Remark to last week's participants: This will be a condensed version of last week's talks. I will drop many details (in particular on the relation to quantum theory) and also drop the introductory slides to algorithmic probability (for this, see Marcus Hutter's introductory talk on Tuesday afternoon, April 10).
Motivated by the conceptual puzzles of quantum theory and related areas of physics, I describe a rigorous and minimal “proof of principle” theory in which observers are fundamental and in which the physical world is a (provably) emergent phenomenon. This is a reversal of the standard view, which holds that physical theories ought to describe the objective evolution of a unique external world, with observers or agents as derived concepts that play no fundamental role whatsoever. Using insights from algorithmic information theory (AIT), I show that this approach admits to address several foundational puzzles that are difficult to address via standard approaches. This includes the measurement and Boltzmann brain problems, and problems related to the computer simulation of observers. Without assuming the existence of an external world from the outset, the resulting theory actually predicts that there is one as a consequence of AIT — in particular, a world with simple, computable, probabilistic laws on which different observers typically (but not always) agree. This approach represents a consistent but highly unfamiliar picture of the world, leading to a new perspective from which to approach some questions in the foundations of physics.