Unpredictable? Randomness, Chance and Free Will

This cross-disciplinary course deals with the undetermined, the unpredictable -- or what appears to be such. Among the questions that will be addressed are:

• How is randomness defined?
• How has randomness, often seen as a nuisance, become a useful resource for communication and computing? How is it generated?
• How can physicists make the astounding claim that there is real randomness in nature?
• Can our apparently free acts be predicted by monitoring the activity of the brain?

Lecture 1: Basic of randomness

• History of randomness
• The fair coin as ideal case
• Definitions of randomness

Lecture 2: Randomness as a resource

• Review of various tasks in which randomness is used
• Randomized algorithms and de-randomization
• Cryptography: randomness for secrecy
• Zero-knowledge proofs

Lecture 3: Characterizing a source of randomness

• The biased coin and other weaker sources of randomness
• Amount of randomness: min-entropy
• Extraction of randomness

Lecture 4: Noise as a random number generator

• Definition of "noise"
• Thermal noise: example of a resistor
• How to extract random numbers from thermal fluctuations

Lecture 5: Deterministic chaos

• Physical (in)determinism
• Definition and examples of chaos

Lecture 6: Quantum physics, a first encounter

• Overview of quantum physics
• Single-particle interferences (Mach-Zehnder, double slit)
• Uncertainty

Lecture 7: Intrinsic randomness and its practical uses

• Bell's theorem and its implication
• Elements of quantum information science

Lecture 8: Introduction to free will in science

• Measurement independence
• Quanta in the brain?
• Libet's experiments