Related papers: On Why and What of Randomness
We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We…
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
The main goal of this article is to put some known results in a common perspective and to simplify their proofs. We start with a simple proof of a result of Vereshchagin saying that $\limsup_n C(x|n)$ equals $C^{0'}(x)$. Then we use the…
A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique"…
Randomization procedures are used in legal and statistical applications, aiming to shield important decisions from spurious influences. This article gives an intuitive introduction to randomization and examines some intended consequences of…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
This short note introduces a formal system of truth and paradoxicality, outlining the main motivation, and proving its $\omega$-consistency. The system is called TP, for 'Truth and Paradoxicality'.
The physics of randomness and regularities for languages (mother tongues) and their lifetimes and family trees and for the second languages are studied in terms of two opposite processes; random multiplicative noise [1], and fragmentation…
Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that…
Herein we consider various concepts of entropy as measures of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
Causal Learning has emerged as a major theme of research in statistics and machine learning in recent years, promising specific computational techniques to apply to datasets that reveal the true nature of cause and effect in a number of…
According to quantum theory, randomness is a fundamental property of the universe yet classical physics is mostly deterministic. In this article I show that it is possible for deterministic systems to arise from random ones and discuss the…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a…