He would have been interested in Ed Lorenz' work (from the butterfly effect fame) I suppose. According to Tim Palmer: "Despite being known for his pioneering w

He would have been interested in Ed Lorenz' work (from the butterfly effect fame) I suppose. According to Tim Palmer: "Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of Lorenz's fractal invariant set relate space-time calculus to deep areas of mathematics such as Gödel's Incompleteness Theorem." "Consider a point p in the three-dimensional Lorenz state space. Is there an algorithm for determining whether p belongs to IL? There are certainly large parts of state space which don’t contain any part of IL. However, suppose p was a point which ‘looked’ as if it might belong to IL. How would one establish whether this really is the case or not? If we could initialise the Lorenz equations at some point which was known to lie on IL, we could then run (1) forward to see if the trajectory passes through p. If the integration is terminated after any finite time and the trajectory still hasn’t passed through p, we can’t really deduce anything. We can’t be sure that if the integration was continued, it would pass through p at some future stage. The Lorenz attractor provides a geometric illustration of the Gödel/Turing incompleteness theorems: not all problems in mathematics are solvable by algorithm. This linkage has been made rigorous by the following theorem [7]: so-called Halting Sets must have integral Hausdorff dimension. IL has fractional Hausdorff dimension - this is why it is called a fractal. Hence we can say that IL is formally non-computational. To be a bit more concrete, consider one of the classic undecidable problems of computing theory: the Post Correspondence Problem [46]. Dube [16] has shown that this problem is equivalent to asking whether a given line intersects the fractal invariant set of an iterated function system [4]. In general, non-computational problems can all be posed in this fractal geometric way." Source: Lorenz, Gödel and Penrose: New Perspectives on Determinism and Causality in Fundamental Physics https://arxiv.org/pdf/1309.2396.pdf https://arxiv.org/pdf/1309.2396.pdf