Where the joule goes
The energy-first turn rests on one measured fact: the arithmetic is not the bill. Moving the operands to the arithmetic is. This is that fact made operable: put the numbers somewhere, decide how hard you work them, and watch the split.
If arithmetic is nearly free, why is AI expensive?
Because a multiply-accumulate cannot happen until its operands arrive, and the trip costs more than the multiply. Choose where the numbers live and how many multiplies each fetched number feeds before it is evicted. That second number is the only lever software has.
Called arithmetic intensity. 1 means every multiply pays for its own fetch.
The ladder, from the physics floor to a frontier query
Every rung is an order of magnitude claim, not a benchmark, and the corpus states them as ranges. The faint bar behind each value is the stated range; the solid bar is its geometric centre. The axis is logarithmic: each gridline is a factor of a thousand, because a linear axis for twenty-six decades is a single pixel and a blank page.
What follows from it
Read the ladder from the bottom and the diagnosis writes itself. Switching a transistor sits two to three orders above the Landauer wall, so devices are not the problem. Arithmetic sits eight orders above it, and the fetch that feeds the arithmetic sits nine to ten: a hundred to a thousand times the operation it exists to serve. Biology runs general intelligence six to seven orders above the wall, which is roughly where an off-chip fetch alone already puts us.
This is why approaches that look nothing alike from outside: processing-in-memory, compute-in-memory crossbars, neuromorphic event-driven silicon, photonics, thermodynamic sampling: are all aimed at the same target. Every one of them shortens the distance between where a number lives and where it is used. The lever above is the software half of that same move: raise reuse and you amortise a fetch you could not avoid.
Where these numbers come from
| Rung | Stated in the review |
|---|---|
| Erase one bit (physics floor, 300 K) | ~3 zJ: 1×, the wall itself |
| Switch one modern transistor | ~1 aJ (order): ~10²–10³ |
| One 8-bit multiply-accumulate | ~0.1–1 pJ: ~10⁸ |
| Fetch operands from on-chip SRAM | ~1–10 pJ: ~10⁹ |
| Fetch from off-chip DRAM | ~100+ pJ per access: ~10¹⁰ |
| One frontier-model query (serving median) | 0.31 Wh ≈ 1,100 J: ~10²³ |
| One biological synaptic event | ~10–100 fJ (order): ~10⁶–10⁷ |
Every figure on this page is read from the energy ladder in The Energy-First Turn (TR-2026-25) and nothing is added to it. The register rung is the one exception and is marked as such below: the review's table starts at on-chip SRAM, so the register figure here is stated as "below the SRAM rung" rather than given a value the review does not publish. Constraint vocabulary: the eight.