Arianna Huffington talks often about how the key to her productivity is sleep.

It's a smart suggestion, not least because so many of us still imagine that the more we work, the more productive we are. For over a hundred years or more, this has been deemed nonsense.

The first productivity studies were conducted by Ernst Abbe at the Zeiss lens laboratories in the 1880s. They indicated what every other productivity study has shown since: that, up to around 40 hours a week, we're all pretty productive but, after that, we become less able to deliver reliable, cost-effective work. Why? Because when we get tired, we make mistakes—and the extra hours we put in are absorbed by correcting our errors. This is demonstrably true in industries like software coding, in which mistakes can cost a lot of time to put right. But it is equally true in manufacturing where more units of production also mean more flaws and waste.

Even though the data around productivity has proved pretty remorseless, humans have found the message hard to accept. It seems so logical that two units of work will produce twice the output. Logical but wrong. The critical measure of work isn't and never should be input but output. What matters isn't how many hours your team puts in, but the quality and quantity of work they produce.

Which is where sleep comes in. Although we might all like to imagine that we can work happily through the night, once again the data's all against us. Lose just one night's sleep and your cognitive capacity is roughly the same as being over the alcohol limit. Yet we regularly hail as heroes the executives who take the red eye, jump into a rental car, and zoom down the highway to the next meeting. Would we, I wonder, be so impressed if they arrived drunk?

The reason sleep is so important is because fatigue isn't simple. When we are tired, our performance doesn't degrade equally. Instead, when you lose a night's sleep, the parietal and occipital lobes in your brain become less active. The parietal lobe integrates information from the senses and is involved in our knowledge of numbers and manipulation of objects. The occipital lobe is involved in visual processing. So the parts of our mind responsible for understanding the world and the data around us start to slow down. This is because the brain is prioritizing the thalamus—the part of your brain responsible for keeping you awake. In evolutionary terms, this makes sense. If you're driven to find food, you need to stay awake and search, not compare recipes.

After 24 hours of sleep deprivation, there is an overall reduction of six percent in glucose reaching the brain. (That's why you crave donuts and candy.) But the loss isn't shared equally; the parietal lobe and the prefrontal cortex lose 12 percent to 14 percent of their glucose. And those are the areas we most need for thinking: for distinguishing between ideas, for social control, and to be able to tell the difference between good and bad.

I've sat in many boardrooms through the night, at the end of which seriously bad deals were done, I've seen the cost of sleep deprivation. Not just in bad tempers, bad diets, and bad decisions. But in the loss of truly productive work and discussion that could have been less heroic but a lot more valuable.