The Self-Similarity of Evidence

Definition

Deutsch names self-similarity the property by which parts of physical reality resemble other parts — concretely, as a planetarium's image resembles the night sky, or, more importantly, abstractly, as a correct statement in a textbook resembles the structure of reality it describes. Galileo's deeper discovery, on this reading, wasn't the heliocentric theory itself but a fact about the universe: it is "saturated with evidence" — every patch of sky, on every clear night, everywhere on Earth, for billions of years, has carried the same evidence bearing on the fundamental laws of astronomy, obtainable by anyone with the right instruments and the right questions, requiring no authorization, initiation, or privileged access.

In the Book

Chapter 4 sets this up by pointing out that Copernicus gathered his evidence in Poland, Tycho Brahe in Denmark, Kepler in Germany, and Galileo in Italy — different observers, different vantage points, converging on the same theory because the same evidence is repeated everywhere the relevant instruments can be pointed. Deutsch treats this "open accessibility... of the whole mechanism of knowledge acquisition" as a substantive, contingent fact about our universe rather than something logically guaranteed: reality could have been arranged so that critical evidence was locked away, rare, or observer-dependent, and much of the book's argument (that science reliably converges on ever-deeper explanations) depends on it not being that way. He extends self-similarity beyond evidence to knowledge itself: books, films, computer memories, and brains all contain structures that "resemble," in the appropriate abstract sense, the physical or abstract things they describe — which is why, in the closing lines of the chapter, he identifies this self-similarity as the very thing that makes both science and, ultimately, universal computation possible (bridging directly into the following chapters on virtual reality and the Turing principle).

Why It Matters

This names a background condition that is easy to take for granted: that a domain's truths are not merely knowable in principle but redundantly, repeatedly demonstrable by independent observers using independent methods, which is what makes decentralized, adversarial verification (peer review, replication, competing labs) work at all. It gives a way to ask, of any field or claim, whether its evidence has this self-similar, universally-accessible character — or whether it depends on privileged access, rare events, or unverifiable testimony — as a diagnostic for how much confidence convergent methods can actually earn.