Ideas

Why they might be asleep

Waiting for a colder universe could increase total computation from a fixed energy supply, under assumptions about heat disposal and long-term survival.

Leans on Thinking in a cooling universe.

Could everyone else be asleep?

In 1950 the physicist Enrico Fermi is said to have asked a lunch table a short question: if the galaxy is so old and so large, where is everybody? A civilization with a few million years' head start should have left something behind, in the form of ships, signals or machines that warm the sky. Through the 2020s, astronomers looked and found nothing. Plenty of answers have been offered. This page is about one of them frontier, and it starts from a fact on Thinking in a cooling universe: the universe is cooling, and a colder universe is a cheaper place to think.

Recall the price from The cost of forgetting. Forgetting a bit sends a little heat into the surroundings, and the heat is proportional to their temperature. Deep space in 2540 is 2.73 kelvin. A hundred billion years later it is below a hundredth of a kelvin. A trillion years later it is so cold that the same joule pays for 1.0 × 10²⁵ times as much forgetting. Out at the far end, where the stretching of space puts a floor under the temperature, it pays for 1.2 × 10³⁰ times as much.

Now imagine a civilization that wants one thing: as much computation as the universe will ever allow it. It has a stock of matter and energy. It can spend that stock at once, in a warm universe, or keep it and spend it in a cold one. Spending it later is worth up to 1.2 × 10³⁰ times more thinking from the very same fuel. A mind that is not in a hurry, and does not age, loses very little by waiting.

In 2017 Anders Sandberg, Stuart Armstrong and Milan Ćirković turned that into a hypothesis and named it after the way some animals sleep through the hot, dry months: aestivation. Early civilizations, they argued, would spread out fast, gather what they could reach, and then remain inactive while waiting for a colder universe. Such civilizations could exist without producing detectable activity during the wait.

Guess first Why would a civilization that could think right away choose to sleep first?

Because it values the total amount of thinking, not how soon it happens. If one joule is worth vastly more thinking later, a mind that cares about the total has every reason to hold its fuel and wait, the way you would wait for a sale if the price were going to drop 1.2 × 10³⁰ times.

The proposal faces two limitations. First, a very cold radiator emits little power per unit area, slowing computation. The paper's authors accounted for this with radiators as wide as a supercluster of galaxies. Second, the gain from waiting depends on which systems can absorb the entropy of erasure. In 2019 Charles Bennett, Robin Hanson and Jess Riedel argued that available reservoirs remove the incentive to wait during the age of stars. The disagreement concerns the available entropy capacity and how a civilization could use it.

What does waiting buy, and what does it cost?

The price of forgetting a bit is

price = k × T × ln 2

where T is the temperature of the place the heat goes. For a fixed stock of energy E, the number of bits it can pay to forget is E divided by that price, so waiting until the sky has cooled from T₀ to T multiplies the total by T₀ ÷ T. Thinking in a cooling universe has the eras in a table. Two entries are enough here: a wait of 100 billion years after 2540 is worth 336 times, and a wait until the floor, about 1,204 billion years after 2540, is worth 1.2 × 10³⁰ times. Most of the gain comes late: a wait of a trillion years is worth 1.0 × 10²⁵ times, and the rest of the way to the floor adds the remaining powers of ten.

Lowering temperature also reduces cooling capacity: a surface at temperature T radiates power in proportion to T⁴. Every erasure sends out kT ln 2 of heat, so the rate at which a radiator can support erasures scales as T³:

bits per second per m² of radiator ≈ σ × T³ ÷ (k × ln 2)

with σ the Stefan-Boltzmann constant. It is an upper bound: a radiator has to run a little warmer than the sky to shed anything at all, and its own temperature then sets the price. Freeman Dyson met the same T³ in 1979, and Sandberg and colleagues work it through in their paper. The table is this page's own sizing, for a radiator of one square kilometre.

Sky	Cheaper than 2540 by	Erasures a radiator can carry, per second per m²	Time to spend one joule's worth, on 1 km²
2540	the baseline	1.2 × 10¹⁷	0.32 seconds
100 billion years on	336 times	3.2 × 10⁹	128 years
The floor	1.2 × 10³⁰ times	6.4 × 10⁻⁷⁴	2.3 × 10¹¹² years

The same five eras twice. The price of forgetting falls, so a joule goes further (left). The heat a fixed radiator can shed falls four times as many powers of ten (right).

At the temperature floor, one joule supports 4.7 × 10⁵² erasures, but a square kilometre of radiator would need on the order of 2 × 10¹¹² years to shed their heat. For comparison, Vesper evaporates in about 3.6 × 10⁷⁰ years. The erasure cost falls as T while the rate per unit radiator area falls as T³. Using the full factor of 1.2 × 10³⁰ therefore requires much more radiator area, much more time, or both.

The useful wake-up temperature depends on radiator area and the time available. The paper's worked example uses a radiator 50 megaparsecs in radius, the size of a supercluster of galaxies. Its authors suggest a realistic sleeper might wake when the sky reaches about 1 × 10⁻⁸ kelvin, below which error correction stops getting easier with cold. On this site's clock (the paper gives about 270 billion years from its own cosmology) that is about 337 billion years after 2540, with erasure still 2.7 × 10⁸ times cheaper than in 2540. The next fold derives the trade.

Open everything

What exactly has to be true for the sleep to pay?The links in the argument, a bit-counting bound and an optimal wake-up temperature

The argument as a chain

The paper lists six assumptions about civilizations: some mature long before humanity, spread over large volumes, solve their coordination problems, hold their territory, aestivate in some non-zero fraction, and do it invisibly. Underneath sits a chain of physics and motive, in this page's own words; each link can be rejected.

The goal is total computation. The civilization wants the most operations over all time. The paper argues that a mature civilization has little reason to discount the future, and that a mind able to pause does not feel the wait. If it values any early outcome (safety, a proof, a copy of itself somewhere else), there is a price for waiting.
Computation is limited by erasure. The costly operations are irreversible ones, such as making fresh memory or correcting errors, at Landauer's price of kT ln 2 each. Reversible computing (Computing without forgetting) avoids the rest, which is why the paper leans on error correction. If almost nothing needs erasing, temperature matters little and the argument loses its engine.
The cold sky is the cheapest place to put entropy. The paper takes the coldest natural bath as the best sink, and in the far future that is the afterglow. (It notes that a giant black hole's horizon is colder still for a long while; The black hole is not your freezer has why that door is narrow.) This is the link the 2019 comment attacks.
The fuel keeps. The stock must survive the wait. The paper tallies the leaks: stars burn a tiny fraction of their mass, some matter falls into black holes or blows out of galaxies, and the expansion of space cuts each cluster of galaxies off from the rest within about a hundred billion years. Its answer is that the multiplier dwarfs the losses: spent late, the resources of one supercluster are worth far more than the whole reachable universe burned early. Stopping the bigger leaks would take engineering on the scale of galaxies, which would be visible, and that is how the paper proposes to test the idea.
The civilization holds together and holds its ground. The strategy needs a goal that holds for hundreds of billions of years, no faction that wakes early and spends, and a domain safe from newcomers. The paper's answer is enforcement: coordination within each civilization and over younger ones in its sphere of influence, and defence against invaders. It rates the coordination assumption hard to judge and notes that one unusual civilization anywhere would break the explanation.
More thinking is worth proportionally more. The paper assumes value grows with resources, possibly faster. If a thousandfold more thinking is only a few times more valuable, nobody bets on patience at these odds.

Counting the bits, and the deadline

Take a stock of energy E to spend on erasing, and sink the heat at temperature T. The number of erasures is

$N_{\text{price}}(T) = \frac{E}{kT\ln 2}$

so the gain from waiting from $T_0$ to $T$ is $T_0/T$ ; with the values on Thinking in a cooling universe the floor gives 1.2 × 10³⁰. But a radiator of area $A$ at temperature $T$ emits at most $\sigma A T^4$ , and every erasure sends out $kT\ln 2$ , so in a time $t_d$ it can carry away at most

$N_{\text{speed}}(T) = \frac{\sigma A T^{4}\, t_d}{kT\ln 2} = \frac{\sigma A T^{3}\, t_d}{k\ln 2}$

erasures. The most the civilization can do by the deadline is the smaller of the two, $N = \min(N_{\text{price}}, N_{\text{speed}})$ . The first falls with $T$ and the second rises with it, so the best $T$ is where they cross:

$\frac{E}{kT\ln 2} = \frac{\sigma A T^{3} t_d}{k\ln 2} \quad\Rightarrow\quad T^{*} = \left(\frac{E}{\sigma A\, t_d}\right)^{1/4}$

By energy conservation, $T^*$ is the temperature at which the radiator, running for the entire available time, sheds exactly the energy stock $E$ . Colder than that, it cannot finish by the deadline; warmer, the higher erasure cost reduces the total. Substituting $T^*$ into $N_{\text{price}}$ gives total erasures proportional to $t_d^{1/4}$ . Dyson encountered the same cooling limit (Thinking in a cooling universe). Sandberg and colleagues likewise conclude that a civilization with a time limit should spend at a steady rate across it, after waiting for the sky to reach its working temperature. They treat the wait as short compared with the available computing time.

A worked case, this page's own sizing: let $E$ be the rest-mass energy of one Sun, 1.8 × 10⁴⁷ J, and the deadline 1 × 10¹⁴ years, about when the last stars form. To shed it at the temperature of the 2540 sky takes a radiator of area 1.8 × 10³¹ m², a sphere 8,022 AU in radius. At the sky temperature of 100 billion years on it takes 2.3 × 10⁴¹ m², a sphere 14,289 light years in radius, the scale of a galaxy, to spend one star's worth. The paper's radiator of 50 megaparsecs, run at one watt, would sit at 2.8 × 10⁻¹¹ K, the figure the authors give. The best wake-up date is a trade between cold and big, not a race to the floor.

Where the entropy goes: the 2019 comment

The comment leaves the arithmetic above alone and goes after link 3. Landauer's bound is really about entropy: erasing a bit means moving $k\ln 2$ of entropy out of the memory. Into a thermal bath at $T$ that costs $kT\ln 2$ of energy. But the universe is full of bounded systems that hold less entropy than they could for their energy: two bodies at different temperatures, a charged battery, a star and the cold space round it. A reversible engine running between the parts of such a system can pump the memory's entropy into the colder part, and the number of bits it can erase is the system's spare capacity (its negentropy, $S_{\max} - S$ ) divided by $k\ln 2$ . The temperature of the sky never enters, so there is nothing to wait for.

Bennett, Hanson and Riedel make this concrete with a toy model, since the original gives none, and Sandberg confirmed their summary of his argument. They find:

Waiting pays only after a civilization controls all the matter it can reach, well enough to stop every irreversible process in it, and has used up that matter's spare entropy capacity. They identify this regime with heat death.
In that late regime they agree with the original: with only a burnt-out reservoir and the cooling bath left, the patient strategy beats the greedy one, and its gain grows as one over the final temperature of the bath.
Even then, a civilization can wall off a patch of the afterglow in an insulated box and use it as a fresh reservoir. Their model therefore gives a civilization reason to take control of more matter and radiation, including inert matter.
Two smaller points: cooling need not be dissipative, as the original said it was, and a real computer pays a friction cost for working fast, which sets a best speed of its own.

Their model, like the original's, treats the afterglow as an infinite bath. A thinning sky that exchanges heat ever more slowly could change both conclusions.

Is this settled? What do the two sides say?The 2017 hypothesis, the 2019 rebuttal and the open question

The case for sleeping

Sandberg, Armstrong and Ćirković start from Landauer's price, a sky that cools toward a floor, and civilizations that mature long before ours. A civilization that wants the most computation, they argue, should expand early to gather resources and then stay inactive until the far future, when each joule buys about 1.2 × 10³⁰ times more. A quiet sky is then what we should expect: the expansion is brief, and the sleepers are compact and cold.

Their strongest point is the size of that factor. It follows from nothing but kT ln 2 and the cooling, and it is big enough to swamp the costs of waiting: they tally stellar burning, black holes, galactic winds, collisions and the expansion of space, and find that one supercluster spent late beats the whole reachable universe spent early. Their second strength is that the idea can be tested. A sleeper that values every joule should stop the losses it can, so the paper predicts suppressed processes that throw matter out of galaxies, or bound structures more massive than standard cosmology allows. The absence of visible galactic engineering already limits one kind of sleeper: those that would value the mass-energy of the dark matter halos, since saving it takes maneuvers bright enough to see.

The case against

Bennett, Hanson and Riedel say the premise is wrong. The original assumes, without saying so, that the entropy of erasure can only go into the afterglow. In fact the universe of stars and galaxies holds vast systems out of equilibrium that can take it, one bit of negentropy per bit erased, at any time and at the same price. So there is no reason to wait until a civilization has taken over and used up everything in reach, and a cooling sky is a reason to grab more, not to sleep.

Their argument makes the entropy destination explicit: a civilization can erase information using reservoirs other than the sky. Their model also recovers the original paper's gain from waiting after those reservoirs are exhausted.

Where the sides actually differ

The two papers agree on the thermodynamics and differ on the inventory. Four questions split them:

Capacity. How much spare entropy capacity do stars, gas, dust and black holes hold, against what a civilization wants to erase? If it is small, the sky wins in the end and the original argument returns, delayed.
Rate. How fast can a real machine move entropy into those reservoirs, or into a thinning sky? The comment flags this and leaves it open; the T³ that limits radiators may limit both.
Time. Is the phase of grabbing and using everything short and quiet enough to have been missed? The original says expansion is brief; the comment's civilization stays busy until every reservoir in reach is spent.
Value. Does a civilization want the largest possible total? One with diminishing returns acts early in both models.

What it does not explain

Aestivation is one answer among many to the question of where everyone is, and it needs the strategy to hold everywhere we look, which the paper answers with enforcement inside each sleeper's domain. A very different silence comes from Inward, not outward: a civilization that grows inward need not leave heat or light behind. A mind that is software (Copy, merge, choose your clock) can be paused at no cost to itself, which is why sleeping is easier to imagine for one than for a body.

The question remains open. The 2019 comment challenges the 2017 hypothesis's assumptions about entropy disposal. A further question raised here is whether the universe's usable spare entropy capacity is sufficient for a civilization's computing goals; neither paper makes that specific reply. Through the 2020s, observations had not distinguished the two proposals. frontier