Cosmologically Unique IDs

The author embarks on a fascinating thought experiment: how to assign truly unique identifiers to every object across an expanding, universe-spanning civilization. This isn't just about identifying a few billion devices; it's about potentially quadrillions of nanobots or even every atom until the heat death of the universe. The exploration delves into both probabilistic and deterministic methods, weighing their theoretical soundness against their practical scalability.

• Probabilistic IDs (Random Numbers): The simplest approach involves generating random numbers. While never truly 'zero' collision probability, increasing the bit length can make collisions 'functionally zero'. The article calculates the bits needed for various cosmic scales: 122 bits for UUIDv4, 372 bits for 1-gram nanobots filling the universe, 532 bits for every atom, and a staggering 798 bits if the entire universe were a 'computronium' assigning IDs until its end.
• Deterministic IDs: These schemes aim for guaranteed uniqueness without relying on probability. Initial ideas include a central counter (impractical due to distance) and hierarchical, 'Dewey'-like IDs (e.g., 13.5.3), which inherently encode provenance. Other variants like 'Binary' and 'Token' schemes are explored, each with different growth characteristics.
• Scaling Challenges & Worst-Case Proof: Through simulations, the article demonstrates how different assignment patterns (subtree expansion vs. linear chains) impact ID length. Critically, it presents a proof that any deterministic scheme will eventually exhibit linear growth in ID length in the worst-case, meaning ID sizes would become unmanageably large.
• Cosmic Extrapolation: Applying observed logarithmic growth from simulations to models of human expansion across planets and galaxies, the author shows that deterministic IDs would require an impossible number of bits (many petabytes per ID) to encode the full provenance across cosmic distances.

The conclusion is clear: despite the allure of guaranteed uniqueness, random IDs with a sufficiently large bit-space remain the only truly practical solution for cosmic-scale identification, as deterministic schemes quickly become unworkably large under realistic (and even speculative) expansion models.