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arxiv: 2605.22840 · v1 · pith:PXJCFBF5new · submitted 2026-05-11 · ⚛️ physics.soc-ph · cs.AI· cs.CY

The Cognitive Kardashev Scale: Quantifying the Material Envelope of Civilisational Computation

Sachin Sharma This is my paper

Pith reviewed 2026-05-25 00:47 UTC · model grok-4.3

classification ⚛️ physics.soc-ph cs.AIcs.CY
keywords cognitive kardashev scalecivilizational computationenergy to compute efficiencyai-grade cognitionkardashev extensionbrain equivalent unitsplanetary power budget
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The pith

Humanity sits at 0.73 on a Cognitive Kardashev Scale that ranks civilizations by sustainable AI-grade computation from total power.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends the original Kardashev scale, which classifies civilizations by power consumption, into a cognitive version that calculates how much AI-grade thinking each tier can sustain. Four factors enter the model: total power output, the share devoted to cognition, the efficiency of converting energy into floating-point operations, and the human brain's processing rate as a normalization unit. Anchored to 2024-2026 hardware efficiency, the calculation places current humanity at K approximately 0.73. At full Type I power with one percent allocated to cognition the scale indicates roughly one personal AI per human; Type II reaches scales that exceed ready comprehension.

Core claim

The Cognitive Kardashev Scale is constructed from total power P, cognitive fraction f, efficiency η set at 10^12 FLOP/J from contemporary hardware, and brain processing rate C_brain to express civilizational compute capacity in brain-equivalent units. Contemporary humanity reaches K ≈ 0.73. A Type I civilization at f = 1% yields compute within an order of magnitude of one personal AI per inhabitant; Type II capacity is described as essentially incomprehensible.

What carries the argument

The Cognitive Kardashev Scale, which converts a civilization's power budget into sustained brain-equivalent AI computation using the product of power, cognitive share, energy-to-FLOP efficiency, and brain-rate normalization.

If this is right

  • At Type I power with f = 1% the available compute reaches one personal AI per human within an order of magnitude.
  • At Type II the resulting cognitive capacity becomes essentially incomprehensible in human terms.
  • Three conditional trajectories for frontier compute through 2035 are supplied as projections rather than forecasts.
  • Whether energy or efficiency forms the long-run limit depends on engineering choices that remain open.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Political decisions about who can access the compute may constrain realized cognition more tightly than total energy or efficiency alone.
  • Large efficiency gains could produce high cognitive capacity without requiring full Type II power levels.
  • The scale supplies a consistent metric for comparing the cognitive ceilings of different technological or societal paths.

Load-bearing premise

The efficiency at which energy becomes compute is taken directly from 2024-2026 hardware performance and the brain's processing rate is treated as a valid reference unit for AI cognition.

What would settle it

Direct measurement showing that future hardware efficiency lies more than an order of magnitude away from 10^12 FLOP/J, or evidence that brain computation cannot be compared quantitatively to AI operations, would invalidate the numerical placements on the scale.

Figures

Figures reproduced from arXiv: 2605.22840 by Sachin Sharma.

Figure 1
Figure 1. Figure 1: Compute efficiency η across workload classes, 2024–2026. Bars on a logarithmic horizontal axis. The roughly two- to three-order-of-magnitude gap between sustained scientific (FP64) and peak ML inference (FP4) reflects the move to lower-precision arithmetic; the further gap of up to two orders of magnitude between peak ML inference and the upper end of biological-brain efficiency bounds the energetic advant… view at source ↗
Figure 2
Figure 2. Figure 2: Cognitive Kardashev Scale. Total brain-equivalents N as a function of civilisational power P, at five energy-allocation fractions f ∈ {0.1%, 1%, 5%, 10%, 50%}. Computed at η = 1012 FLOP/J and Cbrain = 1016 FLOP/s; brain-equivalent values carry roughly ±1 order of magnitude of irreducible uncertainty from the Cbrain literature range. Vertical dotted lines mark the four reference power levels (Earth 2025, Ty… view at source ↗
Figure 3
Figure 3. Figure 3: Per-capita cognitive abundance (log10) under the three [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Frontier training-compute trajectory and three forward scenarios, 2012–2035. Twelve observed frontier models (blue dots, with the historical regression as the thin grey line). Three forward scenarios projected from the 2026 anchor of 3 × 1026 FLOPs to 2035: Current at ×3.51/yr (grey dashed; regression on 2012–2026), Better at ×4.2/yr (green dash-dot; published Sevilla et al. [2022] rate), and Optimistic at… view at source ↗
read the original abstract

How much thinking can a civilisation do? Kardashev's (1964) typology ranks civilisations by total power: planetary (Type I, ~10^16 W), stellar (Type II, ~10^26 W), galactic (Type III). This paper builds an analogous Cognitive Kardashev Scale: how much sustained AI-grade computation each tier could support. Four ingredients enter the calculation: total power P (watts), the share f of it devoted to cognition, the efficiency $\eta$ at which energy becomes compute (operations per joule), and the brain's own processing rate $C_{\mathrm{brain}}$ as a reference unit. Anchoring on 2024-2026 hardware (El Capitan, NVIDIA Blackwell, Vera Rubin) gives $\eta_{2026} = 10^{12}$ FLOP/J. Contemporary humanity sits at $K \approx 0.73$, three-quarters of the way to Type I. At Type I and $f = 1\%$, available compute is, within an order of magnitude, one personal AI's worth of cognition per human inhabitant; at Type II it is essentially incomprehensible. Three trajectories for frontier compute through 2035 are reported as conditional projections, not predictions. Whether the long-run binding constraint is energy or efficiency depends on engineering choices not yet made; the political economy of who has access may matter more than either.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper proposes a 'Cognitive Kardashev Scale' K that extends Kardashev's power-based typology to quantify sustained AI-grade computation supported by a civilization's total power P, the fraction f devoted to cognition, the energy-to-compute efficiency η (FLOP/J), and the brain's processing rate C_brain as a reference unit. Anchoring η on 2024-2026 hardware yields η_2026=10^12 FLOP/J; the manuscript reports contemporary humanity at K≈0.73, states that a Type-I civilization (P=10^16 W) at f=1% supplies roughly one personal-AI brain-equivalent per human, and supplies conditional 2035 projections for frontier compute.

Significance. If the parameterization and normalization choices hold, the scale supplies a compact heuristic linking energy budgets to computational capacity and flags that long-run limits may be set more by allocation and access than by raw efficiency. The conditional projections add a near-term empirical hook. No machine-checked derivations or parameter-free results are present.

major comments (3)
  1. [Abstract] Abstract: the headline claim K≈0.73 for contemporary humanity is obtained by direct substitution of the chosen values η_2026=10^12 FLOP/J and C_brain into the defining expression for K; the text supplies neither the explicit hardware measurement (including cooling overhead) nor any sensitivity analysis, so that a factor-of-10 shift in either anchor moves K by ~0.2 and falsifies the 'three-quarters of the way to Type I' statement.
  2. [Abstract] Abstract (Type-I paragraph): the assertion that Type-I power at f=1% yields 'within an order of magnitude, one personal AI's worth of cognition per human' inherits the identical untested parameter dependence; no error propagation, alternative normalizers, or robustness checks are shown, rendering the order-of-magnitude claim load-bearing on the specific 2026 hardware anchor.
  3. [Abstract] Abstract: the normalization of all results to C_brain is presented without defense of why biological processing rate is the appropriate unit for silicon AI-grade operations; this choice propagates into every K value and every Type-I/II comparison.
minor comments (1)
  1. [Abstract] The abstract states that 'three trajectories for frontier compute through 2035 are reported' but does not indicate the section or figure in which the trajectories, their assumptions, or their conditional nature are presented.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on the abstract's parameterization and normalization choices. We respond point by point below and indicate planned revisions to improve transparency and robustness.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim K≈0.73 for contemporary humanity is obtained by direct substitution of the chosen values η_2026=10^12 FLOP/J and C_brain into the defining expression for K; the text supplies neither the explicit hardware measurement (including cooling overhead) nor any sensitivity analysis, so that a factor-of-10 shift in either anchor moves K by ~0.2 and falsifies the 'three-quarters of the way to Type I' statement.

    Authors: The η_2026 anchor is derived from announced 2024-2026 hardware performance figures (El Capitan, Blackwell, Vera Rubin) as stated in the methods; however, the abstract does not include cooling overhead or sensitivity. We will revise the abstract to qualify the K≈0.73 figure and add a dedicated sensitivity subsection (with tables showing ±1 order of magnitude shifts) in the main text. This is a partial revision because the underlying definition and hardware basis remain unchanged. revision: partial

  2. Referee: [Abstract] Abstract (Type-I paragraph): the assertion that Type-I power at f=1% yields 'within an order of magnitude, one personal AI's worth of cognition per human' inherits the identical untested parameter dependence; no error propagation, alternative normalizers, or robustness checks are shown, rendering the order-of-magnitude claim load-bearing on the specific 2026 hardware anchor.

    Authors: The order-of-magnitude phrasing is intended as an illustrative heuristic rather than a precise prediction. We accept that explicit robustness checks are warranted and will revise the abstract to note the parameter range while adding error-propagation estimates and alternative normalizer comparisons in the results section. revision: yes

  3. Referee: [Abstract] Abstract: the normalization of all results to C_brain is presented without defense of why biological processing rate is the appropriate unit for silicon AI-grade operations; this choice propagates into every K value and every Type-I/II comparison.

    Authors: C_brain is adopted as a reference unit to express capacity in familiar human-brain equivalents, enabling intuitive cross-scale comparisons of cognitive output. We will add a concise justification in the revised abstract and introduction, clarifying that it functions as a benchmark for sustained cognitive throughput rather than an architectural equivalence claim between biological and silicon systems. revision: yes

Circularity Check

0 steps flagged

No circularity: K value is explicit output of openly stated parameterization

full rationale

The paper defines the Cognitive Kardashev Scale explicitly in terms of four inputs (P, f, η, C_brain) and states that it anchors η on 2024-2026 hardware values before computing the numerical position K≈0.73. This is a direct model evaluation rather than a claimed first-principles derivation or prediction that reduces to its inputs by hidden construction. No equations are presented as independent results; the text frames the output as the consequence of the chosen ingredients. No self-citations, uniqueness theorems, or ansatzes are invoked in the provided text. The numerical claims are therefore self-contained within the model's transparent assumptions and do not meet the criteria for any enumerated circularity pattern.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on chosen values for efficiency and cognitive fraction, plus the assumption that brain processing rate provides a meaningful normalization for AI computation. No independent evidence is supplied for these modeling choices.

free parameters (2)
  • f = 0.01
    Fraction of power devoted to cognition, set to 1% in the Type I example
  • η_2026 = 10^12 FLOP/J
    Compute efficiency anchored on 2024-2026 hardware benchmarks
axioms (1)
  • domain assumption Brain processing rate C_brain is a valid reference unit for AI-grade computation
    Used to normalize the K scale
invented entities (1)
  • Cognitive Kardashev Scale K no independent evidence
    purpose: Quantify sustained AI-grade computation capacity per civilization tier
    New scale definition introduced without external falsifiable test

pith-pipeline@v0.9.0 · 5782 in / 1454 out tokens · 32239 ms · 2026-05-25T00:47:07.625127+00:00 · methodology

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Reference graph

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