An illustrated exploration of fandom that combines academic essays with artist pages and experimental texts. Fandom as Methodology examines fandom as a set of practices for approaching and writing about art. The collection includes experimental texts, autobiography, fiction, and new academic perspectives on fandom in and as art. Key to the idea of “fandom as methodology” is a focus on the potential for fandom in art to create oppositional spaces, communities, and practices, particularly from queer perspectives, but also through transnational, (...) feminist and artist-of-color fandoms. The book provides a range of examples of artists and writers working in this vein, as well as academic essays that explore the ways in which fandom can be theorized as a methodology for art practice and art history. Fandom as Methodology proposes that many artists and art writers already draw on affective strategies found in fandom. With the current focus in many areas of art history, art writing, and performance studies around affective engagement with artworks and imaginative potentials, fandom is a key methodology that has yet to be explored. Interwoven into the academic essays are lavishly designed artist pages in which artists offer an introduction to their use of fandom as methodology. Contributors Taylor J. Acosta, Catherine Grant, Dominic Johnson, Kate Random Love, Maud Lavin, Owen G. Parry, Alice Butler, SooJin Lee, Jenny Lin, Judy Batalion, Ika Willis. Artists featured in the artist pages Jeremy Deller, Ego Ahaiwe Sowinski, Anna Bunting-Branch, Maria Fusco, Cathy Lomax, Kamau Amu Patton, Holly Pester, Dawn Mellor, Michelle Williams Gamaker, The Women of Colour Index Reading Group, Liv Wynter, Zhiyuan Yang. (shrink)

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’, which is commonly assumed to provide a hierarchy of increasing degrees of (...) class='Hi'>randomness. However, that notion of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems. (shrink)

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows (...) that, conversely, concepts and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

The Element reconstructs, analyses and compares different derivational routes to a grounding of the Arrow of Time in entropy. It also evaluates the link between entropy and visible disorder, and the related claim of an alignment of the Arrow of Time with a development from order to visible disorder. The Element identifies three different entropy-groundings for the Arrow of Time: (i) the Empirical Arrow of Time, (ii) the Universal Statistical Arrow of Time, and (iii) the Local Statistical Arrow of Time. (...) The Element will also demonstrate that it is unlikely that high entropy states will always coincide with visible disorder. Therefore, it will dispute that there is a strong link between the Arrow of Time and visible disorder. (shrink)

Random decision-making (RDM) is a method of choice in which an agent delegates the final selection to a random device (e.g., a coin). When faced with multiple options, RDM is often dismissed as an irrational approach. Even in symmetrical cases where RDM is conceded to be rational, it is typically regarded as merely one among many equally effective methods for making an arbitrary choice. I challenge this prevailing view by pinpointing a unique psychological benefit of RDM – specifically, its capacity (...) to mitigate potential regret – and thereby demonstrating that its rational applicability extends well beyond the narrow confines hitherto acknowledged. Once this capacity is recognized, it becomes clear that RDM is the uniquely rational strategy in certain symmetrical dilemmas while remaining rational in some asymmetrical cases. Furthermore, while factors such as affective and sociocultural influences impose limitations on the practice of RDM, I contend that these constraints are not insurmountable and may be mitigated as a deeper understanding of RDM’s unique value emerges. (shrink)

This open access book addresses the question of how God can providentially govern apparently ungovernable randomness. Medieval theologians confidently held that God is provident, that is, God is the ultimate cause of or is responsible for everything that happens. However, scientific advances since the 19th century pose serious challenges to traditional views of providence. From Darwinian evolution to quantum mechanics, randomness has become an essential part of the scientific worldview. An interdisciplinary team of Muslim, Christian and Jewish scholars—biologists, (...) physicists, philosophers and theologians—addresses questions of randomness and providence. (shrink)

An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL- (...) class='Hi'>randomness. Our first main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n−g. Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic.Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree.Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α<1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. (shrink)

We study the phenomenon of merging of opinions for computationally limited Bayesian agents from the perspective of algorithmic randomness. When they agree on which data streams are algorithmically random, two Bayesian agents beginning the learning process with different priors may be seen as having compatible beliefs about the global uniformity of nature. This is because the algorithmically random data streams are of necessity globally regular: they are precisely the sequences that satisfy certain important statistical laws. By virtue of agreeing (...) on what data streams are algorithmically random, two Bayesian agents can thus be taken to concur on what global regularities they expect to see in the data. We show that this type of compatibility between priors suffices to ensure that two computable Bayesian agents will reach inter-subjective agreement with increasing information. In other words, it guarantees that their respective probability assignments will almost surely become arbitrarily close to each other as the number of observations increases. Thus, when shared by computable Bayesian learners with different subjective priors, the beliefs about uniformity captured by algorithmic randomness provably lead to merging of opinions. (shrink)

We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random (...) reals. We show that Low(ML, Kurtz) coincides with the non-DNR degrees, while both Low(CR, Kurtz) and Low(Schnorr, Kurtz) are exactly the non-high, non-DNR degrees. (shrink)

We investigate the role of continuous reductions and continuous relativization in the context of higher randomness. We define a higher analogue of Turing reducibility and show that it interacts well with higher randomness, for example with respect to van Lambalgen’s theorem and the Miller–Yu/Levin theorem. We study lowness for continuous relativization of randomness, and show the equivalence of the higher analogues of the different characterizations of lowness for Martin-Löf randomness. We also characterize computing higher [Formula: see (...) text]-trivial sets by higher random sequences. We give a separation between higher notions of randomness, in particular between higher weak 2-randomness and [Formula: see text]-randomness. To do so we investigate classes of functions computable from Kleene’s [Formula: see text] based on strong forms of the higher limit lemma. (shrink)

The philosophy of superdeterminism is based on a single scientific fact about the universe, namely that cause and effect in physics are not real. The philosophy of superdeterminism is supported by quantum randomness. Although quantum events at the microscopic level are inherently probabilistic, the macroscopic world we experience appears deterministic due to the sheer number of particles and interactions involved. Quantum mechanics explains that at our scale, the vast multitude of individual quantum probabilities effectively average out, smoothing over the (...) inherent uncertainty of the quantum realm and leading to the predictable, classical behavior we observe in everyday objects and phenomena. The important takeaway is that macroscopic reality is based on a sequence of inherently random events at the quantum scale. The fact that all physical reality consists of a series of inherently random quantum behaviors strongly suggests that cause and effect in physics are not real. True inherent randomness in quantum mechanics implies that an event is uncaused in the deterministic sense, as its outcome cannot be predicted or determined by any prior physical conditions. Consequently, all physical reality consists of a series of uncaused quantum behaviors, which would not have to be the case, if cause and effect in physics were real. Moreover, the spontaneous coming into existence of a random quantum event would violate Dr. Hansson’s proof that we live in a superdeterministic universe. If the spontaneous coming into existence of random quantum events, like the spin measurement results of entangled particles, were real, then this would result in the potential for inconsistent spin measurement results observed from different inertial frames of reference violating Special Relativity. (shrink)

Historically, one of the most controversial aspects of Darwinian evolution has been the prominent role that randomness and random change play in it. Most biologists agree that mutations in DNA have random effects on fitness. However, fitness is a highly simplified scalar representation of an enormously complex phenotype. Challenges to Darwinian thinking have focused on such complex phenotypes. Whether mutations affect such complex phenotypes randomly is ill understood. Here I discuss three very different classes of well-studied molecular phenotypes in (...) which mutations cause nonrandom changes, based on our current knowledge. What is more, this nonrandomness facilitates evolutionary adaptation. Thus, living beings may translate DNA change into nonrandom phenotypic change that facilitates Darwinian evolution. (shrink)

This study aims to disentangle complexity from randomness and chaos, and to present a definition of complexity that emphasizes its epistemically distinct qualities. I will review existing attempts at defining complexity and argue that these suffer from two major faults: a tendency to neglect the underlying dynamics and to focus exclusively on the phenomenology of complex systems; and linguistic imprecisions in describing these phenomenologies. I will argue that the tendency to discuss phenomenology removed from the underlying dynamics is the (...) main root of the difficulties in distinguishing complex from chaotic or random systems. In my own definition, I will explicitly try to avoid these pitfalls. The theoretical contemplations in this paper will be tested on a sample of five models: the random Kac ring, the chaotic CA30, the regular CA90, the complex CA110 and the complex Bak-Sneppen model. Although these modelling studies are restricted in scope and can only be seen as preliminary, they still constitute on of the first attempts to investigate complex systems comparatively. (shrink)

Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f- (...) class='Hi'>randomness relative to a PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree. (shrink)

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 nonstandard notion of chance. The second, a probabilistic* constraining law, impose relative frequency and randomness constraints that every physically possible world must satisfy. The constraining notion removes a major obstacle to a unified governing account of non-Humean laws, on which laws (...) govern by constraining physical possibilities; it also provides independently motivated solutions to familiar problems for the Humean best-system account (the Big Bad Bug and the zero-fit problem). On either approach, probabilistic laws are tied more tightly to corresponding sets of possible worlds: some histories permitted by traditional probabilistic laws are now ruled out as physically impossible. Consequently, the framework avoids one variety of empirical underdetermination while bringing to light others that are typically overlooked. (shrink)

“Random” commonly is associated with determinism, order, prophecy, and the future. Starkly put by one philosopher, “Randomness is unpredictability” (Eagle, 2005), quoting mainstream logician Suppes in saying “Phenomena that we cannot predict must be judged random” (Suppes, 1984, p. 32). People rely upon uncertainty (encryption and defeating bias). Tables of random numbers are based on the supposition that humans subconsciously create patterns and cannot generate randomness. Gambling casinos are about the “luck of the draw”. Human survival depends on (...) remembering patterns of past events in order to adapt to the changing environment, as well as on randomness in science. Our focus is not only on considering whether randomness exists, i.e., ontology, but the reason for it. Turmoil in the field of experts is expressed by “… there is no such thing as a random number - there are only methods to produce random numbers...” (Von Neumann, 1951; Fiorini and De Giacomo, 2014, p. 5). How can one create something that cannot exist? Yet, at the most basic building block level of existence, Planck scale, there is inherent uncertainty (perhaps immanent in the macro world) with which persons have difficulty accepting. A new view of randomness will be presented here, based on the often neglected philosophy of dialectics, apprehension of something in terms of what it is not, a process understanding, rather than one of identifying objects. This short space allows only a small sampling of approaches to the ontology of randomness for the reader to explore in depth through cited references. If one can begin to think beyond the mechanics (as in random number generators) then this encyclopedia entry will have accomplished its purpose. (shrink)

We study genericity and randomness with respect to ITTMs, continuing the work initiated by Carl and Schlicht. To do so, we develop a framework to study randomness in the constructible hierarchy. We then answer several of Carl and Schlicht’s question. We also ask a new question one the equality of two classes of randoms. Although the natural intuition would dictate that the two classes are distinct, we show that things are not as simple as they seem. In particular (...) we show that the categorical analogues of these two classes coincide, in contradiction with the natural intuition. Even though we are not able to answer the question for randomness in this article, we delineate and sharpen its contour and outline. (shrink)

Recently, a connection has been established between two branches of computability theory, namely between algorithmic randomness and algorithmic learning theory. Learning-theoretical characterizations of several notions of randomness were discovered. We study such characterizations based on the asymptotic density of positive answers. In particular, this note provides a new learning-theoretic definition of weak 2-randomness, solving the problem posed by (Zaffora Blando, Rev. Symb. Log. 2019). The note also highlights the close connection between these characterizations and the problem of (...) convergence on random sequences. (shrink)

One of the most fundamental theoretical results in quantum mechanics, the theorem of Simon Kochen and Ernst Specker (1967), is investigated from a rather mathematical and philosophical than physical viewpoint (i.e. unlike as usual). The absence of hidden variables is interpreted philosophically and ontomathematically: as the identity of the mathematical model by the separable complex Hilbert space (equivalent to the qubit Hilbert space) and physical reality. It implies the completeness of just that model to physical reality including in the sense (...) of its cognitive finality. In other words, "hidden variables" are also interpreted as any mismatch between model and reality implied by the theorem not to be. That property of the qubit Hilbert space unique among all other mathematical theories (i.e., all first-order logics) is deduced as a corollary from the theorem as well. The approach at issue to the theorem implies its inherent contextuality to be deduced also in an "apophatic" or holistic version stating that omitting even a single "axis" of Hilbert space or a single value of probability density break its contextuality thus being inconsistent to the theorem. The concept of "fundamental randomness" is newly introduced as originating from the absence of hidden variables in any probability (density or not) distribution, the characteristic function of which is interpreted to be a (qubit) wave function. Then, the Kochen-Specker theorem implies no deviation from that "fundamental randomness" exists once its preconditions have been satisfied. The deviations at issue are seen to be any excluded degrees of freedom in a variable describing whatever. Just this statement is interpreted to be the theorem's "apophatic interpretation". A powerful method for proving statements in Hilbert arithmetic's number theory is offered as a conjecture to be reasoned and proved in a forthcoming paper. (shrink)

An esteemed American philosopher reflects on the nature of luck and its historical role in war, business, lotteries, and romance, and delineates the differences ...

A real x is -Kurtz random if it is in no closed null set . We show that there is a cone of -Kurtz random hyperdegrees. We characterize lowness for -Kurtz randomness as being -dominated and -semi-traceable.

Life increasingly is understood in terms of information. I consider two attempts to formulate life in terms of mathematical information theory. G. J. Chaitin proposes to define life in terms of the relation between order and algorithmic compressibility in biological information. More recently, William Dembski, Winston Ewart, and Robert J. Mark’s suggest that Dembski’s notion of specified complexity can be mathematically expressed in information-theoretic terms through the concept of algorithmic specified complexity. The mathematical approaches are similar and in both cases (...) essentially dependent on the concept of randomness deficiency in algorithmic information theory: to subtract out the degree of randomness from an informational measure, yielding a remainder of organization (Chatin) or specified complexity (Dembski, Ewart, and Marks). I argue that these attempts must fail due the information-theoretic indistinguishability of organization and randomness. The failure is instructive, however, because it illustrates the inability of mathematical information theory to register biological organization. (shrink)

Osvald Demuth studied constructive analysis from the viewpoint of the Russian school of constructive mathematics. In the course of his work he introduced various notions of effective null set which, when phrased in classical language, yield a number of major algorithmic randomness notions. In addition, he proved several results connecting constructive analysis and randomness that were rediscovered only much later.In this paper, we trace the path that took Demuth from his constructivist roots to his deep and innovative work (...) on the interactions between constructive analysis, algorithmic randomness, and computability theory. We will focus specifically on Demuth’s work on the differentiability of Markov computable functions and his study of constructive versions of the Denjoy alternative, Demuth’s independent discovery of the main notions of algorithmic randomness, as well as the development of Demuth randomness, and the interactions of truth-table reducibility, algorithmic randomness, and semigenericity in Demuth’s work. (shrink)

After the introductory first chapter, the second chapter contains the discussion of the concept of randomness in relation to the element of chance with reference to the Commonplace Thesis. Subjective and objective probabilities are viewed from the perspective of modern approaches. The debate between the Frequentist and Bayesian approaches are also discussed. The Compensated Bayes’ rule function is introduced as a dynamic interpretation of classical Bayes’ rule. The facts and artifacts of scientific reality from personal beliefs to chance situations (...) are investigated. Principles of chance are examined as they constitute building blocks for understanding the nature of randomness. The chapter is concluded with the epistemological demarcation between personal beliefs, knowledge and reality. (shrink)

We study degree-theoretic properties of reals that are not random with respect to any continuous probability measure (NCR). To this end, we introduce a family of generalized Hausdorff measures based on the iterates of the “dissipation” function of a continuous measure and study the effective nullsets given by the corresponding Solovay tests. We introduce two constructions that preserve non-randomness with respect to a given continuous measure. This enables us to prove the existence of NCR reals in a number of (...) Turing degrees. In particular, we show that every \(\Delta ^0_2\) -degree contains an NCR element. (shrink)

The ArgumentVisible colleges, in contrast to the “invisible colleges” familiar to historians of science, are the collective places of science, the places where the “creation of phenomena” and theoretical speculation proceed side by side. To understand their spatial form, we must understand first how buildings can structure space to both conserve and generate social forms, depending on how they relate structure in space to randomness. Randomness is shown to play a crucial role in morphogenetic models of many kinds, (...) especially in spatial forms and in social networks. We argue here that it can also play a crucial role in the advance of science. (shrink)

This research is developed primarily within the framework of first-order formal logic. Going beyond the limitations of prior analyses by philosophers such as Galen Strawson, it rigorously examines the problem of free will through a fundamentally different logical approach. Through precise formal investigation, it demonstrates that only deterministic causation and non-subjective randomness are possible, and that no entity capable of ultimate responsibility can exist. Consequently, in fields including ethics, law, theology, and theories of free will, any notion of an (...) agent possessing subjectivity and ultimate moral or legal responsibility is logically impossible. The paper presents fundamental definitions and concepts, such as Autonomy, Contribution, and Existence. It lays out formal premises and propositions, examines the possibility of Autonomy (Au), analyzes counterexamples and equivalence relations, and concludes with the logical implications regarding the impossibility of autonomy and free will. (shrink)

Se examina la interpretación aristotélica del azar como causa accidental en el ámbito de los fines de aquello que puede ser realizado por la naturaleza o por el pensamiento. ¿Por qué un acontecimiento fortuito pertenece al orden de los fines? ¿Qué quiere decir que los sucesos fortuitos son "para algo"? Se repasan las principales respuestas de los especialistas, se indican algunas deficiencias y se propone una lectura no causal-explicativa de la expresión ἓνεκά του, diferente de la teleología del como-si, como (...) explicación de la finalidad del acontecimiento fortuito. The Aristotelian interpretation of randomness is examined as an accidental cause in the sphere of ends of that which can be brought about by nature or by thought. Why would a fortuitous event belong to the order of ends? What does it mean to say that fortuitous events are "for something"? The main responses to specialists are reviewed, some deficiencies are noted, and a non-causal-explicative reading is proposed for the expression ἓνεκά του. This reading differs from the "as-if teleology" as an explanation of the finality of the fortuitous event. (shrink)