New mathematical framework reshapes debate over simulation hypothesis

Summary

The simulation hypothesis — the idea that our universe might be an artificial construct running on some advanced alien computer — has long captured the public imagination. Yet most arguments about it rest on intuition rather than clear definitions, and few attempts have been made to formally spell out what “simulation” even means. A new paper by SFI Professor David Wolpert aims to change that. In Journal of Physics: Complexity, Wolpert introduces the first mathematically precise framework for what it would mean for one universe to simulate another — and shows that several longstanding claims about simulations break down once the concept is defined rigorously. His results point to a far stranger landscape than previous arguments suggest, including the possibility that a universe capable of simulating another could itself be perfectly reproduced inside that very simulation. “This entire debate lacked basic mathematical scaffolding,” Wolpert says. “Once you build that scaffolding, the problem becomes clearer — and far more interesting.” At the core of his approach is a shift in perspective: instead of treating universes as physical systems with unknowable inner workings, treat them as kinds of computers. This lets Wolpert ground his model in the physical Church–Turing thesis, which holds that any physical process we can observe could, in principle, be reproduced by a standard computer program. Seen through this lens, the simulation question becomes a computational one — and mathematics, rather than speculation, sets the boundaries of what is possible. That computational framing allows Wolpert to draw on a classical result from computer science known as Kleene’s second recursion theorem, which explains how a program can generate and run an exact copy of itself. When Wolpert extends this theorem to entire universes, a surprising implication follows: if some universe can simulate ours accurately, nothing prevents our universe from simulating that universe in return. Under...