"Thank you."
Yuki was surprised by Riku's single statement.
"Huh?"
"Yesterday, you lent me your notes. Thank you."
Yuki was stunned for a moment. Riku expressing gratitude?
Aoi watched with interest. "That statement had high information content."
"Information content?" Riku tilted his head.
"Yes. It's rare for Riku to honestly express gratitude. So the information content is large."
Yuki laughed. "True. I was surprised."
"What, I say thanks sometimes."
"Because the frequency is low, calculating with I(x) = -log₂(p), the information content is high."
Aoi explained. "Events with low probability p have high self-information I(x)."
"So when I say 'thank you,' how many bits?" Riku showed interest.
Yuki thought. "I only hear it about once a month, so probability is about 0.03?"
"Then about 5 bits," Aoi calculated.
"5 bits!"
"Conversely, when Aoi-senpai says 'thank you'?" Yuki asked.
"I say it fairly often, so with probability 0.5, about 1 bit?"
"Totally different," Riku was surprised.
"Information content of words changes with speaker and context," Aoi supplemented.
Yuki was amused. "So even the same 'thank you' has different weight."
"Precisely. Rarity creates value."
Riku pondered. "But that means it's valuable because I don't usually give thanks?"
"Ironic, but from an information theory perspective, yes."
"Complicated."
Aoi continued. "However, high-frequency words also have meaning. Value as reliability or habit."
"Reliability?"
"Greeting with 'good morning' every day. Its information content is low, but it has a function of maintaining relationships."
Yuki nodded. "Like a ritual."
"Yes. Even with low information content, social function is high."
Riku laughed. "So should I say 'thank you' every day?"
"That's fine too, but the impact like today decreases."
"It's a trade-off."
Yuki gave another example. "What about confessions?"
"High information content event," Aoi answered immediately. "Because they rarely happen."
"But probability differs depending on the other person, right?" Riku pointed out sharply.
"Exactly. If mutual feelings, probability is high and information content decreases. If one-sided, probability is low and information content is explosively high."
Yuki thought. "So unexpected confessions stay in your heart."
"Because the surprise is large. And surprise is engraved in memory."
Riku joked, "What if I suddenly said 'Actually I'm a genius'?"
"High information content but low credibility," Aoi laughed.
"Credibility?"
"Bayesian update problem. If prior probability is too low, one statement isn't believable."
Yuki supplemented. "You need evidence."
"Right. Even with high information content, without backing it's meaningless."
Riku became serious. "So when saying something really important?"
"Timing and context are crucial," Aoi answered.
"Appropriate situation, appropriate person, appropriate words."
Yuki said quietly. "Can't be measured by information content alone."
"Right. Human communication transcends information theory."
Riku said embarrassed, "But that 'thank you' was sincere."
"I know," Yuki smiled. "That's why I was happy."
Aoi observed. "High information content and sincere. The strongest combination."
"One word can change the world."
Yuki looked out the window. "I want to use rare words carefully."
"But don't forget everyday words too," Aoi added.
"Balance?" Riku asked.
"Yes. High-information rare words and low-information everyday words. Both are needed."
The three nodded to each other. Words carry information. But they convey more than that.
Riku said quietly, "Lend me notes again."
"Sure," Yuki laughed.
Simple exchange. But there was a certain bond there. Something that can't be measured by information content.