We consider the question of randomness of the probability ΩU[X] that an optimal Turing machine U halts and outputs a string in a fixed set X. The main results are as follows: ΩU[X] is random whenever X is $\Sigma _{n}^{0}$-complete or $\Pi _{n}^{0}$-complete for some n ≥ 2. However, for n ≥ 2, ΩU[X] is not n-random when X is $\Sigma _{n}^{0}$ or $\Pi _{n}^{0}$ Nevertheless, there exists $\Delta _{n+1}^{0}$ sets such that ΩU[X] is n-random. There are $\Delta _{2}^{0}$ sets (...) X such that ΩU[X] is rational. Also, for every n ≥ 1, there exists a set X which is $\Delta _{n+1}^{0}$ and $\Sigma _{n}^{0}$-hard such that ΩU[X] is not random. We also look at the range of ΩU as an operator. We prove that the set {ΩU[X]: X ⊆ 2<ω} is a finite union of closed intervals. It follows that for any optimal machine U and any sufficiently small real r, there is a set X ⊆ 2<ω recursive in ∅′ ⊕ r, such that ΩU[X] = r. The same questions are also considered in the context of infinite computations, and lead to similar results. (shrink)

Mark Doyle's Utopian and Dystopian Themes in Tolkien's Legendarium reads Tolkien's work through the history of utopian and dystopian thought. The aim of this new study is not to prove that Tolkien set out to write dystopian fiction or create a blueprint for a utopian society, but that utopian and dystopian societies and settings crucially inform his legendarium. By placing his study outside of its usual fantasy context, Doyle gives us a valuable societally focused and historicized contribution to both Tolkien (...) and utopian studies respectively, yet one occasionally marred by the author's own unexamined value judgments.The book examines several aspects of Tolkien's legendarium, from its utopian and dystopian literary... (shrink)

Another volume in the Bechers' lifelong project of documenting the architecture of industrial structures. Bernd and Hilla Becher's photography can be considered conceptual art, typological study, and topological documentation. Their work can be linked to the Neue Sachlichkeit movement of the 1920s and to such masters of German photography as Karl Blossfeldt, August Sander, and Albert Renger-Patzsch. Their photographs documenting the architecture of industrial structures, taken over the course of forty years, make up the most important body of work (...) to be found in independent objective photography. This volume adds cooling towers to a list of photographic projects that includes book-length studies of water towers, blast furnaces, gas tanks, mineheads, and frame houses.Since the end of the nineteenth century, cooling towers have formed a striking part of electricity and steel works. The first cooling towers were wood-clad structures at coal mines; more recent examples are the steel or concrete constructions seen at nuclear power stations. The simplicity of these forms and their hermetically sealed external skins create an impressive, monumental effect. The Bechers have been photographing cooling towers since the 1960s. This volume contains 236 photographs of cooling towers—in all their different shapes and structural forms—from Belgium, England, France, Germany, Holland, and the United States, and includes a short text by the Bechers. (shrink)

These photographs of grain elevators in America, Germany, Belgium, and France are a major addition to the Bechers' ongoing documentation of the vanishing buildings that once defined the industrial landscape of Europe and America. Bernd and Hilla Becher's almost fifty-year collaboration constitutes the most important project in objective and conceptual photography today. With this volume, grain elevators join the list of building types documented by the Bechers in their book-length studies: water towers, blast furnaces, gas tanks, oil tanks, mineheads, (...) frame houses, and cooling towers. Grain elevators are towering structures in the flat, vast landscape of the world's granaries. Providing a fast and efficient method of loading and unloading grain to keep pace with the industrial production methods of the nineteenth century, they made possible a tremendous increase in the trafficking and processing of grain. Scooping, pouring, and spitting, they both illustrated and inspired Le Corbusier's idea of buildings as functioning machines. Monumental, essential, and visually arresting, grain elevators belong as much to the American imagination and landscape as to the European. The photographs of grain elevators in this volume were taken in Germany, Belgium, France, and America. But the specificity of time and place is erased in these photographs; the monolithic structures evoke the agricultural prosperity of a vanished era and the vacancy that replaces it today. (shrink)

Anna Vaninskaya's Fantasies of Time and Death: Dunsany, Eddison, Tolkien brings together three major writers of fantasy and studies their treatment of temporality and mortality. This book is about our ongoing conversation regarding time and death and the unique ability for fantasy to tackle these biggest of subjects. If writers have long envisioned time as a river and death as the sea, for instance, what Vaninskaya's new book discusses is how fantasy allows us, through the use of impossible creations and (...) new metaphors, to imagine new ways of understanding our ontological trap. The genre attempts to try to see the world as one of the gods creating it, or to understand time as the eternal burden of the elves; we may... (shrink)

The chromosome theory of inheritance was established during the three first decades of the 20th century. During the early stage of its substantiating, there were lots of puzzles and little evidence that could validate it. The cytological processes were obscure and several scientists maintained serious doubts concerning the existence of a connection between Mendel’s principles and the behaviour of chromosomes during cell division. It was vital to associate an external, observable characteristic of the organism to a specific chromosome, and this (...) was achieved when sex was connected to special chromosomes. At that time, however, some important scholars refused to accept or delayed acceptance of the conception that the hereditary factors (later called genes) were physical entities located along the chromosomes. Such was the case of Thomas Morgan (1866-1945) and William Bateson (1861-1926). Their attitudes could be explained by considering the doubtful ground of the hypothesis at that time. It is more difficult, however, to understand the attitude of Edmund Beecher Wilson (1856-1939). Being an expert in cytology he was acquainted with all the difficulties concerning the chromosome hypothesis. Nonetheless, from 1905 onward, he attributed little weight to the problems and dedicated a notable effort to obtaining evidence that could have grounded it. This paper analyses Wilson’s attitude focusing on his studies from 1900 to 1915 and the scientific context of this period. This study led to the conclusion that Wilson’s attitude could be explained in methodological terms by the adoption of an instrumentalist attitude, while Bateson and Morgan adopted a realistic perspective. (shrink)

In this paper, I take a closer look at Hans Reichenbach’s relation to metaphysics and work out some interesting parallels between his account and that of the proponents of inductive metaphysics, a tradition that emerged in the mid- and late 19th century and the early 20th century in Germany. It is in particular Hans Reichenbach’s conception of the relation between the natural sciences and metaphysics, as displayed in his treatment of the question of the existence of the external world, that (...) shows some very interesting similarities with inductive metaphysics. By a comparison with the position of the inductive metaphysician Erich Becher and his handling of the problem of realism, I work out the parallels between Reichenbach’s program and inductive metaphysics. I come to the conclusion that while there are certainly some respects in which Reichenbach’s logical empiricism is closer to the positions of the representatives of the Vienna Circle, it turns out that with regard to his views on metaphysics there is a greater affinity with the program of inductive metaphysics. (shrink)

We define a program size complexity function $H^\infty$ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in ${\{0,1\}}^\omega$ relative to the $H^\infty$ complexity. We prove that the classes of Martin-Löf random sequences and $H^\infty$-random sequences coincide and that the $H^\infty$-trivial sequences are exactly the recursive ones. We also study some properties of $H^\infty$ and compare it with other complexity functions. In particular, $H^\infty$ (...) is different from $H^A$, the prefix-free complexity of monotone machines with oracle A. (shrink)

Using possibly infinite computations on universal monotone Turing machines, we prove Martin-Löf randomness in ∅' of the probability that the output be in some set.

This volume gathers together for the first time are all the key texts in a crucial debate in modern philosophy, centered on Leibniz's famous 1695 essay, the "New System of the Nature of Substances and their Communication," in which he introduced his strikingly original theory of metaphysics. His "system" became increasingly famous and drew him into discussion and development of these ideas, both in public and in private, with a variety of thinkers, most notably the great French philosopher Pierre Bayle. (...) Woolhouse's and Francks's new English edition gives the only full representation of this debate, and will therefore be essential reading for anyone who wishes to gain a proper understanding of Leibniz's philosophy and its intelletual context. All the texts are newly translated and extensively annotated; many appear in English for the first time. (shrink)

This chapter offers a proceduralist argument against capital punishment. More specifically, it contends that the possibility of irrevocable mistakes precludes the just administration of the death penalty. At stake is a principle of political morality: legal institutions must strive to remedy their mistakes and to compensate those who suffer from wrongful sanctions. The incompatibility of remedy and execution is the crux of the irrevocability argument: because the wrongly executed cannot enjoy the morally required compensation, execution is impermissible. Along with defending (...) his key premises, Yost explains the complicated role that sentencing uncertainty plays in the argument. He concludes by noting some of the flaws in substantive consequentialist and retributivist justifications of capital punishment. (shrink)

Plato's dialogues frequently criticize traditional Greek myth, yet Plato also integrates myth with his writing. Daniel S. Werner confronts this paradox through an in-depth analysis of the Phaedrus, Plato's most mythical dialogue. Werner argues that the myths of the Phaedrus serve several complex functions: they bring nonphilosophers into the philosophical life; they offer a starting point for philosophical inquiry; they unify the dialogue as a literary and dramatic whole; they draw attention to the limits of language and the limits of (...) knowledge; and they allow Plato to co-opt cultural authority as a way of defining and legitimating the practice of philosophy. Platonic myth, as a species of traditional tale, is thus both distinct from philosophical dialectic and similar to it. Ultimately, the most powerful effect of Platonic myth is the way in which it leads readers to participate in Plato's dialogues and to engage in a process of self-examination. (shrink)

"Die folgenden Untersuchungen zielen unmittelbar auf eine Einteilung der Realwissenschaften ab, und zwar auf die adäquate, dem Ganzen dieser Wissenschaften angemessene Einteilung. Soll dies Ziel erreicht werden, so sind die Realwissenschaften nach allen Seiten hin eindringender wissenschaftstheoretischer Betrachtung zu unterziehen. So hat dies Buch eine vergleichende Wissenschaftslehre (Gegenstandslehre, Logik und Erkenntnistheorie) sozusagen eine vergleichende Anatomie der Wissenschaften, insbesondere der Realwissenschaften, anzustreben. In dieser Aufgabe liegt die eigentliche Absicht, während das Einteilungsproblem mehr das äussere, unmittelbare Ziel abgibt." (Erich Becher,Vorwort) Erich (...) Becher ( 1882 - 1929 ) war ein deutscher Philosoph und Psychologe. Er studierte an der Universität Bonn Naturwissenschaften, Mathematik, Sozialwissenschaften und Philosophie, u.a. bei Benno Erdmann, und schloss das Studium mit der Promotion zum Dr. phil. sowie dem Staatsexamen für das höhere Lehramt ab. Seine Habilitationsschrift trägt den Titel "Philosophische Voraussetzungen der exakten Naturwissenschaften". Nach einigen Jahren als Privatdozent an der Universität Bonn wurde er 1909 an die Universität Münster berufen, bevor er 1916 auf den Lehrstuhl für Philosophie und Psychologie an der Universität München wechselte. Zudem war er seit 1924 ordentliches Mitglied der Bayerischen Akademie der Wissenschaften. Sorgfältig überarbeiteter Nachdruck des Originals von 1921. (shrink)

many symbols. We define o, as the probability that an arbitrary machine be circular and we prove that o, is a random number that goes beyond..

This comprehensive volume enables readers to develop an understanding of the principles of fluid mechanics and to utilize problem-solving approaches for handling, transferring, and processing fluids.

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

An encyclopedic collection of all known Becher industrial studies, arranged by building type.

Let [Formula: see text] be an integer. We show that the set of real numbers that are Poisson generic in base [Formula: see text] is [Formula: see text]-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base [Formula: see text] and not Poisson generic in base [Formula: see text] is complete for the class given by the differences between [Formula: see text] sets. We also show that the (...) effective versions of these results hold in the effective Borel hierarchy. (shrink)