The Black Vault

David H. Wolpert, a physics-trained computer scientist at the NASA Ames Research Center, has chimed in with his version of a knowledge limit. Because of it, he concludes, the universe lies beyond the grasp of any intellect, no matter how powerful, that could exist within the universe. Specifically, during the past two years, he has been refining a proof that no matter what laws of physics govern a universe, there are inevitably facts about the universe that its inhabitants cannot learn by experiment or predict with a computation. Philippe M. Binder, a physicist at the University of Hawaii at Hilo, suggests that the theory implies researchers seeking unified laws cannot hope for anything better than a “theory of almost everything.”

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Researchers have proved results about the incomputability of specific physical systems before. Wolpert points out that his result is far more general, in that it makes virtually no assumptions about the laws of physics and it requires no limits on the computational power of the inference device other than it must exist within the universe in question. In addition, the result applies not only to predictions of a physical system’s future state but also to observations of a present state and examining a record of a past state.

The theorem’s proof, similar to the results of Gödel’s incompleteness theorem and Turing’s halting problem, relies on a variant of the liar’s paradox—ask Laplace’s demon to predict the following yes/no fact about the future state of the universe: “Will the universe not be one in which your answer to this question is yes?” For the demon, seeking a true yes/no answer is like trying to determine the truth of “This statement is false.” Knowing the exact current state of the entire universe, knowing all the laws governing the universe and having unlimited computing power is no help to the demon in saying truthfully what its answer will be.

ABSTRACT. This paper argues that at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed.