By Steve Kastenbaum, CNN Radio National Correspondent

Listen to CNN Radio's podcast from Steve Kastenbaum about the dangers of texting while walking.

The old joke about a not-so-bright person goes, “He’s so dumb, he can’t walk and chew gum at the same time.”

Very little thought goes into either task. But what happens if you combine walking and texting?

“People aren’t watching where they are walking. They’re texting, they’re on their cell phones, they have their iPods on, and they’re just not aware of their surroundings,” said Thomas Ripoli, the police chief in Fort Lee, New Jersey.

CNN Radio's Steve Kastenbaum reports on the potential dangers of texting

There has been an increase in the number of pedestrians struck by cars in his town this year. Four such incidents ended in death. So Ripoli went on a mission. He told his cops to look out for people who are not paying attention while crossing the street.

“Our focus is to make people aware of their surroundings and to keep their eyes focused on where they’re going,” Ripoli said.

Is texting while walking really dangerous, though? Most of us think we’re capable of doing more than one thing at once. Professor Earl Miller said that may be an illusion.

“We’re not wired to multitask well,” said Miller, a neuroscientist at the Massachusetts Institute of Technology. “So when people think they’re multitasking, they’re actually just switching from one task to another very rapidly. And every time they do, there’s a cognitive cost in doing so.”

In the case of texting while walking, Miller says that cost is potentially the loss of life.

“The danger is that you don’t see what’s coming. The same constraints that make it a bad idea to text while you drive make it a bad idea to text while you walk.”

His studies show that the brain has a limited capacity to take in information at any one time.

“It only takes in the world little bits and chunks at a time,” Miller said. You may think that you have a seamless thread of data coming in about the things going on around you, but according to Miller, the reality is your brain “picks and chooses and anticipates what it thinks is going to be important, what you should pay attention to.”

So if you text, or look at an iPad, or even just listen to music in your headphones while walking, your brain does not receive all the information it may need to keep you safe.

Texting while driving laws are becoming commonplace across the country. So far no one has passed a texting while walking law, but that could change. In New York, a state senator wants to ban using cell phones, iPods and other gadgets while crossing the street. A local lawmaker in Arkansas has proposed similar legislation.