"Is random really random?"
At Yuki's question, Riku laughed. "That's philosophical."
"But it's an important problem," Aoi opened their notebook. "Computer random numbers aren't actually completely random."
"What?" Yuki was surprised.
"Programs run deterministically. Same input always gives same output. So 'random numbers' generated by computers are called pseudorandom numbers."
Riku was intrigued. "So they can be predicted?"
"In theory, yes. If you know the initial value called the seed, you can reproduce the entire random sequence."
At that moment, Professor S. entered the club room.
"You're discussing something interesting."
"Professor!" the three greeted.
"Do you understand the difference between true randomness and pseudorandomness?"
Aoi explained. "Pseudorandom numbers are generated by algorithms. They have patterns, but they're very complex and difficult to predict."
"That's right. Cryptographically secure pseudorandom generators are designed so that even seeing part of the sequence, you can't predict the next value."
Yuki wrote in their notebook. "So how do you make true random numbers?"
"Use physical phenomena," the professor answered. "Radioactive decay, quantum noise, atmospheric noise. These are inherently unpredictable."
Riku raised his hand. "Are dice also true randomness?"
"Subtle," Aoi said. "In classical physics, dice motion is deterministic. But sensitivity to initial conditions is so high that it's practically unpredictable."
"Chaos theory," the professor supplemented. "Deterministic but unpredictable. That's the essence of chaos."
Yuki pondered. "How does information theory distinguish them?"
Aoi drew a diagram. "Information-theoretically, sequences that can't be compressed are 'random.' If there's a pattern, it's compressible, meaning non-random."
"But," Riku countered, "long passwords can't be compressed either, but they're human-made, right?"
"Sharp," the professor was impressed. "There's a concept called Kolmogorov complexity. The length of the shortest program that generates a sequence. If the program is shorter than the sequence itself, there's a pattern."
Aoi continued. "A truly random sequence is its own shortest description. In other words, incompressible."
Yuki's eyes sparkled. "So randomness can be measured by brevity of explanation?"
"Exactly. That's the definition of algorithmic randomness."
Riku took out his smartphone. "Can I trust the random numbers from this app?"
The professor looked. "Depends on the use. For games, pseudorandom is enough. But for generating encryption keys, you need cryptographically secure randomness."
"Security issue?"
"Yes. Weak random number generators can be predicted by attackers."
Aoi supplemented. "In fact, there have been many attacks exploiting pseudorandom number flaws."
Yuki listened seriously. "So how do you make good random numbers?"
"Combine multiple entropy sources," the professor explained. "Keyboard timing, mouse movement, hardware noise. Mix these to create an unpredictable seed."
"I see," Yuki nodded.
Riku laughed. "My behavior patterns would make a good entropy source too."
"You're certainly unpredictable," Aoi smiled wryly.
Before leaving, the professor said, "Randomness is the foundation of information. Complete predictability means zero information content."
The three nodded quietly.
"Random-senpai taught us something important in their whimsical way today too," Yuki murmured.
Outside the window, wind swayed the leaves unpredictably.