resources it offers. The global population has doubled twice in the last hundred years or so. The global economy is doubling in size every 20 years.

A growing number of people are warning that we must avoid the 99th-day scenario—although it is far from clear that we could recognize it if we were in its midst.

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