Tegmark levels
Max Tegmark's four-floor taxonomy of multiverses: repeated space, inflationary bubbles, quantum branches, all mathematics. Fine-tuning lives on floor two.
Lukasz Szramuk ·
Tegmark levels are Max Tegmark's four-tier taxonomy of multiverses, set out in a 2003 Scientific American article and expanded in his 2014 book. Its value is not that it argues for parallel universes; it is that it separates four completely different claims that ordinary conversation runs together. Ask which level someone means and the argument usually resolves itself, because the evidence, the objections and the stakes are different on every floor.
Level I is simply space being bigger than our horizon: same laws, same constants, different initial conditions — and if it is infinite, every arrangement of matter recurs, including this one. The distance to your nearest exact copy is a number you can only write as a tower of exponents. Level II is eternal inflation: bubbles that stop inflating at different moments, with different low-energy constants, different particle content, possibly different numbers of large spatial dimensions. This is the floor the fine-tuning debate lives on, and string theory's landscape of vacua is its usual engine. Level III is Everett's many worlds — quantum branching; Tegmark's own argument is that it adds no possibilities beyond Level II, it just distributes the same outcomes differently. Level IV is the Mathematical Universe Hypothesis: every self-consistent mathematical structure exists physically, and ours holds no special rank among them.
The levels also grade smoothly from mainstream to radical, which is the other reason the taxonomy earns its keep. Level I follows from inflation plus a flat universe and is close to uncontroversial. Level II is a consequence of models many cosmologists already accept — which is what makes it interesting, and what makes its critics uneasy. Level III is an interpretation rather than an extra postulate. Level IV is philosophy with equations, and its problems are severe: there is no accepted measure over mathematical structures, so it predicts nothing, and George Ellis and Joe Silk have argued in Nature that reasoning of this shape erodes the requirement that physics be testable at all.
On this site the Graveyard is a hand-built Level II: an ensemble where the constants vary, most members are stillborn, and the only ones anyone reads about are the ones that got far enough to be worth reading about. That last clause is the anthropic principle doing its work on a very small sample.