"I got it!"
Yuki suddenly exclaimed.
"Got what?" Riku asked in surprise.
"The mutual information equation. I couldn't understand it for so long, but now I finally get it."
Aoi smiled. "That's learning. Your entropy decreased."
"My entropy decreased?"
"Yes. Before understanding, your uncertainty was high. But now that you understand, uncertainty decreased."
At that moment, Professor S appeared at the club room.
"Good timing. What just happened is the very definition of learning in information theory."
"Professor," Aoi greeted.
"Learning is entropy reduction," the professor said concisely. "By gaining knowledge, uncertainty about the world decreases."
Yuki opened the notebook. "Specifically?"
"For example, when you don't know if a coin is heads or tails, entropy is 1 bit. But the moment you see it, entropy becomes zero."
"Observation is learning?"
"Yes. Observation is a special form of learning. Direct information acquisition."
Riku asked, "Then studying is also entropy reduction?"
"Yes. Unknown concepts are high-entropy states. Understanding reduces entropy."
Aoi supplemented, "But new questions can also arise. That's entropy increase."
"Learning isn't unidirectional?" Yuki asked.
"Exactly," the professor nodded. "As understanding deepens, you notice new uncertainties. That's the essence of scholarship."
The professor drew a diagram on the whiteboard.
"Consider knowledge space. Before learning, a wide range is uncertain. After learning, uncertainty in some region decreases. But new unknown regions appear around it."
"Like fractals," Riku said.
"Good metaphor. The more you know, the more you see what you don't know."
Yuki pondered. "Then complete understanding is impossible?"
"Theoretically, reducing all entropy to zero is possible. But in reality, new information is constantly created."
Aoi added, "Plus there's the computational problem. Knowing everything would take longer than the universe's lifetime."
"Then to learn efficiently?" Yuki asked.
"Maximize information gain," the professor answered. "Ask questions that most reduce uncertainty. Choose experiences with most learning."
"Like decision trees in machine learning," Aoi said.
"Yes. Determining branches by information gain. Same principle."
Riku raised his hand. "But like me, people sometimes learn things wrong, right?"
"That's incorrect entropy reduction," the professor explained. "Subjectively uncertainty decreased, but objectively it's false confidence."
"Dangerous."
"That's why verification is important. Feedback. A mechanism to correct false confidence."
Yuki wrote in the notebook. "Learning = correct entropy reduction + verification"
"Concise and accurate," the professor acknowledged.
Aoi asked, "Professor, is teaching also entropy manipulation?"
"Yes. Teachers provide information that reduces students' entropy. But without understanding the student's current entropy state, it's not effective."
"That's why questions are important," Yuki understood.
"Questions are a means to measure student entropy. Where is uncertain, what is unknown."
Riku asked seriously, "So the more we ask, the easier it is for senpai to teach?"
"Exactly," Aoi laughed. "If I can see your entropy, I can provide optimal explanations."
The professor stood up. "Today, too, your entropy seems to have decreased a bit."
"But new questions also arose," Yuki said honestly.
"That's good," the professor smiled. "Learning is an endless journey. Dialogue with entropy continues."
After the professor left, the three fell silent for a moment.
"Today, I gained another understanding," Yuki murmured.
"The moment entropy decreases feels good, right?" Riku said.
"That's learning's reward," Aoi nodded. "The pleasure of uncertainty decreasing. Humans learn seeking that."
Yuki looked out the window. The world is still full of high entropy. But by understanding one thing at a time, it decreases bit by bit. That must be the journey of learning.