Conventionalism in Reid’s ‘geometry of visibles’

The subject of this investigation is the role of conventions in the formulation of Thomas Reid’s theory of the geometry of vision, which he calls the ‘geometry of visibles’. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid’s ‘geometry of visibles’ and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a choice of conventions regarding the construction and assignment of its various properties, especially metric properties, and this fact undermines the claim for a unique non-Euclidean status for the geometry of vision. Finally, a suggestion is offered for trying to reconcile Reid’s direct realist theory of perception with his geometry of visibles.While Thomas Reid is well-known as the leading exponent of the Scottish ‘common-sense’ school of philosophy, his role in the history of geometry has only recently been drawing the attention of the scholarly community. In particular, several influential works, by N. Daniels and R. B. Angell, have claimed Reid as the discoverer of non-Euclidean geometry; an achievement, moreover, that pre-dates the geometries of Lobachevsky, Bolyai, and Gauss by over a half century. Reid’s alleged discovery appears within the context of his analysis of the geometry of the visual field, which he dubs the ‘geometry of visibles’. In summarizing the importance of Reid’s philosophy in this area, Daniels is led to conclude that ‘there can remain little doubt that Reid intends the geometry of visibles to be an alternative to Euclidean geometry’;¹ while Angell, similarly inspired by Reid, draws a much stronger inference: ‘The geometry which precisely and naturally fits the actual configurations of the visual field is a non-Euclidean, two-dimensional, elliptical geometry. In substance, this thesis was advanced by Thomas Reid in 1764 ...’² The significance of these findings has not gone unnoticed in mathematical and scientific circles, moreover, for Reid’s name is beginning to appear more frequently in historical surveys of the development of geometry and the theories of space.³Implicit in the recent work on Reid’s ‘geometry of visibles’, or GOV, one can discern two closely related but distinct arguments: first, that Reid did in fact formulate a non-Euclidean geometry, and second, that the GOV is non-Euclidean. This essay will investigate mainly the latter claim, although a lengthy discussion will be accorded to the first. Overall, in contrast to the optimistic reports of a non-Euclidean GOV, it will be argued that there is a great deal of conceptual freedom in the construction of any geometry pertaining to the visual field. Rather than single out a non-Euclidean structure as the only geometry consistent with visual phenomena, an examination of Reid, Daniels, and Angell will reveal the crucial role of geometric ‘conventions’, especially of the metric sort, in the formulation of the GOV (where a ‘metric’ can be simply defined as a system for determining distances, the measures of angles, etc.). Consequently, while a non-Euclidean geometry is consistent with Reid’s GOV, it is only one of many different geometrical structures that a GOV can possess. Angell’s theory that the GOV can only be construed as non-Euclidean, is thus incorrect. After an exploration of Reid’s theory and the alleged non-Euclidean nature of the GOV, in 1 and 2 respectively, the focus will turn to the tacit role of conventionalism in Daniels’ reconstruction of Reid’s GOV argument, and in the contemporary treatment of a non-Euclidean visual geometry offered by Angell ( 3 and 4). Finally, in the conclusion, a suggestion will be offered for a possible reconstruction of Reid’s GOV that does not violate his avowed ‘direct realist’ theory of perception, since this epistemological thesis largely prompted his formulation of the GOV.     

<Emphasis Type="Italic">Newton's Argument for Proposition 1 of the</Emphasis> Principia

The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane) and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward a fixed center' – we describe two serious flaws in the Principia's argument for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious, for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption. Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion – namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given' – two using polygonal approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.' (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

Hepatic effects of <Emphasis Type="Italic">Cimicifuga racemosa</Emphasis> extract <Emphasis Type="Italic">in vivo</Emphasis> and <Emphasis Type="Italic">in vitro</Emphasis>

Extracts of Cimicifuga racemosa are used frequently for menopausal complaints. Cimicifuga is well tolerated but can occasionally cause liver injury. To assess hepatotoxicity of cimicifuga in more detail, ethanolic C. racemosa extract was administered orally to rats, and liver sections were analyzed by electron microscopy. Tests for cytotoxicity, mitochondrial toxicity and apoptosis/necrosis were performed using HepG2 cells. Mitochondrial toxicity was studied using isolated rat liver mitochondria. Microvesicular steatosis was found in rats treated with > 1,000 mg/kg [DOSAGE ERROR CORRECTED] body weight cimicifuga extract. In vitro, cytotoxicity was apparent at concentrations > or =75 microg/mL, and mitochondrial beta-oxidation was impaired at concentrations > or =10 microg/mL. The mitochondrial membrane potential was decreased at concentrations > or =100 microg/mL, and oxidative phosphorylation was impaired at concenq trations > or =300 microg/mL. The mechanism of cell death was predominantly apoptosis. C. racemosa exerts toxicity in vivo and in vitro, eventually resulting in apoptotic cell death. The results are compatible with idiosyncratic hepatotoxicity as observed in patients treated with cimicifuga extracts.     

Prediction of α‐stable GARCH and ARMA‐GARCH‐M models

The best prediction of generalized autoregressive conditional heteroskedasticity (GARCH) models with α‐stable innovations, α‐stable power‐GARCH models and autoregressive moving average (ARMA) models with GARCH in mean effects (ARMA‐GARCH‐M) are proposed. We present a sufficient condition for stationarity of α‐stable GARCH models. The prediction methods are easy to implement in practice. The proposed prediction methods are applied for predicting future values of the daily SP500 stock market and wind speed data.     

Athanasius Kircher’s magical instruments: an essay on ‘science’, ‘religion’ and applied metaphysics

In this paper I endeavour to bridge the gap between the history of material culture and the history of ideas. I do this by focussing on the intersection between metaphysics and technology—what I call ‘applied metaphysics’—in the oeuvre of the Jesuit scholar Athanasius Kircher. By scrutinising the interplay between texts, objects and images in Kircher’s work, it becomes possible to describe the multiplicity of meanings related to his artefacts. I unearth as yet overlooked metaphysical and religious meanings of the camera obscura, for instance, as well as of various other optical and magnetic devices. Today, instruments and artefacts are almost exclusively seen in the light of a narrow economic and technical concept. Historically, the ‘use’ of artefacts is much more diverse, however, and I argue that it is time to historicize the concept of ‘utility’.     

IP<Subscript>3</Subscript> receptor signaling and endothelial barrier function

The endothelium, a monolayer of endothelial cells lining vessel walls, maintains tissue-fluid homeostasis by restricting the passage of the plasma proteins and blood cells into the interstitium. The ion Ca²⁺, a ubiquitous secondary messenger, initiates signal transduction events in endothelial cells that is critical to control of vascular tone and endothelial permeability. The ion Ca²⁺ is stored inside the intracellular organelles and released into the cytosol in response to environmental cues. The inositol 1,4,5-trisphosphate (IP₃) messenger facilitates Ca²⁺ release through IP₃ receptors which are Ca²⁺-selective intracellular channels located within the membrane of the endoplasmic reticulum. Binding of IP₃ to the IP₃Rs initiates assembly of IP₃R clusters, a key event responsible for amplification of Ca²⁺ signals in endothelial cells. This review discusses emerging concepts related to architecture and dynamics of IP₃R clusters, and their specific role in propagation of Ca²⁺ signals in endothelial cells.     

Structure and dynamics of rotary V<Subscript>1</Subscript> motor

Rotary ATPases are unique rotary molecular motors that function as energy conversion machines. Among all known rotary ATPases, F₁-ATPase is the best characterized rotary molecular motor. There are many high-resolution crystal structures and the rotation dynamics have been investigated in detail by extensive single-molecule studies. In contrast, knowledge on the structure and rotation dynamics of V₁-ATPase, another rotary ATPase, has been limited. However, recent high-resolution structural studies and single-molecule studies on V₁-ATPase have provided new insights on how the catalytic sites in this molecular motor change its conformation during rotation driven by ATP hydrolysis. In this review, we summarize recent information on the structural features and rotary dynamics of V₁-ATPase revealed from structural and single-molecule approaches and discuss the possible chemomechanical coupling scheme of V₁-ATPase with a focus on differences between rotary molecular motors.     

Newton’s “satis est”: A new explanatory role for laws

In this paper I argue that Newton’s stance on explanation in physics was enabled by his overall methodology and that it neither committed him to embrace action at a distance nor to set aside philosophical and metaphysical questions. Rather his methodology allowed him to embrace a non-causal, yet non-inferior, kind of explanation. I suggest that Newton holds that the theory developed in the Principia provides a genuine explanation, namely a law-based one, but that we also lack something explanatory, namely a causal account of the explanandum. Finally, I argue that examining what it takes to have law-based explanation in the face of agnosticism about the causal process makes it possible to recast the debate over action at a distance between Leibniz and Newton as empirically and methodologically motivated on both sides.     

Ga<Subscript>q</Subscript> proteins: molecular pharmacology and therapeutic potential

Seven transmembrane G protein-coupled receptors (GPCRs) have gained much interest in recent years as it is the largest class among cell surface receptors. G proteins lie in the heart of GPCRs signalling and therefore can be therapeutically targeted to overcome complexities in GPCR responses and signalling. G proteins are classified into four families (G_i, G_s, G_12/13 and G_q); G_q is further subdivided into four classes. Among them G_αq and G_αq/11 isoforms are most crucial and ubiquitously expressed; these isoforms are almost 88% similar at their amino acid sequence but may exhibit functional divergences. However, uncertainties often arise about G_αq and G_αq/11 inhibitors, these G proteins might also have suitability to the invention of novel-specific inhibitors for each isoforms. YM-254890 and UBO-QIC are discovered as potent inhibitors of G_αq functions and also investigated in thrombin protease-activated receptor (PAR)-1 inhibitors and platelet aggregation inhibition. The most likely G protein involved in PAR-1 stimulates responses is one of the G_αq family isoforms. In this review, we highlight the molecular structures and pharmacological responses of G_αq family which may reflect the biochemical and molecular role of G_αq and G_αq/11. The advanced understanding of G_αq and G_αq/11 role in GPCR signalling may shed light on our understanding on cell biology, cellular physiology and pathophysiology and also lead to the development of novel therapeutic agents for a number of diseases.     

Revisiting Galison’s ‘Aufbau/Bauhaus’ in light of Neurath’s philosophical projects

In his article entitled ‘Aufbau/Bauhaus’ and related work, Peter Galison explores the connections between the Vienna Circle and the Dessau Bauhaus. Historically, these groups were related, with members of each group familiar with the ideas of the other. Galison argues that their projects are related as well, through shared political views and methodological approach. The two main figures that connect the Vienna Circle to the Bauhaus—and the figures upon which Galison focuses—are Rudolf Carnap and Otto Neurath. Yet, in our view, the connections that Galison develops do not properly capture the common themes between the Bauhaus and Neurath’s philosophical projects. In this paper, we will examine a few of the historical connections between the Dessau Bauhaus and the Vienna Circle, as well as the philosophical connections that Galison draws between these two groups. By examining in greater depth Neurath’s philosophical commitments, we aim to demonstrate that some of these philosophical connections fail to resonate with Neurath’s projects. And, finally, we develop different connections between Neurath’s projects and the Bauhaus. In our view, these new connections between Neurath and the Dessau Bauhaus are both substantive and philosophically interesting.     

<Emphasis Type="Italic">C</Emphasis>-<Emphasis Type="Italic">Raf</Emphasis> deficiency leads to hearing loss and increased noise susceptibility

The family of RAF kinases transduces extracellular information to the nucleus, and their activation is crucial for cellular regulation on many levels, ranging from embryonic development to carcinogenesis. B-RAF and C-RAF modulate neurogenesis and neuritogenesis during chicken inner ear development. C-RAF deficiency in humans is associated with deafness in the rare genetic insulin-like growth factor 1 (IGF-1), Noonan and Leopard syndromes. In this study, we show that RAF kinases are expressed in the developing inner ear and in adult mouse cochlea. A homozygous C-Raf deletion in mice caused profound deafness with no evident cellular aberrations except for a remarkable reduction of the K⁺ channel Kir4.1 expression, a trait that suffices as a cause of deafness. To explore the role of C-Raf in cellular protection and repair, heterozygous C-Raf ^+/? mice were exposed to noise. A reduced C-RAF level negatively affected hearing preservation in response to noise through mechanisms involving the activation of JNK and an exacerbated apoptotic response. Taken together, these results strongly support a role for C-RAF in hearing protection.     

‘This inscrutable principle of an original organization’: epigenesis and ‘looseness of fit’ in Kant’s philosophy of science

Kant’s philosophy of science takes on sharp contour in terms of his interaction with the practicing life scientists of his day, particularly Johann Blumenbach and the latter’s student, Christoph Girtanner, who in 1796 attempted to synthesize the ideas of Kant and Blumenbach. Indeed, Kant’s engagement with the life sciences played a far more substantial role in his transcendental philosophy than has been recognized hitherto. The theory of epigenesis, especially in light of Kant’s famous analogy in the first Critique (B167), posed crucial questions regarding the ‘looseness of fit’ between the constitutive and the regulative in Kant’s theory of empirical law. A detailed examination of Kant’s struggle with epigenesis between 1784 and 1790 demonstrates his grave reservations about its hylozoist implications, leading to his even stronger insistence on the discrimination of constitutive from regulative uses of reason. The continuing relevance of these issues for Kant’s philosophy of science is clear from the work of Buchdahl and its contemporary reception.