Scale Theory: Exploring Scales of Description
Scale Theory investigates how physical and cognitive phenomena transform across different scales of description. This theoretical framework seeks to understand the mathematical relationships and symmetries that govern transitions between micro and macro scales in both physical systems and cognitive processes.
Research Overview
Scale Theory provides a unified approach to studying scale-dependent phenomena in various fields:
- Physics: Understanding how microscopic interactions give rise to emergent macroscopic properties
- Cognitive Science: Exploring how neural activity relates to higher-level cognitive functions
- Machine Learning: Developing models that can learn and reason across different levels of abstraction
- Complex Systems: Analyzing self-organization and emergent properties in complex systems
Key Concepts
Scale Symmetry
Scale symmetry examines the mathematical transformations that preserve essential properties across different scales. This perspective offers insights into the conditions under which information is preserved or lost when changing the scale of observation.
Dissipative Systems
Scale Theory provides new mathematical tools for understanding dissipative systems and their dynamics across different scales. This work bridges concepts from thermodynamics, information theory, and dynamical systems.
Hamiltonian Dynamics and Canonical Transformations
We explore how Hamiltonian dynamics can be extended and transformed across scales, providing insights into conservation laws and invariants in both physical and abstract systems.
Applications
- Development of more robust and interpretable machine learning models
- Better understanding of emergent phenomena in complex systems
- New approaches to the measurement problem in quantum mechanics
- Insights into the scale-dependence of cognitive processes
Current Research
The current focus is on developing mathematical formalisms that can describe transitions between scales and identifying the invariants that are preserved across these transitions. This includes work on:
- Information-theoretic measures of scale transformations
- Symmetry principles in multi-scale systems
- Computational models that explicitly incorporate scale as a dimension
- Experimental tests of scale-theoretic predictions
Collaborations
This research is conducted in collaboration with researchers from:
- The Hebrew University of Jerusalem
- Max Planck Institute for Dynamics and Self-Organization
- Santa Fe Institute