Reach of Explanations
The extent to which a good explanation applies beyond the phenomena it was originally designed to explain.
Also known as: Explanatory Reach, Theory Reach, Scope of Explanation
Category: Philosophy & Wisdom
Tags: philosophy, epistemology, science, thinking, rationality, mental-models, knowledge, learning
Explanation
Reach, as articulated by David Deutsch in 'The Beginning of Infinity,' refers to an explanation's ability to correctly address phenomena it was never designed for. A theory with great reach does not only explain what it was built to explain - it tells you true things about situations the original designer never considered. A theory with little reach is narrowly tied to its specific target and cannot be extrapolated.
Newton's theory of gravity is a classic example of high reach. Newton formulated it to explain planetary motion and falling apples near Earth. The same theory correctly describes the motion of moons of planets unseen at the time, the trajectories of comets, the tides, the orbits of artificial satellites, binary star systems, and so on. The theory was never 'updated' for these applications - its internal structure already accommodated them.
By contrast, ad hoc or easy-to-vary explanations have almost no reach. A myth invented to explain one season tells you nothing about any other. A conspiracy theory tailored to one event does not generalize to other events because its details were chosen to fit that one case.
Why reach matters:
- **Indicator of truth**: An explanation with reach is constrained by real structure, not by the phenomenon the author was staring at. The structure likely reflects something real.
- **Source of progress**: Most scientific and technological progress comes from exploiting the reach of existing explanations - applying deep theories to new domains.
- **Leverage**: A high-reach idea pays dividends across many contexts. Time invested in learning it compounds.
- **Test of understanding**: If you cannot apply a theory to a new problem, you have a surface understanding. If you can, you have grasped the structure.
- **Basis for optimism**: Deutsch argues that because good explanations have unbounded reach, knowledge itself can be extended indefinitely - there is no inherent ceiling to what we can understand.
Reach is closely tied to hard-to-vary explanations. An explanation that is hard to vary tends to have high reach, because the internal constraints are real and apply wherever those constraints apply. Conversely, an easy-to-vary story fails in new contexts because nothing in its structure forces it to be right.
Seeking reach is a practical heuristic. When learning, invest in ideas that apply everywhere. When explaining, ask whether your explanation tells you anything about adjacent problems. When evaluating theories, prefer those whose consequences extend beyond the specific case that motivated them.
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