05 · Infinity
Approach, never arrive
The slider's far end is 1. You move toward it. The closer you come, the slower the dial moves, the faster the years behind it grow. The years approach infinity. You do not.
The immortalitesimal
An infinitesimal is a step so small it is treated as zero. An immortalitesimal is a step so small it is treated as zero — but the path it walks is infinite. The closer the ratio is to 1, the smaller the immortalitesimal step, the longer the life behind it.
Why the limit is reached only in death
You cannot arrive at 1 while living, because arriving would be a step of finite size, and the framework's only finite step is the last one. Every step before it is a smaller step than the last. The sum of infinitely many smaller-and-smaller steps is the whole of a life.
The collective immortalitesimal
In a room of two, the product approaches 1 from the same direction, on a different curve. The alchemical gold compounds at second order. The shared lifetime grows faster than either of the two lives it lives inside. The room outlives the room.