"Have you decided on your future path?"
Aoi asked Yuki. They were in a corner of the library, facing career survey forms.
"Not yet. Too many options..."
"High uncertainty."
"Exactly. But I don't know how to decide."
Mira sat down beside them and wrote in her notebook. "H(Y|X) - conditional entropy"
Aoi nodded. "Conditional entropy. After obtaining information X, how much uncertainty in Y remains."
"Is this related to career choice?"
"Very much. For example, let Y be 'future satisfaction', X be 'path chosen now'. With perfect information, conditional entropy is zero. But in reality..."
"Uncertainty remains," Yuki said.
"Yes. But by gathering information, you can reduce conditional entropy."
Mira wrote a new equation. "I(X;Y) = H(Y) - H(Y|X)"
"Mutual information. How much uncertainty in Y decreases by knowing X," Aoi explained.
Yuki pondered. "So going to open campus, talking to seniors, that's..."
"Information acquisition. Actions that reduce conditional entropy."
"But," Yuki said anxiously. "We can never get perfect information, right?"
"Exactly. That's why Bayes' theorem becomes important."
Aoi wrote an equation on the whiteboard.
"P(H|E) = P(E|H) × P(H) / P(E)"
"You have prior probability P(H), observe evidence E, and update to posterior probability P(H|E)."
Yuki held their head. "Difficult..."
"Think of a concrete example," Aoi said gently. "You have hypothesis H: you want to pursue science. You get evidence E: you enjoyed open campus. How much does this evidence support the hypothesis?"
"It was fun, so science suits me?"
"Not necessarily. You need to compare 'probability of enjoying it if science suits you' with 'probability of enjoying it in other cases'."
Mira drew a diagram. Partitioning of probability space.
"So you can't decide with just one piece of evidence," Yuki summarized.
"Exactly. Collect multiple pieces of evidence and gradually update posterior probability. That's rational decision-making."
"But," Yuki said quietly. "Even after calculating, uncertainty remains at the end, right?"
Aoi smiled. "True. But that's also what makes life interesting."
"Interesting?"
"A completely predictable future has zero information content. No surprise, no growth, no discovery."
Mira showed a new note. "Uncertainty = Possibility"
"Uncertainty is also possibility," Aoi translated. "Because we don't know which choice is correct, any choice can be correct."
Light returned to Yuki's eyes. "From an information theory perspective, uncertainty isn't bad."
"Rather, it's the source of information. Because entropy is high, new information has value."
"So I should gather information and gradually reduce uncertainty."
"And the uncertainty that remains at the end," Aoi said. "Accept it with courage."
Mira nodded. Unusually, she spoke. "The future is not decided, but created."
Yuki was surprised. It was the first time hearing Mira speak.
"Thank you, both of you. I'm starting to see."
Yuki faced the survey form. There's no perfect choice. But with current information, she can calculate the best posterior probability.
Aoi said quietly. "Youth might be a time to learn decision-making amidst uncertainty."
"Training to live with conditional entropy," Yuki laughed.
Mira smiled. The three continue accumulating their own information toward an uncertain future.
Outside the window, the sunset was fading. Tomorrow's weather, future paths, still unknown. But that uncertainty itself is information and possibility.