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)
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