How did you learn about the world of the military?

Hathaway I was shown unbelievable generosity and openness by the Air Force, and I was taken to Creech Air Force Base. I was shown around and allowed to fly a simulator drone — sorry, R.P.A. [remotely piloted aircraft]. And then the next day I went to Nellis and was taken around the base there, and they really went out of their way to make sure I could speak with female fighter pilots. It grounded me in the humanity of the story.

Julie, you are known for your visual gifts — my colleague Ben Brantley has called you “the director who redefined spectacle on Broadway.” How do you start to think about a monologue?

Taymor I reduce everything when I’m working, even “Lion King,” to an ideograph — to the most simple image that represents the play or the character. In this case, I felt invulnerability. The beginning is a fighter pilot in a helmet, and whatever mortars or bombs, in this case represented by sand falling, it bounces off. It bounces off her as she stands there in front of a black mirror that is endless.

Like you said, I’m known for spectacle, and there is a derogatory attitude in that sentence. In the world of France, spectacle is theater, le spectacle. Spectacle in our culture takes second place to the spoken word. And that is a big mistake. It’s not spectacle as in Barnum and Bailey spectacle. It’s there to give theatrical depth. The idea of visuals has been very maligned in our culture, to think that it’s second place to the script. It’s a complete knitting together when it’s done well. It’s not one more than the other. It’s there to give a visceral experience to the words.

One idea in the play is that we’re all being watched all the time. Anne, you are someone who is watched all the time — at the end of the performance I saw a woman whip out her phone to take your picture. What’s the resonance for you?

Hathaway The reason I was late today was because paparazzi appeared up where I live, and I can’t walk to work anymore because it’s a waste of everyone’s everything — I’m not breathing properly, I’m not able to run my lines, because I’ve got somebody with a camera in front of me. So there is that aspect of my life, but I’d rather not focus on me — I’d rather take it out of the specifics of when a celebrity loses their privacy and say we’re all losing our privacy. Everything is witnessed. I think about my nieces and nephews. They will have no idea what privacy really, really is, and I wonder if they’re going to care? Or if you’ve never had it, if you will have the ability to miss it.

Taymor What she’s saying in the end is bigger than that — bigger than Big Brother. It’s the idea that drones are going to be a part of our life. And we think of them, most people think of them, in a kind of Fisher-Price [way]. Wow — the pizza delivery. How great when the medicine can go to a place where there’s no medicine.