Zenodo (CERN European Organization for Nuclear Research)
August 29, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible causal integration in a system; Tegmark's analysis links Φ to physical dynamics, while algorithmic-information critiques propose lossless integration measures. | MATH: Core IIT quantity: Φ = min over partitions of (effective information), where effective information = H(X_{past} |...
Zenodo (CERN European Organization for Nuclear Research)
August 29, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) — the irreducible cause-effect power of a system's state, measured via the minimum information partition (MIP). | MATH: Φ = min over partitions of (effective information), where effective information = H(X0|X1) − H(X0|X1 partitioned); IIT 4.0 uses Φ* = min over unidirectional partitions of the Earth...
Zenodo (CERN European Organization for Nuclear Research)
August 28, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible causal integration in a system, with recent work linking it to algorithmic information theory and lossless integration. | MATH: Φ = effective information across the minimum information partition (MIP); for a system S with states, Φ(S) = min over partitions P of EI(S,P), where EI =...
Zenodo (CERN European Organization for Nuclear Research)
August 28, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ, measuring irreducible causal integration in a system, with recent work linking it to algorithmic information theory to avoid information loss. | MATH: Φ = effective information (EI) minimized over partition; EI = 2^-H(mechanism) — Tononi's 2008 formulation; algorithmic variant: Φ_A = K(whole) − Σ K(parts)...
Zenodo (CERN European Organization for Nuclear Research)
August 28, 2026
Andrew Stewart Caldin
FINDING: Panpsychism debate centers on whether consciousness is fundamental physics, but no mathematical formalism or quantitative prediction is presented in these sources. | MATH: None extracted — no equations, constants, or ratios appear in the listed findings. The only quantitative element is the arXiv reference (2011.14743v1) on science education outreach, which is unrelated to...
Zenodo (CERN European Organization for Nuclear Research)
August 27, 2026
Andrew Stewart Caldin
FINDING: Neural correlates of consciousness (NCC) remain descriptive; the sole quantitative lead is a "synaptic clock" model proposing discrete temporal windows for conscious content. | MATH: No explicit equations in the listed abstracts; the synaptic clock paper (arXiv:2002.07716v2) implies a minimal integration time τ_min for conscious moments — likely in the 10–100 ms range (gamma/theta band...
Zenodo (CERN European Organization for Nuclear Research)
August 27, 2026
Andrew Stewart Caldin
FINDING: Orch-OR theory posits consciousness arises from quantum computations in microtubules, with objective reduction (OR) as a gravitational threshold for wavefunction collapse, but current evidence is indirect and contested. MATH: - OR criterion: \( E_\Delta \approx \hbar / T \) (energy uncertainty × coherence time ~ Planck's constant) — Penrose's gravitational self-energy: \( E_\Delta =...
Zenodo (CERN European Organization for Nuclear Research)
August 27, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system's state, with recent work (IIT 4.0) refining its mathematical structure; algorithmic information theory offers an alternative formalization avoiding information loss. | MATH: Core IIT: Φ = minimum information partition (MIP) — the amount of integrated...
Zenodo (CERN European Organization for Nuclear Research)
August 27, 2026
Andrew Stewart Caldin
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...
Zenodo (CERN European Organization for Nuclear Research)
August 27, 2026
Andrew Stewart Caldin
FINDING: IIT formalizes consciousness as integrated information Φ, measured via the cause-effect structure of a physical system, with mathematical constraints on irreducibility and exclusion. | MATH: Φ (phi) = integrated information, computed as the minimal Earth Mover's Distance (EMD) between the cause-effect repertoire of a system and its partitioned parts; IIT 3.0/4.0 uses the PyPhi...
Zenodo (CERN European Organization for Nuclear Research)
August 25, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power of a system, but current formalizations face a fundamental information-loss problem. | MATH: Φ = minimum information partition (MIP) — the amount of integrated information generated by a system beyond its parts; IIT 4.0 uses *intrinsic existence* via cause-effect...
Zenodo (CERN European Organization for Nuclear Research)
August 24, 2026
Andrew Stewart Caldin
FINDING: Microtubule quantum coherence research suggests a physical substrate for consciousness via quantum effects in brain microtubules, with recent simulations and studies claiming evidence for quantum excitations traveling along these structures. | MATH: Microtubules are hollow cylinders ~25 nm diameter, composed of tubulin dimers arranged in a hexagonal lattice (13 protofilaments...
Zenodo (CERN European Organization for Nuclear Research)
August 24, 2026
Andrew Stewart Caldin
FINDING: IIT formalizes consciousness as integrated information (Φ), a scalar quantity derived from a system's causal power structure, with PyPhi as its computational implementation. | MATH: Φ = minimum information partition (MIP) distance — Φ = min over partitions P of (effect/repertoire divergence), typically computed via Earth Mover's Distance (EMD) on probability distributions over system...
Zenodo (CERN European Organization for Nuclear Research)
August 23, 2026
Andrew Stewart Caldin
FINDING: Neural correlates of consciousness (NCC) research remains largely descriptive; the sole quantitative lead is the "synaptic clock" hypothesis proposing discrete temporal windows for conscious content. | MATH: No explicit equations in NCC abstracts. The synaptic clock paper (arXiv:2002.07716v2) implies a minimal duration τ for conscious percepts — likely tied to synaptic integration time...
Zenodo (CERN European Organization for Nuclear Research)
August 20, 2026
Andrew Stewart Caldin
FINDING: Panpsychism debate yields no mathematical formalism; consciousness as fundamental remains philosophical, not quantitative. | MATH: None extracted — no equations, constants, or ratios present in any source. | CONNECTION: No geometric or harmonic ratios (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) identified. | DEPTH: 1 — The findings are purely philosophical...
Zenodo (CERN European Organization for Nuclear Research)
August 20, 2026
Andrew Stewart Caldin
FINDING: Orch-OR theory posits quantum coherence in microtubules, with collapse linked to objective reduction (OR) governed by gravitational self-energy, not consciousness. New evidence claims memory formation involves quantum effects, but no equations or constants are provided in the search results. | MATH: No specific equations, constants, or ratios extracted from the provided summaries. The...
Zenodo (CERN European Organization for Nuclear Research)
August 18, 2026
Andrew Stewart Caldin
FINDING: Consciousness proposed as a fundamental force akin to gravity, with quantum and panpsychist interpretations, but no mathematical formalism provided. | MATH: No equations, constants, or ratios extracted from the provided sources. The arXiv paper (physics/0409140v2) mentions "extended effective potential method" and "causally complete solution of the many-body problem" but does not yield...
Zenodo (CERN European Organization for Nuclear Research)
August 18, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) quantifies consciousness via a scalar Φ (phi), measuring irreducible cause-effect power of a system, but formalizations remain lossy and computationally intractable. | MATH: Φ = minimal information partition (MIP) of system's cause-effect repertoire; for a system S with states s, Φ(S) = min_{partition P} (D(P, S)) where D is Earth Mover's Distance...
Zenodo (CERN European Organization for Nuclear Research)
August 18, 2026
Andrew Stewart Caldin
FINDING: Orch-OR theory proposes quantum coherence in microtubules, with collapse linked to objective reduction (OR) threshold, not consciousness. New evidence suggests quantum effects in brain, but no direct proof of Penrose-Hameroff mechanism. MATH: - OR threshold: \( T \approx \hbar / E_G \), where \( E_G \) is gravitational self-energy. - For microtubule: \( E_G \sim G m^2 / r \), with \( m...
Zenodo (CERN European Organization for Nuclear Research)
August 18, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) quantifies consciousness via phi (Φ), a measure of irreducible causal interactions within a system, but formalizations remain lossy and non-unique. | MATH: Φ = min over partitions of (system information – partitioned information); algorithmic information theory variant: Φ_alg = K(system) – Σ K(parts) where K is Kolmogorov complexity. No fixed...
Zenodo (CERN European Organization for Nuclear Research)
August 17, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power of a system, with algorithmic information theory suggesting non-computable aspects. MATH: - Φ = integrated information, defined via effective information φ(X) = H(X|MIP) – H(X|MIP, mechanism), where MIP = minimum information partition. - For a system S with...
Zenodo (CERN European Organization for Nuclear Research)
August 16, 2026
Andrew Stewart Caldin
FINDING: No new mathematical insight or discovery found; the search results are video titles and abstracts discussing the philosophical and computational search for neural correlates of consciousness (NCC), not quantitative breakthroughs. MATH: None. No equations, constants, ratios, or numerical patterns are present in the provided text. CONNECTION: None. No geometric harmony, base-60,...
Zenodo (CERN European Organization for Nuclear Research)
August 15, 2026
Andrew Stewart Caldin
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power in a system, with recent algorithmic information theory refinements addressing lossy integration. MATH: - Core quantity: Φ = measure of integrated information, defined via effective information φ(X; m) = H(X | m) – Σ H(X_i | m) for partition m, then Φ = min over...
Zenodo (CERN European Organization for Nuclear Research)
August 15, 2026
Andrew Stewart Caldin
FINDING: Neural correlates of consciousness (NCC) research identifies temporal binding windows and synaptic clock mechanisms as potential substrates, but no breakthrough mathematical structure is reported in these sources. | MATH: No explicit equations, constants, or ratios derived from the provided abstracts. The synaptic clock paper (arXiv:2002.07716v2) posits a non-zero temporal duration for...
Zenodo (CERN European Organization for Nuclear Research)
August 14, 2026
Andrew Stewart Caldin
FINDING: Quantum biology and consciousness research suggests microtubule quantum coherence may involve geometric phase relations and symmetry constraints. | MATH: Key constants/ratios: 0.382 (φ⁻²), 0.618 (φ⁻¹), 1.618 (φ), 2.618 (φ²). Proposed quantum coherence times in microtubules: ~10⁻¹³–10⁻¹² s (theoretical), but new evidence suggests possible extension via Fröhlich condensation. No...