The structure and interpretation of cosmology: Part I—general relativistic cosmology

The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general relativistic cosmology. The opening section reviews and clarifies the Friedmann–Robertson–Walker models of general relativistic cosmology, while Section 2 deals with the spatially homogeneous models. Particular attention is paid in these opening sections to the topological and geometrical aspects of cosmological models. Section 3 explains how the mathematical formalism can be linked with astronomical observation. In particular, the informal, observational notion of the celestial sphere is given a rigorous mathematical implementation. Part II of this work will concentrate on inflationary cosmology and quantum cosmology.     

The archaean controversy in britain: Part IV—Some general theoretical and social issues

The main theoretical issues in the study of the history of the Archaean Controversy in Britain, which arose in the first three papers of the present series, are summarized and discussed—in particular the problem of stratigraphical work in rocks where no fossils can be discerned. The ‘Archaean’ geologists showed some leanings towards Neo-Neptunism and this, together with the fact that their work challenged the Murchison/Survey view of British geology, was one of the reasons for the controversy. At a deeper level, however, the question concerned the doctrine of uniformitarianism: Were metamorphic rocks to be found at any part of the stratigraphical column, or were they confined to the earliest period of the Earth's history? The establishment of the concept of Precambrian rocks and a suitable stratotype boundary is essentially a social question that has to be determined within the geological community. Some of the social processes whereby these matters are decided internationally are considered, and it is noted that the best location of the ‘Golden Spike’ for the Precambrian/Cambrian boundary has only just been settled (by vote). The paper also explores some nineteenth-century ideas about the nature of metamorphism, and the early conditions of the world.     

The making of an intrinsic property: “Symmetry heuristics” in early particle physics

Mathematical invariances, usually referred to as “symmetries”, are today often regarded as providing a privileged heuristic guideline for understanding natural phenomena, especially those of micro-physics. The rise of symmetries in particle physics has often been portrayed by physicists and philosophers as the “application” of mathematical invariances to the ordering of particle phenomena, but no historical studies exist on whether and how mathematical invariances actually played a heuristic role in shaping microphysics. Moreover, speaking of an “application” of invariances conflates the formation of concepts of new intrinsic degrees of freedom of elementary particles with the formulation of models containing invariances with respect to those degrees of freedom. I shall present here a case study from early particle physics (ca. 1930–1954) focussed on the formation of one of the earliest concepts of a new degree of freedom, baryon number, and on the emergence of the invariance today associated to it. The results of the analysis show how concept formation and “application” of mathematical invariances were distinct components of a complex historical constellation in which, beside symmetries, two further elements were essential: the idea of physically conserved quantities and that of selection rules. I shall refer to the collection of different heuristic strategies involving selection rules, invariances and conserved quantities as the “SIC-triangle” and show how different authors made use of them to interpret the wealth of new experimental data. It was only a posteriori that the successes of this hybrid “symmetry heuristics” came to be attributed exclusively to mathematical invariances and group theory, forgetting the role of selection rules and of the notion of physically conserved quantity in the emergence of new degrees of freedom and new invariances. The results of the present investigation clearly indicate that opinions on the role of symmetries in fundamental physics need to be critically reviewed in the spirit of integrated history and philosophy of science.     

The Archaean Controversy in Britain: Part III—The rocks of Anglesey and Caernarvonshire

A detailed account is given of the development of the Archaean Controversy in Caernarvonshire and Anglesey. Sedgwick had found no base for his Cambrian in North Wales, but had intimated that some of the unfossiliferous rocks of the Lleyn Peninsula and Anglesey might be older than his Cambrian. He also described two ‘ribs’ of igneous rock: one running from Caernarvon to Bangor; the other inland, parallel to the first and crossing the Llanberis Pass at Llyn Padarn. The early Surveyors (especially Ramsay) supposed that these ‘ribs’ had altered the surrounding rocks, and the resulting ‘Altered Cambrian’ could be traced across the Menai Strait to Anglesey, where it formed the various metamorphic rocks of that island. This view (which thus denied the occurrence of Precambrian on Anglesey) was challenged by the usual coalition of ‘amateurs’ (Hicks, Hughes, Bonney, Callaway, Blake, etc.) with attempts being made to recognize a sequence of Archaean rocks in North Wales similar to that in Pembrokeshire. However, vigorous debate occurred amongst the ‘Archaean’ geologists themselves, especially about a rock at Twt Hill, Caernarvon, and about a claimed unconformity at the base of the Cambrian in the Llanberis Pass, perhaps adjacent to the Llyn Padarn ‘rib’. (This was at first regarded as a Precambrian ‘island’ like those claimed at St David's, the Malverns, etc.) Vigorous debate took place about the location of the claimed Llanberis unconformity, but the ‘Archaeans’ were united in regarding the metamorphic rocks of Anglesey as Precambrian (or Archaean). Eventually, the greywackes of Anglesey, and around Bangor and Caernarvon, were identified as Ordovician, not Cambrian. Very detailed map-work in Anglesey was carried out privately by Edward Greenly, and his results were published by the Survey in the form of a map and a high-quality Memoir. Greenly utilized for Anglesey tectonic ideas derived from his earlier fieldwork in the Scottish Highlands, so that although his mapping and stratigraphical divisions have proved to be of permanent value it is believed that his structures for Anglesey were mistaken and his stratigraphic sequence inverted. The Survey eventually abandoned its earlier (Ramsay) model of Anglesey without too much difficulty; and the igneous ‘rib’ of Llyn Padarn is now construed as an ignimbrite. However, a definite base for the Cambrian has still not been found in Caernarvonshire, and the stratigraphical evidence for the Precambrian age of the Anglesey rocks (by perceived unconformity with known Cambrian strata) remains incomplete. The study reveals the great difficulty experienced by early geologists when working in unfossiliferous rocks, the evidence from included fragments proving particularly uncertain. The paper also examines further the community of nineteenth-century British geologists, with their various factions and competing interests.     

The story of ‘Scientist: The Story of a Word’

This examination of an important paper by Sydney Ross is the first in a projected series of occasional reflections on ‘Annals of Science Classic Papers’ that have had enduring utility within the field of history of science and beyond. First the messages of the paper are examined, some well known but others, particularly Ross's own contemporary concerns about the use of the word ‘scientist’, less so. The varied uses made of the paper by scholars are then traced before Ross's biography is examined in order to try to understand how a figure professionally marginal to the field of history of science came to write such a significant piece. Ross’s interest in the topic appears to have been informed by a romantically tinged scientific progressivism and a deep concern with the importance of linguistic precision in science and in public affairs. The inspirations of the author and the interests of his audience have been only partially aligned, but the paper's insights remain of broad historical interest and have wider ramifications since the denotation ‘scientist’ and its proper application are much debated today in contests over the authority of science.     

The growth of mathematical knowledge—Introduction of convex bodies

The article addresses the topic of the growth of mathematical knowledge with a special focus on the question: How are mathematical objects introduced to mathematical practice? It takes as starting point a proposal made in a previous paper which is based on a case study on the introduction of Riemann surfaces. The claim is that (i) a new object first refers to previously accepted objects, and that (ii) reasoning is possible via a correspondence to the objects with reference to which it is introduced. In addition Riemann surfaces are geometrical objects, i.e., they are placed in a geometrical context, which makes new definitions possible. This proposal is tested on a case study on Minkowski’s introduction of convex bodies. The conclusion is that the proposal holds also for this example. In both cases we notice that in a first stage is a close connection between the new object and the objects it is introduced with reference to, and that in a later stage, the new object is given an independent definition. Even though the two cases display similarity in these respects, we also point to certain differences between the cases in the process of the first stage. Overall we notice the fruitfulness of representing problems in different contexts.     

The physiology of the smooth muscle: an interdisciplinary review—part II

Summary In the guinea pig taenia coli, when glycogen is depleted by repeating Ca-induced contracture in excess K solution containing no glucose, the tension cannot be maintained. The decrease in tension is accompanied by reduction of high energy phosphate compounds and oxygen consumption. When substrate is readmitted to the glycogendepleted preparation in the presence of 2.4 mM Ca and 20 mM K, the first response is hyperpolarization of the membrane and relaxation, and this is followed by depolarization and development of contracture. The latter response is blocked by verapamil, suggesting that energy supply increases the Ca conductance of the plasma membrane. The early response is considered to be due to activation of electrogenic Ca pump, since this is not affected by ouabain as well as removal of Na and K. ATP produced by substrate readmission is probably preferentially utilized for Ca pump activation to reduce the intracellular. Ca. The recovery of tension is likely to be brought about by ATP supply not only to the contractile machinery but also to the plasma membrane to remove inactivation of Ca conductance. It is postulated that as the energy source is depleted, energy consumption is automatically limited by suppressing Ca influx, as a selfdefence mechanism. Since HB is as effective as glucose in the recovery of these processes, and also in the activation of electrogenic Na pump, the matabolic pathway of oxidative phosphorylation alone can support these functions without a contribution of the glycolytic pathway.     

Maxwell’s contrived analogy: An early version of the methodology of modeling

The term “analogy” stands for a variety of methodological practices all related in one way or another to the idea of proportionality. We claim that in his first substantial contribution to electromagnetism James Clerk Maxwell developed a methodology of analogy which was completely new at the time or, to borrow John North’s expression, Maxwell’s methodology was a “newly contrived analogue”. In his initial response to Michael Faraday’s experimental researches in electromagnetism, Maxwell did not seek an analogy with some physical system in a domain different from electromagnetism as advocated by William Thomson; rather, he constructed an entirely artificial one to suit his needs. Following North, we claim that the modification which Maxwell introduced to the methodology of analogy has not been properly appreciated. In view of our examination of the evidence, we argue that Maxwell gave a new meaning to analogy; in fact, it comes close to modeling in current usage.     

The ‘Chemistry of Space’: The Sources of Hermann Grassmann's Scientific Achievements

Albert Lewis's article (Annals of Science, 1977) analysing the influence of Friedrich Schleiermacher on Hermann Grassmann, stimulated many different studies on the founder of n-dimensional outer algebra.

Following a brief outline of the various, sometimes diverging, analyses of Grassmann's creative thinking, new research is presented which confirms Lewis's original contribution and widens it considerably. It will be shown that:

i.?Grassmann, although a self-taught mathematician, was at the centre of a hitherto understated intellectual trend, which was defining for Germany. Initiated by Pestalozzi's concept of elementary mathematical education and culminating in the modern mathematics of the late 19th Century, it was reflected in the contributions of Grassmann, Riemann, Jacobi and Eisenstein.

ii.?Hermann Grassmann, his father Justus, and his brother Robert were all demonstrably influenced by Schleiermacher's dialectic; however the two brothers responded to it in very different ways.

iii.?Whilst the more philosophical parts of Hermann's 1844 Extension Theory are characterised by the influence of Schleiermacher and also by the mathematical knowledge of his father, the entire development of this work is the unfolding of a single idea based on the father's interpretation of combinatorial multiplication as a ‘chemical conjunction‘, which was developed largely dialectically by Hermann.     

The impact on microtubule network of a bracovirus IκB-like protein

Polydnavirus-encoded IκB-like proteins are similar to insect and mammalian IκB, and an immunosuppressive function in the host cells has been inferred to these proteins. Here we show that the expression of one of these IκB-like viral genes, the TnBVank1, in the Drosophila germline affects the localization of gurken, bicoid, and oskar mRNAs whose gene products are relevant for proper embryonic patterning. The altered localization of these mRNAs is suggestive of general defects in the intracellular, microtubule-based, trafficking routes. Analysis of microtubule motor proteins components such as the dynein heavy chain and the kinesin heavy chain revealed defects in the polarized microtubule network. Interestingly, the TnBVANK1 viral protein is uniformly distributed over the entire oocyte cortex, and appears to be anchored to the microtubule ends. Our data open up a very interesting issue on novel function(s) played by the ank gene family by interfering with cytoskeleton organization.