Standing in a Garden of Forking Paths

According to the Path Principle, it is permissible to expand your set of beliefs iff (and because) the evidence you possess provides adequate support for such beliefs. If there is no path from here to there, you cannot add a belief to your belief set. If some thinker with the same type of evidential support has a path that they can take, so do you. The paths exist because of the evidence you possess and the support it provides. Evidential support grounds propositional justification. The principle is mistaken. There are permissible steps you may take that others may not even if you have the very same evidence. There are permissible steps that you cannot take that others can even if your beliefs receive the same type of evidential support. Because we have to assume almost nothing about the nature of evidential support to establish these results, we should reject evidentialism

An overview of adakite, tonalite-trondhjemite-granodiorite (TTG), and sanukitoid; relationships and some implications for crustal evolution.

Abstract Examination of an extensive adakite geochemical database identifies two distinct compositional groups. One consists of high-SiO 2 adakites (HSA) which is considered to represent subducted basaltic slab-melts that have reacted with peridotite during ascent through mantle wedge. The second group consists of low-SiO 2 adakites (LSA) which we interpret to have formed by melting of a peridotitic mantle wedge whose composition has been modified by reaction with felsic slab-melts. The chemical composition of less differentiated (primitive) Archaean tonalite-trondhjemite-granodiorite (TTG) magmas evolved from 4.0 to 2.5 Ga. Mg# (molecular Mg/(Mg+Fe 2+ ), Ni, and Cr contents increased over this period of time and we interpret these changes in terms of changes in the degree to which the TTG magmas interacted with mantle peridotite. Over the same period, concentrations of (CaO+Na 2 O) and Sr also increased, as the amount of plagioclase, residual from basalt melting, decreased in response to increased pressures at the site of slab-melting. In the Early Archaean, it appears that these interactions were very rare or absent thus leading to the conclusion that subduction was typically flat and lacked the development of a mantle wedge. In contrast, the relatively lower heat production by~2.5 Ga meant that slab-melting occurred at greater depth, where plagioclase was no longer stable, and where the development of a thick mantle wedge ensured interaction between the slab-melts and mantle peridotite. Close compositional similarities between HSA and Late Archaean TTG (Tb~3.0 Ga) strongly suggest a petrogenetic analogy. However, an analogy between the older Archaean TTG and HSA is not complete because evidence for mantle wedge interaction is missing in most Early Archaean TTGs. Late Archaean sanukitoids and the compositionally similar Closepet-type granites have compositions significantly different from TTG of all ages. However, they show some affinity with LSA which could be considered as their possible analogue. These magmas are all thought to result from melting of a mantle peridotite whose composition has been modified by reaction with slab-melts. We propose that all these magmas are directly linked to slab-melting. Archaean TTG and HSA represent slab-melts that have interacted with peridotite to varying extent, whereas sanukitoids, Closepet-type granites, and LSA correspond to melts of peridotite previously metasomatised by slab-melt. The changes observed from Early Archaean TTG to Late Archaean TTG and to sanukitoids reflect change in both the nature and efficiency of interaction between slab-melt and mantle wedge peridotite. Comparisons between all of these rocks suggest that ancient styles of subduction that have operated since at least~3.3 Ga persist in a limited way today. The secular changes in the degree and style of these interactions is a direct consequence of the cooling of Earth that modified the thermal and dynamic parameters at the subducted slab-mantle wedge interface.

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint

Genetic contributions to generalized arousal of brain and behavior

We have identified a generalized arousal component in the behavior of mice. Analyzed by mathematical/statistical approaches across experiments, investigators, and mouse populations, it accounts for about 1/3 of the variance in arousal-related measures. Knockout of the gene coding for the classical estrogen receptor (ER-α), a ligand-activated transcription factor, greatly reduced arousal responses. In contrast, disrupting the gene for a likely gene duplication product, ER-β, did not have these effects. A combination of mathematical and genetic approaches to arousal in an experimentally tractable mammal opens up analysis of a CNS function of considerable theoretical and practical significance

Angiotensin-converting enzyme and male fertility

The angiotensin-converting enzyme (ACE; EC 3.4.15.1) gene (Ace) encodes both a somatic isozyme found in blood and several other tissues, including the epididymis, and a testis-specific isozyme (testis ACE) found only in developing spermatids and mature sperm. We recently used gene targeting to disrupt the gene coding for both ACE isozymes in mice and reported that male homozygous mutants mate normally but have reduced fertility; the mutant females are fertile. Here we explore the male fertility defect. We demonstrate that ACE is important for achieving in vivo fertilization and that sperm from mice lacking both ACE isozymes show defects in transport within the oviducts and in binding to zonae pellucidae. Males generated by gene targeting that lack somatic ACE but retain testis ACE are normally fertile, establishing that somatic ACE in males is not essential for their fertility. Furthermore, male and female mice lacking angiotensinogen have normal fertility, indicating that angiotensin I is not a necessary substrate for testis ACE. Males heterozygous for the mutation inactivating both ACE isozymes sire wild-type and heterozygous offspring at an indistinguishable frequency, indicating no selection against sperm carrying the mutation

Magmatic ore deposits in mafic–ultramafic intrusions of the Giles Event, Western Australia

More than 20 layered intrusions were emplaced at c. 1075 Ma across > 100 000 km2 in the Mesoproterozoic Musgrave Province of central Australia as part of the c. 1090–1040 Ma Giles Event of the Warakurna Large Igneous Province (LIP). Some of the intrusions, including Wingellina Hills, Pirntirri Mulari, The Wart, Ewarara, Kalka, Claude Hills, and Gosse Pile contain thick ultramafic segments comprising wehrlite, harzburgite, and websterite. Other intrusions, notably Hinckley Range, Michael Hills, and Murray Range, are essentially of olivine-gabbronoritic composition. Intrusions with substantial troctolitic portions comprise Morgan Range and Cavenagh Range, as well as the Bell Rock, Blackstone, and Jameson–Finlayson ranges which are tectonically dismembered blocks of an originally single intrusion, here named Mantamaru, with a strike length of > 170 km and a width of > 20 km, constituting one of the world's largest layered intrusions. Over a time span of N200 my, the Musgrave Province was affected by near continuous high-temperature reworking under a primarily extensional regime. This began with the 1220–1150 Ma intracratonic Musgrave Orogeny, characterized by ponding of basalt at the base of the lithosphere, melting of lower crust, voluminous granite magmatism, and widespread and near-continuous, mid-crustal ultra-high-temperature (UHT) metamorphism. Direct ascent of basic magmas into the upper crust was inhibited by the ductile nature of the lower crust and the development of substantial crystal-rich magma storage chambers. In the period between c. 1150 and 1090 Ma magmatism ceased, possibly because the lower crust had become too refractory, but mid-crustal reworking was continuously recorded in the crystallization of zircon in anatectic melts. Renewed magmatism in the form of the Giles Event of the Warakurna LIP began at around 1090 Ma and was characterized by voluminous basic and felsic volcanic and intrusive rocks grouped into the Warakurna Supersuite. Of particular interest in the context of the present study are the Giles layered intrusions which were emplaced into localized extensional zones. Rifting, emplacement of the layered intrusions, and significant uplift all occurred between 1078 and 1075 Ma, but mantle-derived magmatism lasted for N50 m.y., with no time progressive geographical trend, suggesting that magmatism was unrelated to a deep mantle plume, but instead controlled by plate architecture. The Giles layered intrusions and their immediate host rocks are considered to be prospective for (i) platinum-group element (PGE) reefs in the ultramafic–mafic transition zones of the intrusions, and in magnetite layers of their upper portions, (ii) Cu–Ni sulfide deposits hosted within magma feeder conduits of late basaltic pulses, (iii) vanadium in the lowermost magnetite layers of the most fractionated intrusions, (iv) apatite in unexposed magnetite layers towards the evolved top of some layered intrusions, (v) ilmenite as granular disseminated grains within the upper portions of the intrusions, (vi) iron in tectonically thickened magnetite layers or magnetite pipes of the upper portions of intrusions, (vii) gold and copper in the roof rocks and contact aureoles of the large intrusions, and (viii) lateritic nickel in weathered portions of olivine-rich ultramafic intrusions

MARS spectral molecular imaging of lamb tissue: data collection and image analysis

Spectral molecular imaging is a new imaging technique able to discriminate and quantify different components of tissue simultaneously at high spatial and high energy resolution. Our MARS scanner is an x-ray based small animal CT system designed to be used in the diagnostic energy range (20 to 140 keV). In this paper, we demonstrate the use of the MARS scanner, equipped with the Medipix3RX spectroscopic photon-processing detector, to discriminate fat, calcium, and water in tissue. We present data collected from a sample of lamb meat including bone as an illustrative example of human tissue imaging. The data is analyzed using our 3D Algebraic Reconstruction Algorithm (MARS-ART) and by material decomposition based on a constrained linear least squares algorithm. The results presented here clearly show the quantification of lipid-like, water-like and bone-like components of tissue. However, it is also clear to us that better algorithms could extract more information of clinical interest from our data. Because we are one of the first to present data from multi-energy photon-processing small animal CT systems, we make the raw, partial and fully processed data available with the intention that others can analyze it using their familiar routines. The raw, partially processed and fully processed data of lamb tissue along with the phantom calibration data can be found at [http://hdl.handle.net/10092/8531].Comment: 11 pages, 6 fig