The problem with weather is that our knowledge of its initial conditions is highly imperfect, both in theory and practice. A meteorologist at the National Oceanic and Atmospheric Administration told me that it wasn’t unheard-of for a careless forecaster to send in a 50-degree reading as 500 degrees. The more fundamental issue, though, is that we can observe our surroundings with only a certain degree of precision. No thermometer is perfect, and it isn’t physically possible to stick one into every molecule in the atmosphere.

Weather also has two additional properties that make forecasting even more difficult. First, weather is nonlinear, meaning that it abides by exponential rather than by arithmetic relationships. Second, it’s dynamic — its behavior at one point in time influences its behavior in the future. Imagine that we’re supposed to be taking the sum of 5 and 5, but we keyed in the second number as 6 by mistake. That will give us an answer of 11 instead of 10. We’ll be wrong, but not by much; addition, as a linear operation, is pretty forgiving. Exponential operations, however, extract a lot more punishment when there are inaccuracies in our data. If instead of taking 55 — which should be 3,125 — we instead take 56, we wind up with an answer of 15,625. This problem quickly compounds when the process is dynamic, because outputs at one stage of the process become our inputs in the next.

Given how daunting the challenge was, it must have been tempting to give up on the idea of building a dynamic weather model altogether. A thunderstorm might have remained roughly as unpredictable as an earthquake. But by embracing the uncertainty of the problem, their predictions started to make progress.

Perhaps because chaos theory has been a part of meteorological thinking for nearly four decades, professional weather forecasters have become comfortable treating uncertainty the way a stock trader or poker player might. When weather.gov says that there’s a 20 percent chance of rain in Central Park, it’s because the National Weather Service recognizes that our capacity to measure and predict the weather is accurate only up to a point. “The forecasters look at lots of different models: Euro, Canadian, our model — there’s models all over the place, and they don’t tell the same story,” Ben Kyger, a director of operations for the National Oceanic and Atmospheric Administration, told me. “Which means they’re all basically wrong.” The National Weather Service forecasters who adjusted temperature gradients with their light pens were merely interpreting what was coming out of those models and making adjustments themselves. “I’ve learned to live with it, and I know how to correct for it,” Kyger said. “My whole career might be based on how to interpret what it’s telling me.”