Por Álvaro Perales Eceiza (Universidad de Alcalá).

In this 8-hour course with contents of physics, mathematics and philosophy of science, we will study the theories that a priori suppose a limit to the knowledge we can acquire about nature and the predictions of its future behavior, focusing on Undecidability (Gödel, Turing) and its manifestations in physics.

Contents of the course:

1. Introduction
   Can we know everything with science? Determinism, Reductionism, Predictability, Emergence
    
2. Chaos and Quantum Mechanics
   Chaos. Nonlinear equations and sensitivity to initial conditions. Examples
   QM. Uncertainty principle. Wave function and Schördinger equation. Superposition and entanglement. Measurement problem and interpretations of QM
    
3. Undecidability in Mathematics
   Axiomatic systems: From Euclid to Principia Mathematica
   K. Gödel: Undecidability and Incompleteness in Maths
   A. Turing. Universal Turing machine and halting problem
   Algorithmic Information Theory. Kolmogorov-Chaitin Complexity
   Extensions to other mathematical systems
    
4. Undecidability in Physics
   Undecidability in the physical world?
   Mappings from mathematical systems to physical systems
   Some results of undecidability in classical and quantum systems
    
5. Summary, open problems and discussion
   Are there fundamental limits to knowledge about nature?

Schedule:

• 23/05, Tue: 10h-13h
• 24/05, Wed: 10h30-13h
• 25/05, Thu: 10h30-13h