In this scene, the Doctor's nemesis, the only other Time Lord in existance called the Master, has subdued Earth and is only a minute or two away from using it as a launching point of ships and weapons designed to subdue the rest of the universe. He's kept the Earth under his control by inducing fear in her inhabitants through a set of telepathic satellites orbiting the planet. He's also about to execute recently capture Martha Jones (the Doctors current companion) in front of the Doctor, who's been his prisoner and is a shadow of his original self. The Master thinks he's got it all it now, a future of power and dominion all at his control.
But Martha starts to laugh. The Master lowers his weapon as she begins to tells him her capture was not a coincidence, that she and the Doctor planned it this way so that she would be there at just this time.
Master: But you're still going to die.
Martha: Do you want to know what I was doing, traveling the world?
The Master rolls his eyes, and says sarcastically--
Master: Tell me.
Martha: I told a story, that's all. No weapons. Just words. I did just what the Doctor said. I went across the continents all on my own. And everywhere I went I found the people and I told them my story.
We flash back to a time when she spoke to a group of surviors huddle in a house when Martha told them: "He saved your life so many times and you never even knew he was there. I know him."
Martha: I told them about the Doctor.
We flash back again as Martha continued her story to the surviors: "I love him."
Martha: And I told them to pass it on, to spread the word so that everyone would know about the Doctor.
Master (sarcastically): Faith and hope? Is that all?!
Martha's smile grows and she starts to stand up.
Martha: No, because I gave them an instruction, just as the Doctor said.
Another flash back to the Doctor whispering in Martha's ear: "Use the countdown."
Martha: I told them that if everyone thinks of one word at one specific time--
Master: --Nothing will happen. Is that your weapon: Prayer?!
Martha: Right across the world, one word, just one thought at one moment. . .
Martha pauses and her smile grows--
Martha: But with 15 satellites . . .
The Master eyes widen.
Jack (friend of the Doctor and Marth): The Archangel Network.
Martha: A telephathic field binding the whole human race together, all of them, every single person on Earth thinking the same thing at the same time--and that word is Doctor.
At that moment, the countdown reaches 0 and the Doctor starts to transform. Blue ethereal light surrounds him. We see the people in the room and across the Earth start saying the Doctor's name. He transforms back into his original self. He floats slowly towards the Master, who tries to shoot him, but the light protects him. The Master shrinks back as the Doctor approaches, his face sad.
Doctor: I'm sorry. I'm so sorry.
The Master is now deeply afraid and continues to back away.
Master: You can't do this. You can't do this. No! It's not fair.
Doctor: And you know what happens now.
Realizing he can't kill the Doctor, he tries to shoot others in the room, but the Doctor telepathically knocks the weapon out of his hand and across the room. The Master continues to back away, finally crumbling against a wall.
Master: No! No! No! No!
Doctor: You wouldn't listen. Because you know what I'm going to say.
The Doctor lowers to the floor and walks over to the Master, who's curled over on the floor. The Doctor's face is peaceful as he embraces the Master in his arms and holds him close. Then he says something extraordinary, something that the Master in all his evil and anger can't bear to hear--
Doctor: I forgive you.
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