Faced with a rising curve, the mind extends the line by itself. This is useful: without that faculty we could anticipate nothing. But the spontaneous gesture becomes misleading as soon as it is applied to distant horizons, because it implicitly assumes nothing will change. This notion explains what trend extrapolation is, why it errs, and how to read a projection without mistaking it for a forecast.
1 The definition
Extending an observed movement.
The definition
The past stretched out, not the future predicted
Extrapolating a trend means extending into the future a movement observed in the past, assuming the observed pace holds. It underpins most long-term projections: public spending, demography, energy consumption, market shares. The operation is legitimate and often the only one available: to speak of tomorrow, we have only yesterday's data. But its nature must be clear: an extrapolation does not predict the future, it describes what the future would be if the forces at work kept acting exactly as before. It is an assumption put into numbers.
2 The horizon effect
A small gap in pace, a vast gap on arrival.
The mechanics
The error does not add up, it compounds
An extrapolation can be nearly right in the short run and badly wrong in the long run, because the error does not add up: it compounds. Suppose a quantity is projected to grow 5% a year when it will in fact grow 3.5%. The gap looks negligible in year one. After twenty years the first path has multiplied by 2.65 and the second by 1.99: the projection exceeds reality by more than 30%. On magnitudes counted in trillions, this apparently minor difference in pace produces staggering divergences. The further the horizon, the less the result says about the world, and the more it says about the starting assumption.
The key idea
In a long-term projection, the growth assumption matters more than the starting point. Reading the final figure without reading the rate used is reading the conclusion without the argument.
3 The inflections
What the straight line never sees coming.
The blind spots
Saturation, adaptation, reversion to the mean
Extrapolation is blind to everything that bends a curve. Saturation first: a market ends up equipped, a population ends up covered, and growth slows of its own accord. Adaptation next: when a cost becomes unbearable, behaviour changes, substitutes appear, rules are altered, and the alarming trend triggers its own correction. Reversion to the mean last: an exceptional period, of sharp rise or sharp fall, tends to be followed by a more ordinary pace. A straight-line projection ignores all three mechanisms; that is precisely where it most often goes wrong.
4 Evaluating a projection
The question we forget to ask.
The discipline
Compare yesterday's forecast with today's outturn
A projection is worth something only if one goes back to check what it announced. It is the comparison between the past forecast and what actually happened that allows the method to be judged, and nothing else. Yet that check is almost never made in public debate: the alarming figure circulates, its refutation does not, and the forecast turns into a belief. Three reflexes suffice, though. Ask what growth rate is assumed. Ask when the projection was made and whether it has been revised. And ask whether the previous version came true. A forecast that is never evaluated is not information, it is a habit.
5 Takeaways
Worth remembering.
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Trend extrapolation: extending a past movement assuming its pace holds; it describes the past stretched out, it does not predict.
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The horizon effect: the error compounds; a tiny gap in pace becomes a considerable gap on arrival over twenty years.
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The blind spots: saturation, behavioural adaptation and reversion to the mean bend curves; the straight line does not see them.
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The right question: not "what does this figure predict?" but "what did the previous version predict, and did it come true?"
This notion illuminates an analysis
First published: 16 July 2026