The meaning of πλασμαтιкό<Emphasis Type="Italic">ν</Emphasis> in Diophantus’ <Emphasis Type="Italic">Arithmetica</Emphasis>

Three problems in book I of Diophantus’ Arithmetica contain the adjective plasmatikon, that appears to qualify an implicit reference to some theorems in Elements, book II. The translation and meaning of the adjective sparked a long-lasting controversy that has become a nonnegligible aspect of the debate about the possibility of interpreting Diophantus’ approach and, more generally, Greek mathematics in algebraic terms. The correct interpretation of the word, a technical term in the Greek rhetorical tradition that perfectly fits the context in which it is inserted in the Arithmetica, entails that Diophantus’ text contained no (implicit) reference to Euclid’s Elements. The clause containing the adjective turns out to be a later interpolation, that cannot be used to support any algebraic interpretation of the Arithmetica.     

Analysis of <Emphasis Type="Italic">Dictyostelium</Emphasis> TACC reveals differential interactions with CP224 and unusual dynamics of <Emphasis Type="Italic">Dictyostelium</Emphasis> microtubules

We have localized TACC to the microtubule-nucleating centrosomal corona and to microtubule plus ends. Using RNAi we proved that Dictyostelium TACC promotes microtubule growth during interphase and mitosis. For the first time we show in vivo that both TACC and XMAP215 family proteins can be differentially localized to microtubule plus ends during interphase and mitosis and that TACC is mainly required for recruitment of an XMAP215-family protein to interphase microtubule plus ends but not for recruitment to centrosomes and kinetochores. Moreover, we have now a marker to study dynamics and behavior of microtubule plus ends in living Dictyostelium cells. In a combination of live cell imaging of microtubule plus ends and fluorescence recovery after photobleaching (FRAP) experiments of GFP-α-tubulin cells we show that Dictyostelium microtubules are dynamic only in the cell periphery, while they remain stable at the centrosome, which also appears to harbor a dynamic pool of tubulin dimers.     

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.     

Intrinsic protein disorder in oncogenic <Emphasis Type="Italic">KRAS</Emphasis> signaling

How Ras, and in particular its most abundant oncogenic isoform K-Ras4B, is activated and signals in proliferating cells, poses some of the most challenging questions in cancer cell biology. In this paper, we ask how intrinsically disordered regions in K-Ras4B and its effectors help promote proliferative signaling. Conformational disorder allows spanning long distances, supports hinge motions, promotes anchoring in membranes, permits segments to fulfil multiple roles, and broadly is crucial for activation mechanisms and intensified oncogenic signaling. Here, we provide an overview illustrating some of the key mechanisms through which conformational disorder can promote oncogenesis, with K-Ras4B signaling serving as an example. We discuss (1) GTP-bound KRas4B activation through membrane attachment; (2) how farnesylation and palmitoylation can promote isoform functional specificity; (3) calmodulin binding and PI3K activation; (4) how Ras activates its RASSF5 cofactor, thereby stimulating signaling of the Hippo pathway and repressing proliferation; and (5) how intrinsically disordered segments in Raf help its attachment to the membrane and activation. Collectively, we provide the first inclusive review of the roles of intrinsic protein disorder in oncogenic Ras-driven signaling. We believe that a broad picture helps to grasp and formulate key mechanisms in Ras cancer biology and assists in therapeutic intervention.     

Mean Motions in Ptolemy’s <Emphasis Type="Italic">Planetary Hypotheses</Emphasis>

In the Planetary Hypotheses, Ptolemy summarizes the planetary models that he discusses in great detail in the Almagest, but he changes the mean motions to account for more prolonged comparison of observations. He gives the mean motions in two different forms: first, in terms of ‘simple, unmixed’ periods and next, in terms of ‘particular, complex’ periods, which are approximations to linear combinations of the simple periods. As a consequence, all of the epoch values for the Moon and the planets are different at era Philip. This is in part a consequence of the changes in the mean motions and in part due to changes in Ptolemy’s time in the anomaly, but not the longitude or latitude, of the Moon, the mean longitude of Saturn and Jupiter, but not Mars, and the anomaly of Venus and Mercury, the former a large change, the latter a small one. The pattern of parameter changes we see suggests that the analyses that yielded the Planetary Hypotheses parameters were not the elegant trio analyses of the Almagest but some sort of serial determinations of the parameters based on sequences of independent observations.     

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.     

<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     

Redundant and unique roles of coronin proteins in <Emphasis Type="Italic">Dictyostelium</Emphasis>

Dictyostelium discoideum harbors a short (CRN12) and a long coronin (CRN7) composed of one and two beta-propellers, respectively. They are primarily present in the cell cortex and cells lacking CRN12 (corA ⁻) or CRN7 (corB ⁻) have defects in actin driven processes. We compared the characteristics of a mutant cell line (corA ⁻ /corB ⁻) lacking CRN12 and CRN7 with the single mutants focusing on cytokinesis, phagocytosis, chemotaxis and development. Cytokinesis, uptake of small particles, and developmental defects were not enhanced in the corA ⁻ /corB ⁻ strain as compared to the single mutants, whereas motility and phagocytosis of yeast particles were more severely impaired. It appears that although both proteins affect the same processes they do not act in a redundant manner. Rather, they often act antagonistically, which is in accordance with their proposed roles in the actin cytoskeleton where CRN12 acts in actin disassembly whereas CRN7 stabilizes actin filaments and protects them from disassembly.     

The Role of Geometrical Construction in Theodosius’s <Emphasis Type="Italic">Spherics</Emphasis>

This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius’s Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams.     

Conventions for recreational problems in Fibonacci’s <Emphasis Type="Italic">Liber Abbaci</Emphasis>

Fibonacci’s treatment of so-called recreational problems in his Liber Abbaci has been interpreted as an early episode both in the history of systems of linear equations, and in the history of negative numbers. However, these problems are also interesting in their own right. We discuss some of the conventions which seem to have governed these problems. By considering certain pairs of problems, where one problem is unsolvable and its partner is solvable, we show that Fibonacci went to a significant effort to conform to these conventions. We also examine the methods which he could have used to construct his problems.     

Proposition 10, Book 2, in the <Emphasis Type="Italic">Principia</Emphasis>, revisited

In Proposition 10, Book 2 of the Principia, Newton applied his geometrical calculus and power series expansion to calculate motion in a resistive medium under the action of gravity. In the first edition of the Principia, however, he made an error in his treatment which lead to a faulty solution that was noticed by Johann Bernoulli and communicated to him while the second edition was already at the printer. This episode has been discussed in the past, and the source of Newton’s initial error, which Bernoulli was unable to find, has been clarified by Lagrange and is reviewed here. But there are also problems in Newton’s corrected version in the second edition of the Principia that have been ignored in the past, which are discussed in detail here.     

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’.     

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.     

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.