The simulation hypothesis, suggesting our universe could be an artificial construct on an advanced computer, has fascinated many. However, discussions often rely on intuition without clear definitions or a formal understanding of what ‘simulation’ truly entails.
SFI Professor David Wolpert addresses this gap in a new paper published in Journal of Physics: Complexity. Wolpert presents the first mathematically rigorous framework for defining how one universe might simulate another. His analysis reveals that several long-held beliefs about simulations do not hold up under formal scrutiny. The findings suggest a more complex reality than previously imagined, even allowing for a universe capable of simulating another to be perfectly replicated within its own simulation.
Wolpert states, “This entire debate lacked basic mathematical scaffolding. Once you build that scaffolding, the problem becomes clearer — and far more interesting.”
His approach involves a fundamental shift: viewing universes not as physical systems with unknown internal mechanisms, but as types of computers. This perspective grounds the model in the physical Church–Turing thesis, which posits that any observable physical process can, in theory, be replicated by a standard computer program. Through this lens, the simulation question transforms into a computational one, with mathematics, rather than speculation, defining the limits of what is possible.
This computational framing allows Wolpert to apply Kleene’s second recursion theorem, a classic computer science result explaining how a program can generate and execute an exact copy of itself. When this theorem is extended to entire universes, a surprising implication emerges: if one universe can accurately simulate another, there is nothing to prevent the simulated universe from simulating the first in return. Under specific conditions, the two become mathematically indistinguishable, dismantling the traditional hierarchy of ‘higher’ and ‘lower’ realities.
The framework also challenges the common assumption that deeper levels of simulation must be computationally weaker than the levels above them, an argument often used to suggest that such chains must eventually end. Wolpert demonstrates that mathematics does not require this: simulations do not necessarily degrade, and infinite chains of simulated universes remain entirely consistent within the theory.
This research does not provide experimental tests or predictions. Instead, it establishes a conceptual foundation for future work by philosophers, physicists, and computer scientists. By formalizing the simulation hypothesis, the framework also opens up new avenues of inquiry. For instance, it prompts questions about the possibility of not only infinite chains of simulated universes (where one universe contains a computer simulating another, and so on) but also closed loops of universes simulating each other. Other questions arise concerning how the framework alters philosophical concepts of identity, by suggesting the potential for multiple versions of an individual existing across different simulations, all of whom are mathematically considered the same ‘you’.
Wolpert concludes, “You think you’re asking a simple question — are we in a simulation? — but once you formalize it, an entire landscape of new questions opens up. It turns out the structure beneath the idea is richer than anyone realized.”
