Understand
We introduce and explore the notion of "spaces of input histories", a broad family of combinatorial objects which can be used to model input-dependent, dynamical causal order.
- We motivate our definition with reference to traditional partial order- and preorder-based notions of causal order, adopted by the majority of previous literature on the subject, and we proceed to explore the novel landscape of combinatorial complexity made available by our generalisation of those notions.
- In the process, we discover that the fine-grained structure of causality is significantly more complex than we might have previously believed: in the simplest case of binary inputs, the number of available "causally complete" spaces grows from 7 on 2 events, to 2644 on 3 events, to an unknown number on 4 events (likely around a billion).
- For perspective, previous literature on non-locality and contextuality used a single one of the 2644 available spaces on 3 events, work on definite causality used 19 spaces, derived from partial orders, and work on indefinite causality used only 6 more, for a grand total of 25.