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National University of Singapore

Unpredictable? Randomness, Chance and Free Will

National University of Singapore via Coursera

This course may be unavailable.


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


Taught by

Valerio Scarani


4.0 rating, based on 4 Class Central reviews

Start your review of Unpredictable? Randomness, Chance and Free Will

  • Krassimir Kostadinov
    The course introduces the interface between modern Science (in particular Physics) and Philosophy with respect to topics around randomness, chance, and (un-)predictability. It gives a unique perspective over a topic that is quite technical and at the same time very philosophically oriented.

    Students who expect deeper information and more intellectually challenging content might be disappointed. The course is intended to be an introduction, and often ends by just providing links and hints for further resources.
  • Stephane Mysona
  • Daniel Finol

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