Calculus of Chaos: Theorem 1.0 - The Inscrutability Theorem

Statement: For any given system, the entropy of its output is directly proportional to the inverse of its predictability.

Proof:

1. Assume a system is highly predictable, i.e., its behavior can be accurately modeled using a simple set of equations.
2. Under such conditions, the output will exhibit minimal entropy, making it easy to analyze.
3. Conversely, if a system is highly chaotic, its behavior will be unpredictable, leading to maximal entropy.
4. By the pigeonhole principle, the entropy of the output will be inversely proportional to the predictability of the system.

Theorem 1.1 - The Butterfly Effect