Straight Locally, Curved Globally
The principle that many complex systems appear linear or straight when viewed locally, but are actually curved or nonlinear when viewed globally. This explains why linear reasoning often seems plausible but leads to errors when extended beyond a limited scope.
THE IDEA
STRAIGHT LOCALLY, CURVED GLOBALLY
You might not have thought you needed a professional mathematician to tell you that not all curves are straight lines. But linear reasoning is everywhere. You’re doing it every time you say that if something is good to have, having more of it is even better. Political shouters rely on it: “You support military action against Iran? I guess you’d like to launch a ground invasion of every country that looks at us funny!” Or, on the other hand, “Engagement with Iran? You probably also think Adolf Hitler was just misunderstood.”
Why is this kind of reasoning so popular, when a moment’s thought reveals its wrongness? Why would anyone think, even for a second, that all curves are straight lines, when they’re obviously not?
One reason is that, in a sense, they are. That story starts with Archimedes.
When to use it
When evaluating long-term investments, consider that short-term growth trends may not hold as markets mature or conditions change.
In policy debates, avoid assuming that a moderate action leads to an extreme outcome without evidence of a direct causal chain.
In science, recognize that linear approximations are valid only within a limited range and can become inaccurate when extrapolated beyond that range.
In personal behavior, be cautious of 'more is better' thinking—for example, that working longer hours always leads to greater productivity.
FROM THEORY TO EVERYDAY LIFE
In practice
Political Slippery Slope
Assuming that supporting limited military action automatically implies supporting a full-scale invasion, as in the Iran example. This is a fallacy of linear extrapolation.
Economic Growth Projections
If a company's profits grow 10% per year for two years, that is percentage growth, not a straight-line increase. Assuming the same 10% rate indefinitely still extends a short-term pattern beyond the evidence and may overlook market saturation or other limits.
A MOMENT TO REFLECT
Put it to work.
Can you think of a situation where you assumed a trend would continue linearly, but it turned out to be part of a larger curve?
How might this concept help you avoid the slippery slope fallacy in arguments?
Give an example of a political debate where linear reasoning is used to distort the opposing view.
CONTINUE THE CONVERSATION
Source texts
- How Not to Be Wrong The Power of Mathematical Thinking (Ellenberg, Jordan)