When the World Curves

A note on linearity bias — or what I like to call false linearity.

Christian Keil (@pronounced_kyle) tweet: My 3-month-old son is now TWICE as big as when he was born. He's on track to weigh 7.5 trillion pounds by age 10. Two side-by-side photos: a dad holding his newborn, then holding the visibly bigger baby three months later.
The original tweet — @pronounced_kyle, Mar 16, 2024.

That joke has always been funny to me. Every time I see that tweet by @pronounced_kyle, I end up thinking about the same thing: how often we assume the world works in straight lines when it really doesn’t.

Take a baby’s early weight gain and extend it forever, and the result becomes absurd very quickly. The arithmetic can be perfectly fine. The model is what breaks. That, in a simple way, is what false linearity is.

Child weight: reality vs. false linearity

Typical child weight (WHO growth pattern) If weight doubled every 3 months
0204060801001200246810Age (years)Weight (kg)… ~3.7 trillion kgby age 10

The dotted line runs off the top of the chart before the second birthday. I just cut it and wrote the number. Real growth (green) barely looks like it is moving next to it.

Why the shortcut feels natural

Linear thinking is not bad. In many everyday situations it is useful, cheap, and intuitive. If 10 km takes an hour, 20 km takes two. If 1 kg of plov feeds 4 people, 2 kg feeds 8. The problem starts when we carry that same shortcut into systems that bend, flatten, accelerate, or hit limits.

The mistake is not using a line. The mistake is forgetting that the line is only a simplification.

Hero visual drawn from WHO child growth-chart medians; the doubling line is an illustrative extrapolation.

Where the line bends

Once you notice it, you start seeing false linearity everywhere. A lot of important relationships in life are not straight lines. They flatten, peak, bend, or change direction entirely.

1. Money and happiness

Money matters — especially when you do not have enough of it. But the jump from too little to enough changes life much more than the jump from comfortable to richer.

Based on income and well-being research (Kahneman & Deaton).

2.02.53.03.54.04.55.05.56.00255075100125150175200Annual income (USD, thousands)Reported well-beingroughly where gainsstart to flatten

2. Study hours and exam performance

The first extra hours of study often help a lot. Later hours may add less, and at some point fatigue starts eating into performance.

An inverted-U: more is better, until it isn’t.

657075808590024681012Study hours per dayExpected exam performanceuseful range

3. Work hours and useful output

Longer hours are not the same as better work. Past a certain point, fatigue, mistakes, and diminishing returns start showing up.

Hours present is not the same as work produced.

50556065707580859002468101214Work hours per dayUseful outputpeak zone

4. Savings and compound interest

Here the line fails the other way: reality curves up faster than we expect. Interest earns interest, so the balance bends away from the steady climb we imagine.

Wonderful in a savings account, brutal on a credit card.

04080120160010203040YearsBalance (USD, thousands)interest earns interestwhat we picture

5. Technology adoption

New things often look like a failure early on, then spread all at once, then level off as the market fills. Slow, then sudden, then saturated — an S, not a line.

Judging the slow start as the whole story is the trap.

0204060801000246810Time (years)Adoption (%)slow, then sudden,then saturatedsteady guess

A few other places this shows up

  • exercise and recovery
  • product features and usability
  • advertising spend and new customers
  • medication dose and effect

So it is worth holding three ideas apart. Linear thinking is a tool — a simplification, and often a good one. Linearity bias is our preference for that tool: the reflex to reach for the line even when it does not fit. And false linearity is the last, quietest step — mistaking the line for the world itself, and then being genuinely surprised when the world curves.

Sources. Child weight — WHO Child Growth Standards. Income and well-being — Killingsworth, Kahneman & Mellers, PNAS 2023. Study hours — IJETT 2024. Charts are illustrative, drawn to reflect the shape of these findings.