Mathematics Is Physics

In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within ..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics. This version of the essay contains an addendum responding to Slyvia Wenmackers' essay and comments that were made on the FQXi website.Comment: 15 pages, LaTeX. Second prize winner in 2015 FQXi Essay Contest (see http://fqxi.org/community/forum/topic/2364

Explanation and Quasi-Miracles in Narrative Understanding: The Case of Poetic Justice

This is the peer reviewed version of the following article: Craig Bourne, and Emily Caddick Bourne, ‘Explanation and Quasi‐miracles in Narrative Understanding: The Case of Poetic Justice’, Dialectica, Vol. 71 (4): 563-579, January 2018, which has been published in final form at https://doi.org/10.1111/1746-8361.12201. Under embargo until 29 January 2020. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.David Lewis introduced the idea of a quasi-miracle to overcome a problem in his initial account of counterfactuals. Here we put the notion of a quasi-miracle to a different and new use, showing that it offers a novel account of the phenomenon of poetic justice, where characters in a narrative get their due by happy accident (for example, when the murderer of King Mitys happens to be crushed by a falling statue of Mitys). The key to understanding poetic justice is to see what makes poetically just events remarkable coincidences. We argue that remarkable coincidence is to be understood in terms of a distinctive type of experience quasi-miracles offer. Cases of poetic justice offer a dual awareness of the accidental nature of the events and of a non-accidental process, involving intention, which it appears would explain them. We also extend this account to incorporate how we might experience magic tricks. An account of poetic justice as quasi-miraculous allows us to account for the experience of encounters with poetic justice, as involving the incongruity of seeing design in accident.Peer reviewedFinal Accepted Versio

ARAS: an automated radioactivity aliquoting system for dispensing solutions containing positron-emitting radioisotopes.

BackgroundAutomated protocols for measuring and dispensing solutions containing radioisotopes are essential not only for providing a safe environment for radiation workers but also to ensure accuracy of dispensed radioactivity and an efficient workflow. For this purpose, we have designed ARAS, an automated radioactivity aliquoting system for dispensing solutions containing positron-emitting radioisotopes with particular focus on fluorine-18 ((18)F).MethodsThe key to the system is the combination of a radiation detector measuring radioactivity concentration, in line with a peristaltic pump dispensing known volumes.ResultsThe combined system demonstrates volume variation to be within 5 % for dispensing volumes of 20 μL or greater. When considering volumes of 20 μL or greater, the delivered radioactivity is in agreement with the requested amount as measured independently with a dose calibrator to within 2 % on average.ConclusionsThe integration of the detector and pump in an in-line system leads to a flexible and compact approach that can accurately dispense solutions containing radioactivity concentrations ranging from the high values typical of [(18)F]fluoride directly produced from a cyclotron (~0.1-1 mCi μL(-1)) to the low values typical of batches of [(18)F]fluoride-labeled radiotracers intended for preclinical mouse scans (~1-10 μCi μL(-1))

Recovering a Basic Space from Issue Scales in<i>R</i>

Basicspace is an R package that conducts Aldrich-McKelvey and Blackbox scaling to recover estimates of the underlying latent dimensions of issue scale data. We illustrate several applications of the package to survey data commonly used in the social sciences. Monte Carlo tests demonstrate that the procedure can recover latent dimensions and reproduce the matrix of responses at moderate levels of error and missing data

Large Scale Cosmic Microwave Background Anisotropies and Dark Energy

In this note we investigate the effects of perturbations in a dark energy component with a constant equation of state on large scale cosmic microwave background anisotropies. The inclusion of perturbations increases the large scale power. We investigate more speculative dark energy models with w<-1 and find the opposite behaviour. Overall the inclusion of perturbations in the dark energy component increases the degeneracies. We generalise the parameterization of the dark energy fluctuations to allow for an arbitrary const ant sound speeds and show how constraints from cosmic microwave background experiments change if this is included. Combining cosmic microwave background with large scale structure, Hubble parameter and Supernovae observations we obtain w=-1.02+-0.16 (1 sigma) as a constraint on the equation of state, which is almost independent of the sound speed chosen. With the presented analysis we find no significant constraint on the constant speed of sound of the dark energy component.Comment: 7 pages, 8 figures, minor changes to match version accepted for publication in MNRA

Creep curve measurement to support wear and adhesion modelling, using a continuously variable creep twin disc machine

Predictive modelling of wear and adhesion at rolling-sliding contacts such as a railway rail and wheel depends on understanding the relationship between slip and shear force at the contact surface, i.e. the creep verses force curve. This paper describes a new approach to creep curve measurement using a twin disc machine running with a continuous programmed variation of creep, enabling an entire creep curve to be defined in a single experiment. The work focuses on very low levels of creep, ranging from zero to 1%, and shows clear correlation between the creep curve gradient and the full slip friction coefficient for dry and lubricated contacts. Comparison of data generated using the new approach with that generated using multiple tests each at a single creep level shows good agreement. Comparison is also made between the twin disc data and results for full size three dimensional rail-wheel contacts to examine how two and three dimensional contact adhesion data are related. The data generated has application in wear and rolling contact fatigue modelling, but the original motivation for the research was generation of creep curves to support prediction of low adhesion conditions at the rail-wheel interface based upon monitored running conditions prior to brake application. The range of contact conditions investigated includes those experienced in service and during driver training, with the correlation found between creep curve gradient (measurable prior to braking) and full slip friction coefficient (not measurable until brakes are applied) representing a key finding

Probing the neutrino mass hierarchy with CMB weak lensing

We forecast constraints on cosmological parameters with primary CMB anisotropy information and weak lensing reconstruction with a future post-Planck CMB experiment, the Cosmic Origins Explorer (COrE), using oscillation data on the neutrino mass splittings as prior information. Our MCMC simulations in flat models with a non-evolving equation-of-state of dark energy w give typical 68% upper bounds on the total neutrino mass of 0.136 eV and 0.098 eV for the inverted and normal hierarchies respectively, assuming the total summed mass is close to the minimum allowed by the oscillation data for the respective hierarchies (0.10 eV and 0.06 eV). Including information from future baryon acoustic oscillation measurements with the complete BOSS, Type 1a supernovae distance moduli from WFIRST, and a realistic prior on the Hubble constant, these upper limits shrink to 0.118 eV and 0.080 eV for the inverted and normal hierarchies, respectively. Addition of these distance priors also yields percent-level constraints on w. We find tension between our MCMC results and the results of a Fisher matrix analysis, most likely due to a strong geometric degeneracy between the total neutrino mass, the Hubble constant, and w in the unlensed CMB power spectra. If the minimal-mass, normal hierarchy were realised in nature, the inverted hierarchy should be disfavoured by the full data combination at typically greater than the 2-sigma level. For the minimal-mass inverted hierarchy, we compute the Bayes' factor between the two hierarchies for various combinations of our forecast datasets, and find that the future probes considered here should be able to provide `strong' evidence (odds ratio 12:1) for the inverted hierarchy. Finally, we consider potential biases of the other cosmological parameters from assuming the wrong hierarchy and find that all biases on the parameters are below their 1-sigma marginalised errors.Comment: 16 pages, 13 figures; minor changes to match the published version, references adde

Low-Friction, High-Stiffness Joint for Uniaxial Load Cell

A universal-joint assembly has been devised for transferring axial tension or compression to a load cell. To maximize measurement accuracy, the assembly is required to minimize any moments and non-axial forces on the load cell and to exhibit little or no hysteresis. The requirement to minimize hysteresis translates to a requirement to maximize axial stiffness (including minimizing backlash) and a simultaneous requirement to minimize friction. In practice, these are competing requirements, encountered repeatedly in efforts to design universal joints. Often, universal-joint designs represent compromises between these requirements. The improved universal-joint assembly contains two universal joints, each containing two adjustable pairs of angular-contact ball bearings. One might be tempted to ask why one could not use simple ball-and-socket joints rather than something as complex as universal joints containing adjustable pairs of angularcontact ball bearings. The answer is that ball-and-socket joints do not offer sufficient latitude to trade stiffness versus friction: the inevitable result of an attempt to make such a trade in a ball-and-socket joint is either too much backlash or too much friction. The universal joints are located at opposite ends of an axial subassembly that contains the load cell. The axial subassembly includes an axial shaft, an axial housing, and a fifth adjustable pair of angular-contact ball bearings that allows rotation of the axial housing relative to the shaft. The preload on each pair of angular-contact ball bearings can be adjusted to obtain the required stiffness with minimal friction, tailored for a specific application. The universal joint at each end affords two degrees of freedom, allowing only axial force to reach the load cell regardless of application of moments and non-axial forces. The rotational joint on the axial subassembly affords a fifth degree of freedom, preventing application of a torsion load to the load cell

Low-Impact Mating System for Docking Spacecraft

A document describes a low-impact mating system suitable for both docking (mating of two free-flying spacecraft) and berthing (in which a robot arm in one spacecraft positions an object for mating with either spacecraft). The low-impact mating system is fully androgynous: it mates with a copy of itself, i.e., all spacecraft and other objects to be mated are to be equipped with identical copies of the system. This aspect of the design helps to minimize the number of unique parts and to standardize and facilitate mating operations. The system includes a closed-loop feedback control subsystem that actively accommodates misalignments between mating spacecraft, thereby attenuating spacecraft dynamics and mitigating the need for precise advance positioning of the spacecraft. The operational characteristics of the mating system can be easily configured in software, during operation, to enable mating of spacecraft having various masses, center-of-gravity offsets, and closing velocities. The system design provides multi-fault tolerance for critical operations: for example, to ensure unmating at a critical time, a redundant unlatching mechanism and two independent pyrotechnic release subsystems are included

Activated lymphocyte recruitment into the tumor microenvironment following preoperative sipuleucel-T for localized prostate cancer.

BackgroundSipuleucel-T is a US Food and Drug Administration-approved immunotherapy for asymptomatic or minimally symptomatic metastatic castration-resistant prostate cancer (mCRPC). Its mechanism of action is not fully understood. This prospective trial evaluated the direct immune effects of systemically administered sipuleucel-T on prostatic cancer tissue in the preoperative setting.MethodsPatients with untreated localized prostate cancer were treated on an open-label Phase II study of sipuleucel-T prior to planned radical prostatectomy (RP). Immune infiltrates in RP specimens (posttreatment) and in paired pretreatment biopsies were evaluated by immunohistochemistry (IHC). Correlations between circulating immune response and IHC were assessed using Spearman rank order.ResultsOf the 42 enrolled patients, 37 were evaluable. Adverse events were primarily transient, mild-to-moderate and infusion related. Patients developed T cell proliferation and interferon-γ responses detectable in the blood following treatment. Furthermore, a greater-than-three-fold increase in infiltrating CD3(+), CD4(+) FOXP3(-), and CD8(+) T cells was observed in the RP tissues compared with the pretreatment biopsy (binomial proportions: all P &lt; .001). This level of T cell infiltration was observed at the tumor interface, and was not seen in a control group consisting of 12 concurrent patients who did not receive any neoadjuvant treatment prior to RP. The majority of infiltrating T cells were PD-1(+) and Ki-67(+), consistent with activated T cells. Importantly, the magnitude of the circulating immune response did not directly correlate with T cell infiltration within the prostate based upon Spearman's rank order correlation.ConclusionsThis study is the first to demonstrate a local immune effect from the administration of sipuleucel-T. Neoadjuvant sipuleucel-T elicits both a systemic antigen-specific T cell response and the recruitment of activated effector T cells into the prostate tumor microenvironment