"Mira laughed!"
Yuki shouted in surprise. In the club room, Mira had smiled slightly.
"That's rare," Aoi said quietly.
Mira looked away bashfully.
"Why was I so surprised?" Yuki murmured.
Aoi answered with interest. "Self-information. Rarer events have larger information content."
"So that's why I'm surprised?"
"Yes. The brain estimates event probabilities. When low-probability events occur, 'surprise' measured as -log₂(p) is generated."
Mira wrote in her notebook. "Surprise ∝ -log p"
"I thought the probability of Mira laughing was about 0.01," Yuki said.
"Then self-information is about 6.6 bits," Aoi calculated.
"Meanwhile, probability of Riku being late is 0.9, so information content is about 0.15 bits."
"That's why Riku being late doesn't surprise us."
"More precisely, surprise is small."
Yuki pondered. "So can emotions be measured by information content?"
"To some extent. Surprise, excitement, disappointment. All arise from gaps with expectation."
Mira showed a new note. "Emotion = information gain"
"Emotion is information gained..." Aoi read aloud. "Interesting view."
"What does it mean?"
"When gaining new information, world model gets updated. Larger update width, larger emotional response."
Yuki considered an example. "If a friend suddenly confesses, I'd be really surprised."
"Low probability event. But if you vaguely sensed it, surprise is small."
"Because prior probability was high."
"Yes. Surprise parties succeed when target's prior probability is low."
Mira said quietly. "I surprised you."
"Huh? On purpose?" Yuki was surprised.
"Experiment," Mira smiled. Smiled again.
"Experiment, you were watching our reactions?"
Aoi was impressed. "That's like Mira. Demonstration of information theory."
"But the second time wasn't as surprising, right?"
Yuki realized. "True. Got used to it."
"That's adaptation. Prior probability updated."
Mira wrote details in her notebook.
"1st time: p=0.01 → I=6.6 bits 2nd time: p=0.3 → I=1.7 bits"
"Probability increased, so surprise decreased," Aoi explained.
"But," Yuki said, "same event, different people have different surprise levels, right?"
"Sharp. Because each person's subjective probability differs."
"If I knew Mira less well, would I be more surprised?"
"Might be opposite. Completely unexpected events can be too abnormal to accept."
Mira supplemented. "Optimal surprise exists."
"Optimal surprise?" Yuki asked.
"Too small is boring, too large is confusing. Moderate surprise moves hearts most."
Aoi nodded. "Movies and novels have moderate unpredictability. That's the source of interest."
"Information theory can discuss art."
"Surprise design is fundamental to creativity."
Mira stood and looked out the window.
"Hearts move by surprise."
"Hearts move by surprise..." Yuki murmured.
"So new experiences matter," Aoi continued. "Living an information-rich life."
Yuki wrote in her notebook. "Today, gained about 6.6 bits of surprise."
"Good record," Aoi laughed.
Mira smiled slightly. Third time. Yuki wasn't surprised anymore. But she was happy. Emotions aren't just information. But they start from information.