"Is this the information theory club?"
As Yuki timidly opened the door, an orderly club room came into view.
"Welcome," Aoi turned around. "New member?"
"Yes. I'm not good at math, but... information theory seemed interesting."
"You don't need to be good at math. Curiosity is enough."
At that moment, someone rushed in from behind.
"Made it! Aoi-senpai, what are we doing today?"
"Riku, late again?"
"No, this isn't late, it's last-minute arrival!" Riku laughed.
Aoi sighed. "Whatever. Today I'll explain the overview of information theory to our new member Yuki."
"Overview? I don't really understand it either," Riku admitted honestly.
"I know that," Aoi smiled wryly. "Alright, both of you sit down."
As Yuki and Riku took their seats, Aoi wrote in large letters on the whiteboard.
"What is Information Theory"
"In 1948, a mathematician named Claude Shannon founded this field. It deals with the essence of information mathematically."
"Essence of information?" Yuki tilted their head.
"Information is what reduces uncertainty. It can be quantified with a concept called entropy."
Riku raised his hand. "Entropy, like what we learned in science class?"
"Similar to thermodynamic entropy, but in information theory, it's a measure of 'diversity of choices.'"
Aoi drew three boxes.
"The first box contains only white balls. The second box has white and black, half and half. The third box has white, black, red, and blue equally. Which has the highest entropy?"
"The third!" Yuki answered immediately.
"Correct. When there are many choices and each is equally likely, entropy is at its maximum."
"So what do we do in information theory club?" Riku was curious.
Aoi held up three fingers. "There are three main areas."
"First, data compression. Technology to store information efficiently."
"Like zip files?" Yuki asked.
"Yes. Photos, music, videos. All compressed using information theory principles."
"Second, communication. Technology to transmit information accurately in noisy environments."
"Like cell phones?"
"Exactly. Radio waves are unstable, but thanks to error-correcting codes, we can make calls."
Riku was amazed. "Wow! So what's the third?"
"Cryptography. Technology to keep information secret. The foundation of security."
"These are all things we use every day!" Yuki's eyes sparkled.
"Right. Information theory is invisible, but it's the foundation of modern society."
Riku's face became serious. "Sounds kind of cool."
Aoi smiled. "But there will be equations. Are you ready?"
Yuki looked a bit anxious. "How difficult is it?"
"Within high school math. Logarithms, probability, summation notation. That's all you need for the basics."
"I think I can do it!"
"I'm not great with logarithms..." Riku complained.
"Don't worry. With club practice, you'll get used to it quickly."
Aoi took out two notebooks. "These are club notebooks. Feel free to write in them."
Yuki received one. "What should I write?"
"What you learn, questions, ideas. Information theory is a way of thinking, so summarizing in your own words is important."
Riku flipped through pages. "Senpai's notebook is super neat."
"Organization is kind of my hobby."
Yuki said with determination, "I'll do my best."
"Don't push yourself too hard. Having fun is most important."
Riku stood up. "Then from today, we're information theory comrades!"
Aoi nodded. "I want you to learn many things in this club room. Communication, compression, prediction, randomness. It's all connected."
Yuki looked out the window. An ordinary after-school seemed to look a bit different.
Information exists everywhere. The journey to understand it began today.