"What's information theory actually good for?"
Riku asked frankly. He seemed tired from studying for exams.
"It's magic," Aoi laughed.
"Magic?"
"Invisible, but we use it every day. If that's not magic, what is?"
Yuki asked curiously, "For example?"
Aoi took out a smartphone. "How much information theory is packed into just this?"
"Communication?" Riku guessed.
"Yes. 4G, 5G, WiFi. All use error-correcting codes. Radio waves are unstable, but data arrives accurately."
Mira quietly approached and wrote in her notebook. "LDPC, Turbo codes"
"Low-density parity-check codes and turbo codes. Powerful codes approaching Shannon's limit," Aoi explained.
"Shannon's limit, I heard that before," Yuki recalled.
"The theoretical maximum efficiency. Codes approaching it support modern communication."
Riku looked convinced. "So watching videos too?"
"Compression technology. H.264, H.265. Applications of source coding."
"An hour of video is a few hundred megabytes. Without compression, it'd be many gigabytes."
"Amazing reduction," Yuki was surprised.
"It exploits human visual characteristics. Removes inconspicuous information, keeps important parts."
Mira pointed at the smartphone. "Encryption"
"Cryptography. The third pillar of information theory," Aoi continued.
"Banking apps, messaging apps. All protected by encryption."
Riku became serious. "Cryptography is information theory too?"
"Shannon also laid the theoretical foundation for cryptography. Mathematically defined conditions for perfect secrecy."
"Perfect secrecy?"
"A state where the ciphertext reveals nothing about the original message. One-time pad is an example."
Yuki pondered. "But practical cryptography isn't perfectly secret, right?"
"Sharp. It relies on computational security. Takes enormous time to decrypt, so practically safe."
Mira wrote another example. "QR code"
"QR codes!" Riku exclaimed.
"Those are also information theory. Using Reed-Solomon codes for error correction. That's why they're readable even when dirty."
Aoi gave more examples. "Hard drives, SSDs. Won't work without error correction."
"CDs and DVDs too. Music doesn't skip despite scratches, thanks to error correction."
"Internet communication as well. TCP protocol ensures reliability through packet retransmission."
Yuki was overwhelmed. "Information theory really is everywhere..."
"Machine learning too," Mira said quietly. Unusually, she explained in words.
"Machine learning?" Riku was surprised.
"Cross-entropy loss. KL divergence. Information theory concepts are fundamental," Aoi supplemented.
"Neural networks can also be seen as information compression and decompression."
"Everything's connected," Yuki was moved.
Aoi smiled gently. "Information is the common language of the modern world."
Riku gazed at his smartphone. "So much magic packed into this little box."
"But we can understand the principles of magic. That's the beauty of information theory."
Mira nodded. "Understanding breaks the illusion, but creates new wonder"
"Understanding destroys illusion, but creates new amazement," Aoi translated.
Yuki said with determination, "I want to study more. I want to be able to use this magic myself."
"You can. You already are," Aoi smiled.
"Huh?"
"Using a smartphone. Sending messages. Watching videos. All using information theory."
Riku laughed. "So we were magicians without knowing it."
"But understanding the principles lets you use it more deeply."
Mira wrote lastly. "Magic is science we don't yet understand"
"Science not yet understood is magic. But once we learn, magic becomes science."
Outside the window, the sun was setting. The magic of information continues moving the world today too.