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

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 May 10h-13h
24 May 10h30-13h
25 May 10h30-13h