Finite Factored Sets

This is an introduction to a new way of thinking about time, based on finite factored sets.

A factored set is a set understood as a Cartesian product, in the same sense that a partition is a way to understand a set as a disjoint union.

This sequence begins by applying finite factored sets to temporal inference, showing some advantages of this framework over Judea Pearl’s theory of causal inference. Finite factored sets have many potential applications outside of temporal inference, however, and future writing will explore embedded agency and other topics through the lens of finite factored sets.

The “Details and Proofs” section of this sequence is also available as an arXiv paper: “Temporal Inference with Finite Factored Sets.”

Overview

Finite Fac­tored Sets

Details and Proofs

Finite Fac­tored Sets: In­tro­duc­tion and Factorizations

Finite Fac­tored Sets: Orthog­o­nal­ity and Time

Finite Fac­tored Sets: Con­di­tional Orthogonality

Finite Fac­tored Sets: Polyno­mi­als and Probability

Finite Fac­tored Sets: In­fer­ring Time

Finite Fac­tored Sets: Applications

Applications and Discussion

Sav­ing Time

AXRP Epi­sode 9 - Finite Fac­tored Sets with Scott Garrabrant

[AN #163]: Us­ing finite fac­tored sets for causal and tem­po­ral inference

Countably Fac­tored Spaces