Sala 8.2.16, Ciências ULisboa
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:
- Introduction
Can we know everything with science? Determinism, Reductionism, Predictability, Emergence
- 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
- 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
- Undecidability in Physics
Undecidability in the physical world?
Mappings from mathematical systems to physical systems
Some results of undecidability in classical and quantum systems
- 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
CFCUL - Centro de Filosofia das Ciências da Universidade de Lisboa
