A body in vacuum can think only as much as it can shed heat.

That sounds like a side condition. It is the main condition. And it can be written down:

Ṅ_max = εσAT³ / (k_B ln 2)

On the left is the number of operations a body can sustain per second. On the right is what that number depends on. ε is the emissivity of its surface, a value between zero and one. σ is the radiation constant. A is the area through which it releases heat. T is that area's temperature. k_B is the Boltzmann constant, ln 2 the natural logarithm of two.

I did not discover this equation. I laid two known ones on top of each other. The first describes how much heat a surface radiates. The second describes the minimum cost of a single computational operation. Divide the first by the second, and what remains is a number counting how much thinking fits through a surface each second.

Energy supply does not appear anywhere in it. That is not an oversight. The rest of this brief takes the equation apart, symbol by symbol.

What a Thought Costs

In 1961 Rolf Landauer showed that computation carries a physical price. Not the computing itself, but the forgetting. Erasing a bit requires releasing heat. The minimum is k_B times temperature times ln 2. At room temperature that comes to roughly three sextillionths of a joule per erased bit.

The figure is tiny. It is still the reason a laptop grows warm. Not the only reason, but the only one that cannot be engineered away. Real electronics today consume around a billion times more than this floor. That gap is the room in which engineering can still achieve something. The floor itself is fixed.

Landauer's point, then: thinking is a process that leaves heat behind. Not as a side effect of poor design. As a condition.

That accounts for the lower half of the equation. It sits there because it prices a single thought.

Why Energy Alone Does Nothing

The upper half is the more surprising one.

A temperature appears inside the Landauer limit. The price of a thought depends on how warm the surroundings are into which it releases its heat. In colder surroundings, the same thought costs less.

This is where the common picture of energy as the ultimate resource falls apart. A star supplies no work. A gradient supplies work. A civilization takes in light at six thousand kelvin. It releases it again at three hundred. That difference is what it lives on. Without the cold side, the largest energy source in the universe is a furnace from which nothing can be drawn.

In the cosmos, energy is abundant. What is scarce is cold.

I call what a civilization has available of it a cold budget. It is not the quantity of watts it collects. It is the ability to release heat into something colder than itself.

The Surface That Releases

On Earth this budget stays invisible. Air absorbs heat. Water absorbs heat. A data centre pushes its waste heat into the atmosphere and pays for it in electricity and cooling water. The amount shows up on a bill. The physical limit stays far away.

In vacuum there is no air. There is no convection. Heat leaves a body only as radiation, through its surface.

Every orbital data centre therefore becomes an object with two surfaces. One collects sunlight. The other releases heat. The first is what gets advertised. The second determines how large the installation can grow.

The operators know this. Starcloud describes all of its heat loss as running through infrared radiation, with a radiator held at roughly fifty degrees Celsius. Google's Suncatcher paper lists thermal management of power-dense processors in vacuum explicitly as a critical task. Two prototype satellites are due to fly in early 2027.

My point is not that anyone is concealing something. My point is which category this quantity gets filed under.

The Third Power

Insert the radiation equation into the Landauer limit and something notable cancels. Radiated power grows with the fourth power of temperature. The price of a thought grows with the first. The third remains.

A rule follows, and it carries its condition with it. At fixed radiating area, radiating hotter means computing more. At fixed energy supply the reverse holds, because the price of every thought falls with temperature. What follows in this section takes the first case, because a built installation has a fixed area. One square metre at three hundred kelvin carries, in theory, about 1.6 times ten to the twenty-third operations per second. At four hundred kelvin it is three times that. 

But temperature is not free to choose. The semiconductors set the ceiling. Staying cool enough for the chips to survive is paid for in area.

The figures are known, because one object has been measuring them for over twenty years. The external thermal system of the International Space Station rejects up to seventy kilowatts. It needs roughly four hundred and twenty-two square metres of radiator to do so. That is about one hundred and sixty-six watts per square metre in sustained operation. In theory, room temperature would allow around four hundred and fifty. The gap between those two numbers is what operation costs.

Now the extrapolation. A data centre drawing one gigawatt produces, at an optimistic forty per cent efficiency, some six hundred megawatts of waste heat. Scaling the station's figures linearly, the radiators alone weigh around two thousand two hundred and fifty tonnes. At two hundred dollars per kilogram of launch mass, that is roughly four hundred and fifty million dollars spent purely on getting heat back out.

The number is an estimate, not a construction drawing. Better radiators are possible, higher operating temperatures too. The order of magnitude shifts with them. The structure of the calculation does not.

What Cannot Be Negotiated

Look at the equation again and the room for manoeuvre becomes visible.

σ is a constant of nature. k_B is a constant of nature. ln 2 is mathematics. Three of the six quantities are fixed before anyone builds anything.

ε can be improved, but it is capped at one. Good radiator coatings already sit close to it. Little is to be gained there.

That leaves A and T. Area and temperature. Everything that can be decided in this question at all gets decided at those two points. Both cost mass, and mass costs launch capacity.

Here is where I disagree. In the operators' publications, heat rejection is filed as an optimization task, alongside reliability, radiation tolerance and downlink capacity. Optimization tasks yield to engineering. This one does not. The area follows from the fourth power of a temperature that the components dictate. What appears to be a detail of system design in fact determines how large the whole thing can ever become.

An analysis from July 2026 puts it this way: once compute leaves the ground, the scarce resource is no longer colder air but the radiating itself. That is precisely what the cold budget means.

The Same Arithmetic, One Level Up

There is a second place where a surface governs information, and it comes from an entirely different corner of physics.

In 1972 Jacob Bekenstein proposed that black holes possess entropy. In 1974 Stephen Hawking showed that they have a temperature and radiate. Together these yield a formula binding a black hole's entropy to the area of its horizon. Not to its volume. To its area.

That is unusual. Almost everything else in physics scales with volume. Here the maximum information content of a region stands in relation to its surface.

So two entirely independent arguments say the same thing. What a region can hold in information depends on its surface. What it can accomplish in thinking does too.

The consequence for very large engineered structures is rarely spoken aloud. A Dyson sphere is not an energy collector. It is a radiator. Its size does not follow from how much light it is meant to capture. It follows from how much heat it must shed.

This is exactly why astronomy searches for such structures in the infrared. For decades we have hunted alien civilizations by their waste heat. In our own case we treat the same quantity as a line item in system design.

The Budget for All Time

That leaves the question of how much cold there is in total.

In 1979 Freeman Dyson argued that a civilization could have infinitely many thoughts on finite energy, provided it keeps lowering its operating temperature and thinking correspondingly slower. Lawrence Krauss and Glenn Starkman contradicted this in 2000. Their result: the total recoverable information stays finite, and with it the integrated conscious lifetime of any civilization, however long that may be. The reason is erasure again. To observe is to forget. To forget is to release heat.

Their argument carries a precondition. It holds for a universe whose expansion is accelerated by a constant dark energy. In that case a horizon exists, beyond which nothing can be sent and from which nothing can be received. That horizon sets a floor temperature, and below it nothing goes.

A paper from 2003 showed the calculation comes out differently if dark energy is not constant. In models with evolving dark energy the horizon can fail to appear. Then the budget is not finite.

Which of the two holds is being measured right now. Data from the Dark Energy Spectroscopic Instrument point toward a dark energy that looks like a constant today but weakens over time. How strong that indication is depends on which supernova catalogues are combined with it. George Efstathiou showed that the significance ranges from two and a half to nearly four standard deviations depending on the choice. A 2026 paper in Physical Review D concludes that the indication vanishes and that the underlying datasets contradict one another. A recalibration of the Dark Energy Survey in the same year finds it again.

The question is open. It will not be settled at a desk.

On 30 August 2026 the Nancy Grace Roman Space Telescope launched from Kennedy Space Center, nine months ahead of schedule. It is on its way to Lagrange point L2, some one and a half million kilometres from Earth. The transit takes about three months. After that it will measure roughly twenty-one thousand supernovae from a single instrument under uniform calibration. That is exactly the objection on which the present debate turns.

Roman is an infrared instrument. It works because it is kept cold, and it sits at L2 because sun and Earth can be moved out of its field of view there and its own heat released outward. An instrument whose operation depends on cold is measuring whether cold is the scarce good in the long run.

What a space can know is limited by its surface. What it can think, equally. Which quantity in your work have you treated as unlimited because its limit sits outside it?

Homepage: https://planet-futures.org