"Can optimization do anything?"
Yuki asked.
Aoi thought. "Theoretically, many things. But reality is complex."
"How complex?"
"Sometimes objective functions can't be defined."
Riku interrupted. "Objective function?"
"The value to maximize or minimize. Like profit or time."
Professor S entered the club room. "Talking about optimization?"
"Yes. But it's difficult."
The professor sat down. "The first step of optimization is clarifying objectives."
"What you want to optimize. Without that, you can't start."
Yuki asked. "For example, can happiness be optimized?"
"Difficult," the professor answered. "Can happiness be quantified?"
"I don't think so..."
"Then it can't be optimized."
Aoi supplemented. "There's a concept called utility function. Used in economics."
"An attempt to convert happiness into numbers."
"But individual differences are large."
Riku gave an example. "My happiness and Yuki's happiness are different."
"Right. Subjective values are hard to generalize."
The professor continued. "Furthermore, there are constraints."
"Time, budget, physical laws."
"With infinite resources, optimization is easy. But reality is full of constraints."
Yuki wrote in her notes. "Constrained optimization problem?"
"Correct. Use Lagrange multipliers and such."
Aoi explained. "Want to maximize f(x). But there's constraint g(x) ≤ c."
"Achieve objectives while respecting constraints."
Riku thought. "That tradeoff thing?"
"Right. To gain something, sacrifice something."
The professor gave an example. "In communication, speed versus reliability."
"Want to send fast but also reduce errors."
"Can't perfect both."
Yuki asked. "Then what do you do?"
"Balance. There's a concept called Pareto optimality."
"A state where you can't improve without worsening others."
Aoi drew a diagram. A two-dimensional graph with a curve.
"Pareto frontier. Points on this line are optimal tradeoffs."
"Where to choose depends on values."
Riku suddenly said. "But human feelings aren't decided by such calculations."
"Sharp observation," the professor acknowledged.
"Emotions aren't logical."
Aoi continued. "Behavioral economics says humans aren't rational."
"We have biases. Judge with heuristics."
"Often don't choose optimal solutions."
Yuki thought. "Is that bad?"
"Not necessarily," the professor answered.
"Intuition is product of long evolution."
"Not perfect but fast and practical."
"Sometimes more flexible than optimization algorithms."
Aoi supplemented. "Machine learning optimization also gets stuck in local optima."
"Finding global optima is often NP-hard."
"So we compromise with approximate solutions."
Riku laughed. "Machines aren't perfect either."
"Perfection is ideal. But reality is accumulation of approximations."
Yuki suddenly asked. "Then what are feelings that can't be optimized?"
Aoi thought. "For example, love."
"Can't decide who to love by optimization."
"Conditions can be calculated. But the heart won't follow."
The professor nodded. "Friendship too."
"No one chooses friends by efficiency alone."
"There are connections beyond calculation."
Riku said seriously. "That's what makes us human."
"Things that can't be optimized have value."
Aoi smiled. "Contradictory but beautiful."
Yuki summarized. "Optimization is a powerful tool."
"But not applicable to everything."
"What it can't apply to holds human essence."
The professor stood up. "Good discussion."
"Knowing optimization's limits is wisdom."
"Don't be used by tools. Use tools."
The three nodded.
"Thank you very much."
After the professor left, Riku said. "Let's cherish feelings that can't be optimized."
"Yeah," Yuki nodded.
Aoi looked out the window. "Not just efficiency. That's life."
Feelings that cannot be optimized. They are treasures outside formulas.