"Senpai, nothing interesting happened today."
Yuki sighed.
"Really?" Aoi asked. "From morning until now, nothing?"
"Just a normal day. Classes, lunch, more classes."
Aoi opened the notebook. "Information-theoretically, that's interesting too."
"What do you mean?"
"There's a concept called self-information. An event's information content is determined by how unlikely it is to occur."
Yuki thought. "The less likely it is, the more information?"
"Exactly. In formula terms, I(x) = -log₂ P(x). Lower probability means higher self-information."
"But today nothing unusual happened..."
"Wait," Aoi interrupted. "This morning, was Riku late?"
"No, he was on time for once."
"That's a low-probability event. It has high information content."
Yuki laughed. "True, that's rare."
"What about lunch?"
"The usual cafeteria, usual menu."
"High-probability event. Low information content," Aoi explained. "But that has its own meaning."
"Low information content also has meaning?"
"Yes. Predictability creates comfort. If every day were full of surprises, we'd be exhausted."
Yuki started writing in the notebook. "High and low information events, balance is important?"
"Yes. Daily life consists of events with various probabilities. High-information events are memorable. Low-information events provide stability."
"Interesting perspective."
Aoi continued. "For example, conversation with friends. Predictable responses have low information content but show trust. Unexpected responses have high information content and bring new perspectives."
"So information content alone doesn't measure conversation's value?"
"It can be measured, but that's not all," Aoi corrected. "High information content brings surprise and learning. Low information content brings stability and confirmation. Both are needed."
Yuki looked out the window. "Today's sunset is beautiful."
"What about it?"
"Seeing a sunset on an ordinary day has high probability. But I feel like I'm seeing it from this angle for the first time."
Aoi smiled. "When perspective changes, probability distribution changes too. For you, it's low probability—meaning high information content."
"From an information theory perspective, maybe there's no such thing as a day with nothing."
"Accurate understanding," Aoi acknowledged. "Every moment contains some information. The question is whether we notice it."
Yuki took a deep breath. "Tomorrow I'll observe more carefully."
"Good attitude. But," Aoi added, "trying to observe everything is exhausting. Selective attention matters too."
"Observe in moderation?"
"Yes. Environments with too much entropy are chaotic. Too little is boring. Moderate complexity feels comfortable."
"How was your day, senpai?"
Aoi thought briefly. "Riku came on time. That had high information content. Also, Yuki saying 'nothing happened.'"
"That also has high information content?"
"In a sense. Since you're usually positive, that statement was unexpected."
Yuki laughed embarrassedly. "Sorry."
"No need to apologize. Because of that statement, we're having this information theory discussion. A chain of low-probability events."
"Coincidences piled up."
"In information theory, coincidence is the source of information. In a completely deterministic world, no new information emerges."
Yuki closed the notebook. "Today I learned a lot from a 'day with nothing.'"
"That's the fascination of information theory," Aoi said. "It changes how you see the world."
The two discussed the meaning of daily life in the sunset classroom.
Information theory illuminates boring daily life from a new perspective.
If you notice, every moment contains information.