  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 G\"{o}del's Incompleteness Theorem. These properties,
combined with some recent developments in theoretical and observational
cosmology, motivate what is referred to as the `cosmological invariant set
postulate': that the universe $U$ can be considered a deterministic dynamical
system evolving on a causal measure-zero fractal invariant set $I_U$ in its
state space. Symbolic representations of $I_U$ are constructed explicitly based
on permutation representations of quaternions. The resulting `invariant set
theory' provides some new perspectives on determinism and causality in
fundamental physics. For example, whilst the cosmological invariant set appears
to have a rich enough structure to allow a description of quantum probability,
its measure-zero character ensures it is sparse enough to prevent invariant set
theory being constrained by the Bell inequality (consistent with a partial
violation of the so-called measurement independence postulate). The primacy of
geometry as embodied in the proposed theory extends the principles underpinning
general relativity. As a result, the physical basis for contemporary programmes
which apply standard field quantisation to some putative gravitational
lagrangian is questioned. Consistent with Penrose's suggestion of a
deterministic but non-computable theory of fundamental physics, a
`gravitational theory of the quantum' is proposed based on the geometry of
$I_U$, with potential observational consequences for the dark universe.
