In the late 1970s, a physicist and textiles engineer in Texas named Robert Steadman published a paper called “The Assessment of Sultriness.” The title reflected an unpleasant sort of steaminess—how temperature and humidity combine to make life hard on the body. To do it, he drew on a long history of experimentation. In the 18th century, people climbed into ovens warmed to 250 degrees Fahrenheit to see how long they could suffer, as they watched steaks cook beside them. In the 19th and early 20th centuries, researchers observed people sweat in Turkish baths and reported from mines where they measured the ambient conditions as workers collapsed from heat exhaustion. Later on, the military picked up more of the testing, deriving equations for how blood flow, sweat, and breathing respond to atmospheric extremes.

What was unique to Steadman was his intimate knowledge of clothes; he was known for projects like a universal sizing system for garments, and motors that could spin fine cotton yarn. After all, he theorized, people are rarely naked in the heat, so our perception of it must be mediated by a combination of physiology and clothing. His formulas assumed precise percentages of how much skin would be covered with fabric, and how specific mixes of air and fiber would transfer heat from the air.

What’s surprising is that, for a set of calculations developed by a textiles researcher, Steadman’s measure of sultriness proved useful for weather forecasters, especially in the United States. In 1990, a scientist at the National Weather Service adapted them with Steadman’s key features more or less intact. Henceforth, the sultriness index came to be known more (or perhaps less) pithily as the “heat index,” though it’s also sometimes called the “apparent temperature” or “real feel.” If you have been caught in this summer’s heat waves, this is likely a number you have consulted to better understand the torturous outdoors. It’s the measure that’s supposed to include an overlooked factor in the human experience with heat: humidity. That wetness in the air slows the evaporation of sweat off your skin—a key way of staying cool.

What made Steadman’s index successful was that the numbers felt right, in a literal sense. The heat index reads like a temperature, but it’s wobblier than that, a perception rooted in physiological reality. When two different combinations of heat and humidity result in the same heat index—say, 96 degrees Fahrenheit/50 percent humidity and 86 degrees/95 percent humidity, which both have a heat index of 108—this is meant to signal that the body in each scenario is under a similar level of stress as it tries to cool down. As the heat index rises, the miracle of internal thermoregulation that fixes our bodies at 98.6 degrees begins to crumble. Our core temperature rises, which starts off as unpleasant and then gets dangerous. There’s a roughly 10 degree window before all the chemistry that sustains life begins to fail. That means death.

But there’s a problem with Steadman’s calculations: They weren’t actually built to handle those sorts of extreme conditions. At a certain threshold—one that includes a plausibly steamy combination of 80 percent humidity and 88 degrees Fahrenheit—the heat index veers into predicting what David Romps, a physicist and climate scientist at the University of California, Berkeley, calls “unphysical conditions” that rarely happen in the lower parts of atmosphere. This includes supersaturated air making contact with the skin—that is, air that’s more than 100 percent saturated with water.

Temperature and humidity conditions beyond that threshold are somewhat rare—and when they do happen, it’s possible to extrapolate from Steadman’s model to come up with an estimated heat index value. But estimates are estimates, and those kinds of heat waves are becoming more common as temperatures rise. So Romps and his graduate student, Yi-Chuan Lu, began taking a look at the model’s fundamentals. They quickly realized that, for the long list of assumptions in the equations, certain things were missing. For one thing, there is a natural solution to the supersaturation problem: When the air is too wet for human sweat to evaporate, it can still bead and drip off the skin, providing some relief.