Mathematics

Element n. 11. Mathematics: an entity that satisfies all the conditions of belonging to a given set.

^..^

The Doctor lunged to his feet, with Mike a beat behind pulling up Lady Toshana with him, and ran over to the door of Rose's isolation booth. She stood, hands still bound behind her with the electrical tie, and met her husband's eyes at last. "I'm sorry. I messed it up. I didn't stay put like you asked."

He stared at her, incredulous that she was focusing on that bit at that moment. "Are you kidding? No, Rose, you didn't mess it up. If it hadn't been for you, we would have lost." He flashed her his old grin. "Besides, you wouldn't be the woman I love if you weren't jeopardy friendly." Then the screeching alarm caught his attention again. "Oh my god. It's going into overload. We've got to get you out of there!"

Mike had run up to the other door, reading the gauges through the glass. "We've got about two minutes before the radiation floods the booths." The Doctor pulled out his sonic screwdriver to whiz open her door, but Mike grabbed his arm. "You can't. It'll open the circuit and the entire room will be flooded! We'll all be fried!" He winced at his own bad choice of words as the others glared at him.

The Doctor took a deep breath. "Then there's only one way to get her out." He started to move past Mike to the other booth, but Rose cried out, stopping him.

"No! No, Mike don't let him! NOOO!" She began looking around at her controls, trying to figure out what to hit with her elbow to speed up the end.

"Rose! No, stop!" he twisted back to her door, desperate. "Please, love, no! You won't survive – you can't survive. I can."

She looked at him, tragic. "No, you won't!" she sobbed. "You'll regenerate. And everything you are, everything that makes you my husband, will die. Please, John. Don't end our marriage this way. I could never live with myself if you kill yourself to save me. I couldn't go on. Please, Doctor. Please!"

He shook his head. "You expect me to just let you die? Rose, how can I do that?"

"Oh, and you're the only one in this room who can survive it?" came a new voice from behind him, calm and dry as toast.

He froze for an instant, then swiveled around to face the speaker: Lady Toshana. She looked at him, a hint of sympathetic pain flickering in her eyes. "I think you've been alone for far too long, my son."

He swallowed. "You'll regenerate," he warned, a bit inanely.

"Good!" came her reply. "I've worn this face too long. Thanks to this incredibly brave young woman," she flashed a smile at Donna, "against all odds, I have a chance for a new life. I think a new face to go along with it is quite appropriate." She stepped past Mike into the other booth, brushing him back with a smile, and he gallantly closed the door behind her. "Rose, is it?" The younger woman nodded, and Lady Toshana pushed the red button, switching the door locks. "Out you go."

She looked at the dials; about a minute to go. Taking a deep breath, she looked sideways at her son, who had pulled his wife out and was holding her tightly, tears streaming down both their faces, as Donna sawed at the bindings with a pair of scissors she'd found on a nearby desk. "I take it this is going to hurt," she said drily sideways to Mike, still at the door.

"Yeah," he agreed, shaky but matching her light tone.

"Well, I will remind you, I did bear you – and I even did it the old fashioned way. Although, I will admit to being glad that at the time, there was only one of you." They shared a shaky but ironic smile – and then the alarm shrieked itself into high gear, announcing the radiation surge. She stiffened, bracing herself – and then screamed as a wave of pain sliced through her every nerve and cell, blistering and burning through to her core. She collapsed onto the floor in a heap as the Doctor whirled back to her door, Rose and Donna crowding behind. While the four of them watched agonizingly through the glass, she jerked and moaned for an endless minute. Then, as it seemed to start to ease, the alarm finally shut off, along with all the lights in the booths – and sparks flew from the controls. A loud double click sounded in the sudden silence. The Doctor reached tentatively for the door handle, then snatched it wide when he discovered it unlocked.

"Is the radiation gone?" asked Mike. His human-dulled senses couldn't quite catch it anymore.

"Yes. She's absorbed it all," came the Doctor's choked, guilty reply. He gently pulled his mother into his arms, picking her up and carrying her out to the center of the room, then he melted down to the floor with her, holding her close.

Rose and Donna stood close together, arms around each other, watching the pair on the floor. Mike walked slowly over to the step under the ruined Gate and sat heavily, his head melting down onto his hands. After a moment, he felt Donna's presence beside him, and she reached for his hand. He resisted for a moment, then let her take it. "I'm sorry," he whispered.

"For what?" she quietly asked, puzzled.

"I'm sorry you were stuck with the dud." He couldn't articulate more than that.

"What in the world are you talking about?"

He raised his head, but couldn't look at her. "I used the Gate first. I was just trying to... take the edge off everyone. Just tone down the aggression and fear all over the world, just a bit. But it went too far. It let the Master take over."

The Doctor looked up at his twin. "No, that doesn't work. You can't just tweak anyone's psychology a tiny bit, let alone an entire planet's worth – you throw everything out of balance, and there's just no way to predict what will happen." He watched for a moment, as Mike shook his head, feeling guilty as sin. "So you made a mistake, Mike. So what?" He grimaced. "You think you have to be perfect or something? I thought I was the one with the god complex." As his twin continued to stare at him, he thought back to his realization a few minutes before (was that all it was?), of how his own harsh words all those years ago had wounded his brother so deeply. "Mike... I'm sorry."

Mike shook his head. "Isn't that my line? I'm the one who..." he couldn't say it.

The Doctor didn't have the same problem. "Committed genocide?" Mike nodded. "And I couldn't forgive you for it," continued the Doctor softly. "Not then. But that was a long time ago. I never told you... you were right. It was the only real solution. Nothing less would have ended that war. We've seen what a single Dalek can do. You were right to leave none alive to come back. Mike... I forgave you a long time ago. I'm sorry I never told you till now." There was more that could be said, but Lady Toshana began to stir and moan, and he dropped his eyes to her again.

Mike closed his eyes against unexpected, stinging tears, and Donna squeezed his hand. "Listen, you," she whispered for his ears alone. "You're not a dud. I never wanted to marry the Doctor, or anyone else. I wanted you, and I still do – and I always will." He squeezed her hand back, and she put her head on his shoulder, tenderly breathing with him.

Lady Toshana gasped shakily. Her eyes flew open, and she held her hands up before her to see the old familiar golden sheen sparkle across her fingers, repairing the radiation burns. "It's starting! Put me down!"

The Doctor gently eased her to the floor and shuffled back a pace on his knees, giving her room, and Rose dropped to her own knees beside him. Their hands met automatically, interlacing fingers as they had a million times through the years, and would a million more.

The Time Lady cried out as regeneration hit for real, the Vortex energy bursting through her skin and streaming out, rebuilding her from the inside, then fading quickly away. She collapsed back again, moaning softly, then gathered herself up, abruptly feeling more lively and energetic than she had in centuries. A shiver of the sheer joy of living shimmied through her, and she gave her son a broad smile, then set about examining her new self: slender, shapely hands; slim, athletic figure. She put her hands to her head, bringing down and around silky locks of long, bright ginger hair.

Bright... ginger...

The Doctor's face twisted. "Aw, that's just not fair!" he whined.