"Riku, try guessing what you'll say next."
Aoi suddenly suggested.
"What? Impossible. I'm random," Riku laughed.
"Truly random?"
Yuki became interested in their conversation. "What do you mean?"
Aoi opened the notebook. "I've been observing Riku's behavior patterns. You're actually not that random."
"How rude! I'm free-spirited!"
"Free-spirited and truly random are different," Aoi said quietly. "Humans can seem random, but can't become true random numbers."
Yuki asked. "What are true random numbers?"
"Unpredictable sequences. You can't infer the future from past values."
Riku pondered. "So my behavior is predictable?"
"To some extent," Aoi showed a list. "Riku always goes to buy drinks at 3 PM. When stuck in conversation, you say 'well.' When problems are difficult, you touch your hair."
"You observe too much!" Riku blushed.
Yuki laughed. "True, Riku-senpai's habits are pretty obvious."
"This is the reduction of conditional entropy," Aoi explained. "If completely random, the next action is always uncertain. But with context or history, entropy decreases."
"Entropy decreases..." Yuki thought. "Meaning it becomes predictable."
"Yes. For coin flips, even knowing past results, the next probability stays 50%. Entropy rate is 1 bit. But human behavior depends on the past, so entropy rate is low."
Riku countered. "Then I'll just act more randomly!"
Aoi smiled. "Try it."
Riku stood up and made strange movements. Jumping, spinning, waving hands.
"How's that!"
"Interesting attempt, but that's also a pattern," Aoi pointed out. "'Behavior trying to appear random' is a predictable pattern."
Yuki was impressed. "True, the intention to 'act unpredictably' is itself predictable."
"Humans can't generate randomness. That's why cryptography and random number generation use physical phenomena. Radioactive decay, thermal noise."
Riku sat back down. "Then what's good about being unpredictable?"
"Security," Aoi's expression became serious. "If passwords are patterned, they're broken. If random numbers are predictable, encryption is useless."
"I see."
"But in communication, it's the opposite," Aoi continued. "Completely random conversation doesn't transmit information. Some predictability is why we can understand."
Yuki agreed. "Like redundancy. Because there are patterns, we can fill in gaps."
"Exactly. Language entropy rate is about 1 bit per character. For 26 alphabet letters, theoretically 4.7 bits, but context actually reduces it."
Riku wrote on the whiteboard. "So I'm not random, but that's okay?"
"Not just okay, it's necessary," Aoi said. "A completely random Riku would be impossible to communicate with."
Yuki laughed. "But having some unpredictable parts is also Riku-senpai's charm."
"That unpredictability generates information value," Aoi supplemented. "Because there's surprise, conversation is interesting."
Riku looked pleased. "So moderately random is best?"
"Information-theoretically, yes."
The sunset illuminated the club room. Random-kun remained moderately unpredictable today too.