Energy at Three Scales

The pillar of thermodynamics names its own three scales in a single sentence: "Landauer's limit at the computational floor, the electricity grid powering the data centers, and the metabolic 20-watt budget of the human brain." That sentence is the order of this section. Each scale is stated with the figure, the arithmetic that reaches it, and the source that carries it.

The point of setting them side by side is not to rank them. It is to see that the same rule — nothing can be had from nothing — holds at every one of them, and that the distance between the physical floor and what an architecture actually spends is where a design decision lives.

Human scale

About 20 watts. The brain is roughly 2% of the body's weight and takes roughly 20% of its resting oxygen, which works out at about 20 watts, or a quarter of a kilocalorie a minute. It runs on that budget continuously, with no respite. It is on that budget that a person notices, examines and chooses — and on that budget that a person can be asked a question they cannot answer by recognizing the test.

Basis

Cerebral oxygen consumption of about 3.5 ml per 100 g per minute across a 1,400 g brain, converted at the energy equivalent of carbohydrate oxidation.

Source

Clarke & Sokoloff, "Regulation of Cerebral Metabolic Rate", Basic Neurochemistry (NCBI Bookshelf); Raichle & Gusnard, "Appraising the brain's energy budget", PNAS 99 (2002); "Brain power", PNAS 118 (2021).

Planetary scale

415 terawatt-hours a year, rising to about 945 by 2030. The world's data centres drew an estimated 415 TWh of electricity in 2024, roughly 1.5% of global consumption, and the projection for 2030 is around 945 TWh — slightly more than Japan uses in a year now. Averaged across the year, 415 TWh is about 47 gigawatts of continuous power; 945 TWh is about 108. Against the 20-watt brain, the 2024 figure is the standing equivalent of some 2.4 billion brains running for a year.

Basis

415 TWh/yr = 1.49 x 10^18 J/yr, divided by 3.156 x 10^7 s, gives 4.73 x 10^10 W. Dividing the same energy by 20 W held for one year (6.31 x 10^8 J) gives 2.37 x 10^9.

Source

International Energy Agency, Energy and AI, special report, 10 April 2025.

Universal scale

2.87 x 10^-21 joules per bit erased. Physics sets a floor under any computation performed anywhere, by any substrate, on any planet: erasing one bit of information at temperature T must dispose of at least kT ln 2 of energy as heat. At 300 kelvin that is 2.87 x 10^-21 joules. No architecture, human or engineered, gets below it.

The 2024 grid, spent at that floor, would stand for 5.2 x 10^38 bit erasures. A 20-watt brain running for one second is worth 7.0 x 10^21 of them. The distance between what the floor allows and what an architecture actually spends is where the design lives — and no honest architecture, biological or engineered, is allowed to spend nothing.

Basis

k = 1.380649 x 10^-23 J/K, T = 300 K, ln 2 = 0.6931; kT ln 2 = 2.871 x 10^-21 J. The other two figures follow by division.

Source

R. Landauer, "Irreversibility and Heat Generation in the Computing Process", IBM Journal of Research and Development 5(3), 1961, pp. 183-191.

A note on supply

For a fourth figure that keeps the planetary scale honest: the Earth intercepts about 173.5 petawatts of sunlight, of which roughly 121 petawatts is absorbed after the ~30% the planet reflects. Computed from the solar constant of 1361 W/m2 across the Earth's cross-section. The whole data-centre grid of 2024 is about one two-and-a-half-millionth of what the Sun delivers to this planet.

Scarcity at the human scale is therefore not a shortage of energy in the universe. It is a question of architecture, of placement, and of who is asked to pay the cost. That is the ledger this book is written to keep.