On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases.

Using numerical simulations, we compare properties of knotted DNA molecules that are either torsionally relaxed or supercoiled. We observe that DNA supercoiling tightens knotted portions of DNA molecules and accentuates the difference in curvature between knotted and unknotted regions. The increased curvature of knotted regions is expected to make them preferential substrates of type IIA topoisomerases because various earlier experiments have concluded that type IIA DNA topoisomerases preferentially interact with highly curved DNA regions. The supercoiling-induced tightening of DNA knots observed here shows that torsional tension in DNA may serve to expose DNA knots to the unknotting action of type IIA topoisomerases, and thus explains how these topoisomerases could maintain a low knotting equilibrium in vivo, even for long DNA molecules.

PHYTOCHROME KINASE SUBSTRATE1 regulates root phototropism and gravitropism.

Light promotes the expression of PHYTOCHROME KINASE SUBSTRATE1 (PKS1) in the root of Arabidopsis thaliana, but the function of PKS1 in this organ is unknown. Unilateral blue light induced a negative root phototropic response mediated by phototropin 1 in wild-type seedlings. This response was absent in pks1 mutants. In the wild type, unilateral blue light enhanced PKS1 expression in the subapical region of the root several hours before bending was detectable. The negative phototropism and the enhanced PKS1 expression in response to blue light required phytochrome A (phyA). In addition, the pks1 mutation enhanced the root gravitropic response when vertically oriented seedlings were placed horizontally. The negative regulation of gravitropism by PKS1 occurred even in dark-grown seedlings and did not require phyA. Blue light also failed to induce negative phototropism in pks1 under reduced gravitational stimulation, indicating that the effect of pks1 on phototropism is not simply the consequence of the counteracting effect of enhanced gravitropism. We propose a model where the background level of PKS1 reduces gravitropism. After a phyA-dependent increase in its expression, PKS1 positively affects root phototropism and both effects contribute to negative curvature in response to unilateral blue light.

[Album autour de l'exposition "Art treasures of the United Kingdom" tenue à Manchester en 1857] / [constitué par George Barker]

Collectionneur : Ricci, Seymour de (1881-1942)

[Album autour de l'exposition "Art treasures of the United Kingdom" tenue à Manchester en 1857] / [constitué par George Barker]

Collectionneur : Ricci, Seymour de (1881-1942)

楊淇園先生超性事蹟Yang qi yuan xian sheng chao xing shi ji.Vie et conversion de Yang Qi yuan.

Ce personnage, postnom Ting jun, docteur en 1592, fut converti par le P. Ricci. Ouvrage de Ding Zhi lin (XVIIe ou XVIIIe siècle).

Chinois 1320

Lettre de Sixte V au Maître de l'Empire des Ming. Texte Chinois relatant l'envoi de présents et la présence en Chine de missionnaires, parmi lesquels Matteo [Ricci] ; datée de la capitale des Indes (1590).La Bibliothèque nationale possède la planche gravée servant à l'impression de cette feuille.

Chinois 1321

Rapport sur la vie du P. Ricci, daté de 1586 (date erronée, il faut sans doute lire 1616) ; présenté par les PP. de Pantoja (1571-1618) et Sabbathinus de Ursis (1575-1617).

乾坤體義Qian kun ti yi.Principes du système du monde.

Cat. imp., liv. 106, f. 16 (en 2 livres).Par le P. Ricci (1552-1610). Texte relatif à la cosmographie et à la géographie, avec figures.

記法Ji fa.Traité de mnémotechnie.

Publié par les PP. Alfonso Vagnoni (1566-1640) et Francesco Sambiaso (1582-1649), avec l'autorisation du P. Emmanuel Diaz (1574-1659). Préface par Zhu Yu huan, de Dong yong, à l'église catholique dite Jing jiao tang. Auteur : le P. Matteo Ricci (1552-1610).

重刻畸人十篇

Cat. imp., liv. 125, f. 29.Chong ke ji ren shi pian.Dix conversations sur la doctrine chrétienne, réédition.Par le P. Ricci ; préface de la première édition (1608) par Li Zhi zao, de Hu lin.2 livres.

辯學遺牘

Cat. imp., liv. 125, f. 27.Bian xue yi du.Mémoires et lettres sur le christianisme.Lettre de Yu Shun xi De yuan et réponse du P. Ricci ; mémoires du bonze Lian chi Zhu chuang et réfutation du P. Ricci ; notice finale par Liang an ju shi. Gravé au pavillon Xi shi.26 feuillets.

The role of water in determining structure and function of macromolecules and macromolecular assemblies /

The interaction of biological molecules with water is an important determinant of structural properties both in molecular assemblies, and in conformation of individual macromolecules. By observing the effects of manipulating the activity of water (which can be accomplished by limiting its concentration or by adding additional solutes, "osmotic stress"), one can learn something about intrinsic physical properties of biological molecules as well as measure an energetic contribution of closely associated water molecules to overall equilibria in biological reactions. Here two such studies are reported. The first of these examines several species of lysolipid which, while present in relatively low concentrations in biomembranes, have been shown to affect many cellular processes involving membrane-protein or membrane-membrane interactions. Monolayer elastic constants were determined by combining X-ray diffraction and the osmotic stress technique. Spontaneous radii of curvature of lysophosphatidylcholines were determined to be positive and in the range +30A to +70A, while lysophosphatidylethanolamines proved to be essentially flat. Neither lysolipid significantly affected the bending modulus of the monolayer in which it was incorporated. The second study examines the role of water in theprocess of polymerization of actin into filaments. Water activity was manipulated by adding osmolytes and the effect on the equilibrium dissociation constant (measured as the criticalmonomer concentration) was determined. As water activity was decreased, the critical concentration was reduced for Ca-actin but not for Mg-actin, suggesting that 10-12 fewer water molecules are associated with Ca-actin in the polymerized state. Thisunexpectedly small amount of water is discussed in the context of the common structural motif of a nucleotide binding cleft.

The effects of gramicidin on the structure of phospholipid assemblies /

Gramicidin is an antibiotic peptide that can be incorporated into the monolayers of cell membranes. Dimerization through hydrogen bonding between gramicidin monomers in opposing leaflets of the membrane results in the formation of an iontophoretic channel. Surrounding phospholipids, with various associated mechanical properties, have been shown to influence the gating properties of this channel. Conversely, gramicidin incorporation has been shown to affect the structure of spontaneously formed lipid assemblies. Using small-angle x-ray diffraction and model systems composed of phospholipids and gramicidin, the physical effects incurred by gramicidin incorporation were measured. The reverse hexagonal (H^) phase composed of dioleoylphosphatidylethanolamine (DOPE) monolayers decreased in lattice dimension with increasing incorporation of gramicidin. This indicated that gramicidin was adding negative curvature to the monolayers. In this system, gramicidin was measured to have an apparent intrinsic radius of curvature (Rop*™") of -7. 1 A. The addition of up to 4 mol% gramicidin in mixtures with DOPE did not result in the monolayers becoming stiffer, as indicated by unaltered bending moduli for each composition. Dioleoylphosphatidylcholine (DOPC) alone forms the lamellar (LJ phase when hydrated, but undergoes a transition into the H^ phase when mixed with gramicidin. The lattice repeat dimension decreases systematically with increased gramicidin content. Again, this indicated that gramicidin was adding negative curvature to the monolayers. At 12 mol% gramicidin in mixtures with DOPC, the apparent radius of intrinsic curvature of gramicidin (Rop*"^) was measured to be -7.4 A. This mixture formed monolayers that were very resistant to bending under osmotic pressure, with a measured bending modulus of 1 15 kT. The measurements made in this study demonstrate that peptides are able to modulate the spontaneous curvature and other mechanical properties of phospholipid assemblies.