!The Boundary Must Not Fracture
When a mechanical dial turns, or a voltage slowly rises, it must eventually cross a boundary from one digital state to the next.
In standard binary, moving from 3 (011) to 4 (100) requires three separate bits to flip simultaneously. But in the physical world, nothing is perfectly simultaneous. One switch will always close a microsecond before the others.
If the system reads the dial during that microscopic transition, it might see 111 (7) or 000 (0). For a fraction of a second, the system is hallucinating a value that does not exist, simply because the boundary fractured during the crossing.
To prevent this, engineers abandon standard counting and use Gray code.
In Gray code, the numbers are reordered so that every adjacent state differs by exactly one bit. Moving from 3 to 4 requires only a single switch to flip.
There is no intermediate state. There is no race condition. The boundary is absolute. The system is either entirely on one side, or entirely on the other.
The boundary must not fracture.
