Related papers: On Why and What of Randomness
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
The main goal of this paper is to put some known results in a common perspective and to simplify their proofs. We start with a simple proof of a result from (Vereshchagin, 2002) saying that $\limsup_n\KS(x|n)$ (here $\KS(x|n)$ is…
This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We…
Randomness comes in two qualitatively different forms. Apparent randomness can result both from ignorance or lack of control of degrees of freedom in the system. In contrast, intrinsic randomness should not be ascribable to any such cause.…
The systematic biases seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory, but instead use heuristics which sometimes yield reasonable…
The randomness rate of an infinite binary sequence is characterized by the sequence of ratios between the Kolmogorov complexity and the length of the initial segments of the sequence. It is known that there is no uniform effective procedure…
The education system for students in physics suffers (worldwide) from the absence of a deep course in probability and randomness. This is the real problem for students interested in quantum information theory, quantum optics, and quantum…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
This paper avers that science is not demarcated from other disciplines by a specific unique methodology, but by its specific scientific rationality and rational grounds. In this context, the notion and structure of scientific reason are…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
Algorithmic theories of randomness can be related to theories of probabilistic sequence prediction through the notion of a predictor, defined as a function which supplies lower bounds on initial-segment probabilities of infinite sequences.…
One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…
The effective teaching and learning of statistics persist as a challenge in K-12 education and has clear impacts in developing competence and confidence of students in entering STEM fields especially in today's digital age of data science.…
It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of "What is quantum in quantum randomness", i.e. what is the impact of…
This essay is a two-step reflection on the question 'Which events (can be said to) occur in quantum phenomena?' The first step regiments the ontological category of "statistical phenomena" and studies the adequacy of "probabilistic event…
The paper studies discrete time processes and their predictability and randomness in deterministic pathwise setting, without using probabilistic assumptions on the ensemble. We suggest some approaches to quantification of randomness based…
Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of…
Despite provable unknowables in recursion theory, indeterminism and randomness in physics is confined to conventions, subjective beliefs and preliminary evidence. The history of the issue is very briefly reviewed, and answers to five…