If someone had estimated that their risk was 50 percent and we told them, “Good news: The average likelihood is much better, only 30 percent,” the next time around they would say, “You know what? Maybe my likelihood is only 35 percent.”

However, if someone started off estimating their cancer risk was 10 percent and we told them, “Bad news: The average likelihood is about 30 percent,” they would scale up only gradually. The next time, they might say that their likelihood of contracting cancer was only 11 percent. It is not that they did not learn at all. They simply decided that the figures we provided were not pertinent to them.

This disconnect is related to something scientists call prediction errors, which describe the difference between what you expect and what actually happens.

When we gave our research volunteers information about future likelihoods, we scanned their brains looking for changes that might relate to the gap between their estimates and the information they received.

A few brain areas, including the left inferior frontal gyrus 1, responded to unexpected good news. For example, when someone thought his likelihood of cancer was 50 percent and we told him it was only 30 percent, this region responded fiercely.

On the other side of the brain, the right inferior frontal gyrus responded to unexpected bad news. But it did not do a very good job. In fact, the more optimistic a person was, the less this region seemed to process bad news.

These findings are striking: When people learn, their neurons encode desirable information that can enhance optimism, but the neurons fail at incorporating unexpectedly undesirable information.

Why would our brains be wired in a way that makes us prone to optimistic illusions? It is tempting to speculate that optimism was selected by evolution precisely because, on balance, positive expectations enhance the odds of survival.

Research findings that optimists live longer and are healthier, along with the fact that most humans display optimistic biases — and emerging data that optimism is linked to specific genes — all strongly support this hypothesis.

But the optimism bias also protects and inspires us: It keeps us moving forward, rather than to the nearest high-rise ledge. To make progress, we need to be able to imagine a better reality, and we need to believe that we can achieve it. Such faith helps motivate us to pursue our goals.

Tali Sharot is a research fellow in cognitive, perceptual and brain sciences at University College London and author of “The Optimism Bias: A Tour of the Irrationally Positive Brain.” This article was excerpted from the new TED e-book “The Science of Optimism.”