In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics and a set of logical constants (with specified arities). The first generator returns formulae of exactly the given depth, using all or some of the propositional letters. The second does the same but samples up-to the given depth. The third generator outputs formulae with (...) exactly the desired depth and all the atomics in the set. To make the generators uniform (i.e. to make them return every formula in their space with the same probability), we will prove various cardinality results about those spaces. (shrink)

Left distributive algebras arise in the study of classical structures such as groups, knots, and braids, as well as more exotic objects like large cardinals. A long-standing open question is whether the set of left divisors of every term in the free left distributive algebra on any number of generators is well-ordered. A conjecture of J. Moody describes a halting condition for descending sequences of left divisors in the free left distributive algebra on an arbitrary number of generators. (...) In this paper we present progress toward an affirmative answer to the open question mentioned above, namely we prove that the many generator form of Moody’s conjecture holds if each member of the free left distributive algebra has a “division form” representation in an expanded algebra. (shrink)

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C2 is generated by two Pauli matrices iσ2 and iσ3; C3 is generated by the three Pauli matrices σ1, σ2, σ3; C4 is generated by four Dirac matrices γ0, γ1, γ2, γ3 and C5 is generated by five Dirac matrices iγ0, iγ1, iγ2, iγ3, iγ5. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained (...) with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation. (shrink)

This study investigates how patterns of media use and exposure to media messages are related to attitudes about artificial intelligence (AI) image generators. In doing so, it builds on theoretical accounts of media framing and public opinion about science and technology topics, including AI. The analyses draw on data from a survey of the US public (N = 1,035) that included an experimental manipulation of exposure to tweets framing AI image generators in terms of real art, artists’ concerns, (...) artists’ outrage, or competing interpretations. The results show that technology news use and science fiction viewing predicted support for AI art but also predicted belief that AI image generators will take jobs and steal art styles from human artists. In addition, the experimental results demonstrate that exposure to specific media messages can influence these responses. The findings carry implications for understanding the future adoption, use, and regulation of AI image generators. (shrink)

The relation is developed between rotation generators of the Lorentz group and the magnetic fields of free-space electromagnetism. Using these classical relations, it is shown that in the quantum field theory there exists a longitudinal photomagneton, a quantized magnetic flux density operator which is directly proportional to the photon spin angular momentum. Commutation relations are given in the quantum field between the longitudinal photomagneton and the usual transverse magnetic components of quantized electromagnetism. The longitudinal component is phase free, but (...) the transverse components are phase dependent. All three components can magnetize material in general, but only the transverse components contribute to Planck's law. The photon therefore has three, not two, relativistically invariant degrees of polarization, an axial, longitudinal, polarization, and the usual right and left circular transverse polarizations. Since the longitudinal polarization is axial, it is a phase- free magnetic field. (shrink)

Many experiments have been conducted over the past eight decades to explore whether the ostensible psychic ability of psychokinesis (PK, or "mind over matter") might be a genuine human potential, and the most extensive of these have involved attempts to mentally influence the output of electronic, binary-bit random number generators (RNGs). Research of this type can generally be divided into two lines: proof-oriented (concerned with the accumulation and statistical evaluation of data from controlled experiments designed specifically to test for (...) the presence of PK effects on the microscopic scale) and process-oriented (concerned with conducting exploratory experiments designed to systematically vary certain test conditions in order to search for and identify any physical, biological, and psychological factors which might have a role in improving or moderating PK effects). To help orient novice investigators and cross-disciplinary researchers who may be considering work along these lines (as well as offer some initial guiding insight on possible directions for future research), this paper provides a general review of some of the notable proof- and process-oriented findings that have been obtained to date in experimental microscopic PK research using RNGs. The review generally indicates that although a considerable amount of proof-oriented data for micro-PK has accumulated over the years, the relatively sparse amount of process-oriented data available at present leaves a lot of open questions regarding the underlying factors involved, providing ample opportunity for novice investigators and cross-disciplinary researchers to make valuable research contributions in the future. (shrink)

Affectively uncomfortable concern, anxiety, indecisionand disputation over ‘right’ action are among the expressions of moral tension associated with ethical dilemmas. Moral tension is generated and experienced by people. While ethical principles, rules and situations must be worked through in any dilemma, each occurs against a backdrop of people who enact them and stand much to gain or lose depending on how they are applied and resolved. This paper attempts to develop a taxonomy of moral tension based on its intrapersonal and (...) interpersonal sources and expressions. The proposed ‘ethics of incongruity’ (EoI) outlines ways in which values, actions and needs can find themselves mismatched in morally relevant ways between patients and their clinicians, their own psychologies and their societies. Patient–clinician incongruities may manifest as discord, value misalignment and deception. Patient–patient (ie, intrapersonal) incongruities may manifest as incapacity, akrasia and self-deception. Patient–society incongruities may manifest as disenfranchisement, disaffiliation and disregard. Brief explanations of the incongruities in this scheme are provided, as are suggestions on working within them. Using concepts from moral philosophy when applicable, these suggestions may either ease direct resolution of problems arising from the incongruities, or make sense of the moral tension that arises from the human context of the ethical dilemma at hand. This presentation of content and resolution methods for the EOI is no doubt incomplete. Hopefully, refinement of this preliminary proposal will follow, particularly from clinicians, as the ones who, along with their patients, experience medical ethics in directly tension-inducing ways. (shrink)

This book candidly reports the experiences of one middle school principal for 160 consecutive days with little or no editing. The material is much more than the typical case study. The events are presented in context; the results of actions taken are seen in the daily lives of all affected.

Aberrant consumer behaviour costs firms millions of pounds a year, and the Internet has provided young techno-literate consumers with a new medium to exploit businesses. This paper addresses Internet related ethics and describes the ways in which young consumers misdemean on the Internet and their attitudes towards these. Using a sample of 219 generation Y consumers, the study identified 24 aberrant behaviours which grouped into five factors; illegal, questionable activities, hacking related, human Internet trade and downloading. Those perceived as least (...) wrong were; "Downloading movie and music files from the Internet for free". The consequences of these behaviours have implications for educators, consumer policy and marketers. (shrink)

For the last thirty years or so, there has been a search underway for a theory that can accommodate our intuitions in regard to moral duties to future generations. The object of this search has proved surprisingly elusive. The classical moral theories in the literature all have perplexing implications in this area. Classical Utilitarianism, for instance, implies that it could be better to expand a population even if everyone in the resulting population would be much worse off than in the (...) original. The main problem has been to find an adequate population theory, that is, a theory about the moral value of states of affairs where the number of people, the quality of their lives, and their identities may vary. Since, arguably, any reasonable moral theory has to take these aspects of possible states of affairs into account when determining the normative status of actions, the study of population theory is of general import for moral theory. A number of theories have been proposed in the literature that purport to avoid counterintuitive implications such as the one mentioned above. The suggestions are diverse: introducing novel ways of aggregating welfare into a measure of value, revising the notion of a life worth living, questioning the way we can compare and measure welfare, counting people’s welfare differently depending on the temporal location or the modal features of their lives, and challenging the logic of axiological and normative concepts. We investigate the concepts and assumptions involved in these theories as well as their implications for population theory. In our discussion, we propose a number of intuitively appealing and logically weak adequacy conditions for an acceptable population theory. Finally, we consider whether it is possible to find a theory that satisfies all of these conditions. We prove that no such theory exists. (shrink)