The human mind does not easily grasp the explosive nature of exponential growth. This was demonstrated more than 40 years ago in a series of pioneering psychological experiments conducted in the Netherlands by Willem Wagenaar and his colleagues. In one study, participants were shown a hypothetical index of air pollution beginning in 1970 at a low value of 3 and rising yearly in an exponential way to 7, 20, 55 and, finally, 148 by 1974. Asked to intuitively predict the index value for 1979, many of the respondents produced estimates at or below 10 percent of the correct value of about 21,000 (which can be determined from the underlying exponential equation). Subsequent experiments have observed similarly dramatic underestimation of exponential growth and showed that it typically results from straight-line projections based on early small increases.

The deceptive nature of exponential growth is similarly conveyed by the riddle of a single lily pad in a pond. Suppose each member of this species reproduces once a day so that on the second day there are two lily pads, on the third day there are four, on the fourth day there are eight, etc. On Day 48, the pond is covered completely. How long did it take to be covered halfway? The answer is 47 days. Moreover, even after 40 days of exponential growth, you would barely know the lily pads are there, as they would cover only 1/256th (0.4 percent) of the pond at that time. For a period of time, we can easily ignore the steady exponential growth of lily pads—until they smother the pond.

With respect to the coronavirus, the initial doubling of the relatively small numbers of infected cases and deaths evoked little concern outside China in January and most of February, since, for weeks, people around the world had little or no personal exposure to the virus or its victims. But the deceptively mild and seemingly faraway beginnings of the current pandemic led health officials and governments to squander many opportunities for early intervention. As a result, in the past few weeks, the numbers have quickly become a torrent overwhelming our capacity to stop the virus’ spread and care for the victims. It took 67 days to reach 100,000 coronavirus cases worldwide. The second 100,000 cases took 11 days, and the third 100,000 took only four days. Public-health authorities are now scrambling to communicate just how steep and damaging the coronavirus growth curve has or could become, and urgent response is becoming the law of the land.

Aside from the coronavirus pandemic, the biggest, most destructive exponential growth processes that we must grapple with today are those associated with global climate change. While it might be hard for humans to detect that carbon emissions and their concentration in the atmosphere are growing exponentially right now, that doesn’t mean we should rest easy. The opposite is true. As with the coronavirus, we need to anticipate the climate crisis and act quickly and aggressively to minimize further damages before they overwhelm us.