Since Edward Snowden’s revelations about government surveillence, we know more about how the National Security Agency has been interpreting Section 215 of the Patriot Act and Section 702 of the Foreign Intelligence Surveillance Act. We’ve learned some new words —“bulk metadata,” “selector,” “reasonable articulable suspicion,” “emphatic-access restriction”—but we don’t really know how much of this works in practice.

The intelligence community isn’t used to explaining itself in public, but over the past few months, with much prodding by Congress and the press, it has taken some small, tentative steps. Last week, I spent an hour with General Keith B. Alexander, who retired in March after eight years as the director of the N.S.A. The forces pushing for omnivorous data collection are larger than any one person, but General Alexander’s role has been significant. We met on Wednesday morning, in the conference room of a public-relations firm in the Flatiron District. He is a tall man with a firm handshake and steady eyes who speaks rapidly and directly.

Here are excerpts from the interview.

In January, President Obama claimed that the N.S.A. bulk-metadata program has disrupted fifty-four terrorist plots. Senator Patrick Leahy said the real number is zero. There’s a big difference between fifty-four and zero.

Those [fifty-four events] were plots, funding, and giving money—like the Basaaly Moalin case, where the guy is giving money to someone to go and do an attack. [Note: Moalin’s case is awaiting appeal.] It’s fifty-four different events like that, where two programs—the metadata program and the 702 program—had some play.

I was trying to think of the best way to illustrate what the intelligence people are trying to do. You know “Wheel of Fortune”? Here’s the deal: I’m going to give you a set of big, long words to put on there. Then I’m going to give you some tools to guess the words. You get to pick a vowel or a consonant—one letter. There’s a hundred letters up there. You’ll say, I don’t have a clue. O.K., so you’ve used your first tool in analysis. What the intelligence analysts are doing is using those tools to build the letters, to help understand what the plot is. This is one of those tools. It’s not the only tool. And, at times, it may not be the best tool. It evolved from 9/11, when we didn’t have a tool that helped us connect the dots between foreign and domestic.

Around 9/11, we intercepted some of [the hijackers’] calls, but we couldn’t see where they came from. So guys like [Khalid al-]Mihdhar, [one of the 9/11 hijackers who was living] in California—we knew he was calling people connected to Al Qaeda in Yemen. But we thought he was in the Middle East. We had no way to connect the dots. If you rewound 9/11, what you would have done is tipped the F.B.I. that a guy who is planning a terrorist attack is in San Diego. You may have found the other three groups that were with him.

The C.I.A. could have simply told the F.B.I. that al-Mindhar was in the country. Which they didn’t do, for whatever reason.

But, you see, not everybody is looking at the same picture. So you’re thinking, We’re solving this puzzle. C.I.A. is over here, solving this puzzle. There are a lot of these puzzles that many of us are trying to work. Thousands at any given time. You might ask: What’s the best way for you to figure out who bad guys are? I’m going to tell you there’s a bad guy. What would you start with? You’d say, Well, I need to know who his network for friends are, because chances are many of them are bad, too.

Metadata is the least intrusive, most efficient way to do it. You don’t want to translate millions and millions of calls; you want to get to the most efficient approach. Then, once you know that’s a terrorist, then you can go and get content. So how can you do that in the U.S.? The first thing that people will say is: if you take our data, you’re going to be looking at what we’re doing. You’ve entered into a huge debate—a constitutional debate. You’ve got the Fourth Amendment. So the Administration and Congress set up a program where all three branches of government agree to the approach, such that it comports with the Constitution.

[Earlier this year, the Privacy and Civil Liberties Oversight Board (P.C.L.O.B.) recommended that the N.S.A. reduce its ability to dig into a targeted number’s chain of contacts. Previously, analysts had three hops—they could see a target’s friends’ friends’ friends. The P.C.L.O.B. recommended reducing this to two hops—a target’s friends’ friends. President Obama agreed.] Are we less safe now with two hops than we were with three hops?

I don’t think so. You can always go to the court with a reasonable articulable suspicion (R.A.S.) on a number. You just have to go through another step. But I think it’s doable. So I actually agreed with that.

Let me give you another case: Najibullah Zazi. [Note: Zazi was one of three men who pled guilty to plotting to bomb the New York City subway in 2009.] This one is in Colorado. And so this gives you the 702 [program]. We’re tracking a guy who is doing e-mail with somebody. And we think, Oh, we think he’s in the U.S. They’re talking about making for a bomb.

Zazi is e-mailing about quantities and ingredients.

We get this e-mail, and there’s a number in that, and we see all that and we pass that to the F.B.I. We say, Doesn’t it look like there’s something there? And they come back and say, Zazi, that number’s his. He’s associated with them. Based on that, we were able to get R.A.S. on that number, get it approved, and see that Zazi’s talking to this guy Adis Medunjanin.

There are people on one side saying that these N.S.A. programs could have stopped these plots. And then there are people who dispute that.

We know we didn’t stop 9/11. People were trying, but they didn’t have the tools. This tool, we believed, would help them. Let’s look at what’s happening right now. You ought to get this from the START Program at the University of Maryland. They have the statistics on terrorist attacks. 2012 and 2013. The number of terrorist attacks in 2012—do you know how many there were globally?

How many?

Six thousand seven hundred and seventy-one. Over ten thousand people killed. In 2013, it would grow to over ten thousand terrorist attacks and over twenty thousand people killed. Now, how did we do in the United States and Europe? How do you feel here? Safe, right? I feel pretty safe.

But the P.C.L.O.B. said that there weren’t any more plots [that were disrupted by the N.S.A. programs]. I don’t know if these are things that couldn’t be shared.

They should have had access to those.

I imagined they would have.

Sometimes, people don’t ask all the right questions.… Going back to “Wheel of Fortune,” 702 is like getting the free vowels. It helps you get all the key things that you need. It’s the base program. And, then, all the rest of your things are one-offs. Like the [telephone-metadata program]. It’s going to give you a piece, but it’s probably not going to be the key piece. It’s a starting point.