Experimental mathematics, computers and the a priori

In recent decades, experimental mathematics has emerged as a new branch of mathematics. This new branch is defined less by its subject matter, and more by its use of computer assisted reasoning. Experimental mathematics uses a variety of computer assisted approaches to verify or prove mathematical hypotheses. For example, there is “number crunching” such as searching for very large Mersenne primes, and showing that the Goldbach conjecture holds for all even numbers less than 2 × 1018. There are “verifications” of hypotheses which, while not definitive proofs, provide strong support for those hypotheses, and there are proofs involving an enormous amount of computer hours, which cannot be surveyed by any one mathematician in a lifetime. There have been several attempts to argue that one or another aspect of experimental mathematics shows that mathematics now accepts empirical or inductive methods, and hence shows mathematical apriorism to be false. Assessing this argument is complicated by the fact that there is no agreed definition of what precisely experimental mathematics is. However, I argue that on any plausible account of ’experiment’ these arguments do not succeed.     

How activation, entanglement, and searching a semantic network contribute to event memory

Free-association norms indicate that words are organized into semantic/associative neighborhoods within a larger network of words and links that bind the net together. We present evidence indicating that memory for a recent word event can depend on implicitly and simultaneously activating related words in its neighborhood. Processing a word during encoding primes its network representation as a function of the density of the links in its neighborhood. Such priming increases recall and recognition and can have long-lasting effects when the word is processed in working memory. Evidence for this phenomenon is reviewed in extralist-cuing, primed free-association, intralist-cuing, and single-item recognition tasks. The findings also show that when a related word is presented in order to cue the recall of a studied word, the cue activates the target in an array of related words that distract and reduce the probability of the target’s selection. The activation of the semantic network produces priming benefits during encoding, and search costs during retrieval. In extralist cuing, recall is a negative function of cue-to-distractor strength, and a positive function of neighborhood density, cue-to-target strength, and target-to-cue strength. We show how these four measures derived from the network can be combined and used to predict memory performance. These measures play different roles in different tasks, indicating that the contribution of the semantic network varies with the context provided by the task. Finally, we evaluate spreading-activation and quantum-like entanglement explanations for the priming effects produced by neighborhood density.     

Seriousness checks are useful to improve data validity in online research

Nonserious answering behavior increases noise and reduces experimental power; it is therefore one of the most important threats to the validity of online research. A simple way to address the problem is to ask respondents about the seriousness of their participation and to exclude self-declared nonserious participants from analysis. To validate this approach, a survey was conducted in the week prior to the German 2009 federal election to the Bundestag. Serious participants answered a number of attitudinal and behavioral questions in a more consistent and predictively valid manner than did nonserious participants. We therefore recommend routinely employing seriousness checks in online surveys to improve data validity.     

Übertragung und Übertragungsneurose

The authors investigate Freud's concepts of transference, transference neurosis and their mutual relationship. They discuss the current criticism made on the concept of transference neurosis and raise the question, why patients accept the analyst's interpretations? They suggest understanding transference neurosis as conscious manifestations of transference referring to the analyst which are the outcome of successive interpretations of the type "just-like" followed, changed, and removed again by "just-like-it-was"-interpretations. They conclude that the patient does accept these interpretations not for reasons that are rational, but for reasons pertaining the transference situation.     

Does The Necessity of Mathematical Truths Imply Their Apriority?

It is sometimes argued that mathematical knowledge must be a priori, since mathematical truths are necessary, and experience tells us only what is true, not what must be true. This argument can be undermined either by showing that experience can yield knowledge of the necessity of some truths, or by arguing that mathematical theorems are contingent. Recent work by Albert Casullo and Timothy Williamson argues (or can be used to argue) the first of these lines; W. V. Quine and Hartry Field take the latter line. I defend a version of the argument against these, and other objections.     

Judging the plausibility of arguments in scientific texts: a student–scientist comparison

The ability to evaluate scientific claims and evidence is an important aspect of scientific literacy and requires various epistemic competences. Readers spontaneously validate presented information against their knowledge and beliefs but differ in their ability to strategically evaluate the soundness of informal arguments. The present research investigated how students of psychology, compared to scientists working in psychology, evaluate informal arguments. Using a think-aloud procedure, we identified the specific strategies students and scientists apply when judging the plausibility of arguments and classifying common argumentation fallacies. Results indicate that students, compared to scientists, have difficulties forming these judgements and base them on intuition and opinion rather than the internal consistency of arguments. Our findings are discussed using the mental model theory framework. Although introductory students validate scientific information against their knowledge and beliefs, their judgements are often erroneous, in part because their use of strategy is immature. Implications for systematic trainings of epistemic competences are discussed.     

THE ATOMIC PRIESTHOOD AND NUCLEAR WASTE MANAGEMENT: RELIGION,SCI‐FI LITERATURE,AND THE END OF OUR CIVILIZATION

This article discusses the idea of an “Atomic Priesthood,” a religious caste that would preserve and transmit the knowledge of nuclear waste management for future generations. In 1981, the US Department of Energy commissioned a “Human Interference Task Force” (HITF) that would examine the possibilities of how to maintain the security of nuclear waste storage sites for 10,000 years, a period during which our civilization would likely perish, but the dangerous nature of nuclear waste would persist. One option that was discussed was the establishment of an “atomic priesthood,” an idea that science fiction writers like Isaac Asimov and Arsen Darney had already toyed with. Reading the HITF report alongside sci‐fi novels, my article will shed light on the question of how the sheer force of nuclear power (and the longevity of nuclear waste) lends itself to religious interpretations and how the idea of the atomic priesthood is connected with the utopian/dystopian aspects of nuclear power.