"How much information does a confession carry?"
Riku said this while gazing vaguely at the sky. Lunch break on the rooftop, three people eating their bentos.
"You're thinking strange things again," Yuki chuckled wryly.
"But it's an intriguing problem," Aoi put down her chopsticks. "Information content is proportional to surprise."
"Surprise?"
"Yes. The lower the probability of an event, the greater its information content when it occurs."
Riku leaned forward. "So the information content changes depending on who confesses to whom?"
"Theoretically yes. For example, if an obviously mutual couple confesses to each other, the information content is small."
"Because you can predict it," Yuki understood.
"Precisely. I(x) = -log₂(p). The higher the probability p, the smaller the self-information I(x)."
Riku pondered. "Conversely, if someone you thought was absolutely impossible confesses to you?"
"The information content becomes explosively large. Because the probability was nearly zero."
"Surprise itself is information."
Aoi nodded. "That's why in information theory, entropy is also called 'average surprise.'"
Yuki suddenly thought of something. "Then, is probing the other person's feelings before confessing?"
"A problem of mutual information," Aoi opened her notebook. "How much uncertainty is reduced by observation."
"For example, watch the other person's reactions. If there are many smiles, the probability of affection increases. That's mutual information."
Riku laughed. "So that's why everyone goes on dates before confessing. They're gathering information."
"Exactly. Reduce uncertainty, then make the final confession."
"But," Yuki said, "if you gather too much information, doesn't the confession itself lose information content?"
Aoi showed an impressed expression. "Sharp observation. It's exactly a tradeoff."
"If you confess after having complete certainty, the other person also expects it, so there's less surprise."
Riku's eyes sparkled. "Conversely, confessing suddenly has large information content but high risk?"
"Yes. Low probability means possibly low success rate too."
Aoi looked up at the sky. "So leaving moderate uncertainty might be the aesthetic."
"Moderate surprise," Yuki murmured.
"In information theory, there's the concept of expected value. The average of all results weighted by probability."
"Expected value of confession?"
"Multiply the joy of success and the sadness of failure by their respective probabilities and add them."
Riku began thinking seriously. "So around 50 percent probability has maximum information content?"
"From an entropy perspective, yes. But considering expected utility, a slightly higher probability might be better."
Yuki drank her tea. "In the end, romance can't be measured by information content alone."
"Of course," Aoi smiled. "Emotions transcend information theory."
"But it's interesting that confession is an act of information transmission," Riku said.
"Yes. The words 'I like you' are an information channel that discloses internal state to the outside."
Yuki pondered. "How the other person interprets that information is also important."
"Information transmission asymmetry," Aoi supplemented. "The sender's intention and the receiver's interpretation don't necessarily match."
"So you carefully choose words."
"Add redundancy to prevent misunderstanding. Like error correction codes."
Riku burst out laughing. "Error correction in confessions, that's not romantic."
"But it's important," Yuki said. "To accurately convey feelings."
Aoi said quietly. "Information theory mathematically captures human activities. But it can't express the emotions behind them."
"What lies outside equations."
"Yes. We should use information theory without forgetting that."
The bell rang. End of lunch break.
"So Riku, who are you confessing to?" Yuki asked mischievously.
"Huh, me? I'm still gathering information!" Riku panicked.
Aoi laughed. "You're enjoying the uncertainty."
The three returned to the classroom. Information transmission called confession quietly occurs somewhere in the world today too.