Evidence For Simulation
The recent article on overcomingbias suggesting the Fermi paradox might be evidence our universe is indeed a simulation prompted me to wonder how one would go about gathering evidence for or against the hypothesis that we are living in a simulation. The Fermi paradox isn't very good evidence but there are much more promising places to look for this kind of evidence. Of course there is no sure fire way to learn that one isn't in a simulation, nothing prevents a simulation from being able to perfectly simulate a non-simulation universe, but there are certainly features of the universe that seem more likely if the universe was simulated and their presence or absence thus gives us evidence about whether we are in a simulation. In particular, the strategy suggested here is to consider the kind of fingerprints we might leave if we were writing a massive simulation. Of course the simulating creatures/processes may not labor under the same kind of restrictions we do in writing simulations (their laws of physics might support fundamentally different computational devices and any intelligence behind such a simulation might be totally alien). However, it's certainly reasonable to think we might be simulated by creatures like us so it's worth checking for the kinds of fingerprints we might leave in a simulation. Computational Fingerprints Simulations we write face several limitations on the computational power they can bring to bear on the problem and these limitations give rise to mitigation strategies we might observe in our own universe. These limitations include the following: 1. Lack of access to non-computable oracles (except perhaps physical randomness). While theoretically nothing prevents the laws of physics from providing non-computable oracles, e.g., some experiment one could perform that discerns whether a given Turing machine halts (halting problem = 0') all indications suggest our universe does not provide such oracles. Thus our simulatio
This is best understood in terms of models. Prove doesn't assert that something is provable in our normal sense it asserts that there are numbers encoding a proof. So what "PA |- Prov(phi) -> phi" really asserts is that any structure that satisfies the axioms of PA must believe that phi is true iff it believes there is a number coding a proof of phi.
But there are lots of structures other than the usual non-negative integers that satisfy PA. Including ones with infinite 'numbers.'. In fact, anything consistent with the axioms of PA is going to be true in one of these non-standard models.
So what this is really saying is that if phi isn't a consequence of PA then there is some structure which contains a fake 'infinite proof' of phi but in which phi isn't true. No paradoxes at all.