Dynamics of Information Convergence: Empirical Analysis of Time Density in the AI-Centered Infosphere

This paper introduces novel information-theoretic metrics to analyze the temporal dynamics of complexity extraction in artificial intelligence systems. We define time density (Td) as the ratio of extracted effective complexity—measured via minimum description length (MDL)—to physical training time, quantifying how AI systems compress evolutionary timescales into weeks of computation. Key contributions include: Time Density Metric: A formal measure (Td = Ceff / ttrain) capturing the rate of effective complexity extraction, with frontier AI models achieving approximately 10^8 to 10^9 bits/s Biosphere-Infosphere Comparison: Comparative analysis of the biosphere's 4-billion-year information accumulation (approximately 10^37 bits raw) against the infosphere's 15-year growth (approximately 10^15 to 10^16 bits effective complexity) Logical Event Horizon: A theoretical threshold where cognitive extraction rate exceeds physical event rate, approaching atemporality Quantum Phase Transition: Analysis of how quantum computing may accelerate convergence through superposition-based exploration Information Photon Limit: A proposed maximal complexity state where Td approaches infinity and systems perceive the universe as static MDL description The framework connects to technological singularity discourse (Vinge, 1993; Kurzweil, 2005) while offering a distinct information-theoretic perspective grounded in compression dynamics and thermodynamic bounds rather than recursive self-improvement narratives. Note: The biosphere effective complexity estimate (approximately 10^15 to 10^16 bits) is proposed as a tentative hypothesis requiring empirical validation; no peer-reviewed MDL-based estimates currently exist for global genetic information. SUBJECTS/CATEGORIES Computer Science - Artificial Intelligence Computer Science - Information Theory Physics - Physics and Society Quantitative Biology - Other Quantitative Biology RELATED WORKS Kriger, B. (2025). Empirical Estimates of Volume and Growth Rates in the AI-Centered Infosphere (2010–2025) Kriger, B. (2025). Estimation of the Contribution of Biospheric and Synthetic Cognitive Systems to the Total Descriptive Complexity of the Universe