"Can I write this more briefly?"
Riku stared at a long message.
"What are you writing?" Yuki peeked over.
"A confession. But it's too long, feels wrong somehow."
Aoi approached with interest. "A compression problem."
"Compression?"
"In information theory, there's a concept called Kolmogorov complexity. The length of the shortest program that generates a given string."
Yuki asked, "Program?"
"For example, the string '0000000000' can be expressed with a short program like 'repeat 0 ten times.'"
"True."
"But a random sequence like '0101100111' has to be written as is. It can't be compressed."
Riku's eyes widened. "So my feelings can't be compressed either?"
"Perhaps," Aoi smiled. "Things that are truly random, essentially complex, can't be shortened."
Yuki started writing in the notebook. "But if there's a pattern, it can be compressed, right?"
"Yes. The feeling 'I like you,' if repeated as 'I like you I like you I like you,' doesn't increase information. Rather, it becomes redundant."
"But," Riku's face became serious, "the same words can change meaning with context, right?"
Aoi showed an impressed expression. "Sharp. There's a concept called conditional Kolmogorov complexity. The required information changes depending on whether you know the other person's state."
"Meaning?"
"If you know the other person is in an 'I like you too' state, a short phrase like 'likewise' suffices. But if their feelings are unknown, you need to explain carefully from the start."
Yuki said, "This relates to mutual information."
"Accurate. The more shared knowledge, the more efficient the communication."
Riku reread the message. "But I feel what I really want to convey can't be compressed."
Aoi said quietly, "That might be fine. Shannon entropy shows the average compression limit, but Kolmogorov complexity measures the essential complexity of individual objects."
"Essential complexity..."
"Yes. Truly random strings, truly complex feelings, can't be expressed shorter than themselves. That's what being Kolmogorov random means."
Yuki said gently, "Riku's feelings might be Kolmogorov random."
"Is that a compliment?"
"It is. It means they're not boilerplate, they're your unique words."
Aoi supplemented, "Incompressible things have value. Information-theoretically, they contain maximum information."
Riku stared at the message. "Then I'll send it as is."
"Yes," Yuki nodded.
"But," Riku said anxiously, "what if it's too long to read?"
Aoi laughed. "That's a channel capacity problem. You need to fit information to the receiver's attention bandwidth."
"Difficult..."
"In short, readability matters too," Yuki translated.
"So even incompressible messages need good presentation?"
"Exactly," Aoi confirmed. "The content's complexity might be irreducible, but the packaging matters. It's like the difference between raw data and a well-designed interface. The information content stays the same, but the accessibility changes."
Riku took a deep breath. "Got it. No compression. But I'll organize paragraphs."
"Good decision," Aoi acknowledged. "Maintain essence while improving readability. That's good encoding."
Yuki patted Riku's shoulder. "It'll get through. Your Kolmogorov complexity, properly."
"Weird encouragement," Riku laughed.
The three discussed feelings that cannot be compressed in the sunset club room.
Information theory can sometimes apply to hearts too. But hearts are always more complex than algorithms.