Schnorr randomness is a notion of algorithmic randomness for real numbers closely related to Martin-Löf randomness. After its initial development in the 1970s the notion received considerably less attention than Martin-Löf randomness, but recently interest has increased in a range of randomness concepts. In this article, we explore the properties of Schnorr random reals, and in particular the c.e. Schnorr random reals. We show that there are c.e. reals that are Schnorr random but not Martin-Löf random, and provide a new (...) characterization of Schnorr random real numbers in terms of prefix-free machines. We prove that unlike Martin-Löf random c.e. reals, not all Schnorr random c.e. reals are Turing complete, though all are in high Turing degrees. We use the machine characterization to define a notion of "Schnorr reducibility" which allows us to calibrate the Schnorr complexity of reals. We define the class of "Schnorr trivial" reals, which are ones whose initial segment complexity is identical with the computable reals, and demonstrate that this class has non-computable members. (shrink)
We show that there is a limit lemma for enumeration reducibility to 0 e ', analogous to the Shoenfield Limit Lemma in the Turing degrees, which relativises for total enumeration degrees. Using this and `good approximations' we prove a jump inversion result: for any set W with a good approximation and any set X< e W such that W≤ e X' there is a set A such that X≤ e A< e W and A'=W'. (All jumps are enumeration degree jumps.) (...) The degrees of sets with good approximations include the Σ0 2 degrees and the n-CEA degrees. (shrink)
In Heidegger’s Being and Time certain concepts are discussed which are central to the ontological constitution of Dasein. This paper demonstrates the interesting manner in which some of these concepts can be used in a reading of T.S. Eliot’s The Love Song of J. Alfred Prufrock. A comparative analysis is performed, explicating the relevant Heideggerian terms and then relating them to Eliot’s poem. In this way strong parallels are revealed between the two men’s respective thoughts and distinct modernist sensibilities. Prufrock, (...) the protagonist of the poem, and the world he inhabits illustrate poetically concepts such as authenticity, inauthenticity, the ‘they’, idle talk and angst, which Heidegger develops in Being and Time. (shrink)
This essay, which is the editor's introduction to part 1 of a multipart symposium on quietism, also constitutes his call for symposium papers. The symposium is meant be comprehensive. It is described as political and broadly cultural as well as religious, and in religious terms is said to cover not only the Catholic and Protestant quietisms (most properly so called) of the late seventeenth and eighteenth centuries, but also the proto-quietisms of the medieval Western church and reputedly quietist aspects of (...) the Gnostic, Eastern Orthodox, early Hasidic, Shi'ite, Jain and other Indic, Taoist, and Zen religious traditions. This introduction emphasizes the secular approaches, mostly antipolitical or postphilosophical, that wear the adjective “quietist” metaphorically, including the postmodern currents that Martha Nussbaum has named “hip quietism” and the “minimalist” philosophical version developed by Wittgenstein and some of his successors, notably Richard Rorty. This introduction concludes with attention to Rorty's late essay “Naturalism and Quietism,” then with a dedication of the entire symposium to Rorty's memory. (shrink)
We report on simple shaking experiments to measure the compaction of a column of Firth oat grain. Such grains are elongated anisotropic particles with a bimodal polydispersity. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical shaking evolve to a dense state with evidence of nematic-like structure at the surface of the confining tube. This is accompanied by an increase in the packing fraction of the grain.
This essay describes and commends the treatment of tears and weeping in Augustine’s Confessions. It shows that Augustine depicts these acts as communicative of a particular judgment about the way things are; and that he understands these acts as a species of confession appropriate to the human condition. To become, or attempt to become, the kind of person who does not weep is to distance oneself from God; Augustine therefore commends weeping to Christians as a mode of establishing intimacy with (...) God. (shrink)