Definition
A doubling line is any quantity that doubles per fixed unit of time — every year, every decade, every transistor generation. On a linear chart it looks like an explosion late in the series; on a log chart it is a straight line whose slope encodes the doubling time.
Computing power per dollar, early-pandemic infection counts, compound interest, viral content reach, and historical human population over millennia have all behaved as doubling lines for stretches at a time.
Why it matters
How it works
The 'rule of 70' converts growth rate into doubling time: divide 70 by the percent growth rate to get the years per doubling. A quantity growing 7% per year doubles every 10 years; one growing 1% per year doubles every 70. This gives you a fast sense of whether an apparently small percentage is harmless or transformative on a decadal horizon.
Plotting on a log y-axis turns multiplicative dynamics into additive ones — a constant doubling rate becomes a straight line. The visual is more honest because human intuition reads linear distance as additive. On a log chart, departures from doubling become obvious as kinks; on a linear chart they hide inside the explosion.
The corrective Rosling stresses is to pair every doubling story with an upper bound. Population doubled many times historically but is approaching a ceiling. Transistors doubled for decades but physics caps the next round. The question is always: when does this bend?