Microbes,mathematics, and models

Microbial model systems have a long history of fruitful use in fields that include evolution and ecology. In order to develop further insight into modelling practice, we examine how the competitive exclusion and coexistence of competing species have been modelled mathematically and materially over the course of a long research history. In particular, we investigate how microbial models of these dynamics interact with mathematical or computational models of the same phenomena. Our cases illuminate the ways in which microbial systems and equations work as models, and what happens when they generate inconsistent findings about shared targets. We reveal an iterative strategy of comparative modelling in different media, and suggest reasons why microbial models have a special degree of epistemic tractability in multimodel inquiry.     

Structural realism,mathematics, and ontology

Over the last two decades structural realism has been given progressively more elaborated formulations. Steven French has been at the forefront of the development of the most conceptually sophisticated and historically sensitive version of the view. In his book, The Structure of the World (French (2014)), French shows how structural realism, the view according to which structure is all there is (ontic structural realism), is able to illuminate central issues in the philosophy of science: underdetermination, scientific representation, dispositions, natural modality, and laws of nature. The discussion consistently sheds novel light on the problems under consideration while developing insightful and provocative views. In this paper, I focus on the status of mathematics within French's ontic structural realism, and I raise some concerns about its proper understanding vis-à-vis the realist components of the view.     

Biosynthesis and roles of phospholipids in mitochondrial fusion,division and mitophagy

Mitochondria move, fuse and divide in cells. The dynamic behavior of mitochondria is central to the control of their structure and function. Three conserved mitochondrial dynamin-related GTPases (i.e., mitofusin, Opa1 and Drp1 in mammals and Fzo1, Mgm1 and Dnm1 in yeast) mediate mitochondrial fusion and division. In addition to dynamins, recent studies demonstrated that phospholipids in mitochondria also play key roles in mitochondrial dynamics by interacting with dynamin GTPases and by directly changing the biophysical properties of the mitochondrial membranes. Changes in phospholipid composition also promote mitophagy, which is a selective mitochondrial degradation process that is mechanistically coupled to mitochondrial division. In this review, we will discuss the biogenesis and function of mitochondrial phospholipids.     

Abduction, tomography, and other inverse problems

Charles S. Peirce introduced in the late 19^th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane functions from their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon’s theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.     

Number and measure: Hermann von Helmholtz at the crossroads of mathematics, physics, and psychology

In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics (Grassmann / Du Bois), on the possibility of quantitative psychology (Fechner / Kries, Wundt / Zeller), and on the meaning of temperature measurement (Maxwell, Mach). Late nineteenth-century scrutinisers of the foundations of mathematics (Dedekind, Cantor, Frege, Russell) made little of Helmholtz’s essay. Yet it inspired two mathematicians with an eye on physics (Poincaré and Hölder), and a few philosopher-physicists (Mach, Duhem, Campbell). The aim of the present paper is to situate Helmholtz’s contribution in this complex array of nineteenth-century philosophies of number, quantity, and measurement.     

Evidence of mitotic division of coelomocytes in the normal,wounded and grafted earthwormEisenia foetida

Summary In the oligochaeteEisenia foetida the free amoebocytes, once released into the coelomic fluid were observed to remain mitotically active following the trauma of receiving a body wall graft or wound.Special thanks to Dr.A. Terry for her help.     

Comparison of prospective Hawkes and recursive point process models for Ebola in DRC

Point process models, such as Hawkes and recursive models, have recently been shown to offer improved accuracy over more traditional compartmental models for the purposes of modeling and forecasting the spread of disease epidemics. To explicitly test the performance of these two models in a real-world and ongoing epidemic, we compared the fit of Hawkes and recursive models to outbreak data on Ebola virus disease (EVD) in the Democratic Republic of the Congo in 2018–2020. The models were estimated, and the forecasts were produced, time-stamped, and stored in real time, so that their prospective value can be assessed and to guard against potential overfitting. The fit of the two models was similar, with both models resulting in much smaller errors in the beginning and waning phases of the epidemic and with slightly smaller error sizes on average for the Hawkes model compared with the recursive model. Our results suggest that both Hawkes and recursive point process models can be used in near real time during the course of an epidemic to help predict future cases and inform management and mitigation strategies.     

Genetic structure and division of labor in honeybee societies

Summary Recent studies have demonstrated a genotypic component to the division of labor among worker honeybees. However, these studies used artificially-selected strains of bees or colonies derived from queens that were instrumentally inseminated with the semen from very few males. We present evidence for genotypic variability among groups of workers performing tasks in colonies with naturally-mated queens. These results demonstrate that genetic structure is a level of social organization in honeybees.     

Francesco Patrizi’s two books on space: geometry, mathematics, and dialectic beyond Aristotelian science

Francesco Patrizi was a competent Greek scholar, a mathematician, and a Neoplatonic thinker, well known for his sharp critique of Aristotle and the Aristotelian tradition. In this article I shall present, in the first part, the importance of the concept of a three-dimensional space which is regarded as a body, as opposed to the Aristotelian two-dimensional space or interval, in Patrizi’s discussion of physical space. This point, I shall argue, is an essential part of Patrizi’s overall critique of Aristotelian science, in which Epicurean, Stoic, and mainly Neoplatonic elements were brought together, in what seems like an original theory of space and a radical revision of Aristotelian physics. Moreover, I shall try to show Patrizi’s dialectical method of definition, his geometrical argumentation, and trace some of the ideas and terms used by him back to Proclus’ Commentary on Euclid. This text of Proclus, as will be shown in the second part of the article, was also important for Patrizi’s discussion of mathematical space, where Patrizi deals with the status of mathematics and redefines some mathematical concepts such as the point and the line according to his new theory of space.     

The power of images: mathematics and metaphysics in Hobbes's optics

This paper deals with Hobbes's theory of optical images, developed in his optical magnum opus, ‘A Minute or First Draught of the Optiques’ (1646), and published in abridged version in De homine (1658). The paper suggests that Hobbes's theory of vision and images serves him to ground his philosophy of man on his philosophy of body. Furthermore, since this part of Hobbes's work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics in Hobbes's philosophy. The paper points to some difficulties in the thesis of Shapin and Schaffer, who presented geometry as a ‘paradigm’ for Hobbes's natural philosophy. It will be argued here that Hobbes's application of geometry to optics was dictated by his metaphysical and epistemological principles, not by a blind belief in the power of geometry. Geometry supported causal explanation, and assisted reason in making sense of appearances by helping the philosopher understand the relationships between the world outside us and the images it produces in us. Finally the paper broadly suggests how Hobbes's theory of images may have triggered, by negative example, the flourishing of geometrical optics in Restoration England.     

Polynomials and equations in arabic algebra

It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. I thank Mahdi Abdeljaouad, who provided comments on an earlier version of this paper, and Haitham Alkhateeb, for his help with some of the translations. Notes on references: When page numbers are separated by a “ / ”, the first number is to the Arabic text, and the second to the translation. Also, a semicolon separates page number from line number. Example: [Al-Khwārizmī, 1831, 31;6/43] refers to page 31 line 6 of the Arabic text, and page 43 of the translation.     

A demonstrable local and geometric increase in the chromosomal DNA ofChironomus

Zusammenfassung Mikrospektrophotometrische Messungen an den Speicheldrüsenchromosomen des Bastards zweierChironomus thummi-Unterarten ergeben Differenzen des DNS-Gehalts von homologen Querscheiben. Diese Differenzen folgen der Beziehung 1:2ⁿ (n=1, 2, 3 oder 4). Für bestimmte Querscheiben wurden Verdopplungsstufen des DNS-Gehalts von unterschiedlicher Höhe gefunden. Mechanismen, die geeignet sind, das Duplikationsphänomen zu erklären, werden diskutiert.     

The intelligibility of motion and construction: Descartes’ early mathematics and metaphysics, 1619-1637

I argue for an interpretation of the connection between Descartes’ early mathematics and metaphysics that centers on the standard of geometrical intelligibility that characterizes Descartes’ mathematical work during the period 1619 to 1637. This approach remains sensitive to the innovations of Descartes’ system of geometry and, I claim, sheds important light on the relationship between his landmark Geometry (1637) and his first metaphysics of nature, which is presented in Le monde (1633). In particular, I argue that the same standard of clear and distinct motions for construction that allows Descartes to distinguish ‘geometric’ from ‘imaginary’ curves in the domain of mathematics is adopted in Le monde as Descartes details God’s construction of nature. I also show how, on this interpretation, the metaphysics of Le monde can fruitfully be brought to bear on Descartes’ attempted solution to the Pappus problem, which he presents in Book I of the Geometry. My general goal is to show that attention to the standard of intelligibility Descartes invokes in these different areas of inquiry grants us a richer view of the connection between his early mathematics and philosophy than an approach that assumes a common method is what binds his work in these domains together.