The Problem of Emergence
One of the deepest questions in science is: when is a whole greater than the sum of its parts? We intuitively recognize that some systems—brains, ecosystems, societies—exhibit properties that seem to transcend what any individual component could produce alone. But how do we formalize this intuition? How do we measure emergence?
My research uses multivariate information theory to develop rigorous, quantitative answers to these questions.
Partial Information Decomposition
A key framework in this work is partial information decomposition (PID), which breaks down the information that multiple sources provide about a target into:
- Redundant information: What all sources share in common
- Unique information: What each source contributes independently
- Synergistic information: What only emerges from considering sources together
Synergy is particularly interesting—it represents genuinely emergent information that cannot be localized to any single component. When synergy dominates a system, the whole truly is more than the sum of its parts.
Key Questions
- How do we measure the “emergent” information in a system that cannot be reduced to its components?
- What mathematical structures give rise to synergy and emergence?
- How does information flow and transform across scales in complex systems?
- Can we use information-theoretic tools to identify the “right” level of description for a given system?
Methods
My work combines theoretical development with computational analysis:
- Mathematical frameworks: Developing new information-theoretic measures and proving their properties
- Network analysis: Applying these tools to understand information flow in neural and biological networks
- Time series analysis: Extracting higher-order statistical dependencies from empirical data
- Computational modeling: Testing theoretical predictions in simulated systems
Selected Publications
- Varley, T. F., et al. (2023). “Emergence as the conversion of information: A unifying theory.” Philosophical Transactions of the Royal Society A.
- Varley, T. F., & Hoel, E. (2022). “Emergence and information: A formal framework.” arXiv preprint.
- Varley, T. F. (2024). “Flickering emergence in the dynamics of complex systems.” Physical Review E.
For a complete list of publications, see my Google Scholar profile.