Abstract
The brain is said to use $2$ per cent of the body’s mass and $20$ per cent of its energy. This paper asks where that factor of $10$ comes from——the answer is not that the brain is high but that the denominator is low. No new mathematical theorem and no new law is claimed.
First, a $70$ kg body with a $1.4$ kg brain gives a mass fraction of $\mathbf{2.0000}$ per cent (Section 2).
Second, a basal rate of $100$ W with $20$ W to the brain gives $\mathbf{20.0000}$ per cent, a ratio of $\mathbf{10}$ (Section 2).
Third, the brain’s specific power is $\mathbf{14.2857}$ W/kg against a whole-body $1.4286$ (Section 2).
Fourth, this is the core of the paper. Skeletal muscle in exercise runs at $\mathbf{100}$ W/kg, seven times the brain (Section 3).
Fifth, per neuron it is only $\mathbf{232.5581}$ pW (Section 4).
Sixth, the separator is what the denominator is, not a property of the brain (Section 5).
Scope (what is not claimed)
No new mathematical theorem and no new law is claimed——the brain’s metabolic rate, specific power, and basal metabolic rate are all standard. We do not build neuroscience——how the energy divides between synaptic transmission and action potentials is not entered. It is named and no more. We measure nothing——$70$ kg body, $1.4$ kg brain, $100$ W basal, $20$ W brain are stated assumptions. They follow representative figures from the literature. Evolution is not discussed——the expensive-tissue hypothesis is named and no more. We do not compare with computers——a processor is mentioned once for reference and not used as a comparison. The purposes differ. Individual variation is not treated——age, build, and activity level are not the subject. Relation to earlier papers: Paper 345 showed one logarithm counting a ratio in one place and items in another——there too what one divided by did the work. Paper 364 showed selection alone raising a mean——there too the denominator (the visible group) made the number. Paper 300 showed whether two things share a root is decidable——by that test, “the brain is high” and “the whole-body average is low” have distinct roots. Paper 362 showed the bottleneck lying where nobody was looking——here the source of the surprise lies there. What is added is giving the mass and power fractions as numbers, obtaining the same factor of $10$ by two routes, showing the brain is not high against exercising muscle, giving the $232.5581$ pW per neuron, and putting the separator on the denominator.
1. Notation and the Question
Setting: Take a $70$ kg body with a $1.4$ kg brain, a basal rate of $100$ W with $20$ W to the brain.
$$f_{\text{mass}}=\frac{m_{\text{brain}}}{m_{\text{body}}},\qquad f_{\text{power}}=\frac{P_{\text{brain}}}{P_{\text{body}}},\qquad \text{specific power}=\frac{P}{m}$$Observation 1.1 “$2$ per cent for $20$ per cent” is a ratio of two fractions. $0.20/0.02=10$——and both numerator and denominator carry a chosen reference.
Observation 1.2 The denominator is the basal rate — the whole body at rest. Doing nothing——and in that state the muscles use almost no power.
Observation 1.3 So changing the comparison changes the number. This paper gives how much it changes——looking at where the factor of $10$ actually comes from.
Question: What does the factor of $10$ tell us about the brain?
2. The Factor of $10$ Arrives by Two Routes
Calculation 2.1: Fractions and specific powers (computed in this paper).
| Quantity | Value |
|---|---|
| Mass fraction | $\mathbf{2.0000}$ per cent |
| Power fraction | $\mathbf{20.0000}$ per cent |
| Ratio (power / mass) | $\mathbf{10.0000}$ |
| Brain specific power | $\mathbf{14.2857}$ W/kg |
| Whole-body specific power | $1.4286$ W/kg |
| Ratio of specific powers | $\mathbf{10.0000}$ |
Observation 2.2 Two routes return the same $10.0000$. The ratio of fractions and the ratio of specific powers——the same quantities divided in a different order. A check that the formulae close.
Observation 2.3 The brain’s specific power is $14.2857$ W/kg. $20$ W over $1.4$ kg——that is the absolute figure for how much power the brain draws.
Observation 2.4 The whole-body average is $1.4286$ W/kg. $100$ W over $70$ kg——a single $100$ W bulb is the whole of a resting person.
Observation 2.5 That low denominator is what does the work. $1.4286$ W/kg——a body at rest is doing almost nothing.
3. Exercising Muscle Is Seven Times the Brain
Calculation 3.1: Specific powers side by side (computed in this paper; the muscle figure from the literature).
| Object | Specific power [W/kg] | Relative to the brain |
|---|---|---|
| Whole body (resting average) | $1.4286$ | $0.1000$ |
| Brain | $\mathbf{14.2857}$ | $\mathbf{1.0000}$ |
| Skeletal muscle (exercising) | $\mathbf{100}$ | $\mathbf{7.0000}$ |
Observation 3.2 This is the core of the paper. Exercising muscle has seven times the brain’s specific power——the brain is not the body’s most power-hungry tissue.
Observation 3.3 The factor of $10$ comes from the low denominator. Not that $14.2857$ is high, but that $1.4286$ is low——the same number reads as a property of the comparison rather than of the brain.
Observation 3.4 So during exercise the $20$ per cent falls. Because the denominator grows——the brain’s $20$ W has not changed and the fraction drops.
Observation 3.5 To be stated honestly——$100$ W/kg is a representative figure from the literature, not computed here. It varies greatly with intensity——it is used as a comparison and no precision is claimed.
Observation 3.6 Something about the brain is still unusual. Not that its specific power is high, but that it does not fall at rest——muscle drops below $1$ W/kg when idle; the brain does not.
4. Per Neuron It Is $232.5581$ pW
Observation 4.1 $20$ W over $8.6\times10^{10}$ neurons is $\mathbf{232.5581}$ pW. $2.3256\times10^{-10}$ W——not even a nanowatt.
Observation 4.2 Seen from the individual, it is strikingly small. While the total is $20$ W——being numerous and being individually large are different things.
Observation 4.3 One number gives two impressions. “$20$ per cent” and “$232.5581$ pW”——the first sounds large and the second small. They are the same $20$ W.
Observation 4.4 The same shape as Paper 345. There one logarithm counted a ratio and items——here one $20$ W makes different impressions as a fraction and as a per-unit figure.
Observation 4.5 To be stated honestly——this paper does not compare the brain with a processor. Setting operations per watt beside it compares different purposes——the form “numbers side by side therefore a comparison” is not taken.
5. The Separator: What the Denominator Is
Observation 5.1 The separator——what one divided by; not a property of the brain.
| Compared with | Its specific power | Brain relative to it | Impression |
|---|---|---|---|
| Whole body (resting) | $1.4286$ W/kg | brain is $\mathbf{10}\times$ | the brain is greedy |
| Skeletal muscle (exercising) | $100$ W/kg | brain is $\mathbf{1/7}$ | the brain is frugal |
Observation 5.2 Nothing on the brain’s side has changed. $14.2857$ W/kg in both rows——only the comparison changed, and the impression reverses.
Observation 5.3 Distinct roots by the criterion of Paper 300. “The brain’s specific power is high” is fixed by the brain’s metabolism; “it is ten times” by the whole-body average——the latter is not a statement about the brain.
Observation 5.4 The separator can be moved. Change the denominator from resting to exercising——which is the “right” comparison is settled by what one wants to know.
Observation 5.5 To be stated honestly——$14.2857$ and $232.5581$ pW are values on stated assumptions. Another build gives other numbers——what does not move is the structure: the factor of $10$ arises from the low denominator.
Observation 5.6 One last thing——a figure of the form “$N$ times” is also a statement about what it was compared with. Saying the brain is ten times, half the sentence is about the whole-body average——be surprised without checking where the surprise came from, and you are surprised at the wrong thing.
6. The Census and the Close
- Mass fraction $2.0000$ per cent (Calculation 2.1): $1.4$ kg of $70$ kg.
- Power fraction $20.0000$ per cent (Calculation 2.1): $20$ W of $100$ W.
- Ratio $10.0000$ (Calculation 2.1): the same by two routes.
- Brain specific power $14.2857$ W/kg (Calculation 2.1): the absolute figure.
- Whole-body $1.4286$ W/kg (Observation 2.4): one light bulb.
- Exercising muscle $100$ W/kg (Calculation 3.1): seven times the brain.
- What is unusual is not falling (Observation 3.6): not being high.
- $232.5581$ pW per neuron (Observation 4.1): not even a nanowatt.
- One $20$ W, two impressions (Observation 4.3): fraction and per-unit.
- The brain’s side did not change (Observation 5.2): only the comparison did.
Closing: The brain is said to use $2$ per cent of the body’s mass and $20$ per cent of its energy——and half of that factor of $10$ is a statement about what it was compared with. The numbers are right——a $70$ kg body with a $1.4$ kg brain gives a mass fraction of $\mathbf{2.0000}$ per cent; a basal rate of $100$ W with $20$ W to the brain gives $\mathbf{20.0000}$ per cent; the ratio is $\mathbf{10.0000}$, and the same $10.0000$ returns whether one takes the ratio of fractions or of specific powers. But in absolute terms the brain is not especially high——its specific power is $\mathbf{14.2857}$ W/kg, and skeletal muscle in exercise, at $\mathbf{100}$ W/kg, is seven times that. The brain is not the body’s most power-hungry tissue. The factor of $10$ appears because the whole-body average is a low $1.4286$ W/kg — a body at rest is doing almost nothing. So during exercise the brain’s $20$ W stays put while the fraction falls. Seen from the individual it is smaller still——$20$ W over $8.6\times10^{10}$ neurons is $\mathbf{232.5581}$ pW, not even a nanowatt. “$20$ per cent” and “$232.5581$ pW” are the same $20$ W, and the first sounds large while the second sounds small. The same shape as one logarithm counting a ratio and items in Paper 345. One thing separates them——what one divided by; not a property of the brain. The brain stays at $14.2857$ W/kg in both rows and only the comparison changes, yet “greedy” and “frugal” swap. By the criterion of Paper 300 they have distinct roots: “the specific power is high” is fixed by the brain’s metabolism, “it is ten times” by the whole-body average — and the latter is not a statement about the brain. To be said honestly——$100$ W/kg is a representative literature figure and not computed here, varying greatly with intensity. And something about the brain is still unusual: not that its specific power is high, but that it does not fall at rest. Muscle drops below $1$ W/kg when idle; the brain does not. One last thing——a figure of the form “$N$ times” is also a statement about what it was compared with. Saying the brain is ten times, half the sentence is about the whole-body average. Be surprised without checking where the surprise came from, and you are surprised at the wrong thing.
References
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- Yamagishi, Y. (2026). The Three Hundredth Census: Whether Two Things Share a Root Is Decidable [Paper 300]. Zenodo. 10.5281/zenodo.22171914
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- Yamagishi, Y. (2026). Lifting the Stones of a Pyramid Is Not the Bottleneck [Paper 362]. Zenodo. 10.5281/zenodo.22697498
- Yamagishi, Y. (2026). Selection Alone Raises the Mean by 1.52 Standard Deviations and Shrinks the Spread to 0.45 [Paper 364]. Zenodo. 10.5281/zenodo.22697530
Reference
Yamagishi, Y. (2026). The Brain Uses “$2$ Per Cent of the Mass and $20$ Per Cent of the Energy” Because What It Is Compared With Is Resting [Paper 382]. YOI: https://www.yamagishiyuuki.com/yoi/382
DOI: 10.5281/zenodo.22698849
ORCID: 0009-0006-8587-3450
PDF (English) · PDF (Japanese) · Date proof of the English PDF (OpenTimestamps .ots) · SHA256SUMS
The record page for this paper (in Japanese, with the PDFs in each language and the date proof): YOI 382. This paper is a preprint and has not been peer reviewed.