Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: Problem solving is an enormous field of study, where so-called “problems” can end up having very little in common. One of the least studied categories of problems is open-ended mathematical modeling research. Cifarelli and Sevim’s framework - although not developed for this purpose - may be a useful lens for (...) studying the development of mathematical modelers and researchers in applied mathematics. (shrink)

This paper presents a new model for how the voting worked at the Athenian dramatic competitions, and demonstrates its viability mathematically. Previous proposals have either failed to take full account of the ancient sources or have not considered all the possible permutations of judging results. As is generally recognized, ten votes were cast, but in most circumstances not all were counted. Sections I-IV consider the tragic competition at the Dionysia, in which three competitors vied for the prize. For the questions (...) we consider, two likely cases are examined (when the votes are divided 4-3-3 and 5-3-2), then a random distribution covering all possible cases, and finally the situation when two competitors are favoured against a third (when the votes are divided 5-5-0, 5-4-1 and 4-4-2). Section I presents the proposal and situates it within the Athenian cultural context. Section II asks how many lots are typically drawn before a victory is obtained. Section III considers how other places are determined. Section IV introduces the question of 'fairness': does the person who receives the most votes actually win? Section V considers adjudication for comedies and at the Lenaia. Section VI considers dithyrambic competitions. (shrink)

A proof is given that there does not exist an event, that is not already in the past for some possible distant observer at the (our) moment that the latter is "now" for us. Such event is as "legally" past for that distant observer as is the moment five minutes ago on the sun for us (irrespective of the circumstance that the light of the sun cannot reach us in a period of five minutes). Only an extreme positivism: "that which (...) cannot yet be observed does not yet exist", can possibly withstand the conclusion concerned. Therefore, there is determinism, also in micro-physics. (shrink)

This paper evaluates several recent efforts to interpret the work of Nāgārjuna through the lens of modern symbolic logic. An attempt is made to uncover the premises that justify the use of symbolic logic for this purpose. This is accomplished through a discussion of (1) the historical origins of those premises in the Indian and Tibetan traditions, and (2) how such assumptions prejudice our understanding of Nāgā rjuna’s insistence that he has no “proposition” (pratijñā). Finally, the paper sets forth an (...) alternative interpretation that takes into account the literary dimensions of Nāgārjuna’s writing. (shrink)

Abstract‘Yellow Rain’, an alleged biological warfare agent thought to be utilized in parts of both South East Asia and Afghanistan, may be composed in part of the mycotoxins, trichothecenes. However, more recent analyses suggest that the ‘Rain’ was mainly honey bee excreta. The history of the controversy together with the biological effects, chemistry as well as the fungi producing these mycotoxins and agricultural commodities affected by trichothecenes are reviewed.

Lying in an area bounded by the Wabash, Ohio, and Mississippi rivers, the Southern Illinois country is rich in history, folklore, scenery, and natural resources. At about the latitude of southern Virginia, and extending from the flat prairie farmland of central Illinois to the rugged "Illinois Ozarks,” the area is the natural terminal boundary for hundreds of plant species reaching out to all points of the compass. It is also the oldest and most sparsely populated part of Illinois, a region (...) of small towns and independent people, typical of the vast heartland of the U.S.A. Surveying the area in words and pictures the authors sensitively and appreciatively portray the region’s special qualities. An uncommon portrayal of American life in a distinctive region, the book provides a memorable journey both in time and place. (shrink)

C W Evers, J C Walker; Knowledge, Partitioned Sets and Extensionality: a refutation of the forms of knowledge thesis, Journal of Philosophy of Education, Volume.

Aristotle's treatise De Interpretatione is one of his central works; it continues to be the focus of much attention and debate. C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system, basing this view upon a detailed chapter-by-chapter analysis.By treating the work systematically, rather than concentrating on certain selected passages, Whitaker is able to show that, contrary to traditional opinion, it forms (...) an organized and coherent whole. He argues that the De Interpretatione is intended to provide the underpinning for dialectic, the system of argument by question and answer set out in Aristotle's Topics; and he rejects the traditional view that the De Interpretatione concerns the assertion and is oriented towards the formal logic of the Prior Analytics. In doing so, he sheds valuable new light on some of Aristotle's most famous texts. (shrink)

Three famous sophists are referred to together in the Apology of Sokrates as still practising their enviably lucrative itinerant profession in 399 B.C. (not, by implication, in Athens): Gorgias of Leontinoi, Prodikos of Keos and Hippias of Elis. The last of these was the least well known to the Athenian demos, having practised mainly in Dorian cities. There is no extant reference to him in Old Comedy, but we can assume that he was sufficiently famous - especially for his fees (...) (possibly the highest charged by any sophist) - to justify his inclusion as the third of this 'triad'; cf. the triad Protagoras - Hippias - Prodikos in the Protagoras, considered further below. Gorgias was by now a grand old man of about ninety (with more than a decade of active life still ahead of him), the last survivor of the first generation of fee-taking educators, associated first and foremost in the popular mind with the suspect arts of political and forensic persuasion. Prodikos and Hippias were probably in their sixties. (shrink)