Anatomy of Multiversal Utility Functions: Tegmark Level IV
Outline: Constructing utility functions that can be evaluated on any possible universe is known to be a confusing problem, since it is not obvious what sort of mathematical object should be the domain and what properties should the function obey. In a sequence of posts, I intend break down the question with respect to Tegmark's multiverse levels and explain the answer on each level, starting with level IV in the current post. Background An intelligent agent is often described as an entity whose actions drive the universe towards higher expectation values of a certain function, known as the agent's utility function. Such a description is very useful in contexts such as AGI, FAI, decision theory and more generally any abstract study of intelligence. Applying the concept of a utility function to agents in the real worlds requires utility functions with a very broad domain. Indeed, since the agent is normally assumed to have only finite information about the universe in which it exists, it should allow for a very large variety of possible realities. If the agent is to make decisions using some sort of utility calculus, it has to be able to evaluate its utility function on each of the realities it can conceive. Tegmark has conveniently arranged the space of possible realities ("universes") into 4 levels, 3 of which are based on our current understanding of physics. Tegmark's universes are usually presented as co-existing but it is also possible to think of them as the "potential" universes in which our agent can find itself. I am going to traverse Tegmark's multiverse from top to bottom, studying the space of utility functions on each level (which, except for level IV, is always derived from the higher level). The current post addresses Tegmark level IV, leaving the lower levels for follow-ups. Some of the ideas in this post previously appeared in a post about intelligence metrics, where I explained them much more tersely. Tegmark Level IV Tegmark defined this lev