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

# Quantifying the Material Envelope of Civilisational Computation
Source: [https://arxiv.org/html/2605.22840](https://arxiv.org/html/2605.22840)
## The Cognitive Kardashev Scale: Quantifying the Material Envelope of Civilisational Computation

###### Abstract

How much thinking can a civilisation do?Kardashev \([1964](https://arxiv.org/html/2605.22840#bib.bib4)\)’s typology ranks civilisations by total power: planetary \(Type I,∼1016\\sim 10^\{16\}W\), stellar \(Type II,∼1026\\sim 10^\{26\}W\), galactic \(Type III\)\. This paper builds an analogousCognitive Kardashev Scale: how much sustained AI\-grade computation each tier could support\. Four ingredients enter the calculation: total powerPP\(watts\), the shareffof it devoted to cognition, the efficiencyη\\etaat which energy becomes compute \(operations per joule\), and the brain’s own processing rateCbrainC\_\{\\text\{brain\}\}as a reference unit\. Anchoring on 2024–2026 hardware \(El Capitan, NVIDIA Blackwell, Vera Rubin\) givesη2026=1012\\eta\_\{2026\}=10^\{12\}FLOP/J\. Contemporary humanity sits atK≈0\.73K\\approx 0\.73, three\-quarters of the way to Type I\. At Type I andf=1%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\.

## 1Introduction

Humanity already lives inside an extended cognitive system whose energy footprint rivals that of medium\-sized countries\. Global data centres consumed∼\\sim415 TWh of electricity in 2024 and are projected to roughly double by 2030\(International Energy Agency,[2025](https://arxiv.org/html/2605.22840#bib.bib17)\)\. A single frontier AI training run now draws power on the order of a small city for weeks at a time\. The hardware racks executing the dominant share of this compute—NVIDIA’s Vera Rubin platform, entering volume production in 2026 at∼\\sim50 PFLOP/s sparse FP4 per accelerator—are being deployed inside vertically integrated, hundred\-billion\-dollar consortia whose announced infrastructure commitments \(Stargate, Terafab\) exceed those of any previous industrial buildout in human history\(OpenAI,[2025a](https://arxiv.org/html/2605.22840#bib.bib24); Carlson and Grush,[2026](https://arxiv.org/html/2605.22840#bib.bib26)\)\. The question this paper asks is not whether such investments will happen—they are happening—but what cognitive capacity they could in principle support, and how that capacity scales as energy budgets grow\.

Kardashev \([1964](https://arxiv.org/html/2605.22840#bib.bib4)\)proposed that civilisations be classified by total power consumption: Type I commands the energy striking a planet from its parent star \(∼1016\\sim 10^\{16\}W\); Type II commands the full luminosity of its star \(∼1026\\sim 10^\{26\}W\); Type III commands a galaxy \(∼1037\\sim 10^\{37\}W\)\. The original typology was framed as a typology for SETI, oriented toward whether a civilisation’s energy output would be detectable across interstellar distances\. Carl Sagan later refined the scale to a continuous logarithmic indexK=\(log10⁡P−6\)/10K=\(\\log\_\{10\}P\-6\)/10, which places contemporary humanity, with primary energy consumption∼2×1013\\sim 2\\times 10^\{13\}W in 2024\(International Energy Agency,[2024](https://arxiv.org/html/2605.22840#bib.bib18)\), atK≈0\.73K\\approx 0\.73\. By Sagan’s measure, humanity has travelled roughly three\-quarters of the way from a pre\-industrial baseline \(K=0K=0\) to commanding the full energy budget of a planet \(K=1K=1\)\.

The original Kardashev scale remains an energy and detectability typology, and this paper does not modify it\. I instead construct an analogous framework—which I call theCognitive Kardashev Scale—that runs in parallel with Kardashev’s original tiers but is calibrated in computational units rather than purely energetic ones\. The contribution is calibration, not a new theoretical construct: the paper reports what total sustained machine\-learning\-grade compute, in floating\-point operations per second, each Kardashev tier could support given a defensible 2024–2026 efficiency anchor\. The arithmetic is straightforward\. Take the total powerPPa civilisation has available \(measured in watts—i\.e\. joules per second\)\. A civilisation does not allocateallof that to thinking; it has to grow food, run factories, move people, heat buildings\. Letffbe the fraction set aside for cognition\. Computation costs energy, but with steadily improving efficiency: letη\\etabe the rate at which a system converts joules of energy into operations of compute \(operations per joule\)\. Then the available cognitive throughput is

Ccog=f​P​η\(operations per second\)\.C\_\{\\text\{cog\}\}\\;=\\;f\\,P\\,\\eta\\quad\\text\{\(operations per second\)\}\.\(1\)This is the primary quantity reported throughout the paper\. To make the result intuitive rather than just a large number, I also expressCcogC\_\{\\text\{cog\}\}in human\-brain\-equivalent units, dividing byCbrainC\_\{\\text\{brain\}\}\(the brain’s own processing rate, in operations per second\)\. The secondary quantity,N=Ccog/CbrainN=C\_\{\\text\{cog\}\}/C\_\{\\text\{brain\}\}, is reported with explicit uncertainty: the literature onCbrainC\_\{\\text\{brain\}\}spans101510^\{15\}–101710^\{17\}FLOP/s depending on which neural events are counted as “operations,” so brain\-equivalent counts carry at minimum±1\\pm 1order of magnitude of irreducible uncertainty\. I use them as an interpretable comparator—a yardstick—not as a literal claim that so many FLOP/s of silicon reproduces a human mind\. The cognitive\-Kardashev framework and the original Kardashev scale are therefore complementary: the former indexes how much sustained ML\-grade compute a given Kardashev\-tier energy budget can in principle support, holding the latter’s energetic typology fixed\.

The paper is organised as follows\. Section[2](https://arxiv.org/html/2605.22840#S2)anchors the efficiency parameterη\\etain 2024–2026 hardware data, comparing six classes of workload from sustained scientific FP64 supercomputing to the Landauer thermodynamic limit\. Section[3](https://arxiv.org/html/2605.22840#S3)adopts a central biological\-baseline estimate\. Section[4](https://arxiv.org/html/2605.22840#S4)establishes the Earth 2024–25 baseline\. Section[5](https://arxiv.org/html/2605.22840#S5)computes the Type I, II, and III cognitive envelopes and presents the scale\. Section[6](https://arxiv.org/html/2605.22840#S6)reports per\-capita capacity under realistic fractional allocation\. Section[7](https://arxiv.org/html/2605.22840#S7)presents three forward scenarios for frontier training compute and connects them to current infrastructure commitments\. Section[8](https://arxiv.org/html/2605.22840#S8)discusses parameter sensitivity\. Section[9](https://arxiv.org/html/2605.22840#S9)discusses what the Scale does and does not show about the political economy of cognitive compute, and Section[10](https://arxiv.org/html/2605.22840#S10)concludes\.

## 2Compute Efficiency in 2026

The relevant efficiencies, expressed as floating\-point operations per joule of electrical input, span roughly twelve orders of magnitude from sustained scientific computing through near\-term ML accelerators to the Landauer thermodynamic limit \(Table[1](https://arxiv.org/html/2605.22840#S2.T1); Figure[1](https://arxiv.org/html/2605.22840#S2.F1)\)\.

Table 1:Compute efficiencyη\\etain 2026, by class of workload\. “Sustained” denotes top\-of\-list HPL benchmarks; “peak ML” denotes vendor\-reported sparse Tensor Core throughput at design power\.![Refer to caption](https://arxiv.org/html/2605.22840v1/x1.png)Figure 1:Compute efficiencyη\\etaacross 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 advantage that biology retains over silicon at the single\-system level; and the approximately six\-order\-of\-magnitude gap between the brain and the Landauer limit at 300 K records the headroom available to thermodynamically optimal computation\. None of the values in Tables[2](https://arxiv.org/html/2605.22840#S5.T2)–[3](https://arxiv.org/html/2605.22840#S6.T3)approach that bound\.The Landauer entry is in irreversible bit\-operations per joule, given by1/\(kB​T​ln⁡2\)=3\.48×10201/\(k\_\{\\mathrm\{B\}\}T\\ln 2\)=3\.48\\times 10^\{20\}atT=300T=300K\(Landauer,[1961](https://arxiv.org/html/2605.22840#bib.bib7)\)\. The other rows are in floating\-point operations per joule\. Because a single double\- or half\-precision FLOP corresponds to many bit\-operations of internal state\-flipping, the Landauer\-limit FLOP/J is much smaller than the bit\-operations\-per\-joule figure quoted; the comparison across rows is therefore qualitative, not strictly commensurable\.Lloyd \([2000](https://arxiv.org/html/2605.22840#bib.bib8)\)establishes higher physical bounds on information processing in mass–energy systems that lie further still beyond the values in Table[1](https://arxiv.org/html/2605.22840#S2.T1)\.

Two notes on the Blackwell\-vs\-Rubin transition warrant highlighting\. First, Rubin’s per\-chip FLOP/J figures are not strictly higher than Blackwell’s, because TDP rose from∼\\sim1 kW \(B200\) to∼\\sim1\.8–2\.3 kW \(R200\) per accelerator\. Rubin’s claimed efficiency advantage is realised at the rack and inference\-throughput level, where much larger HBM4 memory bandwidth \(∼\\sim22 TB/s vs∼\\sim8 TB/s on B200\) and tighter NVLink fabric reduce data\-movement overhead substantially\(NVIDIA Corporation,[2026](https://arxiv.org/html/2605.22840#bib.bib23)\)\. Second, the hierarchy in Table[1](https://arxiv.org/html/2605.22840#S2.T1)is internally consistent across workload precision: each step from FP64 down to FP4 doubles to quadruples efficiency, broadly matching vendor claims of22–4×4\\timesper precision halving once memory and utilisation overheads are properly accounted\.

For the cognitive recalculation in this paper, the relevant efficiency is the rate at which energy can be converted into machine\-learning\-grade compute, since the kind of cognition under discussion is overwhelmingly performed at FP16 or lower precision in current and near\-future systems\. I adopt

η2026=1×1012​FLOP/J\\eta\_\{2026\}\\;=\\;1\\times 10^\{12\}\\ \\text\{FLOP/J\}as a defensible 2026 anchor\. This sits roughly an order of magnitude below B200 peak sparse FP16 and an order of magnitude below R200 peak sparse FP8, because real workloads include data movement, memory access, network traffic, cooling overhead, and utilisation losses that bring sustained efficiency well below vendor peaks\(Strubellet al\.,[2019](https://arxiv.org/html/2605.22840#bib.bib16)\)\. It is also broadly consistent with reported tokens\-per\-joule efficiencies for production\-scale inference on Blackwell\- and Rubin\-class systems, in the range101210^\{12\}–101310^\{13\}effective FLOP/J once memory and fabric overhead is included\.

The biological brain remains, on this measure, between roughly1\.51\.5and3\.53\.5orders of magnitude more efficient per joule than current sustained digital ML substrates\. A useful way to feel that gap: a human cortex running on∼\\sim20 watts—roughly the power draw of a dim incandescent bulb—outperforms several hundred to several thousand watts of contemporary AI hardware on the same kind of pattern\-recognition task\. After more than a decade of relentless progress, the most efficient computer that humans have ever known is still the one humans were born with\. This margin matters for two reasons\. First, it bounds how much of the Kardashev energy budget any digital cognitive architecture can in principle convert into useful thought relative to a hypothetical biological substrate\. Second, it means that “efficiency progress” over the next several decades has a clear destination: closing the silicon\-to\-cortex gap\. Whether engineering will get there—or stall well short—is the open empirical question that determines whether the binding constraint on civilisational cognition is energy or efficiency\. Sensitivity toη\\etais one\-to\-one and explored in Section[8](https://arxiv.org/html/2605.22840#S8)\.

## 3Brain Reference Values

Synaptic\-count and molecular\-state analyses attribute approximately101410^\{14\}–101510^\{15\}synapses to the human cortex, with roughly 4\.7 distinguishable states per synapse\(Bartolet al\.,[2015](https://arxiv.org/html/2605.22840#bib.bib9); Drachman,[2005](https://arxiv.org/html/2605.22840#bib.bib10)\)\. Adopting an order\-of\-magnitude estimate,

Mbrain≈1015​bytes\.M\_\{\\text\{brain\}\}\\;\\approx\\;10^\{15\}\\ \\text\{bytes\}\.For processing capacity, estimates vary from101510^\{15\}to101710^\{17\}operations per second depending on the level at which one counts neural events as “operations”\(Levy and Calvert,[2021](https://arxiv.org/html/2605.22840#bib.bib11); Sandberg and Bostrom,[2008](https://arxiv.org/html/2605.22840#bib.bib12)\)\. The literature uses “operations” loosely; mappings to floating\-point operations are inevitably approximate\. I adopt a central value of

Cbrain=1016​FLOP/s,C\_\{\\text\{brain\}\}\\;=\\;10^\{16\}\\ \\text\{FLOP/s\},in line with computational\-neuroscience reviews that count synaptic events as floating\-point operations and adjust for the fact that∼\\sim95% of neural energy is spent on communication rather than the computational equivalent of multiply\-accumulate\(Levy and Calvert,[2021](https://arxiv.org/html/2605.22840#bib.bib11)\)\. Brain\-equivalent counts in this paper should be read as carrying±1\\pm 1order of magnitude of irreducible uncertainty from this source; full propagation across all parameters is reported in Section[8](https://arxiv.org/html/2605.22840#S8)\. The convention adopted is that “brain\-equivalents” is an interpretable reference unit, not a literal claim thatCbrainC\_\{\\text\{brain\}\}FLOP/s of digital compute reproduces a human mind\. Whole\-brain emulation\(Sandberg and Bostrom,[2008](https://arxiv.org/html/2605.22840#bib.bib12)\)would require structural and data conditions not addressed here\.111For a memory\-side comparator, the global datasphere reached∼1\.75\\sim 1\.75–2\.0×10232\.0\\times 10^\{23\}bytes in 2024 againstMbrain≈1015M\_\{\\text\{brain\}\}\\approx 10^\{15\}bytes per cortex, a ratio of∼108\\sim 10^\{8\}\. I do not use this comparison further: the cognitive claims in this paper concern processing throughput, not storage\.

The hundred\-fold spread inCbrainC\_\{\\text\{brain\}\}is itself worth pausing on\. The literature spans101510^\{15\}to101710^\{17\}FLOP/s not because some studies are sloppy and others careful, but because the question “how much computation does a brain do?” has no canonical answer: it depends on whether one counts only the spike events that cross synapses, or also the dendritic integration upstream of those spikes, or the slower neuromodulatory and glial dynamics on top\. A two\-orders\-of\-magnitude range over what a single cortex represents is a humbling reminder of how much remains unknown about cognition\. The brain\-equivalent is therefore a deliberately rough yardstick—a way of asking “does this number of FLOPs correspond to something like one mind, or a million minds, or a trillion?”—rather than a precise translation\. Throughout the rest of the paper I use the central value and report the band; readers should treat conclusions about specific brain\-equivalent counts as good to within a factor of ten, and conclusions about the qualitative ordering of Kardashev tiers as robust\.

## 4Earth 2024–25 Baseline \(Type 0\.73\)

Global primary energy consumption in 2024 was approximately620620EJ/yr, equivalent to∼2\.0×1013\\sim 2\.0\\times 10^\{13\}W of continuous power\(International Energy Agency,[2024](https://arxiv.org/html/2605.22840#bib.bib18)\)\. On Sagan’s logarithmic refinement of the Kardashev scale \(K=\(log10⁡P−6\)/10K=\(\\log\_\{10\}P\-6\)/10\), this places contemporary humanity atK≈0\.73K\\approx 0\.73\. Of this, data centres accounted for∼\\sim415 TWh in 2024, or about4\.7×10104\.7\\times 10^\{10\}W continuous—roughly0\.24%0\.24\\%of total primary energy\(International Energy Agency,[2025](https://arxiv.org/html/2605.22840#bib.bib17)\)\. The IEA’s Base Case projects this rising to∼\\sim945 TWh \(∼1\.1×1011\\sim 1\.1\\times 10^\{11\}W\) by 2030\(International Energy Agency,[2025](https://arxiv.org/html/2605.22840#bib.bib17),[2026](https://arxiv.org/html/2605.22840#bib.bib19)\)\.

Two intermediate adjustments are needed before applyingη2026\\eta\_\{2026\}\. First, the data\-centre electricity figure includes facility overhead \(cooling, power conversion, network\) at a typical Power Usage Effectiveness \(PUE\) of∼1\.2\\sim 1\.2–1\.51\.5, meaning20%20\\%–33%33\\%of the input is consumed by non\-compute infrastructure\. Compute\-effective power is thereforePcompute=PDC/PUEP\_\{\\text\{compute\}\}=P\_\{\\text\{DC\}\}/\\mathrm\{PUE\}\. Second, only a fraction of compute\-effective workloads are ML\-grade in any meaningful sense: cloud serving, video streaming, and conventional enterprise workloads dominate at present, with AI accelerators growing rapidly but still a minority share of installed compute\. I denote this fractionϕ\\phiand treat it as a free parameter; for the global aggregate I takeϕ∈\[0\.05,0\.30\]\\phi\\in\[0\.05,0\.30\]as a plausible 2024 range, with the upper bound rising as AI buildout proceeds\.

Applyingη2026=1012\\eta\_\{2026\}=10^\{12\}FLOP/J to the compute\-effective, ML\-grade share gives

CML,2024≈ϕ​PDCPUE​η2026=ϕ⋅4\.7×1010​W1\.3⋅1012​FLOP/J\.C\_\{\\text\{ML,2024\}\}\\;\\approx\\;\\frac\{\\phi\\,P\_\{\\text\{DC\}\}\}\{\\mathrm\{PUE\}\}\\,\\eta\_\{2026\}\\;=\\;\\frac\{\\phi\\cdot 4\.7\\times 10^\{10\}\\,\\text\{W\}\}\{1\.3\}\\cdot 10^\{12\}\\,\\text\{FLOP/J\}\.Forϕ∈\[0\.05,0\.30\]\\phi\\in\[0\.05,0\.30\]andPUE=1\.3\\mathrm\{PUE\}=1\.3, this yieldsCML,2024∈\[1\.8,11\]×1021C\_\{\\text\{ML,2024\}\}\\in\[1\.8,11\]\\times 10^\{21\}FLOP/s, equivalent to∼105\\sim 10^\{5\}–10710^\{7\}brain\-equivalents under theCbrainC\_\{\\text\{brain\}\}uncertainty range\. The wide bracket reflects genuine uncertainty in the AI\-share of installed compute; it is not a defect of the analysis but a feature of the underlying empirical situation\. By 2030, on the IEA Base Case projection of data\-centre electricity to∼945\\sim 945TWh \(∼1\.1×1011\\sim 1\.1\\times 10^\{11\}W\) and an upward revision ofϕ\\phitoward the high end of its range, the equivalent figure rises to roughly10710^\{7\}–10810^\{8\}brain\-equivalents in raw capacity\. These figures should not be interpreted as a claim that the existing digital infrastructure already constitutes that many “minds”; they are physical\-capacity ceilings, not realised cognitive throughput\.

It is worth pausing on what this means in human\-scale terms\. The midpoint of the 2024 estimate,∼106\\sim 10^\{6\}brain\-equivalents of ML\-grade compute, is comparable to the population of a major metropolitan area\. Most of this compute is not doing anything one would recognise as cognition: it is serving video, processing payments, indexing search, and running enterprise software\. But the share devoted to AI inference, training, and decision\-support is rising rapidly\. A frontier large\-language\-model service operating continuously at the scale of a few hundred megawatts—comparable to a single Stargate\-class data centre—already commands cognitive capacity equivalent, in raw FLOP/s, to a small city’s worth of human cortex\. When one asks whether AI is becoming a cognitive utility on the scale of electrification or literacy, the order\-of\-magnitude arithmetic is already there\. What remains contingent is who has access to it, on what terms, and toward what ends\.

## 5Type I, II, and III: Cognitive Capacity Envelopes

Recall the core arithmetic: the available cognitive throughput of a civilisation is the product of how much power it has,PP\(in watts\), and how efficiently it can convert that power into computation,η\\eta\(in operations per joule\),

Ccog=P​η\(operations per second\),C\_\{\\text\{cog\}\}\\;=\\;P\\,\\eta\\quad\\text\{\(operations per second\)\},and the corresponding brain\-equivalent count isN=Ccog/CbrainN=C\_\{\\text\{cog\}\}/C\_\{\\text\{brain\}\}, whereCbrainC\_\{\\text\{brain\}\}is the brain’s own processing rate in the same units\. Table[2](https://arxiv.org/html/2605.22840#S5.T2)reports the resulting envelope for Kardashev Types I, II, and III atη2026=1012\\eta\_\{2026\}=10^\{12\}FLOP/J andCbrain=1016C\_\{\\text\{brain\}\}=10^\{16\}FLOP/s; Figure[2](https://arxiv.org/html/2605.22840#S5.F2)plots the same data continuously acrossPPat five values offf\.

Table 2:Cognitive capacity at full energy allocation, Kardashev Types I–III, at central parameter valuesη=1012\\eta=10^\{12\}FLOP/J andCbrain=1016C\_\{\\text\{brain\}\}=10^\{16\}FLOP/s\. The brain\-equivalent columnNNcarries roughly±1\\pm 1order of magnitude of irreducible uncertainty from the literature range onCbrainC\_\{\\text\{brain\}\}alone \(see Section[8](https://arxiv.org/html/2605.22840#S8)\); the FLOP/s columnCcogC\_\{\\text\{cog\}\}is correspondingly tighter\.![Refer to caption](https://arxiv.org/html/2605.22840v1/x2.png)Figure 2:Cognitive Kardashev Scale\.Total brain\-equivalentsNNas a function of civilisational powerPP, at five energy\-allocation fractionsf∈\{0\.1%,1%,5%,10%,50%\}f\\in\\\{0\.1\\%,1\\%,5\\%,10\\%,50\\%\\\}\. Computed atη=1012\\eta=10^\{12\}FLOP/J andCbrain=1016C\_\{\\text\{brain\}\}=10^\{16\}FLOP/s; brain\-equivalent values carry roughly±1\\pm 1order of magnitude of irreducible uncertainty from theCbrainC\_\{\\text\{brain\}\}literature range\. Vertical dotted lines mark the four reference power levels \(Earth 2025, Type I, Type II, Type III\); the dashed horizontal line atN=8\.1×109N=8\.1\\times 10^\{9\}marks current global population\. Type I atf=1%f=1\\%already crosses parity with the human population at the centralCbrainC\_\{\\text\{brain\}\}value; Type II at modestffis a few billion brain\-equivalents per human inhabitant\.Three observations follow\. First, even at present terrestrial power, a hypothetical full allocation of energy to cognition would already support∼2×1025\\sim 2\\times 10^\{25\}FLOP/s, equivalent to∼108\\sim 10^\{8\}–101010^\{10\}brain\-equivalents under theCbrainC\_\{\\text\{brain\}\}uncertainty range\. The ratio of actual to maximum is overwhelmingly an allocation problem rather than a physical\-capacity problem\. Second, the gap from Earth 2025 to Type I is a factor of∼\\sim500 in cognitive capacity \(between two and three orders of magnitude\), the gap from Type I to Type II is ten orders of magnitude, and Type II to Type III another eleven\. Each Kardashev step moves cognitive capacity into a qualitatively different regime\. Third, the Landauer bound\(Landauer,[1961](https://arxiv.org/html/2605.22840#bib.bib7)\),1/\(kB​T​ln⁡2\)≈3\.5×10201/\(k\_\{\\mathrm\{B\}\}T\\ln 2\)\\approx 3\.5\\times 10^\{20\}irreversible bit\-operations per joule at 300 K, lies many orders of magnitude above any value in Table[2](https://arxiv.org/html/2605.22840#S5.T2)\. This doesnotmean current and projected systems have a useful safety margin: it means real computation operates far less efficiently than thermodynamics would in principle permit\. Whether engineering can close any meaningful fraction of the gap between sustained ML\-grade compute and Landauer is a hardware\-physics question well beyond this paper’s scope; I report the bound only as a logical ceiling, not as a target\.

The Kardashev tiers translate into very different human futures\. A Type I civilisation atf=1%f=1\\%commands∼1010\\sim 10^\{10\}brain\-equivalents of digital cognition \(at the central reference value\)—roughly one digital mind per inhabitant, distributed across personal assistants, scientific search, planning, design, and routine decision\-support\. Atf=10%f=10\\%the figure is ten per inhabitant: a society in which ten parallel cognitive collaborators per person is the norm rather than the exception\. Type II is a regime so far beyond present experience that its numbers are hard to make intuitive: atf=1%f=1\\%, the per\-inhabitant cognitive surplus is several billion brain\-equivalents, comparable to the entire human population per individual citizen\. Type III is, on this measure, mostly a placeholder for “what stellar engineering could do if it were possible\.” I include it for completeness, but draw no policy conclusions from it\. The substantive lesson of the envelope is that humanity’s accessible cognitive future, on any reasonable horizon, lies between Type 0\.73 \(where humanity stands today\) and Type I \(where planetary solar capture would put it\)\. Everything beyond that is a thought experiment\.

## 6Realistic Per\-Capita Cognition under Fractional Allocation

Real civilisations do not allocate all their energy to cognition\. Agriculture, manufacturing, infrastructure, mobility, and the environmental and biospheric overheads of civilisation itself absorb the remainder\.222Energy\-allocation overheads at planetary scale are reviewed in the IEA’s annual outlooks\(International Energy Agency,[2024](https://arxiv.org/html/2605.22840#bib.bib18),[2025](https://arxiv.org/html/2605.22840#bib.bib17)\); the 1%–10% range used here is a conservative bracket\. The 2024 data\-centre share of∼\\sim0\.24% of global primary energy is well below 1%, but compute is the most rapidly growing component of demand, plausibly reaching a few per cent by mid\-century\.Letffdenote the fraction of total power allocated to cognition—roughly, “the slice of the energy pie set aside for thinking\.” Per\-capita cognitive capacity, dividing the cognitive throughput across the populationNpopN\_\{\\text\{pop\}\}, is

Cper capita=f​P​ηNpop\.C\_\{\\text\{per capita\}\}\\;=\\;\\frac\{f\\,P\\,\\eta\}\{N\_\{\\text\{pop\}\}\}\.For round\-number arithmetic I assume a stableNpop=1010N\_\{\\text\{pop\}\}=10^\{10\}across the table and the heatmap \(current world population is8\.1×1098\.1\\times 10^\{9\}in 2024 and projected by the UN to∼9\.7×109\\sim 9\.7\\times 10^\{9\}by 2050, so the implied error is∼25%\\sim 25\\%, well below the irreducible uncertainty inCbrainC\_\{\\text\{brain\}\}andϕ\\phi\)\. Table[3](https://arxiv.org/html/2605.22840#S6.T3)reports total and per\-capita brain\-equivalents at the central parameter values, and the corresponding logarithmic cognitive Kardashev indices𝒦cogtot=log10⁡\(Ntot\)\\mathcal\{K\}^\{\\text\{tot\}\}\_\{\\text\{cog\}\}=\\log\_\{10\}\(N\_\{\\text\{tot\}\}\)and𝒦cogpc=log10⁡\(Npc\)\\mathcal\{K\}^\{\\text\{pc\}\}\_\{\\text\{cog\}\}=\\log\_\{10\}\(N\_\{\\text\{pc\}\}\)atf∈\{1%,5%,10%\}f\\in\\\{1\\%,5\\%,10\\%\\\}\. Figure[3](https://arxiv.org/html/2605.22840#S6.F3)visualises the full grid on alog10\\log\_\{10\}heatmap\. Both should be read with the±1\\pm 1\-order\-of\-magnitude band described in Section[8](https://arxiv.org/html/2605.22840#S8)\.

Table 3:Cognitive Kardashev Scale atf∈\{1%,5%,10%\}f\\in\\\{1\\%,5\\%,10\\%\\\}, withη=1012\\eta=10^\{12\}FLOP/J,Cbrain=1016C\_\{\\text\{brain\}\}=10^\{16\}FLOP/s,Npop=1010N\_\{\\text\{pop\}\}=10^\{10\}\.𝒦cogtot=log10⁡\(Ntot\)\\mathcal\{K\}^\{\\text\{tot\}\}\_\{\\text\{cog\}\}=\\log\_\{10\}\(N\_\{\\text\{tot\}\}\),𝒦cogpc=log10⁡\(Npc\)\\mathcal\{K\}^\{\\text\{pc\}\}\_\{\\text\{cog\}\}=\\log\_\{10\}\(N\_\{\\text\{pc\}\}\)\.LevelffPtotP\_\{\\text\{tot\}\}\(W\)PcogP\_\{\\text\{cog\}\}\(W\)CcogC\_\{\\text\{cog\}\}\(FLOP/s\)NtotN\_\{\\text\{tot\}\}NpcN\_\{\\text\{pc\}\}𝒦cogtot\\mathcal\{K\}^\{\\text\{tot\}\}\_\{\\text\{cog\}\}𝒦cogpc\\mathcal\{K\}^\{\\text\{pc\}\}\_\{\\text\{cog\}\}Type 0\.73 \(Earth 2024–25\),Ptot=2×1013P\_\{\\text\{tot\}\}=2\\times 10^\{13\}WType 0\.731%2×10132\\times 10^\{13\}2\.0×10112\.0\\times 10^\{11\}2\.0×10232\.0\\times 10^\{23\}2\.0×1072\.0\\times 10^\{7\}2\.0×10−32\.0\\times 10^\{\-3\}7\.30−2\.70\-2\.70Type 0\.735%2×10132\\times 10^\{13\}1\.0×10121\.0\\times 10^\{12\}1\.0×10241\.0\\times 10^\{24\}1\.0×1081\.0\\times 10^\{8\}1\.0×10−21\.0\\times 10^\{\-2\}8\.00−2\.00\-2\.00Type 0\.7310%2×10132\\times 10^\{13\}2\.0×10122\.0\\times 10^\{12\}2\.0×10242\.0\\times 10^\{24\}2\.0×1082\.0\\times 10^\{8\}2\.0×10−22\.0\\times 10^\{\-2\}8\.30−1\.70\-1\.70Type I \(planetary\),Ptot=1×1016P\_\{\\text\{tot\}\}=1\\times 10^\{16\}WType I1%1×10161\\times 10^\{16\}1\.0×10141\.0\\times 10^\{14\}1\.0×10261\.0\\times 10^\{26\}1\.0×10101\.0\\times 10^\{10\}1\.01\.010\.000\.00Type I5%1×10161\\times 10^\{16\}5\.0×10145\.0\\times 10^\{14\}5\.0×10265\.0\\times 10^\{26\}5\.0×10105\.0\\times 10^\{10\}5\.05\.010\.700\.70Type I10%1×10161\\times 10^\{16\}1\.0×10151\.0\\times 10^\{15\}1\.0×10271\.0\\times 10^\{27\}1\.0×10111\.0\\times 10^\{11\}10\.010\.011\.001\.00Type II \(stellar\),Ptot=3\.8×1026P\_\{\\text\{tot\}\}=3\.8\\times 10^\{26\}WType II1%3\.8×10263\.8\\times 10^\{26\}3\.8×10243\.8\\times 10^\{24\}3\.8×10363\.8\\times 10^\{36\}3\.8×10203\.8\\times 10^\{20\}3\.8×10103\.8\\times 10^\{10\}20\.5810\.58Type II5%3\.8×10263\.8\\times 10^\{26\}1\.9×10251\.9\\times 10^\{25\}1\.9×10371\.9\\times 10^\{37\}1\.9×10211\.9\\times 10^\{21\}1\.9×10111\.9\\times 10^\{11\}21\.2811\.28Type II10%3\.8×10263\.8\\times 10^\{26\}3\.8×10253\.8\\times 10^\{25\}3\.8×10373\.8\\times 10^\{37\}3\.8×10213\.8\\times 10^\{21\}3\.8×10113\.8\\times 10^\{11\}21\.5811\.58Type III \(galactic\),Ptot=4×1037P\_\{\\text\{tot\}\}=4\\times 10^\{37\}WType III1%4×10374\\times 10^\{37\}4\.0×10354\.0\\times 10^\{35\}4\.0×10474\.0\\times 10^\{47\}4\.0×10314\.0\\times 10^\{31\}4\.0×10214\.0\\times 10^\{21\}31\.6021\.60Type III5%4×10374\\times 10^\{37\}2\.0×10362\.0\\times 10^\{36\}2\.0×10482\.0\\times 10^\{48\}2\.0×10322\.0\\times 10^\{32\}2\.0×10222\.0\\times 10^\{22\}32\.3022\.30Type III10%4×10374\\times 10^\{37\}4\.0×10364\.0\\times 10^\{36\}4\.0×10484\.0\\times 10^\{48\}4\.0×10324\.0\\times 10^\{32\}4\.0×10224\.0\\times 10^\{22\}32\.6022\.60![Refer to caption](https://arxiv.org/html/2605.22840v1/x3.png)Figure 3:Per\-capita cognitive abundance \(log10\\log\_\{10\}\) under the three Figure[4](https://arxiv.org/html/2605.22840#S7.F4)scenarios projected to 2035\.Three panels share the same Kardashev\-tier×\\timesallocation\-share grid; the cell value is the logarithm \(base 10\) of the number of brain\-equivalents per human inhabitant, assumingNpop=1010N\_\{\\text\{pop\}\}=10^\{10\}\.Current\(left,η2035=1013\\eta\_\{2035\}=10^\{13\}FLOP/J\): the 2035 endpoint of the Figure[4](https://arxiv.org/html/2605.22840#S7.F4)regression\-based trajectory, attributing roughly 10×\\timesof the underlying nine\-year compute growth to efficiency improvement and the rest to chip\-count and run\-duration scaling\.Better\(centre,η2035=1014\\eta\_\{2035\}=10^\{14\}FLOP/J\): the 2035 endpoint of the Figure[4](https://arxiv.org/html/2605.22840#S7.F4)Sevilla\-rate trajectory, with∼\\sim100×\\timesefficiency improvement consistent with neuromorphic\-adjacent ML hardware\.Optimistic\(right,η2035=1015\\eta\_\{2035\}=10^\{15\}FLOP/J\): the 2035 endpoint of the Figure[4](https://arxiv.org/html/2605.22840#S7.F4)capacity\-led trajectory, requiring∼\\sim1000×\\timesefficiency improvement and reaching the lower bound of biological\-cortex efficiency\. Green borders highlight the cell within each panel closest to per\-capita parity \(one brain\-equivalent per inhabitant\)\. The parity threshold migrates leftward and downward as efficiency improves under the three Figure[4](https://arxiv.org/html/2605.22840#S7.F4)trajectories: from a near\-parity Earth\-scale cell atf=10%f=10\\%inCurrent, to exact parity at Earth×\\timesf=5%f=5\\%inBetter, to above\-parity Earth atf=1%f=1\\%inOptimistic\.The three\-scenario heatmap makes the relative weight of efficiency progress and energy availability visible at the 2035 horizon\. In theCurrenttrajectory, achieving even one brain\-equivalent of digital compute per human inhabitant on Earth alone requires allocating approximately 50% of primary energy to cognition; below that, civilisational\-scale \(Type I\) energy expansion is necessary to clear the parity bar\. In theBettertrajectory, parity is achieved on Earth itself atf=5%f=5\\%, without any expansion of total power\. In theOptimistictrajectory, parity is exceeded on Earth at everyffexamined, includingf=1%f=1\\%, and Type I\-scale energy atf=10%f=10\\%buys roughly10410^\{4\}brain\-equivalents per human inhabitant\.

The structural lesson is that if compute efficiency continues to improve at the rate implicit in Figure[4](https://arxiv.org/html/2605.22840#S7.F4)’s trajectories, the binding constraint on per\-capita cognitive abundance shifts decisively from total energy to the political\-economy variableff\. If efficiency stalls at the present 2026 level, by contrast, the binding constraint remains civilisational energy, and Type I\-scale infrastructure becomes the relevant ceiling\.

The per\-capita parity threshold deserves attention in its own right\. “One brain\-equivalent of digital cognition per inhabitant” sounds abstract, but it has an intuitive interpretation: it is the capacity, in compute units, for every human to have access to a personal AI assistant operating continuously at roughly the throughput of their own cortex\. At present this kind of access is concentrated at the high end of the income distribution, distributed unevenly through paid\-tier subscriptions, professional tools, and infrastructural advantages\. At the Type 0\.73 \(Earth 2025\) tier in theOptimistictrajectory, or at the Type I tier under any trajectory, the total compute supply is sufficient to make universal access of this kind physically possible\. Whether it becomes universally available is a question of political economy and institutional design rather than thermodynamics\. Several further patterns are worth noting\. A Type I civilisation atf=1%f=1\\%commands∼1011\\sim 10^\{11\}brain\-equivalents in theCurrenttrajectory, an order of magnitude above global human population; the same tier in theOptimistictrajectory commands∼1013\\sim 10^\{13\}, three orders of magnitude above\. A Type II civilisation operates at∼1011\\sim 10^\{11\}brain\-equivalents per inhabitant even at modest cognitive allocation in theCurrenttrajectory, rising to∼1013\\sim 10^\{13\}–101410^\{14\}per inhabitant in theOptimistictrajectory\. The numbers at Type III are interpretable only as upper bounds on what stellar engineering would notionally permit\.

## 7The Trajectory toward the Envelope

The static envelope above describes what a Kardashev civilisationcouldsupport at givenffandη\\eta\. The dynamic question is whether and how fast contemporary humanity is moving along the envelope\. Three trends are relevant\.

First, frontier training compute has grown rapidly\.Sevillaet al\.\([2022](https://arxiv.org/html/2605.22840#bib.bib13)\)estimate a factor of∼\\sim4\.2 per year for the deep\-learning era\. A simple log\-linear regression through twelve representative frontier models from AlexNet \(2012,∼1017\\sim 10^\{17\}FLOPs\) to estimated 2026 frontier runs \(∼3×1026\\sim 3\\times 10^\{26\}FLOPs\) yields a slightly more conservative factor of∼\\sim3\.5 per year \(Figure[4](https://arxiv.org/html/2605.22840#S7.F4)\), corresponding to a doubling time of roughly 6\.6 months\. For comparison, the classical Moore’s\-Law doubling time was∼\\sim24 months and applied to a much narrower property \(transistor count per chip\)\. Frontier\-AI compute has, over the past decade, doubled roughly four times faster than transistors did in their long boom—and over a base value many orders of magnitude larger\. There is no industrial precedent in the modern era for sustained scaling of this kind; the closest analogy may be the early electrification of national economies in the late nineteenth century\.

Second, I project three forward scenarios as conditional extrapolations rather than predictions\. From a 2026 anchor of3×10263\\times 10^\{26\}FLOPs I extend through 2035 under: \(a\) aCurrentscenario at×3\.51\\times 3\.51/yr, the regression slope through the twelve observed frontier models—this slope is fragile to point selection \(BERT\-Large is a known low outlier; excluding it raises the slope toward Sevilla’s value\); \(b\) aBetterscenario at∼\\sim×4\.2\\times 4\.2/yr, the publishedSevillaet al\.\([2022](https://arxiv.org/html/2605.22840#bib.bib13)\)estimate for the deep\-learning era; and \(c\) anOptimisticcapacity\-led scenario at∼\\sim×10\\times 10/yr\. The first two are continuations of historical fits; the third is a feasibility benchmark, asked of the data rather than supplied by it\. The Stargate consortium’s announced 10 GW target by 2029\(OpenAI,[2025a](https://arxiv.org/html/2605.22840#bib.bib24)\)and the Terafab venture’s terawatt\-per\-year aspiration\(Carlson and Grush,[2026](https://arxiv.org/html/2605.22840#bib.bib26)\)make theOptimisticrate technically conceivable on the capacity side, but several reports during 2025 indicate Stargate has shifted partly toward leasing rather than de novo build, and Terafab is at announcement rather than groundbreaking stage\. The corresponding 2035 frontier\-training\-run sizes are∼1031\.4\\sim 10^\{31\.4\},∼1032\.1\\sim 10^\{32\.1\}, and∼1035\.5\\sim 10^\{35\.5\}FLOPs respectively\. The third figure is, as I show next, physically infeasible at fixed efficiency and is therefore not a prediction but a stress test\.

![Refer to caption](https://arxiv.org/html/2605.22840v1/x4.png)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 of3×10263\\times 10^\{26\}FLOPs to 2035:Currentat×3\.51\\times 3\.51/yr \(grey dashed; regression on 2012–2026\),Betterat×4\.2\\times 4\.2/yr \(green dash\-dot; publishedSevillaet al\.\([2022](https://arxiv.org/html/2605.22840#bib.bib13)\)rate\), andOptimisticat×10\\times 10/yr \(orange dotted; capacity\-led, Stargate \+ Terafab buildout\)\. 2035 endpoint values shown bold to the right of each scenario\. Sources:Sevillaet al\.\([2022](https://arxiv.org/html/2605.22840#bib.bib13)\); Epoch AI \([2024](https://arxiv.org/html/2605.22840#bib.bib14)\); Maslejet al\.\([2025](https://arxiv.org/html/2605.22840#bib.bib15)\); numerical values are order\-of\-magnitude\.Third, the energetic cost of frontier training is converging on the budgets of medium\-sized cities and small countries\. A frontier3×10263\\times 10^\{26\}\-FLOP run atη2026=1012\\eta\_\{2026\}=10^\{12\}FLOP/J consumes3×10143\\times 10^\{14\}J, or∼\\sim83 GWh—comparable to several days of electricity consumption for a small European country such as Estonia \(∼\\sim21 GWh/day\), or about a third of a day’s consumption for a mid\-sized economy such as Belgium \(∼\\sim220 GWh/day\)\. A single 1\.2 GW data\-centre site operating continuously consumes∼\\sim10\.5 TWh/yr, an order of magnitude more than 100 such training runs\.

Decomposing each scenario into its implied energy and efficiency components clarifies feasibility\. Compute scales asC∝E⋅ηC\\propto E\\cdot\\eta, whereEEis total energy consumed by training runs andη\\etais sustained efficiency\. From a 2026 baseline \(E2026⋅η2026E\_\{2026\}\\cdot\\eta\_\{2026\}\), the 2035 endpoint of each scenario decomposes as

E2035E2026⋅η2035η2026=growth factor\.\\frac\{E\_\{2035\}\}\{E\_\{2026\}\}\\cdot\\frac\{\\eta\_\{2035\}\}\{\\eta\_\{2026\}\}\\;=\\;\\text\{growth factor\}\.For theCurrentscenario this growth is×8×104\\times 8\\\!\\times\\\!10^\{4\}\(i\.e\.3\.5193\.51^\{9\}\), theBetterscenario×4×105\\times 4\\\!\\times\\\!10^\{5\}\(i\.e\.4\.294\.2^\{9\}\), and theOptimisticscenario×109\\times 10^\{9\}\. Distributing this growth between energy expansion and efficiency improvement gives a feasibility envelope\. With energy expansion held to a plausible×102\\times 10^\{2\}–10310^\{3\}over nine years \(consistent with IEA Base Case data\-centre buildout extrapolated to 2035\), theCurrentscenario requiresη\\etato grow by roughly×102\\times 10^\{2\}\(toward101410^\{14\}FLOP/J\), theBetterscenario by roughly×103\\times 10^\{3\}\(toward101510^\{15\}FLOP/J, approaching the lower bound of biological\-cortex efficiency\), and theOptimisticscenario by×106\\times 10^\{6\}–10710^\{7\}\. The latter places sustainedη\\etain the range101810^\{18\}–101910^\{19\}FLOP/J, which approaches or exceeds the Landauer\-FLOP equivalent at 300 K under any reasonable assumption about bit\-operations per FLOP\. TheOptimisticscenario at fixed room\-temperature irreversible computation is therefore at or near the thermodynamic ceiling and is best read as a stress test: an upper bound on what compute scaling alone can deliver under generous capacity assumptions, achievable only by some combination of reversible computation, sub\-room\-temperature operation, and very aggressive capacity buildout\. TheCurrentandBetterscenarios remain feasible on the 2035 horizon, conditional on substantial but not unprecedented efficiency progress\.

The OpenAI–SoftBank–Oracle–MGXStargateconsortium, announced in January 2025 with a $500 billion commitment over four years, targets 10 GW of dedicated AI compute capacity by 2029\(OpenAI,[2025a](https://arxiv.org/html/2605.22840#bib.bib24),[b](https://arxiv.org/html/2605.22840#bib.bib25)\); the Tesla–SpaceX–xAITerafabinitiative, announced by Elon Musk in March 2026 with an initial $55 billion \(projected $119 billion total\) investment, targets vertically integrated production of more than one terawatt of AI compute capacity per year\(Carlson and Grush,[2026](https://arxiv.org/html/2605.22840#bib.bib26); Kolodny,[2026](https://arxiv.org/html/2605.22840#bib.bib27)\)\. The combined committed capital across these and adjacent infrastructure programmes runs into the high hundreds of billions of dollars over a five\-year horizon—a scale that exceeds the inflation\-adjusted cost of the Manhattan or Apollo Programmes by a wide margin and is comparable in magnitude to a major mid\-twentieth\-century rearmament cycle\. Frontier AI compute is no longer an industrial activity in the ordinary sense; it has become geo\-political infrastructure, planned and capitalised at the level normally reserved for war or national reconstruction\. These commitments make the optimistic scenario more plausible than it would otherwise be; they also concentrate the cognitive substrate in the hands of a small set of vertically integrated firms with national\-scale energy footprints\. The distributive implications of that concentration are the subject of Section[9](https://arxiv.org/html/2605.22840#S9)\.

## 8Sensitivity and Parameter Uncertainty

The brain\-equivalent count is the product of six quantities once the per\-capita normalisation and the data\-centre overhead corrections are made explicit:

Npc=f​P​η​ϕCbrain​PUE​Npop,N\_\{\\text\{pc\}\}\\;=\\;\\frac\{f\\,P\\,\\eta\\,\\phi\}\{C\_\{\\text\{brain\}\}\\,\\mathrm\{PUE\}\\,N\_\{\\text\{pop\}\}\},each carrying separate uncertainty\. The qualitative structure of the envelope is robust to plausible joint variation, but combined uncertainty is substantial: the envelope as reported in Tables[2](https://arxiv.org/html/2605.22840#S5.T2)–[3](https://arxiv.org/html/2605.22840#S6.T3)should be read as carrying±1\.5\\pm 1\.5to22orders of magnitude of joint uncertainty when the brain\-compute and AI\-share parameters are propagated together\. Within that range, the qualitative structure—that Type I and beyond carry per\-capita cognitive surpluses many orders of magnitude above what biology supplies, and that Earth 2025 already supplies tens of millions of digital brain\-equivalents in raw capacity—is robust\.

- •PPis the most empirically pinned: world primary energy is well\-measured at∼2\.0×1013\\sim 2\.0\\times 10^\{13\}W, and Type I, II, III are by definition\. Stellar luminosityL⊙=3\.828×1026L\_\{\\odot\}=3\.828\\times 10^\{26\}W is a Solar reference; full\-spectrum capture is a physical idealisation\(Dyson,[1960](https://arxiv.org/html/2605.22840#bib.bib5); Sandberg,[1999](https://arxiv.org/html/2605.22840#bib.bib6)\)\.
- •ffis the policy variable\. Today’s data\-centre share of∼\\sim0\.24% is already an order of magnitude above the level of a decade ago; IEA Base Case projections imply∼\\sim0\.5–1% by 2030\(International Energy Agency,[2025](https://arxiv.org/html/2605.22840#bib.bib17)\)\. I treatf∈\[10−3,0\.5\]f\\in\[10^\{\-3\},0\.5\]as the plausible long\-run policy range\.
- •η\\etais the technical\-progress variable\. The two\- to three\-order\-of\-magnitude gap between sustained FP64 supercomputers and peak FP4 ML inference suggests thatη\\etahas substantial residual room to grow within current physics\. Stagnation at the present sustained\-ML value ofη2026=1012\\eta\_\{2026\}=10^\{12\}FLOP/J is unlikely on a multi\-decade horizon; further increases toward101410^\{14\}–101510^\{15\}FLOP/J are conceivable with neuromorphic, optical, or biological substrates approaching the lower bound of biological\-cortex efficiency\.
- •ϕ\\phi\(AI\-share of compute\) is poorly constrained\. I use\[0\.05,0\.30\]\[0\.05,0\.30\]for the global aggregate in 2024, rising to\[0\.20,0\.60\]\[0\.20,0\.60\]by 2030\. This single parameter introduces approximately one order of magnitude of uncertainty into all aggregate brain\-equivalent figures\.
- •PUE\\mathrm\{PUE\}\(data\-centre overhead\) is empirically narrow: typical hyperscale PUE is1\.11\.1–1\.51\.5, with industry averages at∼1\.3\\sim 1\.3\. I use1\.31\.3throughout\. Variation here is sub\-leading\.
- •CbrainC\_\{\\text\{brain\}\}is the most contested parameter\. The literature spans101510^\{15\}to101810^\{18\}FLOP/s depending on whether one counts synaptic events, dendritic computations, or whole\-brain dynamics\(Bartolet al\.,[2015](https://arxiv.org/html/2605.22840#bib.bib9); Sandberg and Bostrom,[2008](https://arxiv.org/html/2605.22840#bib.bib12); Levy and Calvert,[2021](https://arxiv.org/html/2605.22840#bib.bib11)\)\. My101610^\{16\}FLOP/s is mid\-range; reported brain\-equivalent figures carry±1\\pm 1order of magnitude of irreducible uncertainty from this source alone\.
- •NpopN\_\{\\text\{pop\}\}is well\-measured at8\.1×1098\.1\\times 10^\{9\}in 2024 and projected by the UN to∼9\.7×109\\sim 9\.7\\times 10^\{9\}by 2050\. Tables in this paper use101010^\{10\}as a round number; the implied error is∼25%\\sim 25\\%, well below other parameters’ uncertainty\.

## 9Discussion: What the Scale Does and Does Not Show

The Scale developed in §§[2](https://arxiv.org/html/2605.22840#S2)–[7](https://arxiv.org/html/2605.22840#S7)is descriptive\. It quantifies how much sustained ML\-grade computation each Kardashev tier could in principle support, given a defensible 2024–2026 efficiency anchor and a transparent uncertainty range on the biological reference\. Three observations follow, none of which the analysis itself fully establishes; they are interpretive remarks calibrated against the numerical content\.

First, raw capacity in absolute terms is comfortably in excess of population\-weighted parity at planetary energy scales\. A Type I civilisation atf=1%f=1\\%commands102610^\{26\}FLOP/s, equivalent to between10910^\{9\}and101110^\{11\}brain\-equivalents under theCbrainC\_\{\\text\{brain\}\}uncertainty range, and Earth at present energy levels under full allocation already exceeds the same band\. The implication is that the physical\-capacity question is not the binding constraint at any plausible Kardashev tier: a civilisation at Type I or beyond does not run out of cognitive capacity for any realistic per\-capita demand\. The substantive question is therefore distributional: how the available capacity is allocated across population, jurisdictions, and uses\. The Scale does not measure that distribution and cannot answer the distributional question\.

Second, the trajectory and feasibility analysis of §[7](https://arxiv.org/html/2605.22840#S7)highlights two distinct regimes\. Under stagnation ofη\\etanear the present sustained\-ML value, growth in cognitive output requires linear growth in energy, which the IEA forecasts and contemporary infrastructure announcements \(Stargate, Terafab\) suggest is in fact occurring\. Under continued efficiency progress—toward101410^\{14\}–101510^\{15\}FLOP/J, the lower bound of biological\-cortex efficiency—the same compute growth can be delivered with much less marginal energy\. Which regime obtains determines whether allocable energy or institutional access becomes the binding margin\. The paper does not adjudicate; both regimes are empirically possible on the 2035 horizon\.

Third, the empirical pattern of compute concentration in the contemporary AI infrastructure is independent of the Scale but interacts with it\. A small number of vertically integrated consortia control the bulk of frontier capacity\(OpenAI,[2025a](https://arxiv.org/html/2605.22840#bib.bib24); Carlson and Grush,[2026](https://arxiv.org/html/2605.22840#bib.bib26); International Energy Agency,[2025](https://arxiv.org/html/2605.22840#bib.bib17)\)\. If access to the cognitive surplus implied by Type I\-tier energy is similarly concentrated, the per\-capita brain\-equivalent figures in Table[3](https://arxiv.org/html/2605.22840#S6.T3)describe a population\-weighted average that masks an extreme distributional skew\. The Scale quantifies what is in principle available; whether and how it is socially allocated is a political question this paper does not engage\.

Stepping back: the deeper observation behind this calibration is that humanity is on the cusp of a transition that earlier civilisations encountered only with food, fuel, and information\. For most of history, cognition was scarce in the same way calories were scarce: you had what your body could produce, augmented modestly by tools, books, and trusted advisors\. Mass literacy in the nineteenth century, mass schooling in the twentieth, and now mass\-deployed AI in the twenty\-first are successive expansions of the cognitive supply curve\. Each expansion required physical infrastructure—printing presses, schools, data centres—and was accompanied by political contestation over who had access to it\. The Cognitive Kardashev Scale is the latest scaffolding for that recurring question: when the supply of cognition is no longer the binding constraint, what becomes the binding constraint, and what kind of society does humanity build around it? The arithmetic does not answer the question\. It does suggest that the question is now upon humanity\.

## 10Conclusion

Contemporary humanity sits atK≈0\.73K\\approx 0\.73on Sagan’s logarithmic refinement of the original Kardashev energy scale\. The Cognitive Kardashev Scale developed in this paper runs in parallel with that energetic scale, quantifying what each Kardashev tier could in principle support in sustained ML\-grade compute, given current and near\-future hardware efficiencies and a transparent uncertainty range on the biological reference\. The exercise is calibration, not prediction\.

Three things follow from the calibration\. \(i\) Raisingfffrom 1% to 10% within a Kardashev tier buys a factor of 10 in cognitive capacity\. \(ii\) Moving from Type 0\.73 to Type I at fixedffbuys a factor of∼\\sim500 \(between two and three orders of magnitude\)\. \(iii\) Frontier training compute, growing at the historical regression rate, will exceed reasonable global energy budgets by the mid\-2030s in the absence of substantial efficiency progress; theOptimistic\(×10\\times 10/yr\) trajectory is feasible only ifη\\etaimproves by several orders of magnitude as well, ultimately approaching the biological\-cortex efficiency at the lower end of the brain\-compute range\. TheCurrent\(×3\.5\\times 3\.5/yr\) trajectory is feasible under the more modest efficiency progress empirically observed across the Blackwell\-to\-Rubin transition and prior generations\.

Whether the binding constraint on cognitive abundance is allocable energy or computational efficiency therefore depends on which of these regimes is realised\. The paper does not adjudicate\. What it does establish is that the relevant question is no longer the abstract physical possibility of large\-scale digital cognition—that question has been answered in the affirmative by the analysis above—but the engineering trajectory ofη\\eta, the political and ecological allocation offf, and the institutional distribution of access to compute\. Each of these is the subject of a different literature, and the calibration developed here is offered as a quantitative input to those literatures rather than as a substitute for them\.

The exercise is offered in the spirit ofDyson \([1960](https://arxiv.org/html/2605.22840#bib.bib5)\)’s back\-of\-envelope argument that stellar\-scale energy capture is consistent with known physics, or of Drake’s equation as a scaffolding for thinking about civilisational questions whose answers cannot yet be computed\. What such calibrations do is convert vague intuitions about “vast” or “unimaginable” scales into specific numbers that can be argued with, refined, and updated as evidence accumulates\. The Cognitive Kardashev Scale makes specific the intuition that the long\-run constraint on civilisational thought is energy and politics, not silicon\. Whether that intuition survives the next decade of evidence is for that decade to reveal; the calibration developed here will be the easier to update because it has been written down explicitly, with its parameters, ranges, and conditional structure made plain\.

## References

- T\. M\. Bartol, C\. Bromer, J\. Kinney, M\. A\. Chirillo, J\. N\. Bourne, K\. M\. Harris, and T\. J\. Sejnowski \(2015\)Nanoconnectomic upper bound on the variability of synaptic plasticity\.eLife4,pp\. e10778\.External Links:[Document](https://dx.doi.org/10.7554/eLife.10778)Cited by:[§3](https://arxiv.org/html/2605.22840#S3.p1.2),[6th item](https://arxiv.org/html/2605.22840#S8.I1.i6.p1.5)\.
- K\. Carlson and L\. Grush \(2026\)Elon Musk plans Terafab chip facility in Austin, Texas with Tesla, SpaceX, xAI\.Note:Bloomberg News, 22 March 2026External Links:[Link](https://www.bloomberg.com/news/articles/2026-03-22/elon-musk-says-tesla-xai-spacex-terafab-to-start-in-austin)Cited by:[§1](https://arxiv.org/html/2605.22840#S1.p1.2),[§7](https://arxiv.org/html/2605.22840#S7.p3.9),[§7](https://arxiv.org/html/2605.22840#S7.p6.1),[§9](https://arxiv.org/html/2605.22840#S9.p4.1)\.
- D\. A\. Drachman \(2005\)Do we have brain to spare?\.Neurology64\(12\),pp\. 2004–2005\.External Links:[Document](https://dx.doi.org/10.1212/01.WNL.0000166914.38327.BB)Cited by:[§3](https://arxiv.org/html/2605.22840#S3.p1.2)\.
- F\. J\. Dyson \(1960\)Search for artificial stellar sources of infrared radiation\.Science131\(3414\),pp\. 1667–1668\.External Links:[Document](https://dx.doi.org/10.1126/science.131.3414.1667)Cited by:[§10](https://arxiv.org/html/2605.22840#S10.p4.1),[1st item](https://arxiv.org/html/2605.22840#S8.I1.i1.p1.3)\.
- Epoch AI \(2024\)Tracking compute\-intensive AI models\.Note:Database,[https://epoch\.ai/data/notable\-ai\-models](https://epoch.ai/data/notable-ai-models)Curated database of training compute, dataset size, and parameter counts for frontier AI modelsCited by:[Figure 4](https://arxiv.org/html/2605.22840#S7.F4)\.
- International Energy Agency \(2024\)World energy outlook 2024\.IEA,Paris\.External Links:[Link](https://www.iea.org/reports/world-energy-outlook-2024)Cited by:[§1](https://arxiv.org/html/2605.22840#S1.p2.8),[§4](https://arxiv.org/html/2605.22840#S4.p1.9),[footnote 2](https://arxiv.org/html/2605.22840#footnote2)\.
- International Energy Agency \(2025\)Energy and AI\.IEA,Paris\.Note:World Energy Outlook Special ReportExternal Links:[Link](https://www.iea.org/reports/energy-and-ai)Cited by:[§1](https://arxiv.org/html/2605.22840#S1.p1.2),[§4](https://arxiv.org/html/2605.22840#S4.p1.9),[2nd item](https://arxiv.org/html/2605.22840#S8.I1.i2.p1.4),[§9](https://arxiv.org/html/2605.22840#S9.p4.1),[footnote 2](https://arxiv.org/html/2605.22840#footnote2)\.
- International Energy Agency \(2026\)Data centre electricity use surged in 2025, even with tightening bottlenecks driving a scramble for solutions\.Note:IEA press release, 16 April 2026External Links:[Link](https://www.iea.org/news/data-centre-electricity-use-surged-in-2025-even-with-tightening-bottlenecks-driving-a-scramble-for-solutions)Cited by:[§4](https://arxiv.org/html/2605.22840#S4.p1.9)\.
- N\. S\. Kardashev \(1964\)Transmission of information by extraterrestrial civilizations\.Soviet Astronomy8,pp\. 217–221\.Cited by:[§1](https://arxiv.org/html/2605.22840#S1.p2.8)\.
- L\. Kolodny \(2026\)Elon Musk’s Terafab chip factory in Texas could cost up to $119 billion, filing shows\.Note:CNBC News, 6 May 2026External Links:[Link](https://www.cnbc.com/2026/05/06/elon-musks-spacex-chip-fab-in-texas-to-cost-up-to-119-billion.html)Cited by:[§7](https://arxiv.org/html/2605.22840#S7.p6.1)\.
- R\. Landauer \(1961\)Irreversibility and heat generation in the computing process\.IBM Journal of Research and Development5\(3\),pp\. 183–191\.External Links:[Document](https://dx.doi.org/10.1147/rd.53.0183)Cited by:[§2](https://arxiv.org/html/2605.22840#S2.p2.2),[§5](https://arxiv.org/html/2605.22840#S5.p2.6)\.
- W\. B\. Levy and V\. G\. Calvert \(2021\)Communication consumes 35 times more energy than computation in the human cortex, but both costs are needed to predict synapse number\.Proceedings of the National Academy of Sciences118\(18\),pp\. e2008173118\.External Links:[Document](https://dx.doi.org/10.1073/pnas.2008173118)Cited by:[§3](https://arxiv.org/html/2605.22840#S3.p1.4),[§3](https://arxiv.org/html/2605.22840#S3.p1.7),[6th item](https://arxiv.org/html/2605.22840#S8.I1.i6.p1.5)\.
- S\. Lloyd \(2000\)Ultimate physical limits to computation\.Nature406\(6799\),pp\. 1047–1054\.External Links:[Document](https://dx.doi.org/10.1038/35023282)Cited by:[§2](https://arxiv.org/html/2605.22840#S2.p2.2)\.
- N\. Maslej, L\. Fattorini, R\. Perrault, Y\. Gil, V\. Parli, N\. Kariuki, E\. Capstick, A\. Reuel, E\. Brynjolfsson, J\. Etchemendy, K\. Ligett, T\. Lyons, J\. Manyika, J\. C\. Niebles, Y\. Shoham, R\. Wald, T\. Walsh, A\. Hamrah, L\. Santarlasci, J\. B\. Lotufo, A\. Rome, A\. Shi, and S\. Oak \(2025\)Artificial intelligence index report 2025\.Stanford Institute for Human\-Centered Artificial Intelligence\.External Links:[Document](https://dx.doi.org/10.48550/arXiv.2504.07139),[Link](https://arxiv.org/abs/2504.07139)Cited by:[Figure 4](https://arxiv.org/html/2605.22840#S7.F4)\.
- NVIDIA Corporation \(2026\)NVIDIA Vera Rubin Platform: architectural overview\.Note:NVIDIA Developer Blog, GTC 2026 announcementReports R200 GPU peak performance of∼\\sim50 PFLOP/s sparse FP4 \(inference\),∼\\sim35 PFLOP/s NVFP4 \(training\), and∼\\sim16 PFLOP/s FP8 at a TDP of approximately 1\.8–2\.3 kW per GPUExternal Links:[Link](https://developer.nvidia.com/blog/inside-the-nvidia-rubin-platform-six-new-chips-one-ai-supercomputer/)Cited by:[§2](https://arxiv.org/html/2605.22840#S2.p3.6)\.
- OpenAI \(2025a\)Announcing the Stargate project\.Note:OpenAI press release, 21 January 2025Joint venture of OpenAI, SoftBank, Oracle, and MGX committing $500 billion over four years toward AI compute infrastructure, targeting 10 GW total capacity by 2029External Links:[Link](https://openai.com/index/announcing-the-stargate-project/)Cited by:[§1](https://arxiv.org/html/2605.22840#S1.p1.2),[§7](https://arxiv.org/html/2605.22840#S7.p3.9),[§7](https://arxiv.org/html/2605.22840#S7.p6.1),[§9](https://arxiv.org/html/2605.22840#S9.p4.1)\.
- OpenAI \(2025b\)OpenAI, Oracle, and SoftBank expand Stargate with five new AI data center sites\.Note:OpenAI press release, 23 September 2025External Links:[Link](https://openai.com/index/five-new-stargate-sites/)Cited by:[§7](https://arxiv.org/html/2605.22840#S7.p6.1)\.
- A\. Sandberg and N\. Bostrom \(2008\)Whole brain emulation: a roadmap\.Technical reportTechnical ReportTechnical Report 2008\-3,Future of Humanity Institute, University of Oxford\.Cited by:[§3](https://arxiv.org/html/2605.22840#S3.p1.4),[§3](https://arxiv.org/html/2605.22840#S3.p1.7),[6th item](https://arxiv.org/html/2605.22840#S8.I1.i6.p1.5)\.
- A\. Sandberg \(1999\)The physics of information processing superobjects: daily life among the jupiter brains\.Journal of Evolution and Technology5\(1\)\.Cited by:[1st item](https://arxiv.org/html/2605.22840#S8.I1.i1.p1.3)\.
- J\. Sevilla, L\. Heim, A\. Ho, T\. Besiroglu, M\. Hobbhahn, and P\. Villalobos \(2022\)Compute trends across three eras of machine learning\.InProceedings of the International Joint Conference on Neural Networks \(IJCNN\),External Links:[Document](https://dx.doi.org/10.1109/IJCNN55064.2022.9891914)Cited by:[Figure 4](https://arxiv.org/html/2605.22840#S7.F4),[§7](https://arxiv.org/html/2605.22840#S7.p2.5),[§7](https://arxiv.org/html/2605.22840#S7.p3.9)\.
- E\. Strubell, A\. Ganesh, and A\. McCallum \(2019\)Energy and policy considerations for deep learning in NLP\.InProceedings of the 57th Annual Meeting of the Association for Computational Linguistics,pp\. 3645–3650\.External Links:[Document](https://dx.doi.org/10.18653/v1/P19-1355)Cited by:[§2](https://arxiv.org/html/2605.22840#S2.p4.2)\.