"Mira-san, your outfit today is unusual."
Yuki spoke to Mira.
Mira smiled quietly.
Aoi became interested. "Why did you think it's unusual?"
"She usually wears black or white, but today it's blue."
"That's an event with high information content," Aoi explained. "Information content is proportional to degree of surprise."
Riku asked, "Can surprise be quantified?"
"Yes. Self-information I(x) = -log₂ P(x). Lower probability means greater surprise."
Yuki wrote in the notebook. "Because the probability of Mira wearing blue is low, the information content is high?"
"Exactly," Aoi nodded. "If she wore a different color every day, blue today wouldn't be surprising. The information content would be low."
Mira wrote on paper. "Pattern creates meaning."
"Yes," Aoi translated. "Because we know the pattern, deviation from it holds meaning."
Riku looked at his own clothes. "So me wearing the same T-shirt every day?"
"It's predictable, so the information content is low," Yuki said.
"That's not a compliment, right?"
Aoi laughed. "High or low information content isn't good or bad. It's a difference in role."
"Role?"
"Think about conversation. Predictable responses have low information content but provide comfort. Unpredictable responses have high information content and provide stimulation."
Yuki gave an example. "'Good morning' to 'Good morning' is low information. But 'The Earth rotates' would be high information."
"The latter is a weird response though," Riku laughed.
"Yes. That's why balance of information content matters in conversation," Aoi continued.
Mira showed another paper. "Surprise value = attention."
Aoi supplemented. "Surprise attracts attention. Advertising and news select high-information events."
"The more unusual something is, the more memorable?" Yuki asked.
"As a trend, yes. But moderate predictability is also important. If completely random, patterns aren't visible and meaning is lost."
Riku thought. "So what's the best conversation?"
"Slightly betraying expectations," Aoi answered. "Neither completely predictable nor completely random."
Yuki looked at Mira. "Mira-san's statements are always brief and abstract. But they always hit the essence."
Mira smiled.
"That's high-efficiency encoding," Aoi explained. "Conveying maximum information with minimum words."
Riku asked, "Conversely, talking too much like me?"
"High redundancy. Repeating the same information."
"Wasteful?"
"Not necessarily. Redundancy is robust against noise. Even if part is lost, the message gets through."
Yuki understood. "That's why we repeat important things."
"Yes. The more important the information, the more redundancy we add. To prevent misunderstanding."
Mira showed a new paper. "Balance is wisdom."
Aoi nodded deeply. "Perfect summary. In information theory and in life, balance is wisdom."
Riku said, "But how do we find balance?"
"By understanding the other person's expectations," Aoi answered. "What they know and don't know. If you understand that, you can choose appropriate information content."
Yuki reviewed her notebook. "Does this relate to mutual information?"
"It does. The more shared knowledge between two people, the more can be conveyed with fewer words."
Riku laughed. "So that's why we understand each other?"
"Right. Because we have common context, we can communicate efficiently."
Mira said slowly, "Sometimes silence carries most information."
Aoi's face became serious. "Profound. Silence can also have high information content depending on context."
Yuki asked, "What do you mean?"
"For example, silence after a question. It can carry various information: 'I don't know,' 'I'm thinking,' 'I don't want to answer.'"
"Silence's information content is determined by context?"
"Exactly. Silence that betrays expectations has higher information content."
The four sat quietly.
And each thought about what that silence meant.
After a few seconds, Riku laughed. "Was that silence high in information content?"
"A bit," Aoi smiled. "But it was comfortable silence."
Information theory illuminates not just the surface of conversation, but its depths too.
Surprise and predictability, silence and words—all contain information.