Enter David Dinges, the head of the Sleep and Chronobiology Laboratory at the Hospital at University of Pennsylvania, who has the distinction of depriving more people of sleep than perhaps anyone in the world.

In what was the longest sleep-restriction study of its kind, Dinges and his lead author, Hans Van Dongen, assigned dozens of subjects to three different groups for their 2003 study: some slept four hours, others six hours and others, for the lucky control group, eight hours — for two weeks in the lab. 

Every two hours during the day, the researchers tested the subjects’ ability to sustain attention with what’s known as the psychomotor vigilance task, or P.V.T., considered a gold standard of sleepiness measures. During the P.V.T., the men and women sat in front of computer screens for 10-minute periods, pressing the space bar as soon as they saw a flash of numbers at random intervals. Even a half-second response delay suggests a lapse into sleepiness, known as a microsleep. 

The P.V.T. is tedious but simple if you’ve been sleeping well. It measures the sustained attention that is vital for pilots, truck drivers, astronauts. Attention is also key for focusing during long meetings; for reading a paragraph just once, instead of five times; for driving a car. It takes the equivalent of only a two-second lapse for a driver to veer into oncoming traffic. 

Not surprisingly, those who had eight hours of sleep hardly had any attention lapses and no cognitive declines over the 14 days of the study. What was interesting was that those in the four- and six-hour groups had P.V.T. results that declined steadily with almost each passing day. Though the four-hour subjects performed far worse, the six-hour group also consistently fell off-task. By the sixth day, 25 percent of the six-hour group was falling asleep at the computer. And at the end of the study, they were lapsing fives times as much as they did the first day. 

The six-hour subjects fared no better — steadily declining over the two weeks — on a test of working memory in which they had to remember numbers and symbols and substitute one for the other. The same was true for an addition-subtraction task that measures speed and accuracy. All told, by the end of two weeks, the six-hour sleepers were as impaired as those who, in another Dinges study, had been sleep-deprived for 24 hours straight — the cognitive equivalent of being legally drunk. 

So, for most of us, eight hours of sleep is excellent and six hours is no good, but what about if we split the difference? What is the threshold below which cognitive function begins to flag? While Dinges’s study was under way, his colleague Gregory Belenky, then director of the division of neuroscience at the Walter Reed Army Institute of Research in Silver Spring, Md., was running a similar study. He purposely restricted his subjects to odd numbers of sleep hours — three, five, seven and nine hours — so that together the studies would offer a fuller picture of sleep-restriction. 

Belenky’s nine-hour subjects performed much like Dinges’s eight-hour ones. But in the seven-hour group, their response time on the P.V.T. slowed and continued to do so for three days, before stabilizing at lower levels than when they started. Americans average 6.9 hours on weeknights, according to the National Sleep Foundation. 

Which means that, whether we like it or not, we are not thinking as clearly as we could be.

Of course our lives are more stimulating than a sleep lab: we have coffee, bright lights, the social buzz of the office, all of which work as “countermeasures” to sleepiness. They can do the job for only so long, however. As Belenky, who now heads up the Sleep and Performance Research Center at Washington State University, 

Spokane, where Van Dongen is also a professor, told me about cognitive deficits: “You don’t see it the first day. But you do in five to seven days. Unless you’re doing work that doesn’t require much thought, you are trading time awake at the expense of performance.” 

And it’s not clear that we can rely on weekends to make up for sleep deprivation. Dinges is now running a long-term sleep restriction and recovery study to see how many nights we need to erase our sleep debt. But past studies suggest that, at least in many cases, one night alone won’t do it. 

Not every sleeper is the same, of course: Dinges has found that some people who need eight hours will immediately feel the wallop of one four-hour night, while other eight-hour sleepers can handle several four-hour nights before their performance deteriorates. (But deteriorate it will.) There is a small portion of the population — he estimates it at around 5 percent or even less — who, for what researchers think may be genetic reasons, can maintain their performance with five or fewer hours of sleep. (There is also a small percentage who require 9 or 10 hours.) 

Still, while it’s tempting to believe we can train ourselves to be among the five-hour group — we can’t, Dinges says — or that we are naturally those five-hour sleepers, consider a key finding from Van Dongen and Dinges’s study: after just a few days, the four- and six-hour group reported that, yes, they were slightly sleepy. But they insisted they had adjusted to their new state. Even 14 days into the study, they said sleepiness was not affecting them. In fact, their performance had tanked. In other words, the sleep-deprived among us are lousy judges of our own sleep needs. We are not nearly as sharp as we think we are.