Rate Against Level
Where the current size of something is reassuring and its growth rate is not, so the two framings support opposite conclusions from the same data.
Reviewed July 16, 2026Stable
When not to use it
- Where growth is linear or bounded, in which case current levels are informative and the divergence argument does not apply.
- As automatic alarm. A fast-growing quantity from a tiny base can remain negligible for a long time, and the horizon matters.
- Where the rate is measured by an instrument that changed during the window, which makes the rate the less reliable figure of the two.
Reach for something else instead
- Report both — a level and a doubling time together, which costs one clause and removes the ambiguity entirely.
- Fixed-instrument trends — recompute historical levels under today's detection method so the trend reflects the world rather than the effort spent looking.
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Read more on the blog
- Every chatbot query on earth is 2% of AI's powerTerritory 8 opens on the numbers behind AI's physical footprint, and on the arithmetic in the IEA's own report that almost nobody quotes.
- Inference prices fell 9x a year. Also 900x.The most cited number in AI economics is a single rate. The study behind it reports a range spanning two orders of magnitude, and a caveat that undercuts its own fastest figures.
Further reading
- International Energy Agency (2025), Energy and AI — per-unit efficiency improving while sector consumption rises.
- Epoch AI (2025), LLM inference prices have fallen rapidly but unequally across tasks — why a rate depends on which milestone is chosen.
Primary sources, listed so you can check the claims on this page rather than take them on trust.
Where people go wrong
- Quoting a share to reassure and a growth rate to alarm without stating which question is being answered.
- Treating a per-unit improvement as evidence about a total.
- Reading a detection trend as a production trend when screening effort rose over the same period.
At a glance
FieldFoundations
Distinctionstock against its derivative
Two questionsstock or flow, and what is each doubling time
Three shapesreassuring level with alarming rate, improving unit with rising total, falling price with growing spend
Main trapa detection curve read as a production curve
DifficultyBeginner → Intermediate
Where this sits
A starting point. Nothing needs to come before it.
0Levelstarting point
0Needs firstnothing
0Opens upnothing further
1Areastays here
Computed from the prerequisite graph, not assigned. How this works