"Is random truly random?"
Riku muttered while rolling a die. In the corner of the library, a quiet space with just the three of them.
"That's a philosophical question," Yuki looked up from a book.
Mira silently wrote something in her notebook and showed it to them. "Pseudo-random vs True random"
"Pseudo-random and true random?"
Riku stared at the die. "Is this true random?"
"Physically, if initial conditions are determined, the result is determined too. But initial conditions are too complex to predict, so it appears effectively random," Yuki explained.
"What about computers?"
Mira wrote again. "Deterministic algorithm. Looks random."
"A deterministic algorithm, but it looks random," Yuki translated.
Riku tilted his head. "So randomness is ultimately a product of ignorance?"
"In a sense, yes. But that's what's important," Yuki opened a notebook. "In information theory, randomness is treated as an information source."
"Information source?"
"Precisely because it's unpredictable, there's information. If completely predictable, information content is zero."
Mira nodded and wrote a new equation. "H(X) = max when uniform distribution"
"Entropy is maximum for uniform distribution," Yuki supplemented. "Meaning when completely random, uncertainty is highest."
Riku rolled the die repeatedly. "But when you roll many times, it gets close to the average, right?"
"Law of large numbers," Yuki said. "As the number of trials increases, the sample average converges to the expected value."
"Random, yet predictable long-term?"
"Yes. Individual results are random, but collective behavior is stable."
Mira wrote again. "Monte Carlo simulation"
"Monte Carlo simulation," Yuki's eyes sparkled. "A method to solve complex problems using random sampling."
Riku showed interest. "How?"
"For example, estimating pi. Randomly plot points inside a square. From the proportion that fall inside a circle, you can calculate π."
"Random, yet you get an accurate answer?"
"Increase the number of trials, and precision improves. You use randomness to find deterministic values."
Riku was impressed. "Randomness is useful, huh."
Mira smiled and wrote. "Randomness is powerful tool"
Yuki continued. "It's also used in cryptography. Unpredictability guarantees security."
"So you need completely random numbers?"
"Ideally yes. But cryptographically secure pseudo-random numbers are often sufficient."
Riku stopped the die. "Don't randomness and determinism contradict?"
"Superficially they contradict. But in information theory, they coexist," Yuki explained. "Random processes can be deterministically modeled."
Mira wrote a longer sentence. "Randomness creates uncertainty. Uncertainty creates information. Information creates meaning."
"Randomness creates uncertainty, uncertainty creates information, information creates meaning," Yuki translated.
Riku's eyes widened. "Deep, Mira."
"She always strikes at the core," Yuki acknowledged.
Mira was about to close her notebook but wrote one more thing. "Life is random. But patterns emerge."
"Life is random. But patterns emerge."
Riku laughed. "So we don't have to give up even if things are random."
"Statistically speaking, effort increases the probability of reward," Yuki said.
"Increasing probability... that's a deterministic action."
Mira stood up and quietly left the room. As usual.
Riku stared at the die. "I think I understand what's important despite being random."
"Randomness itself enriches the world," Yuki concluded.
The die continues rolling quietly today. Each individual outcome is unpredictable, but the overall behavior is beautifully stable.