We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into study randomness. In particular, we define several notions randomness associated with interval, rather than precise, forecasting systems, and their properties. The richer mathematical structure that thus arises lets us, amongst other things, better understand place existing results for precise...

In this text we will discuss different forms of randomness in Natural Sciences and present some recent results relating them. In finite processes, randomness differs in various theoretical context, or, to put it otherwise, there is no unifying notion of finite time randomness. In particular, we will introduce, classical (dynamical), quantum and algorithmic randomness. In physics, differing prob...

Humans can easily discriminate a randomly spaced from a regularly spaced visual pattern. Here, we demonstrate that observers can adapt to pattern randomness. Following their adaption to prolonged exposure to two-dimensional patterns with varying levels of physical randomness, observers judged the randomness of the pattern. Perceived randomness decreased (increased) following adaptation to high ...

The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability ...

In general, any observed random process includes two qualitatively different forms of randomness: apparent randomness, which results both from ignorance or lack of control of degrees of freedom in the system, and intrinsic randomness, which is not ascribable to any such cause. While classical systems only possess the first kind of randomness, quantum systems may exhibit some intrinsic randomnes...

We propose studying uniform Kurtz randomness, which is the uniform relativization of Kurtz randomness. This notion has more natural properties than the usual relativization. For instance, van Lambalgen’s theorem holds for uniform Kurtz randomness while not for (the usual relativization of) Kurtz randomness. Another advantage is that lowness for uniform Kurtz randomness has many characterization...