The Exponential Replot Test
Replot an exponential from earlier dates to deflate present-day exceptionalism
- Difficulty
- Easy
- Time to result
- ~days to results
- Steps
- 5
- Confidence
- 98%
Tyson responds to the idea that recent technological progress is uniquely sudden by describing how exponentials look on a linear graph. The curve appears nearly flat before turning sharply upward, but truncating it decades earlier and replotted against the data then available creates the same visual story. People at earlier points could therefore also say that the most important advances had just arrived. The reusable test is to redraw a claimed exponential from multiple historical vantage points and compare the narratives each chart invites. If every era looks like the special takeoff era, the current steepness is partly a property of exponential growth rather than proof of an unprecedented break. Genuine discontinuities can still exist, but they require evidence beyond the familiar hockey-stick shape.
Origin
Extracted from The Diary of a CEO
Core principles
- 01A linear chart makes an exponential look suddenly vertical
- 02Every point on an exponential can feel historically exceptional
- 03Recent progress must be judged against the curve's structure
- 04A dramatic slope does not establish a unique cause or outcome
How to run it
- 1
Confirm the curve
Plot the measure over time and check whether an exponential description is reasonable. Do not infer the process from appearance alone.
Pro tip Compare linear and logarithmic views before naming the growth pattern.
Watch out A short rising series can mimic an exponential.
- 2
Select earlier cutoffs
Choose several historical dates and remove everything observers at those dates could not have known.
Pro tip Use cutoffs far enough apart to cover multiple stages of growth.
- 3
Replot each period
Scale each truncated series as it might have been viewed at the time. Note whether each produces its own apparent takeoff.
Watch out Do not preserve today's axis merely to make earlier change look small.
- 4
Compare the stories
Write the claim an observer at each cutoff might have made about living through exceptional progress. Identify the repeated pattern.
Pro tip Use contemporaneous milestones rather than mocking earlier technology with present-day standards.
- 5
Test for a real break
Look for evidence that the mechanism, growth rate, or constraints changed, rather than relying on the steep visual slope. Update the forecast only to the degree that this evidence supports it.
Watch out The test challenges exceptionalism; it does not prove that all periods are equivalent.
In the wild
Tyson notes that people living through automobiles, transcontinental railroads, and steamships did not regard themselves as backward. From their point on a continuing curve, recent progress also appeared extraordinary.
→ The historical vantage point weakens the inference that a steep recent slope alone makes the present uniquely special.
In an illustrative startup analysis, a founder redraws an adoption curve at three earlier quarter-end dates. Each chart appears to show a sudden breakout, so the team looks for a measured change in retention and acquisition efficiency before declaring a new growth regime.
→ The forecast relies on changed business mechanics rather than the shape of one linear chart.
Common mistakes
Calling every hockey stick a discontinuity
A sharply rising linear plot is a normal visual feature of exponential growth and does not establish a new mechanism.
Using today's axis for every era
Earlier observers evaluated progress against the scale and information available to them, which is the perspective the replot is meant to recover.
Is it for you?
Best for
It is best for evaluating claims about sudden technological, demographic, adoption, or capacity breakthroughs.
Not ideal for
It is not suitable when the data do not follow an exponential pattern or a real discontinuity has changed the process.
From the transcript
“everybody in an exponential thinks they're living in special times”
“if you truncated it somewhere here, let's say, so go back 20 years”
From the episode
Neil deGrasse Tyson On Aliens, Simulation Theory, and What Happens Inside A Black Hole