Mokou knocked casually on the open door of Eirin's study, her other hand in the pocket of her trousers. "How's it going?"
Eirin glanced over her shoulder and nodded in acknowledgment. Her expression was calm: what had once been a bitter relationship between a vengeful earthling and genius Lunarian had eventually transformed into a mutual understanding and finally into an awkward friendship soon after princess Kaguya had settled into Gensokyo.
"I'm doing well, thank you for asking. The practice is flourishing, and I've come up with a superior archiving method for my old files." She gestured at the mountains of books and manuscripts around her. "I'm starting the new catalogue with these. It seems someone has misplaced the old one." She rubbed her forehead and sighed. "However, that's none of your concern. How are you?"
"Same old, same old. Seen Kaguya around? We were supposed to meet this afternoon."
"Another one of your 'brutally murdering each other for fun and out of spite' kind of meetings?"
"You got it."
Mokou bent forward and randomly picked up an ancient piece of yellowing manuscript sticking out from a book. She frowned as she recognised the text to be in Eirin's inhumanly tiny handwriting and more importantly, legible.
"I thought you encrypted all your important research?"
"Mm?" Eirin didn't even bother turning around. "Yes, that is true. Why do you ask?"
"No reason." Mokou kept reading. To her disappointment, she couldn't make much out of it: the paper was crammed full of ludicrously complex math formulae. She was willing to bet Eirin was one of the very few people in Gensokyo who could make anything out of it, let alone come up with it in the first place.
There was one thing she could read, however. At the very end of the manuscript, there was a hastily scribbled formula, far more simple than anything else on it.
"108 to the power of 108? What's this about?"
Eirin started to turn her head, then changed her mind and turned back to her work.
"If you're reading the paper I think you are, it's the number of resurrections the Hourai Elixir grants."
Mokou frowned and looked back at the manuscript. Then the words hit her and figuratively punched all the air out of her.
"...What?" she gasped.
"It's the number of resurrections the Hourai Elixir grants." Eirin repeated. She finally set her quill down and turned to Mokou.
Mokou opened her mouth, but no words came out. It was as if she was frozen, both mind and body, by the sheer shock of the revelation.
Eirin sat in place patiently as she recomposed herself.
"But," she finally sputtered. "But but but..."
"Is there a problem?" Eirin asked calmly.
"But-" Mokou started again, her heart beating in her chest like a drum. Her mouth was dry, and her head felt like she hadn't eaten in weeks. "You mean, the resurrections can run out? That eventually the elixir's not gonna work?"
Eirin sighed again and picked up her quill. "Hypothetically, yes. There isn't a single thing in this universe that will last indefinitely. Even protons will eventually vanish, and like them, the elixir's effects will eventually degrade to the point where they will no longer be felt. However, the process takes so long as to be meaningless. 108 to the power of 108 resurrections might as well be infinite resurrections in common parlance."
Mokou didn't know how to respond. Finally, she asked: "What does 108 to the power of 108 even mean?
"Essentially, 4.07160456 times 10 to the power of 219," Eirin replied without missing a beat.
Mokou tried to imagine the figure in her head.
"That's gibberish to me."
Eirin gave her a blank stare turned around, searching for something to write on. Mokou couldn't see what she was doing, but she heard furious scribbling.
"There," Eirin said, handing a piece of paper over to her. "that is the exact number of resurrections the Hourai Elixir grants."
Mokou wrested the piece of paper from her hand and started reading: "Four-zero-seven-one-six-"
Eirin quirked an eyebrow. "Are you going to read the whole thing out loud?"
Mokou fell silent and instead looked at the figure, going through it from left to right, right to left, up and down, down and up, trying to grasp the ridiculous number and its impact on her life.
"If you want," said Eirin, reaching out for a large book on top of one of the piles on the floor, "I will explain to you the process of degradation and how-"
She turned around to see that Mokou was gone, with nothing but the sound of rapidly receding footsteps.
"Come again?" Kaguya blinked at her like she had never been in sunlight before.
"You didn't know?" Mokou gasped incredulously. Her breath was ragged: she had dashed around Eientei like a woman possessed before finally managing to stumble upon Kaguya outside the mansion.
"Of course not!" Kaguya fell silent, her face was a mask. Only a slight trembling of her hands revealed she was moved on some level.
"How many?" she asked quietly.
"108 to the power of 108."
Mokou could practically see the cogs inside Kaguya's head moving as she tried to wrap her mind around the figure.
"What is that?"
Silently, Mokou handed over the crumbled piece of paper the full figure was written on.
Kaguya straightened the paper and boggled at it just like Mokou had. "4071604564769-"
"Save your breath," Mokou snapped.
Kaguya ignored her and continued stubbornly: "-711221188954455263345246108162335997753967475804 29609457724019890312913685897885530534179482299921 05732456302014169855410209490127305567743365233419 53563223103240077385090699521634068197196328203189 869346816." She looked at Mokou, her eyes as glazed as Mokou's felt like.
"Impossible," she finally said, shaking her head. "There's no way we could ever die that many times, even if we spent all our waking hours killing each other."
Mokou snorted. "You're just too lazy. It's not like we have to do it all at once. I mean, say we kill each twenty times a day for a thousand years-"
"That's not even a fraction of the resurrections we need to get rid of."
"I know that! But say, if we keep doing it for a million years-"
Kaguya gave Mokou a look of mock pity. "You really have no idea of how much 108 to the power of 108 truly is, have you?"
"Oh yeah? And since when have you been such a math whizz?" Mokou asked rather hotly.
"Eirin's showed me some stuff in the past. I didn't pay much attention, but I still know more than you. We could keep going for a billion years and it wouldn't be anywhere near enough." She shrugged. "Forget it. Even if there is some distant limit to our resurrections, we're still immortal for all intents and purposes." She sneered at Mokou. "I suppose someone like you would try to grasp at every possible straw. Learn a little dignity, desperation doesn't suit you in the slightest."
"Shut your face!" Mokou threw a violent punch at Kaguya. The Lunarian sidestepped the attack and chuckled.
"My, don't we get easily riled up today? I already know all of your moves. You can't surprise with crude attacks like-"
Her taunting was interrupted by a sharp punch that hit her squarely in the jaw. She staggered backwards, coughing blood.
Mokou pulled her fist back, her knuckles sore after the impact, and glared at Kaguya.
"I know all of your moves too. You always let your guard down when you think you're being clever."
"You...You brute!" Kaguya's eyes narrowed into tiny slits. "Well, if you're so eager to die..." She rose to the sky and spread her arms. Several glowing magic circles appeared around her.
"Oh yeah? Likewise!" Mokou summoned her aura, the ever-burning fiery mantle of a phoenix, and launched herself into the air. She summoned a large fireball in between her hands. "And none of that spellcard bullshit! Fight properly!" She aimed the fireball at Kaguya's head and send it off.
Kaguya pulled the Jewelled Branch of Hourai from inside the sleeve of her blouse and placed it in front of the approaching fireball. As soon as the fireball came in contact with the branch, it evaporated into smoke.
"It's not my fault I'm not as pathetically feeble as you and won't die from simple ritual duels."
Mokou growled. "I'm going to wipe that smirk right off your face!"
"Bring it on!"
"I've been thinking..."
"Yeah? Must be a first."
"Be quiet for once. About what you said earlier. That there is a limit to the Hourai Elixir. About the 108 to the power of 108 resurrections."
Mokou said nothing, but glared at Kaguya as to make her get on with it.
"I mean, we won't be able to whittle all those resurrections away no matter what we do, but...at some point, far, far into the future, they will run out. It'll take an eternity, but it's not like we're going anywhere. We'll exist through that eternity. And then..."
Mokou made an appreciative grunt. "You're finally starting to make sense."
"I wasn't done yet. Anyway, 108 to the power of 108...I doubt we'll be able to die that many times before the world ends. Then what? We'll float around in nothingness, suffocating to death, unless the lack of air pressure gets us first. And every time we're resurrected, we'll die immediately again, because it's not like our lungs will be magically refilled with air when we are reborn." She lazily turned her head and looked directly at Mokou. "And if what you said is true, after an eternity of torture our 108 to the power of 108 resurrections will run out."She closed her eyes and took a deep breath. "And then we will be free."
"Yeah." Mokou looked up at the sky. Fluffy white clouds were slowly making their way across the clear blue sky. She reached her hand out towards them and closed it into a fist, as if grabbing one of them. "I wonder what will happen to us once we finally die."
"What do you mean? The same as to everyone else, I suppose."
"Will there be an afterlife left for us to go to after all that time?"
They lied still for a while, looking at the clouds. Eventually, Kaguya pushed herself into a sitting position.
"Care for another round? Every death takes off a couple of seconds out of our final torment."
Mokou shook her head. "Not yet. My chest really hurts where your stupid Jewelled Branch hit me."
"Suit yourself." Suddenly, Kaguya smiled. "It's not like there's any rush, we have all the time in the world."
Mokou closed her eyes and let the gentle summer breeze wash over her body. Funny how even after all these years, resting outside on a warm day still felt as good as it had felt back when she had still been mortal.
"That's right. All the time in the world."