The Informational Measure of Existence — Kolmogorov Complexity as a Cosmological Metric
Fuente:
Zenodo
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Langue: | russe |
| Publié: |
Zenodo
2026
|
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866902041249447936 |
|---|---|
| author | Avanesyan, Tigran |
| author_facet | Avanesyan, Tigran |
| contents | <div class="chat-content-container"> <div class="chat-content-list"> <div class="chat-content-item chat-content-item-assistant"> <div class="segment segment-assistant"> <div class="segment-container"> <div class="segment-content"> <div class="segment-content-box"> <div class="markdown-container"> <div class="markdown"> <div class="paragraph">The measure problem stands as one of the deepest unresolved crises in modern cosmology. In the eternally inflating multiverse, where spacetime is infinite and every macroscopic configuration recurs infinitely many times, conventional volume-based and observer-counting measures fail catastrophically: they are non-normalizable, arbitrarily cutoff-dependent, and predict that typical observers should be Boltzmann Brains—transient fluctuations in the vacuum rather than products of biological evolution. This paradox undermines the very possibility of making statistical predictions in cosmology.</div> <div class="paragraph"><strong>Project ERGODICON</strong> proposes a fundamentally new solution: the <strong>Algorithmic Cosmological Measure (ACM)</strong>. Rather than counting volumes or observers, ACM assigns probabilities via the conditional Kolmogorov complexity of a region’s initial conditions, weighted by the Solomonoff universal prior. The key insight is that an evolutionary history of an observer is algorithmically compressible (laws of physics + initial data + evolutionary algorithm), whereas a Boltzmann Brain is incompressible thermal noise. Consequently, evolutionary observers exponentially dominate the measure, naturally resolving the Boltzmann Brain paradox without <em>ad hoc</em> anthropic selection. Furthermore, because the set of evolutionary histories forms a prefix-free set in program space, the measure normalizes automatically via the Kraft–MacMillan theorem—eliminating the need for arbitrary spatial or temporal cutoffs.</div> <h3 class="">Research Objectives</h3> <div class="paragraph"><strong class="">Objective 1: Formal Foundations of ACM</strong><br>We will rigorously define the conditional Kolmogorov complexity <em>K(R | Λ, T̂)</em> for cosmological regions within an inflationary framework, prove that the set of observer-generating histories is prefix-free, and establish the normalization <em>Ω_ACM ≤ 1</em>.</div> <div class="paragraph"><strong class="">Objective 2: The Complexity Gap Theorem</strong><br>We will derive and bound the complexity gap <em>ΔK = K_BB − K_evo</em> between fluctuational and evolutionary paths. Using explicit estimates of thermodynamic entropy for neural tissue (~10²⁸ bits) versus the algorithmic description length of Darwinian evolution, we will prove that <em>P_ACM(evo)/P_ACM(BB) ~ 2^(10²⁸)</em>—a super-exponential suppression of Boltzmann observers.</div> <div class="paragraph"><strong>Objective 3: Decoherence Drift and Copy Lifetime</strong><br>We will introduce the <em>Decoherence Drift Theorem</em>, quantifying the characteristic time <em>τ_d</em> after which two algorithmically identical copies of a macroscopic system diverge due to quantum decoherence and Lyapunov chaos. For planetary biospheres, we estimate <em class="">τ_d ~ 10⁵ seconds</em> (~1 day), establishing that cosmic duplicates are metastable, not eternal.</div> <div class="paragraph"><strong>Objective 4: Spatial Statistics of Duplicates</strong><br>We will construct the algorithmic correlation function <em>C_ACM(r)</em>, demonstrating that inflationary initial-condition correlations induce large-scale clustering of Earth-like copies at scales of ~100 Mpc—predicting “super-clusters of duplicates” rather than a Poisson distribution.</div> <h3 class="">Methodology</h3> <div class="paragraph">The project integrates four domains: (i) algorithmic information theory (Solomonoff, Kolmogorov, Chaitin); (ii) quantum decoherence theory (Zurek’s einselection); (iii) inflationary cosmology (eternal inflation, curvature perturbations); and (iv) non-linear dynamics (Lyapunov spectra of macroscopic systems). Analytical derivations will be supplemented by numerical simulations of decoherence rates in hierarchical quantum systems, from single neurons to planetary atmospheres.</div> <h3 class="">Significance and Impact</h3> <div class="paragraph">ERGODICON will provide the first information-theoretic measure of probability in an infinite universe that is simultaneously <strong>normalizable</strong>, <strong>anthropic-cutoff-free</strong>, and <strong>predictive</strong>. By resolving the Boltzmann Brain paradox through algorithmic compression rather than observer selection, it shifts the foundations of multiverse statistics from geometry to information. The project opens testable connections to CMB large-angle anomalies (regions of anomalously low algorithmic complexity) and establishes a rigorous framework for the statistical physics of cosmic duplicates.</div> <div class="paragraph"><strong>Keywords:</strong> measure problem, algorithmic information theory, Kolmogorov complexity, Solomonoff prior, eternal inflation, Boltzmann Brain, quantum decoherence, ergodic cosmology, multiverse statistics.</div> </div> </div> </div> <div class="okc-cards-container"> </div> <div class="segment-assistant-actions"> <div class="segment-assistant-actions-content"> <div class="icon-button"> </div> <div class="icon-button"> </div> <div class="icon-button"> </div> <div class="icon-button"> </div> <div class="icon-button"> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div class="chat-action"> <div class="bottom-action-container"> <div class="to-bottom to-bottom-show"> </div> </div> <div class="chat-notifications"> </div> <div class="chat-editor"> <div class="chat-input"> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20366409 |
| institution | Zenodo |
| language | rus |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Informational Measure of Existence — Kolmogorov Complexity as a Cosmological Metric Avanesyan, Tigran <div class="chat-content-container"> <div class="chat-content-list"> <div class="chat-content-item chat-content-item-assistant"> <div class="segment segment-assistant"> <div class="segment-container"> <div class="segment-content"> <div class="segment-content-box"> <div class="markdown-container"> <div class="markdown"> <div class="paragraph">The measure problem stands as one of the deepest unresolved crises in modern cosmology. In the eternally inflating multiverse, where spacetime is infinite and every macroscopic configuration recurs infinitely many times, conventional volume-based and observer-counting measures fail catastrophically: they are non-normalizable, arbitrarily cutoff-dependent, and predict that typical observers should be Boltzmann Brains—transient fluctuations in the vacuum rather than products of biological evolution. This paradox undermines the very possibility of making statistical predictions in cosmology.</div> <div class="paragraph"><strong>Project ERGODICON</strong> proposes a fundamentally new solution: the <strong>Algorithmic Cosmological Measure (ACM)</strong>. Rather than counting volumes or observers, ACM assigns probabilities via the conditional Kolmogorov complexity of a region’s initial conditions, weighted by the Solomonoff universal prior. The key insight is that an evolutionary history of an observer is algorithmically compressible (laws of physics + initial data + evolutionary algorithm), whereas a Boltzmann Brain is incompressible thermal noise. Consequently, evolutionary observers exponentially dominate the measure, naturally resolving the Boltzmann Brain paradox without <em>ad hoc</em> anthropic selection. Furthermore, because the set of evolutionary histories forms a prefix-free set in program space, the measure normalizes automatically via the Kraft–MacMillan theorem—eliminating the need for arbitrary spatial or temporal cutoffs.</div> <h3 class="">Research Objectives</h3> <div class="paragraph"><strong class="">Objective 1: Formal Foundations of ACM</strong><br>We will rigorously define the conditional Kolmogorov complexity <em>K(R | Λ, T̂)</em> for cosmological regions within an inflationary framework, prove that the set of observer-generating histories is prefix-free, and establish the normalization <em>Ω_ACM ≤ 1</em>.</div> <div class="paragraph"><strong class="">Objective 2: The Complexity Gap Theorem</strong><br>We will derive and bound the complexity gap <em>ΔK = K_BB − K_evo</em> between fluctuational and evolutionary paths. Using explicit estimates of thermodynamic entropy for neural tissue (~10²⁸ bits) versus the algorithmic description length of Darwinian evolution, we will prove that <em>P_ACM(evo)/P_ACM(BB) ~ 2^(10²⁸)</em>—a super-exponential suppression of Boltzmann observers.</div> <div class="paragraph"><strong>Objective 3: Decoherence Drift and Copy Lifetime</strong><br>We will introduce the <em>Decoherence Drift Theorem</em>, quantifying the characteristic time <em>τ_d</em> after which two algorithmically identical copies of a macroscopic system diverge due to quantum decoherence and Lyapunov chaos. For planetary biospheres, we estimate <em class="">τ_d ~ 10⁵ seconds</em> (~1 day), establishing that cosmic duplicates are metastable, not eternal.</div> <div class="paragraph"><strong>Objective 4: Spatial Statistics of Duplicates</strong><br>We will construct the algorithmic correlation function <em>C_ACM(r)</em>, demonstrating that inflationary initial-condition correlations induce large-scale clustering of Earth-like copies at scales of ~100 Mpc—predicting “super-clusters of duplicates” rather than a Poisson distribution.</div> <h3 class="">Methodology</h3> <div class="paragraph">The project integrates four domains: (i) algorithmic information theory (Solomonoff, Kolmogorov, Chaitin); (ii) quantum decoherence theory (Zurek’s einselection); (iii) inflationary cosmology (eternal inflation, curvature perturbations); and (iv) non-linear dynamics (Lyapunov spectra of macroscopic systems). Analytical derivations will be supplemented by numerical simulations of decoherence rates in hierarchical quantum systems, from single neurons to planetary atmospheres.</div> <h3 class="">Significance and Impact</h3> <div class="paragraph">ERGODICON will provide the first information-theoretic measure of probability in an infinite universe that is simultaneously <strong>normalizable</strong>, <strong>anthropic-cutoff-free</strong>, and <strong>predictive</strong>. By resolving the Boltzmann Brain paradox through algorithmic compression rather than observer selection, it shifts the foundations of multiverse statistics from geometry to information. The project opens testable connections to CMB large-angle anomalies (regions of anomalously low algorithmic complexity) and establishes a rigorous framework for the statistical physics of cosmic duplicates.</div> <div class="paragraph"><strong>Keywords:</strong> measure problem, algorithmic information theory, Kolmogorov complexity, Solomonoff prior, eternal inflation, Boltzmann Brain, quantum decoherence, ergodic cosmology, multiverse statistics.</div> </div> </div> </div> <div class="okc-cards-container"> </div> <div class="segment-assistant-actions"> <div class="segment-assistant-actions-content"> <div class="icon-button"> </div> <div class="icon-button"> </div> <div class="icon-button"> </div> <div class="icon-button"> </div> <div class="icon-button"> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div class="chat-action"> <div class="bottom-action-container"> <div class="to-bottom to-bottom-show"> </div> </div> <div class="chat-notifications"> </div> <div class="chat-editor"> <div class="chat-input"> </div> </div> </div> |
| title | The Informational Measure of Existence — Kolmogorov Complexity as a Cosmological Metric |
| url | https://doi.org/10.5281/zenodo.20366409 |