Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Evolution in software systems: foundations of the SPE classification scheme

The SPE taxonomy of evolving software systems, first proposed by Lehman in 1980, is re-examined in this work. The primary concepts of software evolution are related to generic theories of evolution, particularly Dawkins' concept of a replicator, to the hermeneutic tradition in philosophy and to Kuhn's concept of paradigm. These concepts provide the foundations that are needed for understanding the phenomenon of software evolution and for refining the definitions of the SPE categories. In particular, this work argues that a software system should be defined as of type P if its controlling stakeholders have made a strategic decision that the system must comply with a single paradigm in its representation of domain knowledge. The proposed refinement of SPE is expected to provide a more productive basis for developing testable hypotheses and models about possible differences in the evolution of E- and P-type systems than is provided by the original scheme. Copyright (C) 2005 John Wiley & Sons, Ltd.

The first international workshop on the role and impact of mathematics in medicine: a collective account

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for inter- disciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtaining

Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Cronaca, narrativa, and the unstable foundations of the Institution of Neorealism

The author contends that many of the conventions of Italian film studies derive from the conflicts and the critical vocabulary that shaped the Italian reception of neorealism in the first decade after the Second World War. Those conflicts, and that critical vocabulary, which lie at the foundation of what has been called the ‘institution of neorealism,’ established an irreconcilable binary: Cronaca and Narrativa. For the neorealists and their critics, Cronaca stood for the effort to record data faithfully, while Narrativa represented the effort to employ the shaping force of human invention in the representation of information. This essay’s first section analyzes the earliest reviews of Rossellini’s Roma città aperta alongside the contemporaneous literary debates over Cronaca and Narrativa. The second section reconsiders the reception of Pratolini’s Metello and Visconti’s Senso, which similarly centered upon the conflict between Cronaca and Narrativa. The third section proposes that the concepts which have often been employed to unify neorealism are destabilized by the Cronaca/Narrativa binary. In search of a solution to neorealism’s conceptual instability, this essay proposes more critical and purposeful appropriations of the movement’s problematic genealogy.

The foundations of the rule of law

Formal conceptions of the rule of law are popular among contemporary legal philosophers. Nonetheless, the coherence of accounts of the rule of law committed to these conceptions is sometimes fractured by elements harkening back to substantive conceptions of the rule of law. I suggest that this may be because at its origins the ideal of the rule of law was substantive through and through. I also argue that those origins are older than is generally supposed. Most authors tend to trace the ideas of the rule of law and natural law back to classical Greece, but I show that they are already recognisable and intertwined as far back as Homer. Because the founding moment of the tradition of western intellectual reflection on the rule of law placed concerns about substantive justice at the centre of the rule of law ideal, it may be hard for this ideal to entirely shrug off its substantive content. It may be undesirable, too, given the rhetorical power of appeals to the rule of law. The rule of law means something quite radical in Homer; this meaning may provide a source of normative inspiration for contemporary reflections about the rule of law.

The three faces of bounded reliability: Alfred Chandler and the micro-foundations of management theory

Alfred Chandler, the celebrated business historian, provided detailed descriptions of the reasons for failed human commitments and the managerial tools needed to prevent/remediate such failings in the context of large business firms. Chandler's historical narrative identifies three distinct “faces” of bounded reliability—opportunism, benevolent preference reversal, and identity-based discordance—as the main drivers of commitment failure. Adopting bounded reliability (BRel) as a micro-foundation in management studies will raise the quality and relevance of scholarly recommendations to improve managerial decision making and action, because analysis of BRel challenges closely mirrors the real-world problems facing practicing managers.

Transition of pupils from Key Stage 2 to 3 deemed gifted and talented in mathematics: an initial study

In this article Geoff Tennant and Dave Harries report on the early stages of a research project looking to examine the transition from Key Stage (KS) 2 to 3 of children deemed Gifted and Talented (G&T) in mathematics. An examination of relevant literature points towards variation in definition of key terms and underlying rationale for activities. Preliminary fieldwork points towards a lack of meaningful communication between schools, with primary school teachers in particular left to themselves to decide how to work with children deemed G&T. Some pointers for action are given, along with ideas for future research and a request for colleagues interested in working with us to get in touch.