“Ultimate physical limits to computation”, (1999-08-13):
Computers are physical systems: what they can and cannot do is dictated by the laws of physics. In particular, the speed with which a physical device can process information is limited by its energy and the amount of information that it can process is limited by the number of degrees of freedom it possesses. This paper explores the physical limits of computation as determined by the speed of light c, the quantum scale ℏ and the gravitational constant G. As an example, quantitative bounds are put to the computational power of an ‘ultimate laptop’ with a mass of one kilogram confined to a volume of one liter.
“A Bayesian Approach to the Simulation Argument”, (2020-08-03):
The Simulation Argument posed by Bostrom suggests that we may be living inside a sophisticated computer simulation. If posthuman civilizations eventually have both the capability and desire to generate such Bostrom-like simulations, then the number of simulated realities would greatly exceed the one base reality, ostensibly indicating a high probability that we do not live in said base reality.
In this work, it is argued that since the hypothesis that such simulations are technically possible remains unproven, statistical calculations need to consider not just the number of state spaces, but the intrinsic model uncertainty. This is achievable through a Bayesian treatment of the problem, which is presented here. Using Bayesian model averaging, it is shown that the probability that we are sims is in fact less than 50%, tending towards that value in the limit of an infinite number of simulations. This result is broadly indifferent as to whether one conditions upon the fact that humanity has not yet birthed such simulations, or ignore it.
As argued elsewhere, it is found that if humanity does start producing such simulations, then this would radically shift the odds and make it very probably we are in fact simulated.
[Keywords: simulation argument, Bayesian inference]