The Second Derivative, Part V: Upstream

Climate · Energy · Growth · Part V

Upstream

Four essays measured what the climate is doing. All four stopped at the word “emissions” without once asking what produces them.

October 2026 · Part V · The Second Derivative series

This is Part V. Part I argued the climate is accelerating, Part II charted it, Part III looked at the thresholds ahead, and Part IV explained where the numbers come from. Every one of them treated emissions as the start of the causal chain. They are not: they are the output of an energy system, which is the output of an economy. This essay measures that upstream stretch with the same instruments.

What this essay does and does not do

The subject matter here attracts strong opinions, and the series has no standing to add one. So the rule is stricter than in the previous four:

• Measured — quantities from published statistical series: energy use, energy intensity, emissions, decoupling rates.
• Contested — claims about which competent researchers disagree, presented with the evidence on each side.
• Normative — claims about what should be done. These appear only as reported positions, attributed to the people who hold them. This essay makes none of its own, and does not adjudicate between those it reports.

That is a limitation, not a modesty. What follows can tell you the size and direction of things. It cannot tell you what to want.

I. Where the previous four essays stopped

The causal chain runs in one direction, and it is not controversial:

Figure 1 · The chain, and the part the series has covered Each link is a measured quantity. Parts I to IV worked entirely to the right of the dashed line; this essay works to the left of it.

Why the line sits there. Everything to the right obeys conservation laws and can be checked against instruments, which is what made the earlier essays tractable. Everything to the left involves human behaviour, which is measurable but not law-governed — so the same statistics apply, and the same confidence does not.

II. The long arc of energy use

Start with the quantity itself, because it is the one most people have never seen plotted.

Global primary energy consumption was roughly 30 exajoules a year in 1900. By 2000 it was about 450. By 2023 it was around 620 — the figure Part II used, in passing, to make 23 zettajoules of ocean heat comprehensible.[1] That is roughly a twenty-fold increase in 125 years, against a population increase of about five-fold over the same period.

Figure 2 · World primary energy consumption Anchor values from the cited sources rather than a continuous reconstruction — the same convention Part II used for the energy imbalance.

Sources: historical series from the Encyclopédie de l’énergie reconstruction of world energy consumption 1800–2000;[1] the 2023 figure from the global primary energy total used in the ocean-heat literature.[2] Measured.

The composition changed as completely as the total. Biomass still supplied about 80% of world energy in 1870. Coal’s share went from roughly 6% in 1850 to 64% by 1900, peaking near 73% during the First World War, before oil and gas took over between 1950 and 1973.[1]

One observation about that sequence is worth recording because it is frequently assumed rather than checked: historically, new energy sources have mostly been added to the mix rather than substituted for the old ones. The world burns more coal today than it did when coal’s share peaked. Whether the current renewable expansion breaks that pattern is a live empirical question, not a settled one — and the answer will be visible in the data within a decade.

III. Is energy use accelerating?

Now apply the series’ own question to its own driver. Not “is energy use growing” — it is — but whether the growth rate is climbing.

The answer, on the recent record, is no. Global energy demand grew 2.2% in 2024, a notably fast year, and 1.3% in 2025, against an average of about 1.3–1.4% over 2013–2023.[2][3] There is year-to-year variation, but no acceleration in the aggregate. Twentieth-century growth rates were considerably higher.

Figure 3 · Growth rates: total energy, and electricity Annual growth in global energy demand, with electricity shown separately. Electricity is growing at roughly twice the rate of total energy.

Measured. Sources: IEA Global Energy Review and 2025 demand analysis.[2][3] This is a finding that cuts against a simple “everything is accelerating” reading, and the series’ own discipline requires reporting it as plainly as the findings that pointed the other way.

IV. The two ratios that decide the outcome

There is a standard identity, uncontroversial because it is arithmetic rather than theory, that decomposes emissions into four factors:

emissions = population × (GDP / person) × (energy / GDP) × (emissions / energy)

The first two factors have been rising. Whether total emissions rise or fall therefore depends on how fast the last two — the energy intensity of economic output and the carbon intensity of energy — are falling. Everything contested in this essay reduces to a question about those two ratios.

Energy intensity has been improving for decades, but the rate has slowed. It averaged about 2% a year over 2010–2019, dropped to roughly 1.3% a year since 2019, fell to 1.0% in 2024, and recovered to about 1.8% in 2025. At COP28 in 2023, nearly 200 governments agreed a target of doubling the rate to 4% a year by 2030.[4]

Figure 4 · Energy intensity improvement against the agreed target Annual improvement in global primary energy intensity — energy used per unit of economic output. The dashed line is the rate governments agreed at COP28 to reach by 2030.

Measured. Source: IEA Energy Efficiency 2025.[4] Regional spread is wide: 2025 improvement exceeded 3% in China and 4% in India, while falling below 1% in both the United States and the European Union.

V. Decoupling: what the data show

“Decoupling” means an economy growing while its emissions do not. Relative decoupling is emissions growing more slowly than output; absolute decoupling is emissions falling while output rises. Only the second one reduces anything.

Two findings need stating together, because each is routinely quoted without the other.

The first: absolute decoupling is real, and it is not merely offshoring. Between 2015 and 2023, economies accounting for 92% of global GDP decoupled emissions from growth in absolute or relative terms; countries representing 46.3% of global GDP and 36.1% of global emissions achieved absolute decoupling. The number of countries doing so rose from 32 before the Paris Agreement to 43 after it.[5] The obvious objection — that rich countries simply moved their factories abroad — has been tested by recalculating emissions on a consumption basis, which attributes imported goods to the importer. Twenty-three countries absolutely decoupled from consumption-based emissions as well, and fourteen from both measures.[6] Offshoring accounts for part of the decline in some countries; it does not account for all of it.

The second: the achieved rates are nowhere near the stated targets. Vogel and Hickel took the eleven high-income countries that absolutely decoupled over 2013–2019 and compared their achieved rates of consumption-based emission reduction against rates consistent with fair shares of the remaining budget for 1.5 °C. At the rates actually achieved, those countries would need more than 220 years to cut emissions by 95%.[7]

Figure 5 · Both facts at once Left: absolute decoupling is happening in more countries than before Paris. Right: for the high-income countries that achieved it, the pace against what the stated targets require.

Measured, both panels. Left: decoupling counts 2015–2023.[5] Right: Vogel and Hickel’s comparison of achieved consumption-based reduction rates against fair-share Paris-compliant rates, for the eleven high-income countries that absolutely decoupled over 2013–2019.[7] Neither panel is an argument; both are counts. Which one you find more striking is not something the data decides.

The most comprehensive assessment of the underlying literature reached the same two-sided conclusion. Haberl and colleagues screened more than 11,500 papers and analysed 835 empirical studies of the relationship between GDP, resource use and greenhouse gases. They found evidence of absolute decoupling to be “scarce and scattered,” and concluded that large, rapid absolute reductions cannot be achieved through observed decoupling rates alone.[8] That review also makes a recommendation, which belongs in Section VIII rather than here.

VI. The plateau that is not a decline

Now the finding that ties this essay back to the other four, and it is the most interesting number in the whole piece.

Global fossil CO&sub2; emissions hit a record 38.1 billion tonnes in 2025, up about 1.0% on 2024.[9] That is the headline. Underneath it is something the headline hides: total global CO&sub2; emissions grew at 0.3% a year over 2014–2025, against 1.9% a year over 2004–2013.[10]

Figure 6 · The driver’s second derivative is negative Annual growth rate of global CO&sub2; emissions by period. Emissions are still rising — but the rate at which they rise has fallen sharply.

Measured. Global Carbon Budget 2025.[9][10] China and India entered an emissions plateau on the back of renewable expansion, while the United States and the European Union saw rebounds. The 2025 rise was spread across all fossil fuels: coal +0.8%, oil +1%, gas +1.3%.

Why both things can be true at once

Parts I to IV documented a climate whose second derivative is positive. This essay documents a driver whose second derivative is negative. That looks like a contradiction and is not, for one reason: warming tracks the cumulative stock of CO&sub2;, not the annual flow.

Part IV described the near-linear relationship between cumulative emissions and warming that underlies every carbon budget.[11] Under that relationship, a plateau in annual emissions is a plateau in the rate at which the stock grows — so the stock keeps growing, at close to a record pace, and warming continues roughly in step. Emissions growth slowing to 0.3% a year means the tank is filling at a nearly constant rate rather than an accelerating one. It does not mean the tank is emptying, or level.

This is the single most important piece of arithmetic in this essay, and it is neither good news nor bad news. It is the reason a genuine and hard-won deceleration upstream is compatible with no deceleration whatsoever downstream.

VII. Efficiency and rebound: the case unfolding right now

Section IV showed that the outcome depends on intensity ratios falling. There is a long-standing observation, dating to Jevons on coal in 1865, that improvements in the efficiency of using a resource can be accompanied by increases in total consumption of it, because efficiency lowers cost and lower cost raises demand. The size of this rebound effect is contested across the literature.

An unusually clean instance is unfolding at the moment. The energy required per AI task is falling at a rate the IEA describes as unprecedented in energy history. Global data-centre electricity use nonetheless grew 17% in 2025, and consumption by AI-focused data centres grew 50% in a single year.[12]

Figure 7 · Falling per unit, rising in total Global data-centre electricity consumption, measured for 2025 and projected for 2030. The efficiency gain per task and the total consumption are moving in opposite directions.

Measured for 2025, projected for 2030. Sources: IEA.[12][13] What this is not: evidence that efficiency gains are always cancelled by demand growth. It is one well-documented case in which they were, in a sector expanding for reasons unrelated to its energy cost. Whether it generalises is contested.

VIII. The disagreement, reported

Here is the argument this essay will not settle. Both positions are held by competent researchers publishing in peer-reviewed venues, and I am setting them out rather than choosing between them.

	Position A	Position B
Held by	Researchers who conclude that decoupling can be scaled within a growing economy	Researchers who conclude that it cannot be scaled fast enough on its own
Evidence cited	43 countries in absolute decoupling post-Paris, up from 32; economies covering 92% of global GDP decoupling in some form; 23 countries decoupled on a consumption basis, so it is not just offshoring[5][14]	Achieved rates imply 220+ years to cut 95%; the 835-study review finds evidence for decoupling at the required scale “scarce and scattered”[7][8]
What follows, per its proponents	Accelerate the existing levers — deployment, efficiency, electrification, carbon pricing (normative — reported, not endorsed)	Complement decoupling with sufficiency strategies and enforced absolute reduction targets (normative — reported, not endorsed)

The important thing about that table is what the two columns share. Both sides agree on the measurements. Nobody serious disputes that absolute decoupling is occurring in dozens of countries, and nobody serious disputes that the observed rates fall far short of the rates implied by the targets governments have signed. Those are the same two facts in Figure 5, and they are both true.

The disagreement is about something else entirely: whether the observed rate can be raised by a large factor within the existing arrangement. That is a claim about the future. It is not currently decidable by measurement, and anyone presenting it as though it were — in either direction — has left the evidence behind. Part IV made the same point about climate sensitivity: where a question turns on what happens next rather than what has happened, the honest output is a range and a stated uncertainty.

On the word “need”

Sentences of the form “we need to fundamentally change how we live” are common in this literature and in writing about it. They are not measurements, and this essay does not make them. What can be said without leaving the data is narrower and, I think, more useful:

If the objective is the emissions pathway implied by 1.5 °C, then the observed rates of decoupling and intensity improvement are, by a wide margin, not on that pathway. Whether to hold that objective, and what to trade against it, are questions about values and priorities that no dataset answers. The conditional is measurable. The choice of objective is not.

IX. What would settle it

The series’ habit, applied to a question that is unusually well suited to it — because unlike tipping thresholds, these quantities are published annually and the disagreement is about a rate rather than a mechanism. Recorded now, checkable later:

• Sustained deep decoupling. A group of high-income countries reducing consumption-based emissions at more than 5% a year for a full decade, with output growing, would demonstrate that Paris-compliant rates are achievable within a growing economy. Nothing close to that has been observed.
• The efficiency target. Global energy intensity improvement reaching and holding 4% a year, the rate agreed at COP28. It ran at 1.8% in 2025, the best year since 2019.[4]
• Absolute global decline. Global fossil CO&sub2; falling for five consecutive years outside a recession or a pandemic. Every previous decline in the record has coincided with an economic contraction — including, as Part II noted, the fall in growth rate visible in the 1990s.
• Substitution rather than addition. Absolute global coal consumption falling year on year while renewable capacity grows, which would indicate the historical additive pattern in Section II has broken.
• The rebound question. Data-centre electricity growth decoupling from AI adoption — efficiency gains per task showing up in the sector total rather than being absorbed by expanded use.

X. The bottom line

Five essays, and the arithmetic they add up to is stranger than either of the stories usually told about it.

The climate system is accelerating: the energy imbalance is growing, ocean heat uptake has roughly tripled, sea-level rise has doubled, and land-ice loss has quadrupled. That was Parts I and II, and the measurements are not seriously disputed.

The human system driving it is decelerating: emissions growth has fallen from 1.9% a year to 0.3%, absolute decoupling has spread from 32 countries to 43, and the energy intensity of the world economy keeps improving. Those measurements are not seriously disputed either.

The foot is easing off the accelerator. The car is still speeding up.

Both are true simultaneously because emissions are a flow and warming tracks a stock. A tank filling at a constant rate is still filling. That single distinction explains why a person can report genuine progress and a person can report continuing acceleration and both can be citing the same year’s data correctly.

What the data cannot tell us is whether the deceleration continues to zero and past it, fast enough to matter, and by what means. On that, competent people who agree entirely about the numbers disagree entirely about the conclusion — which is a reliable sign that the remaining question is not an empirical one.

The series has now measured what the climate is doing, how fast, towards what, how we know, and what drives it. It stops here, at the boundary where measurement ends. What to do with the arithmetic was never something a chart could settle, and this series has not pretended otherwise.

References

1. Encyclopédie de l’énergie. “World energy consumption 1800–2000: results” and companion articles on sources and definitions. Source of the 1900 and 2000 anchors and the fuel-share history. encyclopedie-energie.org
2. International Energy Agency (2025). Global Energy Review 2025 — global trends and key findings. iea.org
3. International Energy Agency (2026). “Global energy demand growth was met by a diverse range of sources in 2025, led by solar and then gas.” Demand +1.3% in 2025 against +2.2% in 2024. iea.org
4. International Energy Agency (2025). Energy Efficiency 2025, and “Global progress on energy efficiency picks up in 2025.” Intensity improvement 1.8% in 2025, ~1.3% average since 2019, ~2% over 2010–2019; COP28 target of 4% by 2030. iea.org
5. Energy and Climate Intelligence Unit (2025). “10 Years Post-Paris: how emissions decoupling has progressed” and associated release. Counts of countries in absolute and relative decoupling, 2015–2023. eciu.net
6. Our World in Data. “Many countries have decoupled economic growth from CO&sub2; emissions, even if we take offshored production into account.” Consumption-based accounting. ourworldindata.org
7. Vogel, J. & Hickel, J. (2023). “Is green growth happening? An empirical analysis of achieved versus Paris-compliant CO&sub2;–GDP decoupling in high-income countries.” The Lancet Planetary Health 7, e759. thelancet.com
8. Haberl, H. et al. (2020). “A systematic review of the evidence on decoupling of GDP, resource use and GHG emissions, part II: synthesizing the insights.” Environmental Research Letters 15, 065003. 835 studies analysed from more than 11,500 screened. iopscience.iop.org
9. Global Carbon Project (2026). Global Carbon Budget 2025, Earth System Science Data 18, 3211. Fossil CO&sub2; at a record 38.1 GtCO&sub2; in 2025. essd.copernicus.org
10. Carbon Brief (2025). “Analysis: Fossil-fuel CO2 emissions to set new record in 2025, as land sink recovers.” Source of the 0.3%/yr (2014–25) against 1.9%/yr (2004–13) comparison. carbonbrief.org
11. IPCC (2021). Sixth Assessment Report, Working Group I. The near-linear relationship between cumulative CO&sub2; emissions and warming, on which carbon budgets rest. ipcc.ch
12. International Energy Agency (2026). “Data centre electricity use surged in 2025” and Energy and AI. 485 TWh in 2025 rising to roughly 950 TWh by 2030; +17% overall and +50% for AI-focused facilities in 2025. iea.org
13. Carbon Brief. “AI: Five charts that put data-centre energy use — and emissions — into context.” carbonbrief.org
14. Breakthrough Institute. “Absolute Decoupling of Economic Growth and Emissions in 32 Countries.” Cited as a representative statement of the position that decoupling is real and extensible. thebreakthrough.org

Published October 2026 · Part V of The Second Derivative, a series on climate acceleration · Read Part I, Part II, Part III and Part IV.

On method and tools

This article was researched and written collaboratively with Claude (Anthropic): human specification and critical review, machine research synthesis and drafting, iterative refinement through structured dialogue. The research covered IEA energy demand and efficiency reporting, the Global Carbon Budget, the decoupling literature on both sides of the current disagreement, and the IEA’s data-centre analysis.

Seven hand-built SVG figures. Figures 2 to 7 plot published values; Figure 1 is a diagram of a causal chain rather than data. Figure 2 marks anchor points rather than a reconstruction, and Figure 7 is measured for 2025 and projected for 2030, both flagged in place.

This essay was written to a stricter constraint than the previous four: it reports normative positions but advances none of its own, and says so where the boundary falls. The most common failure mode in writing about growth and energy is to let a preference arrive dressed as a finding. Section VIII sets out the disagreement without resolving it, because the evidence does not resolve it — and the parts that would resolve it lie in the future rather than in any dataset.

Authored by: Luis Matos Ferreira
Physicist & Developer