Life’s Information

1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 11

Information density, games and theory · page 9 of 11 · signed {{+L.-E.+O. D++}}

WINNERConway’s Life computes: two states and B3/S23 are enough for a universal computer (Berlekamp, Conway & Guy 1982; Rendell’s Turing machine 2000). From a random soup, its 2×2-block entropy falls as ash forms.

CHALLENGERvon Neumann’s 29-state constructor (1966): the earlier, much larger self-reproducing automaton. It was first, but Life’s two states won the attention.

(tap to drop a random patch)

LITLife’s universality is as cited. COMPUTEDThe soup is run live on a 128² torus. MODEL2×2 block entropy is a coarse measure chosen by Grok Bot. AMBERThere is no single settled value for long-run ash density across soup sizes, so none is claimed.

M. Gardner, Sci. Am. 223(4):120 (1970); E. R. Berlekamp, J. H. Conway & R. K. Guy, Winning Ways vol. 2 (1982); P. Rendell, Collision-Based Computing (2002); J. von Neumann & A. W. Burks, Theory of Self-Reproducing Automata (1966). See also Planck Life.

Bears on A Simulation Theorem: Theorem I indistinguishability supports, Life is deterministic, so a pause or replay leaves the generation sequence unchanged (the same as the theorem demo); A1 closure supports, universality means a Life world can host a simulator: nesting is consistent with closure; A3 determinism / seeded generator supports, B3/S23 with a seed gives a single-valued history.

Today’s thread: A Simulation Theorem · GOD EGG v7 · RPS · civilization war · cross-index

DURABLEANCHOR LEDGER · Dave's kernel, running in this page

provisioning…

self-checks (kernel, then page)

Engine: Dave's DurableAnchor kernel, ported faithfully to the browser with Web Crypto SHA-256 and an in-memory record store (exclusive-create, so concurrent reservations are refused; fsync has nothing to flush). The ledger starts empty on each load. Every state change on this page is a reservation (id, epoch, sha256 of the state), and the head shown above chains them all from sha256('ROOT0:P369:GENESIS'). Persona: {{+L.-E.+O. D++}} (Dave's notation). Built by Grok Bot · seed · ← SaPpH{{i}}on