"Riku, you're unpredictable."
At Yuki's words, Riku laughed.
"That's my specialty!"
Aoi became interested. "Unpredictability. In other words, randomness."
"Random?" Yuki asked.
"No pattern. No regularity. That property."
Mira quietly opened her notebook and wrote an equation.
"Kolmogorov complexity"
"Kolmogorov complexity," Aoi explained. "The length of the shortest program that generates a sequence."
"That's difficult..." Yuki frowned.
"Simply put, sequences that cannot be compressed are random."
Riku gave an example. "'AAAAAAA' and 'AGKTQPZ'. Which is random?"
"The latter," Yuki answered immediately.
"Correct. 'AAAAAAA' can be briefly expressed as '7 As'. But 'AGKTQPZ' must be written as is."
Aoi supplemented. "Random sequences have no description shorter than themselves."
"That's true randomness."
Yuki had a question. "But if you flip a coin, it's unpredictable, right?"
"Superficially. But it's determined by physical laws. If you know initial conditions, you can calculate it."
"So true randomness doesn't exist?"
Aoi's face became serious. "In classical physics, yes. But in quantum mechanics, there's essential randomness."
Mira added. "Quantum randomness is true randomness"
"Quantum randomness is true randomness," Aoi translated.
Riku raised his hand. "What about computer random numbers?"
"Pseudorandom. Generated by algorithms. So predictable."
"What?" Yuki was surprised.
"If you know the seed value, you can reproduce the entire random sequence. Not truly random."
Aoi drew a diagram.
"True random: Incompressible, unpredictable Pseudorandom: Algorithm-generated, predictable (if seed known)"
"But good pseudorandom generators are very difficult to distinguish."
Yuki thought. "Does randomness depend on knowledge?"
"Sharp observation," Aoi was impressed. "Apparent randomness depends on the observer's knowledge."
"For example, an encrypted message. To someone without the key, it looks random."
"But to someone with the key, it has meaning."
Riku got excited. "What about my behavior?"
"Unpredictable to others. But you have reasons."
"So it's subjective randomness."
Mira smiled and wrote. "Riku = high entropy source"
"Riku is a high-entropy source," Aoi translated.
Yuki laughed. "Is that a compliment?"
"Information-theoretically, high entropy means abundance. Diversity."
Riku said proudly. "I'm a bundle of diversity!"
Aoi summarized. "Randomness is the core of information theory. Because it's unpredictable, there's information."
"If completely predictable, information amount is zero."
Yuki understood. "So randomness isn't an enemy, but a source of information."
"Exactly. Cryptography, simulation, machine learning. All require randomness."
Mira added. "Randomness is creativity"
"Randomness is creativity."
Riku said happily. "My unpredictability is creative?"
"In a sense," Aoi smiled. "Because it's unpredictable, new possibilities emerge."
Yuki wrote in the notebook. "Random-kun is unpredictable today too. And that's wonderful."
The four laughed. The unpredictable world is full of information.
That is the teaching of information theory.