1. The Necessity of 'Logically Impossible Events' in Maintaining a Simulation System
→ Information Theory + Systems Theory + Mathematical Formal Systems
Gödel's Incompleteness Theorems
Any formal system (including a simulation) cannot prove all true statements within itself. In other words, a system must necessarily contain statements that are true but unprovable to maintain its internal consistency. This implies that an inherently unsolvable problem must exist to prevent a system from falling into self-referential collapse.
Turing's Halting Problem
There is no universal algorithm capable of determining whether any given program will eventually halt. In other words, unsolvable problems (non-halting situations) must be preserved within a system to ensure both its computational possibility and structural stability.
The Measurement Problem in Quantum Mechanics
Quantum states exist in superposition until measured. This implies the necessity of unobservable and unmeasurable states as a foundation of the physical system. This can be interpreted as a kind of logical boundary that cannot be approached or resolved from within the system.
2. Every System Requires Mechanisms to Prevent Abnormal Situations
→ Systems Theory + Control Theory + Security Engineering
Fail-safe & Fail-secure Design Principles
All technological systems require a safe failure mechanism to prevent entering abnormal states. For example, nuclear reactors are designed to shut down automatically when power is lost, and elevators engage brakes in emergency situations.
Formal Verification
In software and hardware design, invariant conditions are established to prevent logical errors or external attacks. If these conditions are violated, the system is forced to stop functioning. Allowing a system to run indefinitely without restrictions is considered extremely dangerous.
3. Operating Systems Without a 'Force Quit' Function Are Hazardous
→ Operating Systems Theory + Kernel Design
Kernel Panic & Watchdog Timer
To prevent systems from falling into infinite loops or freezing, operating systems must include a last-resort forced shutdown mechanism such as hardware interrupts (e.g., Ctrl + Alt + Del) or system reboot protocols.
Deadlock Detection & Recovery
Operating systems are designed to detect deadlocks — situations where processes wait for each other indefinitely — and forcibly terminate or recover resources. The very assumption of a living system requires that certain events must never be allowed to occur.
4. The Example of Zero-Cost Transactions in Finance → The Vulnerability of Economic Systems and the Design of Trust
→ Economics + Game Theory + Financial Engineering
No-Arbitrage Principle
Modern financial systems rest on the assumption that risk-free arbitrage is impossible. If transactions with zero cost could occur infinitely, the entire system would collapse immediately. This is a classic example of impossible equilibrium in game theory.
Reserve Requirements & Bankruptcy Prevention Mechanisms
Financial systems are always designed with worst-case scenarios in mind, incorporating ultimate protection mechanisms such as deposit insurance and central bank intervention. This defines an untouchable boundary designed to ensure that the system never completely halts.