Inward, not outward

Leans on The cost of forgetting, Cooling is the economy.

Which way is up?

In 1964 a Soviet astronomer, Nikolai Kardashev, asked how a civilization could be detected across space, and to answer it he ranked civilizations by how much power they use. His Type I used about what the whole Earth of his day used. A Type II uses the entire output of a star. A Type III uses a galaxy's. The ladder points outward: more energy, more sky, more of the universe turned into machinery.

Carl Sagan smoothed the steps into a continuous scale in 1973, and set the first rung much higher. On his version, the Earth of 2026 sits at 0.73, still short of Type I. The Vigil lights its first petawatt in 2540, which is 0.9 on the same scale: past Earth, and far from a star. Its plan aims for 1 × 10²⁰ watts, 1.4 on the scale, a level it reaches in the 2550s if its growth keeps pace simulation.

The cosmologist John Barrow proposed a scale in 1998 based on the smallest thing a civilization can control. Its categories are as follows (Barrow called them Type I-minus to Type Ω-minus; BI to BΩ is shorter):

BI: objects about your own size, which people have managed since before history.
BII: genes.
BIII: molecules.
BIV: single atoms.
BV: the nuclei inside atoms.
BVI: elementary particles.
BΩ: the structure of space and time itself.

Earth in 2026 stands around BIII: its chemists build molecules to order, its biologists edit genes, and in laboratories a few people can push single atoms around. The Vigil stands at BIV. It builds with atom-exact precision, it is reaching for nuclei, and it makes use of the last rung without trying to engineer it: it sits next to a black hole, which is spacetime doing its most extreme work.

Here is why the Vigil prefers Barrow's ladder. Power is the cheap part. A petawatt, a million billion watts, needs only about 0.1 kilograms of black-hole feed every second. What is expensive is getting rid of the heat, because every watt that thinks is a watt that must be radiated away. At 30 K, a petawatt of waste heat needs radiators with a radiating surface of 43 Earths. Climb one more step of Kardashev's ladder and the radiator grows to match.

Going inward pays off in the other direction. Smaller hands unlock denser fuel: burning chemistry yields 1 × 10⁷ joules from a kilogram, and feeding a spinning black hole yields 9 × 10¹⁵. Finer control also means a computer that wastes almost nothing per thought, down to a floor that physics sets. Same heat budget, vastly more thinking.

Guess first A civilization can make its computers ten times more numerous, or make each one waste ten thousand times less heat per thought. Which gets more thinking out of the same radiators?

Reducing the heat per thought. Ten times more computers make ten times more heat, so the existing radiators cannot support them all at once. Wasting ten thousand times less heat per thought allows ten thousand times more thinking with the same radiators. The computers of the 2020s operated further above the minimum than that, as the figures below show.

The Vigil increases precision, lowers operating temperatures where useful, and expands within its cooling capacity. Black holes are relevant to both scales: a black hole holds the most mass-energy a region its size can hold and, according to theories whose details remain disputed, the most information too. These properties motivate the Vigil's location.

How far up is each ladder?

The power ladder is one formula:

K = (log₁₀ P − 6) / 10

P is power in watts. Each step of 1 in K is a factor of ten billion in power. Sagan's Type I is 1 × 10¹⁶ W, Type II is 1 × 10²⁶ W and Type III is 1 × 10³⁶ W. Kardashev's own 1964 anchors were 4 × 10¹², 4 × 10²⁶ and 4 × 10³⁷ W. The top two are within a factor of a few tens of Sagan's; the first is far lower, because it was simply the Earth of 1964. By Kardashev's reckoning the Earth was already Type I; by Sagan's, the Earth of 2026 is still short of it. Here is where some real and imagined civilizations stand:

Civilization	Power	K
Earth, 2026	2 × 10¹³ W	0.73
The Vigil at First Light, 2540	1 × 10¹⁵ W	0.9
The Vigil's goal, 2550s (projected)	1 × 10²⁰ W	1.4
All the light of the Sun	4 × 10²⁶ W	2.1
The Milky Way	4 × 10³⁷ W	3.2

The Vigil's goal is 5 × 10⁶ times Earth's power, 1.4 on the scale.

Barrow's ladder has no formula, and Barrow gave no lengths. The lengths below are this page's choices, a representative size for each rung:

Rung	Controls	Length
BI	Objects of your own size	1 m
BII	Genes (the width of the DNA helix)	2 × 10⁻⁹ m
BIII	Molecules	1 × 10⁻⁹ m
BIV	Atoms (the Bohr radius)	5.3 × 10⁻¹¹ m
BV	Nuclei (what a 200 MeV probe resolves)	9.9 × 10⁻¹⁶ m
BVI	Elementary particles (what a 1 TeV probe resolves)	2.0 × 10⁻¹⁹ m
BΩ	Space and time (the Planck length)	1.6 × 10⁻³⁵ m

The rungs are not evenly spaced. From your own size down to an atom is about 10.3 powers of ten, as long as one whole Kardashev step. From an atom to a nucleus is another 4.7. From a nucleus to the Planck length is 19.8, a long way down that nobody has a plan for.

Two ladders. Kardashev climbs by power, Barrow descends by size, and each tick is a factor of ten on a log scale. K is Kardashev's rating, worked out from the power.

What does going inward buy?

First, fuel. The deeper the control, the more energy each kilogram of fuel can release:

Fuel	Control it needs	Energy per kilogram
Burning methane and oxygen	Nothing finer than a fire (BI)	1 × 10⁷ J
Fusing hydrogen to helium	Nuclei (BV)	6 × 10¹⁴ J
Feeding a spinning black hole (spin 0.7)	Parking next to spacetime (BΩ)	9 × 10¹⁵ J

To run at the Vigil's goal of 1 × 10²⁰ W, a black hole needs 1.1 × 10⁴ kg every second. Chemistry would need 1 × 10¹³ kg a second, and would burn through the mass of the Earth in about 2 × 10⁴ years. Fusion sits in between at 1.6 × 10⁵ kg a second.

Second, thinking. A chip of the 2020s spends between 1 × 10⁻¹⁶ and 1 × 10⁻¹³ joules to switch one logic gate. The floor from The cost of forgetting at 300 K is 2.9 × 10⁻²¹ joules per bit. The gap is a factor of 35,000 to 3.5 × 10⁷, which is 4.5 to 7.5 powers of ten. In Kardashev's currency that is 0.45 to 0.75 of a whole step, and closing it needs no extra watt and no extra square metre of radiator. Dump the heat at the Vigil's 30 K instead of 300 K, and the floor drops tenfold again: the gap becomes 0.55 to 0.85 of a step. Cold does have a price, paid in radiator area rather than watts, and the first fold below weighs it.

Increasing power requires more cooling capacity. The radiating surface for the Vigil's goal, at 30 K, covers 4 × 10⁶ Earths. One more Kardashev step, at the same efficiency and temperature, would require 4 × 10¹⁶ Earths. Cooling is the economy derives the area requirement.

What does the Vigil do with all this?

Its computers are built atom by atom to approach the energy minimum for reliable switching. Its radiators run cold. These choices reduce the power it needs from the black hole. The self-replicating machines described in Doubling build the radiator area needed for further growth.

Open everything

Why do smaller and colder buy so much?Switching energy, the Landauer gap and the temperature trade, with logarithms and a little calculus

What does reliable switching require?

The Landauer limit $kT\ln 2$ is the least heat that forgetting one bit can release, derived on The cost of forgetting. Reliable storage also requires protection against thermal noise. A bit stored behind an energy barrier $E$ flips by thermal noise with probability about

$p \sim e^{-E/kT}$

so a gate that must fail less than once per $1/p$ operations needs

$E \ge kT \ln\frac{1}{p}$

For a flip probability of 1 × 10⁻¹⁵ per operation, a design choice rather than a law of nature, this is $E \approx$ 35 $\,kT$ , which is 50 times the Landauer floor, or 1.4 × 10⁻¹⁹ joules at 300 K. That is roughly the least a conventional gate can spend, one that lets the energy holding its bit in place go as heat every time it switches. The 2020s gates sit 700 to 7 × 10⁵ times above it. The headline gap in the numbers stretch is the bigger figure; the reachable one is smaller, and still large.

Why shrinking helped, and why it stops helping

In 1974 Robert Dennard and his colleagues at IBM showed how to scale a transistor down. Shrink every length and every voltage by a factor $\kappa$ , and dope the silicon to match. Then the capacitance of a gate falls as $1/\kappa$ (its area falls as $1/\kappa^2$ and the insulator gets thinner as $1/\kappa$ ), the voltage falls as $1/\kappa$ , and the energy of a switch, $\tfrac12 C V^2$ , falls as

$E_{\text{switch}} \propto \frac{1}{\kappa}\cdot\frac{1}{\kappa^2} = \kappa^{-3}$

The delay of a gate fell as $1/\kappa$ at the same time, which is why the shrink was worth so much for decades. To close the whole gap to the Landauer floor by scaling alone, a gate would have to shrink in every direction by a factor of 33 to 330.

The rule breaks where the voltage can no longer fall. A transistor turns on and off by lifting electrons over a barrier against thermal noise, so the swing of voltage it needs is set by $kT/q$ , and the supply cannot drop below several times that. Once the voltage is fixed, shrinking lowers the energy only through the capacitance, one power of $\kappa$ instead of three. Further reductions require lower temperatures or a different computing architecture.

What the atom, and the nucleus, actually give you

Confining a particle to a region of size $L$ costs energy, and the smaller the region, the more. For electrons in atoms, the natural unit is the Hartree energy, 27 eV. That is 1,100 times $kT$ at 300 K, which is why atoms make a good building material: their structure shrugs off thermal noise. A gate of the 2020s spends 23 to 23,000 Hartrees per switch, because it moves crowds of electrons where one would do. Atom-exact control lets a designer set each barrier where it is needed, near the reliable floor above, instead of where lithography leaves it. Below that floor, control of atoms is not enough: it takes logic that does not throw bits away, the subject of Computing without forgetting.

For a nucleus the arithmetic turns around. A particle confined to the size of a nucleus has, by the uncertainty principle, a momentum of at least about $\hbar/L$ , and since it is then relativistic, an energy of order

$E \sim \frac{\hbar c}{L}$

That is 3 × 10⁻¹¹ joules at the BV length above, 7 × 10⁶ times a Hartree. Higher energy permits faster operations: by the Margolus-Levitin bound on How fast can anything think?, one operation takes at least $\pi\hbar/2E$ , which is 4 × 10⁻¹⁷ s for a Hartree and 5 × 10⁻²⁴ s at the nuclear scale. The dissipation minimum, $kT\ln 2$ , is independent of size. An efficient nuclear switch would have to recover almost all of its energy on every step, requiring reversible operation with tight error control. Control down to the atomic scale can reduce computing energy; control below it offers denser fuel (the middle row of the fuel table) and faster operations.

Cold, and the other resource

Cooling pays in two different currencies, and they pull in opposite directions. Per joule, the floor falls in proportion to $T$ : ten times colder, ten times more forgotten bits per joule. Per square metre of radiator, run flat out at the floor, the count of operations per second is

$\frac{\sigma T^4}{kT\ln 2} = \frac{\sigma T^3}{k\ln 2}$

which is 2 × 10²⁰ per square metre at 30 K and 2 × 10²³ at 300 K. When area is the scarce thing, a warmer radiator thinks a thousand times more per square metre. When feed is the scarce thing, a colder one thinks ten times more per joule. Which one binds decides the temperature, and the Vigil's choice of 30 K belongs to its heat engine, covered in Cooling is the economy.

Whatever the temperature, the thinking rate of a heat-limited machine is

$\text{operations per second} = \frac{P_{\text{heat}}}{E_{\text{op}}}, \qquad P_{\text{heat}} \le \sigma T^4 A$

Going outward raises $A$ or $P$ ; the radiator grows with it. Going inward lowers $E_{\text{op}}$ toward its floor, which helps at every temperature and at every size. At the Vigil's goal of 1 × 10²⁰ W, 30 K and the floor, that is 3 × 10⁴¹ erasures a second; with 2020s gates the same power gives 1 × 10³³ to 1 × 10³⁶.

Size also buys time

A mind that must act as one has to keep its parts in step, and light covers only 0.30 metres in one cycle of a 1 GHz clock. Smaller parts mean shorter signal paths, so a smaller machine can have both a faster clock and less lag between its halves.

Where the ladders meet

A black hole holds a bit for every $4\ln 2$ Planck areas of its horizon, which comes to 1 × 10⁶⁹ bits per square metre, and no region of space can hold more information per area. Vesper's horizon holds 2 × 10⁷⁹ bits. It also holds the most mass-energy any region of its size can, and matter falling into it, with spin, is the richest fuel in the table. The Vigil uses this existing spacetime structure; it cannot engineer one. frontier

Is this how civilizations really rank, and who says so?The papers, the searches and what is still argued

Where the ladders came from

Kardashev's 1964 paper was about listening. Which civilizations could we hear across the galaxy, and how much power would their transmitters need? The three types were rough anchors for that question: about 4 × 10¹², 4 × 10²⁶ and 4 × 10³⁷ watts. Sagan's 1973 suggestion, in The Cosmic Connection, was to fill the gaps: call a civilization using 1 × 10¹⁶ W Type 1.0, step by a tenth for each tenfold increase, and rate the Earth of that decade around 0.7. Written as a formula, his interpolation is the one at the top of the numbers stretch. Milan Ćirković's 2015 review follows the scale through its first half century, with its refinements and rivals, and argues that Kardashev's emphasis on what can be detected has aged well.

Barrow's ladder comes from Impossibility, a book about the limits of science. He named his types Type I-minus to Type Ω-minus, and the idea is the one on this page: a civilization advances by controlling smaller and smaller things. The seven rungs and their definitions are Barrow's; the labels BI to BΩ and the lengths attached to them here are not. Where the Earth stands is a judgement. This page puts the Earth of 2026 near BIII, because chemists have made new molecules to order since the nineteenth century.

Has anyone looked?

If civilizations grew outward, they should be visible. Freeman Dyson suggested in 1960 that a civilization using a star's whole output would have to radiate the used energy away as infrared light, so astronomers could look for stars that glow warm and dim. The modern version is the Ĝ search. Wright and colleagues set out its logic in 2014, and in 2015 Roger Griffith's team checked about 1 × 10⁵ galaxies in the WISE infrared survey for the waste heat of Type III civilizations. No galaxy in the sample reprocessed more than 85 per cent of its starlight into infrared. Only 50, among them the well-known starburst Arp 220, were bright enough to be reprocessing more than half, and the little-studied red sources looked, in most cases, like galaxies busy forming stars. As of 2026, no search has found a civilization using a galaxy's power.

What the silence might mean

Several readings of that silence are argued, and none is settled.

They are rare or absent. The simplest reading.
They wait. Sandberg, Armstrong and Ćirković argued in 2017 that a civilization that wants to maximize computation should sleep until the universe is colder, because the Landauer cost falls with temperature, a gain they put at about a factor of 1 × 10³⁰. That is the ladder of this page turned into a strategy; see Thinking in a cooling universe. frontier
They go inward. John Smart's transcension hypothesis (2012) proposes that advanced civilizations tend toward ever smaller, denser and more efficient scales, and so stop being visible from outside, ending somewhere very like a black hole. That is Barrow's ladder offered as an answer to the Fermi question, and it is a proposal about civilizations nobody has seen. frontier

What the page assumes

The argument makes three assumptions.

That a civilization wants thinking above all. Kardashev's scale made no such assumption; it counted watts.
That the rungs come in order. Nothing in physics says a civilization must master molecules before nuclei, and the rungs of BII and BIII are close in size.
That the last rung is reachable. No method for engineering spacetime is known. The Vigil uses a naturally occurring black hole. frontier