Chapter 15: Hilbert's Hotel
As the group stood in the Guild, Zara activated her system world map. A shimmering hologram appeared before them, displaying countless locations across the Forgotten Realm. She tapped on a glowing marker labeled "Hilbert's Hotel."
"This is the place," Zara said. "I can teleport us directly there, but once we arrive, be prepared for... unusual experiences."
With a swipe of her hand, a portal materialized, swirling with silver and black energy. It hummed softly, inviting them to step through. Nathan hesitated, but Emily gave him a reassuring nod. Together, they entered the portal, followed by Zara, Mia, and Lily.
The portal deposited them in front of a massive structure. Hilbert's Hotel loomed before them, a breathtaking building of black obsidian and shimmering silver. Its architecture was otherworldly, with spiraling towers and endless corridors that seemed to defy the laws of geometry. Doors stretched infinitely in both directions, each glowing faintly with golden numbers.
"Wow," Emily whispered. "It's... massive."
"And strange," Nathan added, staring at a door that flickered between the numbers 1 and infinity.
A system notification popped up before Nathan and Emily:
Quest Update: Discover the secrets of Hilbert's Hotel. Objective: Understand the implications of infinity in a finite reality. Reward: 20 system points.
The group entered the hotel lobby, which was equally grand. Marble floors reflected the ceiling, a vast tapestry of stars. Behind the reception desk stood a prim clerk, adjusting his tie and smiling warmly.
"Welcome to Hilbert's Hotel," he said. "How may I assist you?"
Nathan stepped forward. "We'd like some rooms, please."
The clerk tilted his head. "Ah, I must inform you that all our rooms are currently occupied."
Nathan frowned. "Then how can we stay here?"
The clerk beamed. "Not to worry, young man. We have an infinite number of rooms, and therefore plenty of vacancies."
"Wait," Emily said, confused. "If all the rooms are full, how can there still be vacancies?"
The clerk chuckled. "Allow me to demonstrate."
He rang a bell, and suddenly the intercom buzzed with an announcement. "Attention guests! Please move from your current room to the next one up. If you are in Room 1, please move to Room 2; Room 2, move to Room 3, and so on."
Doors began opening along the infinite corridors, and guests shuffled from one room to the next. Moments later, the clerk turned back to them. "There you go—Room 1 is now available."
Nathan blinked. "But what about the person in Room 1?"
"Moved to Room 2," the clerk replied.
"And the person in Room 2?"
"Moved to Room 3." The clerk grinned. "You see, in an infinite hotel, there's always room for more."
The group exchanged puzzled looks. "That doesn't make sense," Emily muttered.
The group was shown to their "vacant" room but soon decided to test the hotel further.
"What happens if someone checks out?" Mia asked.
"Let's see," Zara said, pressing the intercom. "Let's ask all guests in even-numbered rooms to check out."
The intercom buzzed, and the hotel erupted into movement. Doors slammed, guests vanished, and within minutes, only odd-numbered rooms were occupied.
"Now the hotel is half-empty," Lily said.
"But," Nathan pointed out, "it still has the same number of rooms—an infinite number!"
The absurdities continued as the group tested more scenarios:
They asked the clerk to fill only the first 100 rooms while keeping the rest vacant. The clerk complied instantly, yet the hotel still had infinite rooms.
They requested every guest to move into a room double their current number, leaving all odd-numbered rooms vacant—yet the hotel remained full with the same infinity of guests.
Each time, the results defied logic. "It's like trying to count forever," Emily said. "You never actually finish."
As the experiments continued, Nathan suddenly paused. "Wait a second," he said. "This whole thing is absurd. It doesn't make any sense."
"Exactly," Zara said. "And that's the point. An actual infinite can't exist in the real world—it leads to contradictions like this. That's why the past can't be infinite. The universe must have had a beginning."
Emily's eyes widened. "If the universe had no beginning, it would be like Hilbert's Hotel. Always full, yet always able to add more. That's... impossible."
"And," Mia added, "if the universe had no beginning, we'd never get to the present moment. It would be like trying to count down from infinity—you'd never arrive."
Nathan nodded, his excitement growing. "It's like trying to run a race where the finish line keeps moving further away. You'd never finish."
A system notification appeared before Nathan and Emily:
Quest Complete: Discover the secrets of Hilbert's Hotel. > Rewards: 20 system points earned.
Zara activated her world map again, and a portal to the Guild appeared. The group stepped through, their minds buzzing with new understanding. As they arrived back in front of the Guild, Nathan turned to Emily.
"I think we're starting to piece this together," he said. "The Cause must exist beyond time and space—because time and space couldn't be infinite."
Emily nodded. "We're getting closer to the truth."
Their next stop was Old Man Reggie, ready to share their findings and take on whatever challenge awaited them next.