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.

The opening of Plutarch's Life of Themistokles

Plutarch begins the biography by selecting incidents and an epigram that anticipate the basic themes of Themistocles' life--his greatness, sometimes ambiguous, and his benefactions to all of Greece.

Feeding rumen-inert fats differing in their degree of saturation decreases intake and increases plasma concentrations of gut peptides in lactating dairy cows

Our objective was to determine the effect of feeding rumen-inert fats differing in their degree of saturation on dry matter intake (DMI), milk production, and plasma concentrations of insulin, glucagon-like peptide 1 (7-36) amide (GLP-1), glucose-dependent insulinotropic polypeptide (GIP), and cholecystokinin (CCK) in lactating dairy cows. Four midlactation, primiparous Holstein cows were used in a 4 x 4 Latin square experiment with 2-wk periods. Cows were fed a control mixed ration ad libitum, and treatments were the dietary addition (3.5% of ration dry matter) of 3 rumen-inert fats as sources of mostly saturated fatty acids (SFA), monounsaturated fatty acids (MUFA), or polyunsaturated fatty acids (PUFA). Daily DMI, milk yield, and composition were measured on the last 4 d of each period. Jugular vein blood was collected every 30 min over a 7-h period on d 12 and 14 of each period for analysis of plasma concentrations of hormones, glucose, and nonesterified fatty acids. Feeding fat decreased DMI, and the decrease tended to be greater for MUFA and PUFA compared with SFA. Plasma concentration of GLP-1 increased when fat was fed and was greater for MUFA and PUFA. Feeding fat increased plasma glucose-dependent insulinotropic polypeptide and CCK concentrations and decreased plasma insulin concentration. Plasma CCK concentration was greater for MUFA and PUFA than for SFA and was greater for MUFA than PUFA. Decreases in DMI in cows fed fat were associated with increased plasma concentrations of GLP-1 and CCK and a decreased insulin concentration. The role of these peptides in regulating DMI in cattle fed fat requires further investigation.

The effects of temperature and light integral on early vegetative growth and chlorophyll fluorescence of four contrasting genotypes of cacao (Theobroma cacao)

The effect of temperature on early vegetative growth, leaf chlorophyll fluorescence and chlorophyll content was examined on four genotypes of cacao (Amelonado, AMAZ 15–15, SCA 6 and SPEC 54/1). A controlled environment glasshouse was used to simulate the temperature conditions of three cacao-growing regions (Bahia, Brazil; Tafo, Ghana and Lower Perak, Malaysia) over the course of a year. Base temperatures calculated from increments in main stem growth varied from 18.6°C for AMAZ 15/15 to 20.8°C for SPEC 54/1. Temporal variation in Fv/Fm observed for two of the clones (SCA 6 and SPEC 54/1) in two of the compartments were correlated with temperature differences over time. Significant differences were also recorded between genotypes in leaf chlorophyll content. It was shown that variation over time in leaf chlorophyll content could be quantified accurately as a function of temperature and light integral. The results imply that genetic variability exists in cacao in response to temperature stress.

13C-2H correlation NMR spectroscopy studies of the in vivo transformations of natural products from Artemisia annua

13C-2H correlation NMR spectroscopy (13C-2H COSY) permits the identification of 13C and 2H nuclei which are connected to one another by a single chemical bond via the sizeable 1JCD coupling constant. The practical development of this technique is described using a 13C-2H COSY pulse sequence which is derived from the classical 13C-1H correlation experiment. An example is given of the application of 13C-2H COSY to the study of the biogenesis of natural products from the anti-malarial plant Artemisia annua, using a doubly-labelled precursor molecule. Although the biogenesis of artemisinin, the anti-malarial principle from this species, has been extensively studied over the past twenty years there is still no consensus as to the true biosynthetic route to this important natural product – indeed, some published experimental results are directly contradictory. One possible reason for this confusion may be the ease with which some of the metabolites from A. annua undergo spontaneous autoxidation, as exemplified by our recent in vitro studies of the spontaneous autoxidation of dihydroartemisinic acid, and the application of 13C-2H COSY to this biosynthetic problem has been important in helping to mitigate against such processes. In this in vivo application of 13C-2H COSY, [15-13C2H3]-dihydroartemisinic acid (the doubly-labelled analogue of the natural product from this species which was obtained through synthesis) was fed to A. annua plants and was shown to be converted into several natural products which have been described previously, including artemisinin. It is proposed that all of these transformations occurred via a tertiary hydroperoxide intermediate, which is derived from dihyroartemisinic acid. This intermediate was observed directly in this feeding experiment by the 13C-2H COSY technique; its observation by more traditional procedures (e.g., chromatographic separation, followed by spectroscopic analysis of the purified product) would have been difficult owing to the instability of the hydroperoxide group (as had been established previously by our in vitro studies of the spontaneous autoxidation of dihydroartemisinic acid). This same hydroperoxide has been reported as the initial product of the spontaneous autoxidation of dihydroartemisinic acid in our previous in vitro studies. Its observation in this feeding experiment by the 13C-2H COSY technique, a procedure which requires the minimum of sample manipulation in order to achieve a reliable identification of metabolites (based on both 13C and 2H chemical shifts at the 15-position), provides the best possible evidence for its status as a genuine biosynthetic intermediate, rather than merely as an artifact of the experimental procedure.

A novel trinuclear nickel(II) complex of an unsymmetrical tetradentate ligand involving bridging oxime and acetylacetone functions

A novel trinuclear nickel(II) complex, [Ni-3(L)(2)(H2O)(2)](ClO4)(2), where L is a bridging unsymmetrical tetradentate ligand, involving o-phenylenediamine, diacetyl monoxime and acetylacetone (H2L = 4-[2-(3-hydroxy-1-methyl-but-2-enylideneamino)-phenylimino]-pentan-2- one oxime) has been synthesized and characterized structurally. In the complex, an octahedral Ni( II) centre is held in the middle by two square planar units with the aid of oxime and ketonic bridges. (c) 2007 Elsevier B. V. All rights reserved.

Prevalence of disorders of the autism spectrum in a population cohort of children in South Thames: the special needs and autism project (SNAP)

Background Recent reports have suggested that the prevalence of autism and related spectrum disorders (ASDs) is substantially higher than previously recognised. We sought to quantify prevalence of ASDs in children in South Thames, UK. Methods Within a total population cohort of 56946 children aged 9-10 years, we screened all those with a current clinical diagnosis of ASD (n=255) or those judged to be at risk for being an undetected case (n=1515). A stratified subsample (n=255) received a comprehensive diagnostic assessment, including standardised clinical observation, and parent interview assessments of autistic symptoms, language, and intelligence quotient (IQ). Clinical consensus diagnoses of childhood autism and other ASDs were derived. We used a sample weighting procedure to estimate prevalence. Findings The prevalence of childhood autism was 38.9 per 10000 (95% CI 29.9-47.8) and that of other ASDs was 77.2 per 10000 (52.1-102.3), making the total prevalence of all AS Ds 116.1 per 10000 (90.4-141.8). A narrower definition of childhood autism, which combined clinical consensus with instrument criteria for past and current presentation, provided a prevalence of 24.8 per 10 000 (17.6-32.0). The rate of previous local identification was lowest for children of less educated parents. Interpretation Prevalence of autism and related ASDs is substantially greater than previously recognised. Whether the increase is due to better ascertainment, broadening diagnostic criteria, or increased incidence is unclear. Services in health, education, and social care will need to recognise the needs of children with some form of ASD, who constitute 1% of the child population.

Mixed initial-boundary value problem in particle modeling of microelectronic devices

The Boltzmann equation in presence of boundary and initial conditions, which describes the general case of carrier transport in microelectronic devices is analysed in terms of Monte Carlo theory. The classical Ensemble Monte Carlo algorithm which has been devised by merely phenomenological considerations of the initial and boundary carrier contributions is now derived in a formal way. The approach allows to suggest a set of event-biasing algorithms for statistical enhancement as an alternative of the population control technique, which is virtually the only algorithm currently used in particle simulators. The scheme of the self-consistent coupling of Boltzmann and Poisson equation is considered for the case of weighted particles. It is shown that particles survive the successive iteration steps.