Wittgenstein’s Remarks on Mathematics, Turing and Computability

Typically, Wittgenstein is assumed to have been apathetic to the developments in computability theory through the 1930s. Wittgenstein’s disparaging remarks about Gödel’s incompleteness theorems, and mathematical logic in general, are well documented. It seems safe to assume the same would apply for Turing’s work. The chief aim of this thesis is to debunk this picture. I will show that: a) Wittgenstein read, understood and engaged with Turing’s proofs regarding the Entscheidungsproblem. b) Wittgenstein’s remarks on this topic are highly perceptive and have pedagogical value, shedding light on Turing’s work. c) Wittgenstein was highly supportive of Turing’s work as it manifested Wittgenstein’s prevailing approach to mathematics. d) Adopting a Wittgensteinian approach to Turing’s proofs enables us to answer several live problems in the modern literature on computability. Wittgenstein was notably resistant to Cantor’s diagonal proof regarding uncountability, being a finitist and extreme anti-platonist. He was interested, however, in the diagonal method. He made several remarks attempting to adapt the method to work in purely intensional, rule-governed terms. These are unclear and unsuccessful. Turing’s famous diagonal application realised this pursuit. Turing’s application draws conclusions from the diagonal procedure without having to posit infinite extensions. Wittgenstein saw this, and made a series of interesting remarks to that effect. He subsequently gave his own (successful) intensional diagonal proof, abstracting from Turing’s. He endorsed Turing’s proof and reframed it in terms of games to highlight certain features of rules and rule-following. I then turn to the Church-Turing thesis (CTT). I show how Wittgenstein endorsed the CTT, particularly Turing’s rendition of it. Finally, I show how adopting a family-resemblance approach to computability can answer several questions regarding the epistemological status of the CTT today

Toward an understanding of players' perceptions of talent development environments in UK female football

This study explored UK female football players' perceptions of their talent development environments using the Talent Development Environment Questionnaire. Participants were 137 UK-based female football players (M age = 16.06, SD = 1.90) from Football Association Girls' Centres of Excellence and Football Association Women's Super League Development Squads. Players had most positive perceptions of long-term development focus and support network, whereas the least positive perceptions were of communication and understanding the athlete. Sport psychologists could offer significant support in (a) planning for football-specific development and career progression, (b) communication with key social agents, and (c) holistic player development and well-being

Spectrophotometric analysis of ternary uranyl systems to replace tri-N-butyl phosphate (TBP) in used fuel reprocessing

In this report, the interaction of monoamide/diamide and monoamide/diglycolamide mixtures with UO2+2 are investigated in pH = 1 methanolic nitric acid media. These monoamides include N,N-dimethylacetamide (DMAA), N,N-diethylacetamide (DEAA), N,N-dibutylacetamide (DBAA) and N,N-dibutylbutanamide (DBBA). N,N,N′N′-tetraethylmalonamide (TEMA) and N,N,N′,N′-tetraethyldiglycolamide (TEDGA), which were chosen as model diamides and diglycolamides, respectively. Complex stability constants for each ligand were modelled using the Stability Quotients Using Absorbance Data program using UV–visible data. Complex stoichiometry of ligand mixtures was determined using Job plots and UV–Vis spectrometry. Monoamides were confirmed to produce only disolvate complexes with UO2+2 in solution. The log10(K) values for monoamides were found to be independent of amine-side chain length, but were slightly dependent on the carbonyl-side chain length. TEDGA was found to produce multiple uranyl complexes in solution. Job plot data indicated that the uranyl cation strongly prefers to bond either only with the monoamide or diamide in ternary monoamide–diamide–UO2 systems. Monoamide–diglycolamide–UO2 systems were more complicated, with Job plot data indicating the potential for multiple ternary species being present is dependent on the monoamide structure

Impairments in sensory-motor gating and information processing in a mouse model of Ehmt1 haploinsufficiency

Regulators of chromatin dynamics and transcription are increasingly implicated in the aetiology of neurodevelopmental disorders (NDDs). Haploinsufficiency of EHMT1, encoding a histone methyl-transferase, is associated with several NDDs, including Kleefstra syndrome, developmental delay and autism spectrum disorder. Using a mouse model of Ehmt1 haploinsufficiency (Ehmt1D6Cre/+), we examined a number of brain and behavioural endophenotypes of relevance to NDDs. Specifically, we show that Ehmt1D6Cre/+ mice have deficits in information processing, evidenced by abnormal sensory-motor gating, a complete absence of object recognition memory and a reduced magnitude of auditory evoked potentials in both paired-pulse inhibition and mismatch negativity (MMN). The electrophysiological experiments show that differences in magnitude response to auditory stimulus were associated with marked reductions in total and evoked beta- and gamma-band oscillatory activity, as well as significant reductions in phase synchronisation. The pattern of electrophysiological deficits in Ehmt1D6Cre/+ matches those seen in control mice following administration of the selective NMDA-R antagonist, ketamine. This, coupled with reduction of Grin1 mRNA expression in Ehmt1D6Cre/+ hippocampus, suggests that Ehmt1 haploinsufficiency may lead to disruption in NMDA-R. Taken together, these data indicate that reduced Ehmt1 dosage during forebrain development leads to abnormal circuitry formation, which in turn results in profound information processing deficits. Such information processing deficits are likely paramount to our understanding of the cognitive and neurological dysfunctions shared across the NDDs associated with EHMT1 haploinsufficiency

A systematic review of the intrapersonal correlates of motivational climate perceptions in sport and physical activity

Objectives: The purpose of this study was to systematically review and appraise the achievement goal literature (1990-2014) with a view to identifying the intra-individual correlates of motivational climate perceptions, and to identify research gaps and avenues in need for further development. Design: Systematic review. Method: Four databases were searched, leading to 104 published studies being sampled (121 independent samples) that met inclusion criteria. Correlates were grouped into 17 categories and qualitative analysis focussed on identifying the associations predicted by achievement goal theory. Effect sizes were calculated using the Hunter-Schmidt method for correcting sampling error. Results: A total population size of 34,156 (χ=316.3, σ=268.1) was sampled in the analysis, with the published mean ages ranging from 10.0 to 38.2 years (χ=16.5 years, σ=4.7). Perceptions of a task or mastery climate were consistently associated with a range of adaptive motivational outcomes including perceived competence, self-esteem, objective performance, intrinsic forms of motivational regulation, affective states, practice and competitive strategies and moral attitudes, and the experience of flow. Perceptions of an ego or performance climate were positively associated with extrinsic regulation and amotivation, negative affect, maladaptive strategy use, antisocial moral attitudes and perfectionism, but negatively associated to positive affect and feelings of autonomy and relatedness. Conclusions: After reviewing the sum total of research in this topic area, the authors appraise the options for future research to make meaningful progress in developing understanding of the social determination of motivation in sport and physical activity settings

Lanthanide speciation in potential SANEX and GANEX actinide/ 2 lanthanide separations using Tetra-N-Donor extractants

Lanthanide(III) complexes with N-donor ex-tractants, which exhibit the potential for the separation of minor actinides from lanthanides in the management of spent nuclear fuel, have been directly synthesized and characterized in both solution and solid states. Crystal structures of the Pr3+, Eu3+, Tb3+, and Yb3+ complexes of 6,6′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin3-yl)-1,10-phenanthroline(CyMe4-BTPhen) and the Pr3+, Eu3+, and Tb3+ complexes of 2,9-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotria-zin-3-yl)-2,2′-bypyridine (CyMe4-BTBP) were obtained. The majority of these structures displayed coordination of two ofthe tetra-N-donor ligands to each Ln3+ ion, even when in some cases the complexations were performed with equimolar amounts of lanthanide and N-donor ligand. The structures showed that generally the lighter lanthanides had their coordination spheres completed by a bidentate nitrate ion, giving a 2+ charged complex cation, whereas the structures of the heavier lanthanides displayed tricationic complex species with a single water molecule completing their coordination environments. Electronic absorption spectroscopic titrations showed formation of the 1:2 Ln3+/LN4‑donor species (Ln = Pr3+, Eu3+, Tb3+) in methanol when the N-donor ligand was in excess. When the Ln3+ ion was in excess, evidence for formation of a 1:1 Ln3+/LN4‑donor complex species was observed. Luminescent lifetime studies of mixtures of Eu3+ with excess CyMe4-BTBP and CyMe4-BTPhen in methanol indicated that the nitrate-coordinated species is dominant in solution. X-ray absorption spectra of Eu3+ and Tb3+ species, formed by extraction from an acidic aqueous phase into an organic solution consisting of excess N-donor extractant in pure cyclohexanone or 30% tri-n-butyl phosphate (TBP) in cyclohexanone, were obtained. The presence of TBP in the organic phase did not alter lanthanide speciation. Extended X-ray absorption fine structure data from these spectra were fitted using chemical models established by crystallography and solution spectroscopy and showed the dominant lanthanide species in the bulk organic phase was a 1:2 Ln3+/LN‑donor species

Diffusion NMR characterization of catalytic silica supports:a tortuous path

Mesoporous silicas have found widespread application within the field of heterogeneous catalysis. Acid functionalization of such materials, through one-pot or postsynthetic grafting of sulfonic acid groups, imparts activity for fatty acid esterification, with the studious choice of pore geometry facilitating significant rate enhancements. Diffusion NMR has been utilized for the first time to characterize the structure of mesoporous silicas through the transport behavior of systematically related carboxylic acids confined within their mesopore networks. A reduced diffusion coefficient is obtained for species constrained within the 3-dimensional interconnected pores of KIT-6 relative to the 2-dimensional noninterconnected pore channels of SBA-15. The effective tortuosity of both porous silicas increases with the acid chain length, with the diffusion behavior of long-chain acids dominated by the alkyl chain and silica architecture. Carboxylic acid diffusion within these two pore networks is unlikely to be rate-limiting in catalytic esterification over sulfonic acid silica analogues. Physicochemical insights from diffusion NMR will aid the future design of optimal silica architectures for catalytic applications

Separation of the minor actinides americium(III) and curium(III) by hydrophobic and hydrophilic BTPhen ligands: exploiting differences in their rates of extraction and effective separations at equilibrium

The complexation and extraction of the adjacent minor actinides Am(III) and Cm(III) by both hydrophobic and hydrophilic pre-organized 2,9-bis(1,2,4-triazin-3-yl)-1,10-phenanthroline (BTPhen) ligands has been studied in detail. It has been shown that Am(III) is extracted more rapidly than Cm(III) by the hydrophobic CyMe4-BTPhen ligand into different organic diluents under non-equilibrium extraction conditions, leading to separation factors for Am over Cm (SFAm/Cm) as high as 7.9. Furthermore, the separation of Am(III) from Cm(III) can be tuned through careful choice of the extraction conditions (organic diluent, contact time, mixing speed, ligand concentration). This ‘kinetic’ effect is attributed to the higher presumed kinetic lability of the Am(III) aqua complex towards ligand substitution. A dependence of the Am(III)/Cm(III) selectivity on the structure of the alkyl groups attached to the triazine rings is also observed, and BTPhens bearing linear alkyl groups are less able to separate Am(III) from Cm(III) than CyMe4-BTPhen. Under equilibrium extraction conditions, hydrophilic tetrasulfonated BTPhen ligands complex selectively Am(III) over Cm(III) and prevent the extraction of Am(III) from nitric acid by the hydrophobic O-donor ligand N,N,N’,N’-tetraoctyldiglycolamide (TODGA), giving separation factors for Cm(III) over Am(III) (SFCm/Am) of up to 4.6. These results further underline the utility of the BTPhen ligands for the extremely challenging separation of the chemically similar minor actinides Am(III) and Cm(III) in future processes to close the nuclear fuel cycle

New horizons: the management of hypertension in people with dementia

The optimal management of hypertension in people with dementia is uncertain. This review explores if people with dementia experience greater adverse effects from antihypertensive medications, if cognitive function is protected or worsened by controlling blood pressure (BP) and if there are subgroups of people with dementia for whom antihypertensive therapy is more likely to be harmful. Robust evidence is scant, trials of antihypertensive medications have generally excluded those with dementia. Observational data show changes in risk association over the life course, with high BP being a risk factor for cognitive decline in mid-life, while low BP is predictive in later life. It is therefore possible that excessive BP lowering in older people with dementia might harm cognition. From the existing literature, there is no direct evidence of benefit or harm from treating hypertension in people with dementia. So what practical steps can the clinician take? Assess capacity, establish patient preferences when making treatment decisions, use ambulatory monitoring to thoroughly assess BP, individualise and consider deprescribing where side effects (e.g. hypotension) outweigh the benefits. Future research might include pragmatic randomised trials of targeted deprescribing, which include patient-centred outcome measures to help support decision-making and studies to address mechanistic uncertainties