Lossless Consciousness: The Integration-Memory Trade-off in Algorithmic IIT — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as irreducible causal structure, but its standard measure (Φ) is lossy; a lossless algorithmic-information reformulation requires a trade-off between integration and memory preservation. MATH: - IIT 4.0: Φ = minimal Earth Mover's Distance (EMD) between cause-effect repertoires of a system and its partitioned parts. For a system S with mechanism M, Φ = min_π EMD(P(M|S), P(M|S_π)) over partitions π. - Algorithmic reformulation (arXiv:1405.0126): replaces Shannon mutual information with algorithmic mutual information: I_alg(X;Y) = K(X) + K(Y) − K(X,Y), where K is Kolmogorov complexity. Lossless integration requires: K(S) ≈ K(parts) + I_alg(parts) − O(1), i.e., no information destruction. - Trade-off: For a system with n components and memory m, lossless integration demands m ≥ n·Φ_lossless, where Φ_lossless = K(S) − ΣK(parts) (excess algorithmic synergy). This is bounded by the system's causal graph's * Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com