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Among the many changes President Obama called for today to prevent future school shootings and other gun violence were four measures to strengthen background checks to keep guns out of the hands of dangerous people. NPR's science correspondent Shankar Vedantam has been tracking the history of our efforts to keep guns out of the hands of specifically the mentally ill. And he joins us in the studio now. Shankar, welcome.

SHANKAR VEDANTAM, BYLINE: Hello, Audie.

CORNISH: So to start - to many Americans, this might seem straightforward - when someone is deeply troubled and their parents or teachers know something is wrong, that there ought to be some way to keep that person from owning weapons. But why is this difficult?

VEDANTAM: You know, once a shooting takes place, Audie, it seems obvious that this person was troubled and shouldn't have been allowed to own guns. But, in fact, in real time, it's very hard to identify these people. If you look at recent cases of mass shooters - Seung-Hui Cho, who was the shooter in Virginia Tech, or Jared Loughner, who was the shooter in Arizona, or even James Holmes was the shooter in Colorado - experts have reached very different conclusions about how troubled these individuals were.

The truth is there are very large number of people who could potentially commit violence and a very small number of people who actually do, and science does not have a very good way of spotting the needles in the haystacks. And you can see this reflected in the policy, because if you look at the national language we use to keep guns out of the hands of dangerous people, we say people who are mentally defective are not supposed to have their hands on guns. That isn't just a crude term. It's a very imprecise term.

CORNISH: And the National Instant Criminal Background Check System, right now, the president says he wants to change it to make sure that instead of just applying to dealers that have to run these checks, that it would apply to anyone selling a gun, say, people at gun shows as well. Would this solve the problem?

VEDANTAM: Well, it would certainly address a loophole in the current system, which is that 40 percent of guns are sold outside of dealerships. But remember, the current system relies on states reporting cases to the federal database, cases where they have involuntarily committed a patient who seems really troubled to psychiatric care. Many states end up not reporting their cases to the federal government. They have different reporting standards. They also have different standards in terms of thresholds about what constitutes somebody who is dangerous enough to be kept from owning weapons.

Now, even if you could get all of the states to cooperate, there are a couple of really big problems. I spoke with James Jacobs. He's a Columbia University law professor. He notes that most people with serious mental illnesses get treated voluntarily. They don't get treated involuntarily. And if you're treated voluntarily, you don't end up in this federal database.

The second big problem is there are 300 million guns in circulation in the United States today. Think about it this way. Imagine there's a swimming pool that has 300 million drops of water, and every drop of water is a gun. Next to that swimming pool is another pool - and this also has 300 million drops - but now, each of these drops is a person - that's the population of the United States. What we've done in this country is mix these two swimming pools together.

You now have 600 million drops sloshing around. Somewhere in there is the next Adam Lanza. Somewhere in there is the next gun that's going to get used in a mass shooting. Most of the current background check system only addresses new guns coming into the system. The idea that it can prevent one of those Adam Lanzas from getting access to one of those guns really seems fanciful.

CORNISH: Now, as the president notes, there are many other aspects of gun violence besides mass shootings. I mean, he's looking at better background checks that would essentially help reduce street corner homicides and suicides. But it seems as though you're saying that when it comes to mass shootings, there's a question here about the affects.

VEDANTAM: Well, I think when it comes to mass shootings, the truth is we really don't know. We know when the system breaks down. We don't know when the system works. We don't know when the system has kept guns out of the hands of somebody who could have become a mass shooter. Every time there's a mass shooting, the intuitively appealing thing to do is to focus on background checks and focus on people with mental illness. These seem to be the lowest hanging fruits.

The truth is there isn't a lot of leverage here because of the number of guns that are sloshing around the system. Now, it's possible that policies that affect guns in general, or that restrict access to high-capacity magazines in general, could potentially have an effect. But the idea that you can single out dangerous people and keep guns away from them, that's really a stretch when you look at the scientific data.

One way we have to evaluate many of these policies is to ask would the policies have made a difference to the shooters who we've had in recent memory. Seung-Hui Cho, Jared Loughner, James Holmes all bought their guns legally from dealers. The Columbine shooters and Adam Lanza in Connecticut didn't buy their guns at all. They just took their guns from relatives, and they would have been completely outside this factual evaluation system.

CORNISH: That's NPR's science correspondent Shankar Vedantam. Shankar, thank you for speaking with us.

Thanks, Audie. Transcript provided by NPR, Copyright NPR.