"What do you think youth is?"
The club room fell silent at Yuki's sudden question.
"That's philosophical," Aoi smiled. "But it might be interpretable through information theory."
"Through information theory?" Riku showed interest.
"Youth is a high-entropy state," Aoi said. "The future is uncertain, with infinite possibilities."
"So it's unstable?" Yuki asked.
"But that's also the charm. High-entropy possibility over low-entropy stability."
At that moment, Professor S. entered the club room.
"Discussing youth?" the professor said quietly.
"Yes. We're attempting an information-theoretic interpretation."
The professor nodded. "Interesting attempt. Let me offer a perspective."
The three paid attention.
"Youth is a learning process. Continuous Bayesian updating."
"Bayesian updating?" Riku asked.
"New experiences update prior probabilities to posterior probabilities. Both failures and successes are information."
Aoi supplemented. "P(hypothesis|data) = P(data|hypothesis)・P(hypothesis) / P(data)"
"That's difficult," Riku held his head.
The professor laughed. "Simply put, learning from experience."
Yuki understood. "Heartbreak also has meaning as information?"
"Of course. Painful data, but it updates your world model."
Aoi added. "The greater the surprise, the larger the update."
"So youth is a period of great change?"
"Yes. Many surprises, much learning."
The professor offered another perspective. "And youth is also a period of acquiring mutual information."
"Mutual information?" Yuki asked.
"Understanding relationships between people. Increasing I(self;others)."
Aoi explained. "Mutual information is information gained by knowing the other person."
"Friendship and love too?" Riku asked.
"All included. Understanding others and being understood."
The professor continued. "In childhood, I(self;others) is low. But it surges in youth."
"That's why relationships become complex," Yuki understood.
"And sometimes, noise also increases," Aoi added.
"Noise?"
"Misunderstandings, miscommunications, communication errors. Unavoidable in youth."
The professor nodded. "But that's also learning. Learning to deal with noise."
Riku thought. "So becoming an adult means entropy decreases?"
"In a sense," the professor acknowledged. "Possibilities narrow, but stability increases."
"Is that sad?" Yuki asked.
"Depends on perspective," Aoi said. "Decreasing entropy is also evidence of choosing."
"Choosing?"
"Selecting your path from infinite possibilities. That's growth."
The professor supplemented. "And information density on the chosen path actually increases."
"Deep understanding?"
"Yes. From broad and shallow to narrow and deep."
Riku looked out the window. "Are we right in the middle of high-entropy youth?"
"Indeed," Aoi smiled. "But we're gradually updating our models."
Yuki said quietly. "Decoding through information theory makes youth look a bit different."
"How different?" the professor asked.
"Instability and confusion all have meaning. Because it's a time to gather information and learn."
"Wonderful understanding," the professor acknowledged.
Aoi added. "And conversations in this club room also increase mutual information."
"The process of understanding each other."
"Yes. That might be the essence of youth."
Riku laughed. "Information theory is surprisingly youthful."
"Mathematics is also human," the professor said. "Tools made by people to understand people."
The four quietly enjoyed their high-entropy state called youth. Uncertain, but full of possibilities. Even decoded through information theory, youth was still youth.