I'm only talking about the physical world - phenomena that don't correspond to something computable, which are very common, and include the next five seconds of

I'm only talking about the physical world - phenomena that don't correspond to something computable, which are very common, and include the next five seconds of the amplifier noise heard on your headphones, are dealt with by being ignored or averaged out. Collective motion is somewhat predictable and includes things like popular opinion or temperature, but individual deviations aren't covered. The problem with translating that into proof of dualism is that everything outside the computable looks the same. A hypothesis is something you can assume to compute a prediction, so if any hypothesis is true, the phenomenon must be computable. If the phenomenon is not computable, no computable hypothesis will match. The second you ascribe properties to a soul that can distinguish it from randomness, or properties of randomness that distinguished it from free will you've made one or the other computable, and whichever is computable won't match reality, if we suppose we're looking for something outside of rational explanation and not a "second material." Here's a concrete example. If you had access to a Halting oracle, it would only be checkable on Turing machines that you yourself could decide the halting problem for. Any answers beyond those programs wouldn't match any conceivable hypothesis.