The wrong comparison of 20 watts

Every so often a sentence returns that seems to end the discussion before it has begun: the human brain runs on about twenty watts, while modern artificial intelligence needs data centers. The sentence works because it places two almost comic images on the same table. On one side, a warm and silent organ; on the other, a data center with its electrical and industrial surroundings. The rhetorical effect is immediate: biological intelligence looks frugal; artificial intelligence looks industrial.

The trouble is that the sentence is true only in the way a measurement can be true when it is taken from too close. The adult brain really is cheap, if we treat it as a machine already switched on. Twenty watts is the right order of magnitude for human brain metabolism: about 2% of body mass and roughly one fifth of resting energy use. But that number is not the energetic outlay needed to arrive at a human mind. It is the running outlay of an organism that has already received, without a visible invoice, a long biological and cultural preparation: body, language, social tools and many generations of error.

The first correction is less elegant than a slogan: there is no single energetic efficiency of intelligence. There are different accounts. The meme compares a narrow, almost marginal line item with a much wider apparatus: the already running brain on one side, the electrical infrastructure of AI on the other. That is not the same question asked twice. If we compare the brain in run mode with the whole industrial machine of AI, we get a simple but dirty moral. If we compare AI as a copyable, queryable, generalist and partially verifiable model with one specialized human being, the target has already moved. The boundary of the account has to be declared before anyone is awarded thermodynamic virtue.

The accounting boundary

It is useful to begin with elementary physics. The energy consumed by a process is mean power multiplied by the duration of the interval:

E = P\,\Delta t

where $P$ is mean power and $\Delta t$ is the time interval under consideration. The relation looks too simple to carry a comparison between biological and artificial cognition, but it already dissolves much of the rhetoric. A brain running for a year at 20 W consumes about 175 kWh. That is small next to an industrial plant and large when multiplied by all the person-years of human history. With rough but not absurd estimates, the energy spent only on active human brains quickly reaches hundreds of thousands of TWh; if we include the body metabolism that sustains them, the account rises again.

For AI the boundary is more visible because it passes through the electrical grid. The IEA estimates that data centers reached about 485 TWh in 2025, with scenarios approaching 950 TWh in 2030. These are enormous numbers. They should not be minimized or disguised as the inevitable price of progress. But they are not the consumption of “pure artificial thought”: they also include ordinary cloud workloads and the material share of infrastructure. A nontrivial share of the energy is spent simply making bits remain stable enough to be useful.

The symmetry with the brain, if we actually look for it, becomes less comfortable. The brain’s 20 W are not “pure reasoning” either. They sustain an organ that perceives, regulates the body, remembers, predicts and remains active even when it is not doing mathematics. And the data center is not a giant mind: it is a technical apparatus inside which part of the computation becomes cognitive because it is connected to data, goals and evaluation criteria.

To avoid changing units halfway through the sentence, I would write the comparison with a subscript on the accounting boundary:

\begin{aligned} \eta_B &= \frac{C(T,\varepsilon,G,R,A,N)}{E_B},\\ E_B &= E_{\mathrm{data}} + E_{\mathrm{training}} + E_{\mathrm{research}} \\ &\quad + E_{\mathrm{inference}} + E_{\mathrm{substrate}} \\ &\quad + E_{\mathrm{verification}} + E_{\mathrm{culture}}. \end{aligned}

Here $B$ is the chosen boundary, $E_B$ the total energy included by that boundary, and $C$ the performance evaluated under declared conditions: $T$ denotes the task, $\varepsilon$ the tolerated error, $G$ grounding, $R$ the required reliability, $A$ the breadth of the domain and $N$ reuse. A narrow boundary counts the task; a middle one includes formation; a broad one brings in the history that made the agent possible. Written this way, $\eta_B$ measures performance per accounted unit of energy and mainly blocks an abuse: taking the local outlay of one case and comparing it with the genealogy of the other.

The dimensional point is simple: if the metric promises performance per joule, energy belongs in the denominator. If the ratio is reversed, the formula does not merely look different; it measures a different quantity.

One more caution is needed. $E_B$ may mean energy physically spent, a share assigned to one use, or a component shared across many effects. Culture was not produced only to answer a prompt, and biological evolution was not aiming at an exercise solution. Widening the boundary does not license charging all of history to every cognitive act. It forces us to say which share we assign, and why.

Account boundary First decide what you are counting

B0 Answer local act only
B1 Body metabolism and service
B2 Formation years and training
B3 History culture and data

On that reading, the comparison breaks into three different questions:

Level	Question	Human	AI
Local	What does the act cost now?	brain and body running	inference and service
Formation	What did it take to obtain the agent?	growth, school, practice	training, evaluation, research
Systemic	What keeps the ecosystem working?	institutions, culture, tools	data centers, datasets, safety, monitoring

The 20 W line often uses the first level for the human and the third for AI. Once the levels are separated, the comparison becomes less quotable and more honest.

At the local level, the human brain remains impressive: an answer, a choice or a piece of reasoning requires little power, especially in domains where body and environment supply strong constraints.

Formation energy is already something else. An adult capable of solving a problem did not simply appear in front of the problem. They were formed for years inside a material and symbolic environment. The 20 W brain, when it does mathematics or physics, never works alone: it carries a didactic, notational and instrumental apparatus with it. Even a formula written on paper is not just passive memory. It is part of the reasoning, a prosthesis that lets the mind re-enter its own thought.

For AI, formation energy is easier to see because it takes the form of a training, evaluation and engineering pipeline. The successful model is the winner, not the tournament. The same is true for humans, except that we are used to narrating individual genius as if it were a local property of the skull. When we say that mankind produced general relativity or frontier mathematics, we are compressing a population, a selective culture and a long educational apparatus.

Embodied historical energy makes the comparison even more ambiguous. AI does not read raw nature. It reads a civilization already metabolized. A quantum mechanics textbook is the compact residue of experiment and failure; a paper shows the endpoint more than the cognitive mud; a repository preserves the solution, not all the abandoned versions. The model therefore receives a privileged curriculum: it reads cultural objects with very high pattern density.

But embodied does not mean fully billable. The energy a society spends on schools, books, instruments, archives and institutions also produces survival, power, art, conflict, economies and relationships. Assigning all of it to one mental act would be the opposite error to the one we are trying to correct. The point is not to add everything; it is to avoid pretending that history vanishes when that is convenient.

But this richness is mutilated. A child does not learn cup from a distribution of sentences about cups. The child handles it and undergoes its effects: stability, breakage, the adult’s reaction. In that small episode there is physics, gesture and social value. Text is highly abstract per bit, but often poor in intervention per bit. For the biological agent, the world is a continuous physical simulator that no GPU has to render.

This does not mean that the environment is thermodynamically free. It is free only relative to the child’s local account. Gravity does not draw from the child’s metabolic budget when a ball falls; the world evolves according to its own physics. If we want to give an artificial system the same amount of causality through simulation, robotics or interactive environments, the cost becomes explicit: a physical channel of intervention has to be built and maintained. Textual AI pays in statistical inference for part of what the human receives as body and world.

The body, then, is not an accessory to the brain. It is a physical prior. Perceptual and motor morphology reduce the hypothesis space before the problem becomes conscious. Many tasks that would look huge if formulated as abstract optimization reach the brain already filtered. The system does not have to infer from zero that an edge cuts or that a slippery object requires care; it learns inside a geometry of consequences.

The substrate enters here. The brain does not simulate neurons: it is neural tissue, local chemistry, rhythms and plasticity. Algorithm and support are not cleanly separated. In modern GPUs and TPUs, by contrast, representational geometry is realized through digital linear algebra and data movement. These are magnificent machines, but magnificent for numerical throughput and scale, not because their physics is already the physics of cognition.

This detail changes the meaning of mental “spontaneity”. In a latent space a relation may be almost obvious: a concept near another, a natural transformation, a trajectory that seems to want to move in that direction. But semantic obviousness does not guarantee physical cheapness. To make that relation occur in silicon, memory still has to be read, data moved and energy dissipated. In the brain, some intuitions look more like the relaxation of a physical system already trained toward an attractor. In current AI, that descent is often approximated through explicit digital steps. I do not mean this as a moral condemnation of AI. It is a sign of a historical moment in which the cognitive model and its material support still do not fit each other very well.

The performance we demand

The 20 W comparison has already lost much of its force. But another asymmetry remains, perhaps even more unfair: the human is often compared as a specialized individual, while the model is judged as if it had to contain a population.

A human being becomes someone. They have a native language, a history, a few deep domains and many perfectly legitimate ignorances. Specialization reduces the space of hypotheses that must be kept alive. It is a form of energetic and personal compression.

A generalist model, instead, remains conditional. It has to cross domains and registers that we normally distribute across different people. We ask it to be a technical assistant, a tutor, a critical reader and sometimes the interpreter of badly formed desires. No single human is evaluated this way. When people say that “humans” can do advanced mathematics, they are using an existential quantifier disguised as a species property: some humans, after years of cultural finetuning, can do it. Often very few.

This breadth is not free. If we want to measure efficiency over a space of domains, the quantity should not be performance on one task, but performance integrated over a task distribution with declared weights:

C = \int_{\mathcal{D}} p(\tau)\,w(\tau)\,\mathrm{d}\tau

Here $\mathcal{D}$ is the space of tasks, $\tau$ one point in it, $p(\tau)$ the performance on that task and $w(\tau)$ the weight assigned to that region of the domain. The expression is schematic, but it forces a simple point: a narrow and deep system cannot be compared with a broad and irregular one without deciding how depth and breadth are weighted. The human brain occupies one point on the frontier: very low power, strong grounding and everyday robustness, paid for with low copyability, slowness and fragile memory. Current AI occupies another: huge symbolic bandwidth and industrial reuse, paid for with incomplete grounding, infrastructure cost and safety overhead.

The cost of reliability deserves its own discussion, because it is often mistaken for the outlay of intelligence. An intelligent answer is rarely enough. We want it to be verifiable and calibrated, but also compatible with social constraints. We want it to refuse certain requests without becoming mute. This is another layer of energy and work.

Humans do not carry all this reliability inside the skull. A doctor is made reliable also by hospitals, licenses and legal responsibility; a theorem becomes reliable through seminars, referees and hostile readings. With AI we often try to put part of the reviewer, supervisor and skeptical colleague inside the system itself. Producing an answer is one thing. Knowing when it can be used is another. Sometimes the second line item dominates the first.

Memory also changes the balance. The human is cheap partly because it forgets. It does not preserve the dataset of life; it compresses and reconstructs. That imperfection produces errors, of course, but it is also an energy technology. We often ask AI for the opposite: long contexts, documentary precision and searchable external memory. Faithful memory does not cost only storage; it costs retrieval and verification. The brain is forgiven because it is an organism; the model is granted much less tolerance.

Then there is copyability, which cuts in the opposite direction. A trained human being cannot be duplicated. You can teach Newton, but you cannot copy Newton. Each new expert requires years and an unrepeatable biography. A model, once trained, can be replicated. This does not erase the outlay of training, but it changes its nature:

\begin{aligned} E_{\mathrm{use}} &= \frac{E_{\mathrm{training}}}{N_{\mathrm{copies}}\,N_{\mathrm{uses}}} + E_{\mathrm{inference}} + E_{\mathrm{service}}. \end{aligned}

If $N_{\mathrm{copies}}$ is the number of replicas and $N_{\mathrm{uses}}$ the number of interactions, the embodied training cost per use can become small. Not always: long contexts, retrieval, multi-step agents and verification can make inference expensive too. But the structural advantage remains. An artificial competence can be distributed without rebuilding the whole biography that produced it.

Reuse Training matters less each time

If the same model is used many times, training weighs little per answer. Inference and service still remain.

Temporal compression is the last part that the local comparison tends to hide. We want AI to absorb in months an amount of culture no human being could read in a lifetime, and then to answer almost immediately. Holding architecture fixed, compressing $\Delta t$ means increasing $P$ . This is not only an economic problem; it is a physical consequence of accelerating the formation of competence. The human is parsimonious in local power, but slow and difficult to parallelize. AI is costly in power, but fast, copyable and distributable.

Perhaps the metric we actually want is not watts per thought, because “thought” is not a good physical unit. Joules per token is not enough either: a token can be filler, error, style, or the decisive step in a solution. The interesting quantity is closer to useful causal information embodied per unit of energy:

\rho_B = \frac{I_{\mathrm{useful}}\!\left(S;M\mid T,\varepsilon,R,G,A\right)}{E_B}

$S$ is the agent and $M$ the world against which it is evaluated; the conditions after the vertical bar are the same as in the previous account. $I_{\mathrm{useful}}$ is not raw information. A terabyte of noise is not worth a good page of physics. What matters here is structure that lets an agent predict, explain, control, transfer and correct regularities in the world. Change $B$ , and the answer changes.

Account

Widen the boundary, change the total

formation

B0 counts the answer. B3 adds body, training, data and history.

Boundary

B

: formation

Reuse

N_{copies} N_{uses}

: 100.000x

Human total: 0
AI total: 0
Largest item: -

This is not an operational formula ready for a spreadsheet. It is a way not to be fooled. A system can have much semantics and little grounding, or much embodied experience and little symbolic range. It can be competent but hard to copy, general but fragile, cheap in the local act and expensive in the history that produced it. The word efficiency is not enough by itself. We need a Pareto frontier between energy, generality, reliability, grounding and reuse. We cannot maximize everything at once without paying somewhere.

Trade-off No one wins on everything

More breadth and control require energy, time or compromises.

For that reason, the question “should it cost 20 W?” has a fairly clear answer for current AI: no, not in this regime. We ask it to reconstruct world, culture, safety and generality from partial traces, on digital hardware that is not perfectly suited to the task, in a few years. The opposite would be stranger.

This does not mean that AI has to remain energetically crude. It probably is crude today. Sparser architectures, hardware closer to the dynamics it must execute, better curricula and separate verifiers could move the frontier a lot. The human brain is not the final limit of cognition; it is a powerful biological compromise, constrained by birth, metabolism, evolutionary history and objective functions that did not have abstract mathematics as their aim.

The most honest formulation, at least for now, seems to me this: the human pays little in the local moment of thought because it uses structures already spread across biology, body and culture; AI pays much in explicit computation because it has to recover parts of that structure in digital form. But pays does not mean that all biological and cultural history becomes the bill for every thought. It means we cannot move the boundary when we switch from one agent to the other. The 20 W brain and the data center are not two alternative answers to the same question. A serious account does not produce one winner: it produces different measures, each fixed by boundary, task, tolerated error, grounding, verification and reuse.