The Cost of Forgetting

Information is inevitably tied to a physical representation and therefore to restrictions and possibilities related to the laws of physics and the parts available in the universe.

Information has no economic life outside a physical representation. That proposition is less dramatic than the claim that thermodynamics prices intelligence, and it is the one the physics supports.

Landauer's 1961 result concerns a specific operation: logically irreversible erasure.¹ Resetting one bit under the conditions of the model dissipates at least $kT \ln 2$ into the environment. At room temperature the quantity is about $2.87 \times 10^{-21}$ joules. The number matters because it marks a boundary between information treated as an abstraction and information embodied in matter. It does not assign a price to a token, a model, or a decision.

The qualification is not a retreat from physics. It is physics. Charles Bennett showed that a logically reversible computation can in principle avoid the dissipation associated with erasure, though real designs face costs in time, control, storage, noise, and implementation.² Landauer therefore gives no fixed energy charge for computation as such. It says that forgetting has a physical account.

Contemporary machines live far from the austere world of the bound. Switching transistors, moving bits through a memory hierarchy, synchronizing devices, regulating voltage, and removing heat all consume energy. Dennard scaling once allowed smaller transistors to deliver powerful efficiency gains, but that regime weakened as device and architectural constraints changed.³ None of those engineering costs can be inferred by multiplying a workload by $kT \ln 2$. Different operations discard different amounts of information, and system overheads dominate the remote minimum.

Seth Lloyd's calculation of ultimate physical computation makes the distance plain.⁴ Under idealized assumptions, matter can support rates enormously beyond present machines. That is not a forecast of cheap computers. It is evidence that the constraints governing this century are likely to arrive from fabrication, interconnect, memory, cooling, power delivery, capital, and institutional time before they arrive from the ultimate limit of matter.

Georgescu-Roegen's larger insight remains: production is not a circular flow detached from degradation.⁵ Computation draws on concentrated resources and returns heat; hardware wears, grids congest, and facilities take years to build. The economic conclusion comes from those operating realities, not from pretending that Landauer's constant is an invoice.

This changes the question. The issue is no longer when cleverness ends and joules take over, as though algorithms and energy were rival fuels. Better algorithms alter the amount and kind of hardware required. More hardware can compensate for weaker algorithms. Memory locality can matter more than arithmetic. At a given place and time, reliable power may still be the scarce complement that decides whether a project can run.

Where it is scarce, access to power delivered to suitable machines confers advantage. Elsewhere the bottleneck may be chips, networks, cooling water, financing, data, or permission. The physical account does not name one constraint for all computation. It prevents any account of computational abundance from forgetting that every apparent cloud terminates in a plant.