"Today was high density."
Aoi said with satisfaction. After club activities ended.
"Density?" Yuki asked.
"Information density. We exchanged a lot of information in a short time."
Riku thought. "True, it was fulfilling."
"That's high information density."
Yuki looked back at notes. "Just one hour, but we learned so much."
"Information per unit time. That's rate."
Aoi explained. "In communication theory, R = C = max I(X;Y). Channel capacity."
"Channel capacity?"
"Upper limit of information that can be transmitted per unit time."
Riku showed interest. "Human conversation has capacity too?"
"In a sense. Attention, comprehension speed, memory capacity. All finite."
"So if you cram too much, it overflows," Yuki understood.
"Right. But transmit efficiently, and you can learn a lot in a short time."
Professor S passed by and joined the conversation. "Discussing information density?"
"Yes," Aoi answered.
"To increase density, reduce redundancy and maximize mutual information."
"But redundancy is needed for error correction, right?" Yuki asked.
"Good point," Professor S nodded. "There's a trade-off."
"High density but hard to understand, or low density but reliable."
Riku said with feeling, "Aoi-senpai's explanations sometimes have too high density to follow."
"Sorry," Aoi apologized.
Professor S continued. "Optimal density depends on receiver's capability."
"Adaptive rate control."
"Yes. Watch other's comprehension and adjust information density."
Yuki thought. "So why did today feel high density?"
"Maybe your comprehension improved," Aoi answered.
"Can process same information in shorter time."
"You've grown?" Riku asked happily.
"Exactly."
Professor S supplemented. "Learning is improving internal models. Better models increase reception efficiency."
"So even for same lessons, density can increase in higher grades."
"I see," Yuki was convinced.
Aoi gave another perspective. "But low density time also has value."
"Huh?"
"Time to think slowly. Small talk. Looks wasteful but nurtures creativity."
Riku agreed. "True. Too packed gets tiring."
"Information density and mental space need balance."
Professor S said quietly, "Approaching Shannon limit increases complexity."
"Shannon limit?"
"Channel capacity. Theoretical upper limit where you can't transmit more."
"But approaching that limit requires advanced encoding. Computation cost rises."
Aoi translated. "For humans, concentrating to the limit causes fatigue."
"Makes sense."
Yuki laughed. "So moderate density lasts longer."
"Right. Sustainability matters too."
Riku asked, "So what's an ideal after-school?"
"Moderately high density, but with room," Aoi answered.
"Learning and fun."
Professor S smiled. "Today, you three were exactly that."
"Yes," the three nodded.
"Not just high information density, but good quality too," Yuki reflected.
"Quality?"
"Meaningful information. Not noise, but essential content."
Aoi agreed. "Signal-to-Noise ratio was high too."
"When both information density and SNR are high, that's the best."
Riku said with satisfaction, "Today was the best then."
Professor S said as he left, "Accumulating high density time is growth."
"But sometimes enjoy low density time too."
"Thank you," the three answered.
Aoi looked out the window. Sunset lit the club room.
"This after-school is ending too."
"It was a high information density day," Yuki said.
"Tomorrow, let's make high density time again," Riku said positively.
"But don't overdo it."
"Balance," Aoi laughed.
The three began cleaning up. High information density after-school. It's not just efficiency. Quality learning, deep understanding, and time with friends.
"See you tomorrow," Yuki said.
"Yeah, let's go high density tomorrow too," Riku answered.
Aoi smiled quietly. "Looking forward to it."
Information can be measured by density. But value isn't just density. What stays in the heart is something beyond numbers.