The nature of randomness: Part 2 – Cognitive constraints

Purpose – The purpose of the paper, in this two-part series, is to consider certain intriguing aspects of randomness, the basic mathematical concept used to model financial risk and other unknown quantities in the physical world. Design/methodology/approach – In Part 2 of the paper, the author describes methods for simulating random variables, and explores whether it is possible in practice to distinguish between the knowable complexity of compressible random variables and the unknowable complexity of incompressible random variables. Findings – In Part 2 of the paper, it is found that because of Chaitin's impossibility result (regarding incompressible sequences) and the possibility of constructing least-surprising sequences, one is left with two cognitive constraints with serious implications for statistical hypothesis testing and the scientific method. Originality/value – This two-part paper explores the underlying nature of randomness in terms of both its physical/mathematical properties and its role in human cognition.