Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Effects of allometry, productivity and lifestyle on rates and limits of body size evolution

Body size affects nearly all aspects of organismal biology, so it is important to understand the constraints and dynamics of body size evolution. Despite empirical work on the macroevolution and macroecology of minimum and maximum size, there is little general quantitative theory on rates and limits of body size evolution. We present a general theory that integrates individual productivity, the lifestyle component of the slow–fast life-history continuum, and the allometric scaling of generation time to predict a clade's evolutionary rate and asymptotic maximum body size, and the shape of macroevolutionary trajectories during diversifying phases of size evolution. We evaluate this theory using data on the evolution of clade maximum body sizes in mammals during the Cenozoic. As predicted, clade evolutionary rates and asymptotic maximum sizes are larger in more productive clades (e.g. baleen whales), which represent the fast end of the slow–fast lifestyle continuum, and smaller in less productive clades (e.g. primates). The allometric scaling exponent for generation time fundamentally alters the shape of evolutionary trajectories, so allometric effects should be accounted for in models of phenotypic evolution and interpretations of macroevolutionary body size patterns. This work highlights the intimate interplay between the macroecological and macroevolutionary dynamics underlying the generation and maintenance of morphological diversity.

Money laundering and the shadow economy in Kazakhstan

Purpose The purpose of this paper is to assess and highlight the approach taken towards the legal control of illicit money laundering taken in the Republic of Kazakhstan, in particular, the role played by an amnesty on the legalisation of illicit funds. This is particularly important as a basis for a wider discussion about the proper limits of the “criminalising” approaches commonly taken in anti-money laundering regulations. Design/methodology/approach The discussion and evaluation in the paper is based upon a conceptual analysis of the money laundering regime in Kazakhstan, in particular, the legal framework and policies of implementation adopted. Findings The paper demonstrates that the problems that are posed by the shadow economy in post-Soviet transition societies can make the blanket criminalisation of money laundering a self-defeating approach, unless accompanied by measures which allow for the achievement of “market-constituting” effects. Research limitations/implications The paper draws on experience and practice in one jurisdiction only (Kazakhstan); it also limits its focus to one particular example of a money laundering amnesty policy. Both of these limitations, therefore, suggest avenues for further comparative research. Originality/value The paper’s conclusions about the interactions between the shadow economies of transitional societies and the global anti-money laundering agenda have wider application in assessments of international law in this area.

New legal texts from the Hermeneumata Pseudodositheana

Several previously unnoticed texts concerning ancient lawcourts can be found in the Colloquia of the Hermeneumata Pseudodositheana, a set of bilingual dialogues composed for language learners during the Roman empire. The texts describe court cases, both criminal and civil; their writers probably taught in law schools between the second and fourth centuries ad. Editions, translations, and summary information about these texts are provided.

Shared authority: courts and legislatures in legal theory

This book advances a fresh philosophical account of the relationship between the legislature and courts, opposing the common conception of law, in which it is legislatures that primarily create the law, and courts that primarily apply it. This conception has eclectic affinities with legal positivism, and although it may have been a helpful intellectual tool in the past, it now increasingly generates more problems than it solves. For this reason, the author argues, legal philosophers are better off abandoning it. At the same time they are asked to dismantle the philosophical and doctrinal infrastructure that has been based on it and which has been hitherto largely unquestioned. In its place the book offers an alternative framework for understanding the role of courts and the legislature; a framework which is distinctly anti-positivist and which builds on Ronald Dworkin’s interpretive theory of law. But, contrary to Dworkin, it insists that legal duty is sensitive to the position one occupies in the project of governing; legal interpretation is not the solitary task of one super-judge, but a collaborative task structured by principles of institutional morality such as separation of powers which impose a moral duty on participants to respect each other's contributions. Moreover this collaborative task will often involve citizens taking an active role in their interaction with the law.

Working with legal pluralism: widowhood, property inheritance and poverty alleviation in urban Senegal

This article explores the role of women's inheritance and ownership of property in urban Senegal. It shows how being able to inherit and own property promotes the economic and emotional security of widows and their children in urban areas, and discusses the challenges posed by legal pluralism in working on poverty alleviation and social protection in the city.

Recovering lost lives: researching women in legal history

Drawing on the research I undertook into the life of Gwyneth Bebb, who in 1913 challenged the Law Society of England and Wales for their refusal to admit women to the solicitors’ profession, this article focuses on the range of sources one might use to explore the lives of women in law, about whom there might be a few public records but little else, and on the ways in which sources, even official ones, might be imaginatively used. It traces the research process from the case that inspired the research (Bebb v The Law Society [1914] 1 Ch 286) through to the creation of an entry in the Oxford Dictionary of National Biography and what this means for women’s history, emphasising the importance of asking the ‘woman question’ and seeking out the broader significance of a woman’s life in the context of her times.

Transreal limits and elementary functions

We extend all elementary functions from the real to the transreal domain so that they are defined on division by zero. Our method applies to a much wider class of functions so may be of general interest.

Half-remembered quotations from mostly forgotten speeches: the limits of Labour’s European policy discourse

This article uses discourse analysis to study the continuities in British foreign policy thinking within the Labour party from the 1960s to the present day. Using representative extracts from speeches by Hugh Gaitskell, Harold Wilson, Tony Blair and Gordon Brown, it identifies the ideational consis- tencies in the leaders’ attitudes to: Empire; federalism in the EEC/EU; and laying down conditions that have to be met before any constructive engagement with ‘Europe’ can be countenanced. We argue that these consistencies, spanning a 50-year period, exemplify a certain stagnation both within Labour’s European discourses and within British foreign policy thinking more widely. We develop the idea that Labour party thinking has been crucially framed by both small ‘c’ conser- vative and upper-case Conservative ideology, popularised by Winston Churchill in his ‘three circles’ model of British foreign policy.

Performing right: legal constraints and Beckett’s plays on BBC television

Drawing on BBC archival documentation, this article outlines how BBC television versions of Beckett’s plays were affected by copyright. Rights to record and broadcast original drama for the screen differ from those governing adaptations of existing theatre plays. Rights can be assigned for specific territories and periods of time, and are negotiated and traded via complex contractual agreements. Examining how Beckett’s agents and the BBC dealt with rights sheds new light on the history of his work on television.

No asylum for “Infiltrators”: the legal predicament of Eritrean and Sudanese nationals in Israel

This article explores the precarious status of Eritrean and Sudanese nationals in Israel. Having crossed the Israeli-Egyptian border without authorisation and not through an official border crossing, Israeli law defines such individuals as ‘infiltrators’, a charged term which dates back to border-crossings into Israel by Palestinian Fedayeen in the 1950s. Eritreans and Sudanese nationals constitute over 90 percent of ‘infiltrators’ in Israel. Their livelihood is curtailed through hostility, sanctions, and detention, while (at the time of writing) Israel refrains from deporting them to their respective countries of origin, recognising that such forced removal could expose them to risks to their lives and/or freedom. Israel was the 10th state to ratify the 1951 Refugee Convention, and has acceded to its 1967 Protocol which removed the 1951 Convention’s temporal and geographic restrictions, yet it has not incorporated these treaties into its domestic law not has it enacted primary legislation that sets eligibility criteria for ‘refugee’ status and regulates the treatment of asylum-seekers. Israeli law also fails to accord subsidiary protection status to persons that the state considers to be non-removable, whether or not they satisfy the definition of a ‘refugee’ under the 1951 Convention. Absent legal recognition of ‘refugee’, ‘asylum-seeker’, and ‘beneficiary of subsidiary protection’ statuses, Eritreans and Sudanese nationals are left in legal limbo for an indefinite period qua irregular non-removable persons. This article takes stock of their legal predicament.

Identifying the generic limits of the Cheilanthoid genus Doryopteris

Morphology-based delimitation of genera in the Cheilanthoid ferns has proved to be problematic and understanding of the phylogeny and relationships amongst Cheilanthoid ferns based on morphological characters has posed even further difficulties, owing perhaps in large part to adaptation by many taxa to xeric habitats, as well as convergent evolution. It is only now with the application of DNA sequence data that relationships of species and genera are becoming clear. Here, we present results of cpDNA sequence data from species that have been traditionally placed in the genus Doryopteris and, based on both these results, and morphological and distribution data, this study helps clarify the concept of the genus Doryopteris its position within the Cheilanthoid ferns and the status of Lytoneuron. As a result, three genera are redefined: Doryopteris, Lytoneuron and Ormopteris.