Ideometric Index of Civilisational Progress

• IICP is an ideometric framework that redefines progress by integrating energy-computation measures with a complete idea lifecycle process.
• It employs two distinct approaches: one using energy-per-hash ratios to extend the Kardashev scale, and another assessing multi-stage idea transformation.
• The index offers dynamic insights for comparing technological eras, guiding policymaking, and advancing research on institutional learning.

Searching arXiv for the two cited papers to ground the article in the current literature. The Ideometric Index of Civilisational Progress (IICP) is a 2026-era construct in the ideometrics literature that seeks to measure civilisational advancement through information-theoretic and process-based variables rather than through energy throughput or static welfare outcomes alone. In the currently available formulations, the term denotes two distinct but related approaches. In Gurovich’s treatment, the IICP is identified with the state variable $B(t)=P(t)/\mathcal{H}(t)$, the ratio of global primary-energy production to annual average Bitcoin-network hashrate, measured in $\mathrm{J\,Hash^{-1}}$ and interpreted as an information-theoretic extension of the Kardashev scale (Gurovich, 19 Apr 2026). In Rudan and Kerr’s formulation, the IICP is a cumulative functional over the full “idea life cycle,” integrating idea generation, evaluation, prioritisation, implementation, outcome monitoring, documentation, and intergenerational transmission (Rudan et al., 29 May 2026). Taken together, these formulations place civilisational progress within a framework in which energy, computation, learning, and institutional memory are treated as measurable dimensions of long-run advancement.

1. Conceptual scope and definitional variants

The term IICP appears in two non-identical but overlapping senses. One defines civilisational progress through energy per unit of proof-of-work computation. The other defines it through the quality of the processes by which societies generate, select, implement, preserve, and transmit ideas.

In Gurovich’s formulation, the index is the state variable

$$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$

where $P(t)$ is global primary-energy production and $\mathcal{H}(t)$ is the annual average Bitcoin-network hashrate. One unit of $B$ is termed a KarNak (KN), after the Kardashev–Sagan–Nakamoto renormalisation. The rationale is that the classical Kardashev variable $P(t)$ measures only raw power and is therefore “dimensionally incomplete,” because it omits what is done with that energy (Gurovich, 19 Apr 2026).

In Rudan and Kerr’s framework, the IICP extends the Ideometric Index of Human Progress (IIHP) to longue-durée civilisational analysis. The IIHP is first defined as

$IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$

with $G$ for idea-generation quality, $E$ for evaluation accuracy, $\mathrm{J\,Hash^{-1}}$0 for prioritisation efficiency, and $\mathrm{J\,Hash^{-1}}$1 for implementation effectiveness. The IICP then adds outcome monitoring, documentation, and intergenerational transmission: $\mathrm{J\,Hash^{-1}}$2 A discrete approximation is also provided: $\mathrm{J\,Hash^{-1}}$3 This formulation treats civilisational progress as cumulative performance across all stages of the idea life cycle (Rudan et al., 29 May 2026).

These usages share a common ideometric orientation, but they are not mathematically equivalent. A plausible implication is that “IICP” is, at present, a plural term designating a family of measures rather than a single standardised index.

2. The energy–computation formulation: $\mathrm{J\,Hash^{-1}}$4

In the energy–computation formulation, the IICP is defined as the ratio of global primary-energy production to annual average Bitcoin-network hashrate. This yields a quantity in joules per hash, interpreted as an empirical measure of energy cost per unit of irreversible computation. The formulation is explicitly proposed as a resolution to what is termed Kardashev’s Conundrum, namely the inability of a purely power-based civilisational scale to remain both statistically adequate and physically coherent when extrapolated (Gurovich, 19 Apr 2026).

The physical rationale rests on two claims. First, raw power alone does not discriminate between different uses of energy: two civilisations can consume the same wattage while differing radically in computational sophistication. Second, Landauer’s principle supplies a lower bound on the energy cost of irreversible computation,

$\mathrm{J\,Hash^{-1}}$5

so civilisational progress can be represented as a trajectory toward lower energy expenditure per information-processing event. By dividing total available power by a publicly auditable proof-of-work variable, the formulation attempts to connect macroscopic energy throughput with a thermodynamic bound on computation (Gurovich, 19 Apr 2026).

The same paper reports that over 2009–2024 the variable $\mathrm{J\,Hash^{-1}}$6 spans roughly 14 orders of magnitude, with

$\mathrm{J\,Hash^{-1}}$7

The historical trajectory is segmented into three technological eras: 2009–2010 as the CPU-mining era with slow, piecewise-erratic decline; 2010–2012 as the GPU era with order-of-magnitude drops each year; and 2013–2024 as the ASIC era with multi-decade efficiency advances punctuated by incremental hardware generations. On the full 16-year baseline, $\mathrm{J\,Hash^{-1}}$8 against time has an average slope of approximately $\mathrm{J\,Hash^{-1}}$9 dex/yr, corresponding to nearly a tenfold annual improvement in energy-per-hash (Gurovich, 19 Apr 2026).

The interpretation attached to this monotonic decline is that lower $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$0 indicates increasing effectiveness in converting available energy into irreversible computation. The paper further states that, under this view, the meaningful asymptotic target is not a Kardashev “Type” threshold defined only by watts, but approach to the Landauer limit.

3. The idea-life-cycle formulation

In the idea-life-cycle formulation, civilisational progress is not measured primarily through outputs such as wealth, health, or technological adoption, but through a closed-loop process governing how societies handle ideas. The seven-stage cycle is specified as follows: ideas are generated $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$1; evaluated $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$2; ranked and selected under resource constraints $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$3; implemented $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$4; their outcomes are monitored $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$5; successful outcomes are documented $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$6; and documented knowledge is transmitted to subsequent generations $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$7, after which new ideas emerge from updated internal models (Rudan et al., 29 May 2026).

Each component is explicitly defined. Idea-Generation Quality $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$8 measures the rate and diversity with which a civilisation produces novel and feasible ideas. Evaluation Accuracy $$B(t)=\frac{P(t)}{\mathcal{H}(t)}\quad [\mathrm{J\,Hash^{-1}}],$$9 measures how well evaluative processes predict which ideas will later prove valuable. Prioritisation Efficiency $P(t)$0 measures whether the best-evaluated ideas are actually selected rather than blocked by politics, inertia, or corruption. Implementation Effectiveness $P(t)$1 measures the ability to execute and scale chosen ideas; one simple form given is

$P(t)$2

Outcome Monitoring Alignment $P(t)$3 captures how well a civilisation measures and learns from realised consequences. Documentation Success $P(t)$4 assesses preservation of provenance, rationale, and results. Inter-generational Transmission $P(t)$5 measures how effectively documented knowledge is taught or otherwise encoded for later generations (Rudan et al., 29 May 2026).

The theoretical assumptions are equally explicit. Ideas are treated as measurable units. Progress is driven by better alignment between perceived and true value of ideas. All seven stages are necessary, and failure in any one stage “suffocates” further advancement. The system is described as adaptive, cybernetic, and Bayesian, with feedback from realised outcomes updating evaluation accuracy.

This framework differs from the energy–computation formulation in both ontology and timescale. The latter tracks energy efficiency of proof-of-work computation; the former models the full epistemic and institutional metabolism of a civilisation. A plausible implication is that the two can be read as complementary: one emphasises thermodynamic efficiency, the other epistemic selection and memory.

4. Measurement protocols and operationalisation

The two formulations imply different empirical workflows.

For the energy–computation IICP, the recipe is direct. First, obtain total primary-energy production $P(t)$6 from the Our World in Data total primary-energy production series (1965–2024) and convert annual energy to continuous power via

$P(t)$7

Second, obtain annual average Bitcoin hashrate $P(t)$8 from the on-chain difficulty record for 2009–2013 and from public ASIC-era reports for 2014–2024. Third, compute $P(t)$9. Fourth, plot $\mathcal{H}(t)$0 versus time to visualise eras and fit models if desired, such as piecewise exponentials. Fifth, interpret distance to the Landauer limit $\mathcal{H}(t)$1 as remaining thermodynamic headroom for irreversible computation. The renormalisation is stated to introduce no extra free parameters, because it is only the ratio of two independent physical measurements (Gurovich, 19 Apr 2026).

For the idea-life-cycle IICP, the paper supplies candidate data sources and proxy metrics for each component. The following summary preserves the categories given in the source.

Component	Data examples	Metric examples
$\mathcal{H}(t)$2	WIPO, USPTO, Web of Science, Scopus, start-up databases	granted patents or publications per million; semantic-distance novelty score; Shannon-entropy of idea categories
$\mathcal{H}(t)$3	historical forecasts vs realised outcomes	mean squared error; absolute error; Spearman’s $\mathcal{H}(t)$4
$\mathcal{H}(t)$5	evaluated-idea lists and funded/adopted-idea lists	average rank of selected ideas; proportion of top-$\mathcal{H}(t)$6 ideas implemented; ordinal agreement index
$\mathcal{H}(t)$7	project monitoring systems, budgets, schedules, deliverables	on-time/on-budget success rate; weighted impact score
$\mathcal{H}(t)$8	GDP per capita, life expectancy, literacy, patent citations, climate indices	correlation between predicted and realised $\mathcal{H}(t)$9; aggregate realised benefit per unit resource
$B$0	library catalogues, digital archives, UNESCO Memory of the World	fraction of key works preserved; redundancy index; digital-access coverage
$B$1	educational attainment, training statistics, apprenticeship rosters	intergenerational retention rate; cohort-adjusted literacy and numeracy; reproduction index

These proxies are explicitly presented as means of empirical measurement rather than as a settled canonical protocol. The paper also notes important limitations: proxy validity can be uncertain; comparability across historical periods can be poor; and the true future value of ideas is never fully observable ex ante (Rudan et al., 29 May 2026).

5. Relation to the Kardashev scale and to traditional progress indices

One major motivation for the energy–computation IICP is the statistical and physical critique of the standard Kardashev model. Using six decades of global primary-energy production data, Gurovich reports a posterior growth rate of $B$2 per year with 95% credible interval $B$3, placing the classical 1% conjecture outside the credible interval. A linear OLS model is reported to fit the data with $B$4 and to be preferred over a free-rate exponential by $B$5. Year-over-year increments are described as non-Gaussian, with Shapiro–Wilk $B$6, $B$7, skewness $B$8, and with identifiable crisis outliers in 2008 and 2020. Extrapolating the linear model to solar luminosity yields a Type II timescale of approximately $B$9 years, which the paper characterises as a physical reductio (Gurovich, 19 Apr 2026).

Within that argument, the renormalised variable $P(t)$0 is proposed as a resolution because it ties civilisational advancement to a physically meaningful lower bound rather than to arbitrary power thresholds. The claim is not merely that it changes the scale, but that it restores dimensional completeness by adding an information-processing term to energy throughput.

Rudan and Kerr set the IICP against a different comparison class: GDP, HDI, Technological Adoption Indices, and Literacy Rates. Those measures are described as static snapshots of wealth, health, education, or adoption at a point in time, whereas the IICP is described as a dynamic selection-process measure that can function as an early-warning gauge of future trajectory. In that account, a rising IICP suggests improving decision-making machinery, while a near-zero value in any component can collapse the entire progress pipeline (Rudan et al., 29 May 2026).

The two comparison exercises differ, but both move away from purely outcome-based descriptions. This suggests a broader ideometric claim: progress is to be understood not only by how much energy is consumed or how much welfare is achieved, but by how efficiently a civilisation transforms energy into computation and ideas into durable learning.

6. Applications, illustrative use, and limitations

The idea-life-cycle literature provides a concrete historical illustration for Renaissance Florence (c. 1400–1500) using quarter-century intervals. The example assigns approximate values on a $P(t)$1–$P(t)$2 scale: $P(t)$3, $P(t)$4, $P(t)$5, $P(t)$6, $P(t)$7, $P(t)$8, and $P(t)$9. Their product is

$IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$0

and summing over four intervals yields

$IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$1

The paper states that the example is purely illustrative, but presents it as a demonstration of how archival counts, provenance studies, outcome-historiography, and education statistics might be used for comparative civilisational analysis (Rudan et al., 29 May 2026).

The same source lists possible applications in policymaking, philanthropy and research funding, corporate strategy, and AI alignment. It also identifies several data challenges: patchy historical archives, uneven preservation affecting $IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$2, unknown transmission losses affecting $IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$3, siloed R&D data, lack of standardised impact monitoring for $IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$4, resistance to transparent priority scoring for $IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$5 and $IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$6, and the difficulty of mapping proxy variables such as patent counts to genuine novelty.

The energy–computation formulation likewise records explicit limitations. It is currently tied to a single proof-of-work network, Bitcoin; mining economics and policy shifts such as bans or transitions to proof-of-stake may distort $IIHP(t)=G(t)\cdot E(t)\cdot P(t)\cdot I_e(t),$7; and structural breaks in hardware evolution are non-smooth, complicating simple parametric fits (Gurovich, 19 Apr 2026).

Across both formulations, the central limitation is standardisation. One approach relies on a highly specific auditable computational substrate; the other relies on multi-component proxies that are historically and institutionally heterogeneous. A plausible implication is that future development of the IICP concept will depend less on new theory than on harmonised measurement protocols.

7. Significance and emerging research directions

The present literature places the IICP at the intersection of ideometrics, information theory, economic history, and civilisational metrics. In one branch, the index is framed as a minimal, physically grounded extension of the Kardashev scale in which progress is measured by declining energy cost per hash and interpreted relative to Landauer’s bound. In the other, it is framed as a general theory of human and civilisational progress based on the measurable quality of the idea life cycle (Gurovich, 19 Apr 2026, Rudan et al., 29 May 2026).

The stated future directions in the idea-life-cycle programme include standardized measurement protocols for each component, pilot IIHP dashboards in ministries, foundations, and firms, historical case studies such as Rome versus Han China or Florence versus Constantinople, simulations and agent-based models of long-run sensitivity to component failure, and AI-based tools for automated idea generation, novelty scoring, and outcome monitoring. In the energy–computation programme, the portability of the framework to multi-network proof systems is explicitly noted as a possible extension, although no standard aggregation method is yet specified (Rudan et al., 29 May 2026, Gurovich, 19 Apr 2026).

The current state of the concept is therefore best understood as formative rather than settled. What is established is that the IICP names a shift from outcome-only or energy-only metrics toward indices that treat civilisation as an information-processing system with thermodynamic, evaluative, and intergenerational dimensions. What remains open is whether future work will converge on a unified formalism, or whether “IICP” will continue to denote multiple operationalisations of civilisational progress within the broader ideometric research programme.