The forest has no census

Nick Bostrom’s simulation argument depends on estimating the fraction of observers like us who are simulated, then applying an indifference principle: absent evidence distinguishing us, our chance of being simulated should match that fraction. The essay argues that this reasoning breaks down if the cosmos contains infinitely many universes. Simulated observers and observers in original, or “root,” universes may both be countably infinite, so their raw numbers cannot establish a proportion. A density-based count can produce different fractions depending on the order in which observers are listed; even the even numbers have different densities under different listings. Thus the simulated fraction is not automatically a fact about the world.

The essay tests two ways of ordering observers across universes. If a shared global time exists and new roots appear exponentially, counting all observers alive at one moment mostly captures young universes that have not yet had time to run simulations. With roots appearing at rate \(e^{\gamma t}\) and simulations beginning only after age \(\Delta\), the simulated fraction is approximately \(Ne^{-\gamma\Delta}/(Ne^{-\gamma\Delta}+1)\), which approaches zero when new roots arrive rapidly. Bostrom’s alternative, counting outward from one root, instead approaches a simulated fraction of one. If no global time exists, there is no privileged ordering across disconnected universes, so the fraction depends on a chosen convention and cannot ground the indifference principle. The conclusion is that the simulation argument does not show we are probably simulated without an additional assumption, such as a finite cosmos or a single base reality.