"Senpai, this doesn't have just one answer, right?"
Yuki was staring at the exercise book. An information theory practice problem.
"Which one?" Aoi looked over.
"The question 'How do you reduce the ambiguity of a message?'"
Riku laughed. "Reduce ambiguity? That's easy. Just add information."
"That's correct," Aoi nodded. "But what information to add. That's what matters."
Yuki tilted their head. "Are there specific examples?"
Aoi wrote on the whiteboard.
"'Tomorrow will be hot.' This message is ambiguous."
"We don't know what temperature is hot," Riku pointed out.
"Correct. But what about 'Tomorrow will be 30 degrees'?"
"The ambiguity decreased!" Yuki said.
"Yes. By adding a specific number, the uncertainty decreases. In information theory, we call this entropy reduction."
Riku thought. "Then 'Tomorrow will be 30.5 degrees' would be even better?"
"Depends on the necessary precision. For temperature, decimals might be within the margin of error. Excessive precision just adds noise."
Yuki wrote in the notebook. "There's an appropriate amount of information."
"Exactly. Too vague is problematic, too detailed is problematic. Balance is important."
Aoi gave another example.
"'I met a friend' versus 'I met Aoi.' Which has more information?"
"'I met Aoi,'" Yuki answered immediately.
"Why?"
"'A friend' is ambiguous. There are many. But 'Aoi' specifies one person."
"Precise. The more ambiguous an expression, the higher the entropy. The more specific an expression, the lower the entropy."
Riku asked curiously. "But sometimes we deliberately speak vaguely, right?"
"Good observation, Riku," Aoi was impressed. "Intentional ambiguity creates flexibility. We use it to protect privacy or leave options open."
Yuki remembered. "Is this related to conditional entropy we learned before?"
"It's related. When conditions become clear, entropy decreases. Meaning ambiguity reduces."
Aoi drew a diagram.
"Initial state: High entropy (ambiguous) Add information: Conditions clarified Result state: Low entropy (clear)"
"Information is a tool to reduce ambiguity," Yuki understood.
Riku joked. "People always say my actions are ambiguous. Does that mean I'm a high-entropy person?"
"Exactly," Aoi laughed. "Your behavior is unpredictable, so information-theoretically, you're high-entropy."
"Is that a compliment?"
"Half of one."
Yuki looked at the exercise book again. "So the answer to this problem is 'Add appropriate information according to the purpose.'"
"Perfect answer," Aoi acknowledged. "The battle with ambiguity is choosing appropriate information. You don't need to clarify everything. Only clarify the necessary parts."
Riku wrote in his notebook. "Information Theory Club activity goal: Find appropriate clarity."
"Good goal," Aoi smiled.
Yuki looked outside the window. The sunset was fading. Ambiguous boundaries were gradually becoming clear.
Learning information theory means confronting the world's ambiguity. Perfect clarity doesn't exist, but we can reduce uncertainty as much as needed.
That was what they learned today.