"Something really surprising happened today."
Riku said excitedly.
"What?" Yuki asked.
"Professor S was reading manga in the library."
Aoi laughed. "That is indeed surprising."
"High information content."
"Information content?" Yuki tilted her head.
Aoi began explaining. "Information content can be measured by degree of surprise. I(x) = -log₂ P(x)"
"Lower probability means greater information content."
Riku understood. "Professor S reading manga has super low probability, so huge information content."
"Precisely. Conversely, expected events have little information content."
Yuki gave an example. "Riku being late doesn't surprise me anymore."
"Harsh," Riku laughed. "But true, low information content."
"Frequent occurrences have high probability. So small information content."
Aoi continued. "In information theory, surprise itself is information."
"Interesting way of thinking," Yuki was impressed.
Riku thought. "So collecting surprises gives lots of information?"
"Yes. New experiences, unexpected events. That's the source of learning."
"But," Yuki said, "isn't constant surprise tiring?"
"Good point," Aoi nodded. "Moderate predictability is also necessary."
"Balance."
"Right. Completely predictable world is boring. Completely unpredictable world is chaos."
Riku asked seriously. "What's optimal surprise level?"
"Medium entropy state," Aoi answered.
"Medium?"
"When probability distribution is close to uniform. Meaning each event is equally likely."
Yuki calculated. "With dice, each face is 1/6. Is this maximum entropy?"
"Correct. When there's no bias, most unpredictable."
Riku pondered. "So same with daily life? Ideal is different things happening every day?"
"Not entirely. Humans prefer some routine."
"Why?"
"To reduce cognitive load. Brain gets tired when everything is new."
Yuki understood. "So mix predictable parts with surprising parts."
"Yes. Insert moderate change into routines."
"Like how we always meet here after school, but our conversations are different each time," Riku observed.
"Perfect example," Aoi confirmed. "The setting is predictable, the content surprising."
Aoi summarized. "Collecting moments of surprise is collecting information. But everything doesn't need to be surprising."
"Efficiently gain surprises," Riku said.
"Exactly. Go to new places, meet new people, learn new things."
Yuki wrote in her notebook. "Surprise = information. But in moderation."
"Balance is important."
Riku looked outside. "Maybe I'll do something new tomorrow."
"Good attitude. But don't overdo it."
"Need capacity to enjoy surprises too," Yuki said.
"Yes. Surprises are most valuable when you have mental space."
Aoi smiled. "Information theory captures surprise mathematically. But can't capture the emotion of surprise."
"What lies outside formulas."
"Right. Don't forget that."
The three laughed. Moments of surprise enrich life. Collecting them is growth.
"Looking forward to Professor S's next surprising behavior," Riku said.
"Let's continue observation," Aoi answered.
"Information gathering," Yuki laughed.
"We should start a surprise journal," Riku suggested. "Rate each day's surprise level."
"That would be quantifying our own entropy," Aoi noted with amusement.
"Meta-learning about learning," Yuki added.
Laughter echoed in the club room. Days of collecting surprises continue today too.