Definition
The Reach of Explanations (or Explanatory Reach) is the ability of a good explanation to correctly predict, describe, and solve phenomena far beyond the specific local problems that originally motivated its creation. It is the property that allows finite human minds to reason about the infinite structure of reality.
Why It Matters
Reach is the litmus test for truth. If an explanation only works for the data you already have, it is just curve-fitting. If it predicts things you haven’t seen yet—like the center of stars or the beginning of time—it is a “good explanation.” Recognizing reach allows us to distinguish between incremental patches and fundamental breakthroughs, ensuring we invest our intellectual and technical resources in models that possess the capacity to solve problems we haven’t even encountered yet.
Core Concepts
- Good Explanations (Hard to Vary): Explanations that are highly constrained by reality. Every detail plays a functional role; if you change any detail, the explanation no longer works. This structural tightness is what grants them reach.
- Appearances Need Interpretation: Observation is not raw access to reality; it is always processed through theory. Empiricism is incomplete because sense experience supplies tests and problems, but does not mechanically generate the explanatory theories.
- Universality: Local laws (e.g., gravity, the jump to universality in computer code, or quantum mechanics) apply everywhere in the cosmos. Once a universal threshold is crossed, local solutions acquire infinite reach.
- Unintended Consequences: A true explanation sheds light on domains the original researcher was not considering. Reach is not added by the researcher; it is an inherent property of the truth of the explanation.
- Infinity is Accessible via Reach: Mathematical and physical infinity are counterintuitive, but they can be reasoned about rigorously because reach allows us to understand the infinite through finite, hard-to-vary explanations that apply without bound.