A Mathematical Foundation for Computability in Physics


When can a model of a physical system be regarded as computable? The formal definition of a computable physical model provides one answer to this question. Students in this course will be introduced to the mathematical background for understanding computable physical models. The theoretical consequences of computable physical models will be explored, and various sorts of applications will be illustrated, including applications to deterministic systems, non-deterministic systems, discrete systems, and non-discrete continuous systems. The course will conclude with an overview of some mathematical techniques for studying computable physical models in more general topological spaces.

Preliminary Syllabus

  1. Physical Models and Dynamical Systems
  2. Computable Physical Models
  3. Discrete Motion
  4. Non-Discrete Continuous Motion
  5. Coarse-Graining
  6. Radioactive Decay
  7. Ensembles of Physical Models
  8. Incompatible Measurements
  9. The Accuracy of Measuring Instruments
  10. Isomorphism Theorems
  11. Oracles and Effective Topologies
  12. Basic Representations of Sets
  13. Basic Representations of Physical Models
  14. Data and Predictions
  15. Kreisel's Criterion

Meet the instructor

Matthew Szudzik is an Assistant Teaching Professor of Mathematics at Carnegie Mellon University. In addition, he served as a research assistant to Dr. Stephen Wolfram from 1998 to 2000. Matthew Szudzik holds a PhD in mathematical logic from Carnegie Mellon University, and a bachelor's degree in physics from the University of Michigan.

General Information

  • Language: English
  • Course starts: To be announced in 2017
  • Course length:TBA
  • Estimated effort:TBA


Dr. Matthew Szudzik
Assistant Teaching Professor of Mathematics, Carnegie Mellon University

Supporting Material

FQXi Foundation
Wolfram Foundation
Sillicon Valley Foundation
Wolfram Research
Complexity Explorer
St Fe Institute
University of Oxford