An Implementation of Causal Emergence 2.0

I implement the computational tools suggested in Erik Hoel's novel Causal Emergence 2.0.

Causal Emergence 2.0 (CE 2.0) attempts to capture causally-important scales of discrete dynamical systems, leveraging first-principles notions of causality.

Overview

The CE 2.0 framework explores how macro-scale representations of a system can exhibit greater causal power than their micro-scale counterparts. This implementation provides tools to:

• Calculate Causal Emergence scores
• Visualize apportionment paths
• Explore merge operations and which causal component is contributory

Core Components

ce.py

Core implementation; components to generate a greedy causal apportionment path.

ce_systems.py

Common/predefined system configurations and example transition probability matrices (TPMs) for testing and analysis.

Analysis Notebooks

ce_explorer.ipynb

The frontend, where you can ask about downstream causal apportionment by providing a microscale TPM.

• explore() function for comprehensive system analysis
• Visualization of CP changes and absolute scores

det_spec_explorer.ipynb

Getting some intuiton for how the greedy merge operates. When do we merge for determinism, when for specificity?

• Side-by-side matrix comparisons for apportionment paths under different metrics
• Path convergence analysis
• Status reporting for different metrics

Usage

Import the core modules and explore a predefined system from the collection in ce_systems.py. The explore function generates and visualizes the complete greedy causal apportionment path for any given transition probability matrix. Examine how causal power changes through successive merges.

For comparative analysis between different merging metrics, use the det_spec_explorer.py to examine how determinism-only and specificity-only forced paths differ from a standard CE 2.0 apportionment. This intution is key in understanding CE 2.0 and underlying causal dynamics.

Provide your own transition probability matrix to the explore() function in ce_explorer.py to generate the apportionment sequence. The system expects $n \times n$ matrices representing the transition probabilities between all possible states of your discrete dynamical system microstate.

Dependencies

• NumPy (matrix operations and numerical computing)
• SciPy (entropy calculations)
• Matplotlib (visualization)
• NetworkX (graph operations in ce_systems.py)

Other

Among other systems, I looked at Boid behavior. Some demonstrations are included in boids_under_CE.zip.