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.

The effects of bilingualism on the white matter structure of the brain

Recent studies suggest that learning and using a second language (L2) can affect brain structure, including the structure of white matter (WM) tracts. This observation comes from research looking at early and older bilingual individuals who have been using both their first and second languages on an everyday basis for many years. This study investigated whether young, highly immersed late bilinguals would also show structural effects in the WM that can be attributed to everyday L2 use, irrespective of critical periods or the length of L2 learning. Our Tract-Based Spatial Statistics analysis revealed higher fractional anisotropy values for bilinguals vs. monolinguals in several WM tracts that have been linked to language processing and in a pattern closely resembling the results reported for older and early bilinguals. We propose that learning and actively using an L2 after childhood can have rapid dynamic effects on WM structure, which in turn may assist in preserving WM integrity in older age.

Does energy efficiency matter to home-buyers? An investigation of EPC ratings and transaction prices in England

This paper investigates whether energy performance ratings, as measured by mandatory Energy Performance Certificates (EPCs), are reflected in the sale prices of residential properties. This is the first large-scale empirical study of this topic in England involving 333,095 dwellings sold at least twice in the period from 1995 to 2012. Applying hedonic regression and an augmented repeat sales regression, we find a positive relationship between the energy efficiency rating of a dwelling and the transaction price per square metre. The price effects of superior energy performance tend to be higher for terraced dwellings and flats compared to detached and semi-detached dwellings. The evidence is less clear-cut for rates of house price growth but remains supportive of a positive association. Overall, the results of this study suggest that energy efficiency labels have a measurable and significant impact on house prices in England

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.

Do consumers want public or private bodies to monitor animal friendly production and marketing schemes? And does trust matter?

Producing according to enhanced farm animal welfare (FAW) standards increases costs along the livestock value chain, especially for monitoring certified animal friendly products. In the choice between public or private bodies for carrying out and monitoring certification, consumer preferences and trust play a role. We explore this issue by applying logit analysis involving socio-economic and psychometric variables to survey data from Italy. Results identify marked consumer preferences for public bodies and trust in stakeholders a key determinant.

Why your customers’ social identities matter

The article looks at the role of consumers' social identities in their purchasing decisions, and hence in the creation of effective marketing strategies. It says that people generally belong to multiple social groups, any one of which may have the most salience for them in a given situation. It reports on social psychology research on how a person's connection with a particular social identity can be triggered and discusses the idea in the context of marketing products including the Toyota Prius hybrid-electric automobile, Nescafé instant coffee, and the Jeep all-terrain vehicle. INSET: Lessons of the Stanford Prison Experiment.

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.

Evaluation of optical techniques for characterising soil organic matter quality in agricultural soils

Soil organic matter (SOM) is one of the main global carbon pools. It is a measure of soil quality as its presence increases carbon sequestration and improves physical and chemical soil properties. The determination and characterisation of humic substances gives essential information of the maturity and stresses of soils as well as of their health. However, the determination of the exact nature and molecular structure of these substances has been proven difficult. Several complex techniques exist to characterise SOM and mineralisation and humification processes. One of the more widely accepted for its accuracy is nuclear magnetic resonance (NMR) spectroscopy. Despite its efficacy, NMR needs significant economic resources, equipment, material and time. Proxy measures like the fluorescence index (FI), cold and hot-water extractable carbon (CWC and HWC) and SUVA-254 have the potential to characterise SOM and, in combination, provide qualitative and quantitative data of SOM and its processes. Spanish and British agricultural cambisols were used to measure SOM quality and determine whether similarities were found between optical techniques and 1H NMR results in these two regions with contrasting climatic conditions. High correlations (p < 0.001) were found between the specific aromatic fraction measured with 1H NMR and SUVA-254 (Rs = 0.95) and HWC (Rs = 0.90), which could be described using a linear model. A high correlation between FI and the aromatics fraction measured with 1H NMR (Rs = −0.976) was also observed. In view of our results, optical measures have a potential, in combination, to predict the aromatic fraction of SOM without the need of expensive and time consuming techniques.

Modeling the photo-oxidation of dissolved organic matter by ultraviolet radiation in freshwater lakes: implications for mercury bioavailability

Uncertainties in projected ultraviolet (UV) radiation may lead to future increases in UV irradiation of freshwater lakes. Because dissolved organic carbon (DOC) is the main binding phase for mercury (Hg) in freshwater lakes, an increase in DOC photo-oxidation may affect Hg speciation and bioavailability. We quantified the effect of DOC concentration on the rate of abiotic DOC photo-oxidation for five lakes (DOC = 3.27–12.3 mg L−1) in Kejimkujik National Park, Canada. Samples were irradiated with UV-A or UV-B radiation over a 72-h period. UV-B radiation was found to be 2.36 times more efficient at photo-oxidizing DOC than UV-A, with energy-normalized rates of dissolved inorganic carbon (DIC) production ranging from 3.8 × 10−5 to 1.1 × 10−4 mg L−1 J−1 for UV-A, and from 6.0 × 10−5 to 3.1 × 10−4 mg L−1 J−1 for UV-B. Energy normalized rates of DIC production were positively correlated with DOC concentrations. Diffuse integrated attenuation coefficients were quantified in situ (UV-A Kd = 0.056–0.180 J cm−1; UV-B Kd = 0.015–0.165 J cm−1) and a quantitative depth-integrated model for yearly DIC photo-production in each lake was developed. The model predicts that, UV-A produces between 3.2 and 100 times more DIC (1521–2851 mg m−2 year−1) than UV-B radiation (29.17–746.7 mg m−2 year−1). Future increases in UV radiation may increase DIC production and increase Hg bioavailability in low DOC lakes to a greater extent than in high DOC lakes.