Abstract Mind-World Correspondence Principle – No actionable investigative leads

180 10 A Mind-World Correspondence Principle tion graph. Given two world-paths P and Q, it’s obvious how to define the composition P*Q one follows P and then, after that, follows Q, thus obtaining a longer path. Similarly for mind-paths. In category theory terms, we are constructing the free category associated with the graph: the objects of the category are the nodes, and the morphisms of the category are the paths. And category theory is the right way to be thinking here we want to be thinking about the relationship between the world category and the mind category. The world-mind transfer function can be interpreted as a mapping from paths to subgraphs: Given a world-path, it produces a set of mind state-sets, which have a number of links between them. One can then define a world-mind path transfer function M(P) via taking the mind-graph M(nodes(P)), and looking at the highest-weight path spanning M(nodes(P)). (Here nodes? obviously means the set of nodes of the path P.) A functor F between the world category and the mind category is a mapping that preserves object identities and so that F(P *Q) = F(P) * F(Q) We may also introduce the notion of an approximate functor, meaning a mapping F so that the average of d(F(P * Q), F(P) * F(Q)) is small. One can introduce a prior distribution into the average here. This could be the Levin universal distribution or some variant (the Levin distribution assigns higher probability to computation- ally simpler entities). Or it could be something more purpose specific: for example, one can give a higher weight to paths leading toward a certain set of nodes (e.g. goal nodes). Or one can use a distribution that weights based on a combination of simplicity and directedness toward a certain set of nodes. The latter seems most interesting, and I will define a goal-weighted ap- proximate functor as an approximate functor, defined with averaging relative to a distribution that balances simplicity with directedness toward a certain set of goal nodes. The move to approximate functors is simple conceptually, but mathematically it’s a fairly big step, because it requires us to introduce a geometric structure on our categories. But there are plenty of natural metrics defined on paths in graphs (weighted or not), so there’s no real problem here. 10.4 The Mind-World Correspondence Principle Now we finally have the formalism set up to make a non-trivial statement about the relationship between minds and worlds. Namely, the hypothesis that: MIND-WORLD CORRESPONDENCE PRINCIPLE For an organism with a reasonably high level of intelligence in a certain world, relative to a certain set of goals, the mind-world path transfer function is a goal-weighted approximate functor. HOUSE_OVERSIGHT_013096