On Why and What of Randomness

TL;DR

This paper clarifies the concept of randomness, differentiates it from lawlessness, and explores its philosophical and computational aspects, emphasizing proper understanding before applying probability theory.

Contribution

It introduces a nuanced classification of randomness, distinguishes it from probability, and advocates for teaching and understanding randomness thoroughly before probability.

Findings

Identifies four types of randomness: ontic, epistemic, pseudo, telescopic.

Explains the role of Kolmogorov complexity in defining randomness.

Encourages a foundational approach to teaching randomness before probability.

Abstract

This paper has several objectives. First, it separates randomness from lawlessness and shows why even genuine randomness does not imply lawlessness. Second, it separates the question -why should I call a phenomenon random? (and answers it in part one) from the patent question -What is a random sequence? -for which the answer lies in Kolmogorov complexity (which is explained in part two). While answering the first question the note argues why there should be four motivating factors for calling a phenomenon random: ontic, epistemic, pseudo and telescopic, the first two depicting genuine randomness and the last two false. Third, ontic and epistemic randomness have been distinguished from ontic and epistemic probability. Fourth, it encourages students to be applied statisticians and advises against becoming armchair theorists but this is interestingly achieved by a straight application of telescopic randomness. Overall, it tells (the teacher) not to jump to probability without explaining randomness properly first and similarly advises the students to read (and understand) randomness minutely before taking on probability.