"Can the world be explained through probability?"
Yuki asked quietly while looking out the window.
"Interesting question," Aoi opened their notebook. "Probability theory is like a language for understanding the world."
"A language?"
"Yes. The world is complex, and we can't know everything perfectly. But using probability, we can draw the shape of the world while including uncertainty."
Riku peeked over. "I got soaked yesterday because the weather forecast was wrong. Is that also a probability issue?"
"Exactly," Aoi nodded. "Weather forecasts express things like '70 percent chance of rain tomorrow.' That's a model of the world."
"A model?" Yuki asked.
"A simplified representation of reality. It's impossible to perfectly track every atmospheric movement, so we approximate with probability."
Aoi drew a diagram on the whiteboard.
"For example, rolling a die. Physically, if the force, angle, and rotation are all determined, the result is determined too. But measuring all that isn't realistic."
"So we think of it as 1/6 probability each," Yuki understood.
"Exactly. Probability is the optimal way to describe things while acknowledging the limits of knowledge."
Riku pondered. "So if we had more information, the probability would change?"
"Sharp," Aoi's eyes lit up. "That's the idea of Bayesian updating. Every time you get new information, you revise the probabilities."
"Bayesian?"
"A theory by mathematician Thomas Bayes. Simply put, it's the process of 'seeing evidence and updating beliefs.'"
Yuki wrote in their notebook. "For example?"
"Say we thought the probability of Riku being late was 90 percent."
"That again!" Riku protested.
"But if Riku said 'I woke up early today,' the probability of being late might decrease. That's updating from prior probability to posterior probability."
"I see..." Yuki nodded.
Riku countered. "But sometimes I'm late even when I wake up early."
"That's why the probability doesn't become 100 percent. Uncertainty remains. That's what makes a realistic model."
Aoi gave another example. "Disease diagnosis is the same. Even if a test result is positive, it doesn't mean you're 100 percent sick. You combine the prior disease rate and test accuracy probabilistically to make a judgment."
"Math is practical, huh," Riku said with feeling.
"Information theory and probability theory are the foundation of all modern technology. Machine learning, communication—everything models the world with probability."
Yuki suddenly thought of something. "So we can't create a perfectly correct model?"
Aoi smiled quietly. "All models are wrong. But some are useful."
"Someone's words?"
"A famous quote by statistician George Box. What's important isn't aiming for perfection, but creating a model that's useful in reality."
Riku looked out the window. "Tomorrow's weather is also only knowable through probability."
"But if that probability is 70 percent, you can make the decision to bring an umbrella," Aoi said. "Probability is a tool for making the best decisions in an uncertain world."
"Deep," Yuki closed their notebook.
"The more you learn information theory, the more your view of the world changes. That's what makes it interesting."
In the dusk-lit club room, the three quietly thought about the uncertain world.