"This classroom is full of variables."
Yuki looked around.
"What do you mean?" Riku asked.
Aoi explained. "Random variables. Each person's behavior appears as a random variable."
"Interesting perspective," Yuki showed interest.
"For example, the probability Riku is late. The number of times Yuki asks questions. All are random variables."
Riku protested. "My lateness isn't random. There are proper reasons."
"Subjectively yes. But to an observer, it appears unpredictable."
Yuki wrote in the notebook. "Random variables are unpredictable things?"
"Precisely, things that aren't deterministic. Can take multiple values."
Aoi drew a diagram on the whiteboard.
"X: Riku's arrival time Y: Weather outside Z: Yuki's mood"
"These are all random variables."
Riku thought. "So is my arrival time related to weather?"
"It might be. Do you tend to be late on rainy days?"
"Actually yes."
"That's correlation. Two variables that aren't independent."
Yuki asked. "What's independence?"
"A state where one doesn't affect the other. Mathematically, P(X,Y) = P(X)P(Y)"
Aoi gave an example.
"Riku's arrival time and Yuki's mood. These are probably independent."
"Right. My mood isn't affected by Riku's arrival time," Yuki nodded.
"But!" Riku protested. "When I'm late, Aoi-senpai's mood worsens."
"That's evidence of non-independence," Aoi laughed.
Yuki asked seriously. "Why is independence important?"
"If independent, calculations become simple. Information amounts can be added."
Aoi wrote equations.
"H(X,Y) = H(X) + H(Y) (independent case) H(X,Y) < H(X) + H(Y) (dependent case)"
"When dependent, information amount decreases," Yuki understood.
"Yes. Knowing one lets you predict the other. So total information amount decreases."
Riku gave an example. "Like twins' behavior?"
"Good example. Twins have high correlation. Seeing one lets you predict the other."
Yuki looked at the notebook. "But do completely independent variables exist in reality?"
"Philosophical question," Aoi pondered. "Complete independence may be an ideal concept."
"Everything is connected somehow?"
"Possibly. But if the influence is small, we can consider it independent."
Riku looked outside. "Are all the people in this classroom affecting each other?"
"Information-theoretically, yes. But the strength of influence varies."
Aoi drew a diagram.
"Strong correlation: Friendships Weak correlation: Classmates Nearly independent: Strangers"
Yuki said quietly. "In a world full of variables, we're connected."
"Yes. Neither completely independent nor completely dependent."
"Somewhere in between."
"Human relationships can also be viewed as correlation of random variables," Aoi answered.
Riku laughed. "The correlation between us three seems high."
"No doubt," Aoi nodded. "Because we have the common factor of the Information Theory Club."
Yuki closed the notebook. "A classroom full of variables isn't bad."
"Rather, there's beauty in it," Aoi said.
The three quietly left the classroom. In a world full of variables, connected probabilistically.
That might be the shape of reality.