A tale of a threshing machine: Images of the Voigt-Leibniz mathematical-agricultural machine at the beginning of the 18th century.

This paper examines how a certain threshing machine was developed and improved by Jobst Heinrich Voigt and Gottfried Wilhelm Leibniz between 1699 and 1700. While this machine was based on various mechanical principles and instruments, including the pinned drum mechanism first noted by Georg Philipp Harsdörffer, it was later reconceptualized as a 'mathematical' machine. I claim that such a positioning was not unique to this machine, but part of a wider movement during the 18th century that considered various artisanal instruments as mathematical, as well as agricultural and artisanal knowledge as scientific. Examining the development and subsequent reception of this machine, I show that during the first decades of the 18th century these conceptions gave rise to a double image of this machine, and hence of agricultural knowledge in general: on the one hand, this machine was considered as more efficient and productive (while still in need of improvement); on the other hand, it was viewed, either implicitly or explicitly, as something that should be studied by mathematicians, thus reflecting a changing image of mathematics.

Heterodox underdetermination: Metaphysical options for discernibility and (non-)entanglement.

Broadly speaking, there are three views on whether Leibniz's Principle of the Identity of Indiscernibles (PII) is violated in the case of similar particles. According to the earliest view, PII is always violated (call this the no discernibility view); according to the more recent weak discernibility view, PII is at least valid in a weak sense. No and weak discernibility have been referred to as orthodoxy. Steven French has argued that although PII is violated, similar particles can still be regarded as individuals, or, alternatively, as non-individuals: French famously concluded therefore that metaphysics is underdetermined by physics. Call this thesis orthodox underdetermination. Most recently, some authors have turned against orthodoxy by arguing that PII is valid in more than a weak sense - call this the new discernibility view, also referred to as heterodoxy. Since heterodoxy is backed up by physical considerations, metaphysics now seems to be determined by physics: physics indicates that PII is valid. In this paper, I argue that with respect to entangled states, there are two ways to establish PII's validity, which yield two different ontological interpretations of entanglement. Therefore, a form of underdetermination returns within the heterodox framework. I argue that heterodox underdetermination deserves some attention, because the two ontological interpretations might yield different explanations of the violation of Bell inequalities.

Protein structure prediction from the complementary science perspective.

A comparative analysis between two problems-apparently unrelated-which are solved in a period of ~400 years, viz., the accurate prediction of both the planetary orbits and the protein structures, leads to inferred conjectures that go far beyond the existence of a common path in their resolution, i.e., observation → pattern recognition → modeling. The preliminary results from this analysis indicate that complementary science, together with a new perspective on protein folding, may help us discover common features that could contribute to a more in-depth understanding of still-unsolved problems such as protein folding.

Aristotle on identity: close enough!

We present what Aristotle wrote on identity in a leisurely manner, which is much more than is generally known, save among the cognoscenti (Aristotle scholars), and mutatis mutandis about the introduction of the identity-symbol [Formula: see text]. We add two codas, one on the so-called Leibniz' Law, which is different (but resembles) what passes for it in logic and philosophy, and one on the status of identity, as accepted by mathematicians and logicians, in physics. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Automata, reason, and free will: Leibniz's critique of Descartes on animal and human nature.

This paper argues that Leibniz's use of the concept of "automaton" to characterize the nature of souls and bodies of living beings constitutes a systematic critique of Descartes' earlier use of automata. Whereas Descartes conceived non-human animals in terms of mechanical automata, he also denied that the human rational soul can be modeled on the nature of an automaton. In contrast, Leibniz understood living things to involve both an organic body, or "natural automaton," as well as an immaterial soul, or "spiritual automaton," that spontaneously produces its own perceptions. In extending the concept of the automaton to souls, Leibniz rejected key Cartesian assumptions about animals and free will and draws on the concept of the automaton to understand a range of cognitive capacities including volition. Leibniz thus occupies a distinctive place in the history of the use of automata to understand the nature of living things.

Rethinking the protein folding problem from a new perspective.

One of the main concerns of Anfinsen was to reveal the connection between the amino-acid sequence and their biologically active conformation. This search gave rise to two crucial questions in structural biology, namely, why the proteins fold and how a sequence encodes its folding. As to the why, he proposes a plausible answer, namely, the thermodynamic hypothesis. As to the how, this remains an unsolved challenge. Consequently, the protein folding problem is examined here from a new perspective, namely, as an 'analytic whole'. Conceiving the protein folding in this way enabled us to (i) examine in detail why the force-field-based approaches have failed, among other purposes, in their ability to predict the three-dimensional structure of a protein accurately; (ii) propose how to redefine them to prevent these shortcomings, and (iii) conjecture on the origin of the state-of-the-art numerical-methods success to predict the tridimensional structure of proteins accurately.

Representation of the Universe as a Dendrogramic Hologram Endowed with Relational Interpretation.

A proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretical implicate order structure given by p-adic numbers. This number field was zero-dimensional, totally disconnected, and disordered. Physical systems (such as electrons, photons) are sub-dendrograms of the universal dendrogram. Measurement process is described as interactions among dendrograms; in particular, quantum measurement problems can be resolved using this process. The theory is realistic, but realism is expressed via the the Leibniz principle of the Identity of Indiscernibles. The classical-quantum interplay is based on the degree of indistinguishability between dendrograms (in which the ergodicity assumption is removed). Depending on this degree, some physical quantities behave more or less in a quantum manner (versus classic manner). Conceptually, our theory is very close to Smolin's dynamics of difference and Rovelli's relational quantum mechanics. The presence of classical behavior in nature implies a finiteness of the Universe-dendrogram. (Infinite Universe is considered to be purely quantum.) Reconstruction of events in a four-dimensional space type is based on the holographic principle. Our model reproduces Bell-type correlations in the dendrogramic framework. By adjusting dendrogram complexity, violation of the Bell inequality can be made larger or smaller.

Spinoza on the resistance of bodies.

Commentators often claim that the bodies of Spinoza's physics resist the changes they undergo. But it's not always clear what they mean when they say this, or whether they are entitled to say it. This article clarifies what it might mean to for Spinoza's bodies to resist change, and examines the evidence for such a view. In the first half, the author argues that there is some limited evidence for such a view, but not nearly as much as people think. In the second half, the author proposes looking for a mental analogue to collision in the realm of ideas and argues that adequacy amounts to a meaningful concept of resistance in Spinoza, albeit one that is incomplete.

New insight into the origins of the calculus war.

The consensus today is that both Newton and Leibniz created calculus independently. Yet, this was not so clear at the beginning of the eighteenth century. A bitter controversy took place at that time, which came to be known as the 'calculus war', probably the greatest clash in the history of science. While it is accepted that the debate started when Fatio de Duillier publicly accused Leibniz of plagiarism in 1699, earlier evidence of its origins can be found in an exchange of letters between Leibniz and Huygens.

Fish and fishpond. An ecological reading of G.W. Leibniz's Monadology §§ 63-70.

One of Leibniz's most original ideas is his conception of the living individual as a hierarchical network of living beings whose relationships are essential to the proper functioning of its organic body. This idea is also valid to explain any existing order in nature that depends on the set of relationships of living beings that inhabit it. Both ideas are present in the conception of the natural world that Leibniz presents in his Monadology (§§ 63-70) through his idea of biological infinitism. According to this idea, nature consists of infinite theatres (some within others and some unfolding from others) where living beings unfold their vital functions. Through this idea Leibniz defines both the biological complexity of nature and the living individual, which is in turn a portion of nature that unfolds from an infinite set of inferior living beings. The thesis that I defend in this work is that this Leibnizian understanding of the living individual and the natural complexity that includes infinite hierarchical levels of individuality has a marked ecological sense, as we would say today. This Leibnizian metaphysics of individuality that we could call biological is also interesting in light of the recent studies in the philosophy of biology.

Articulações entre o Pensamento de Leibniz e Robine: A Gestalt-terapia Inspirada através da Dobra / Joints between Leibniz and Robine's Thought: The Gestalt-therapy Inspired through the Fold / Articulaciones entre el Pensamiento de Leibniz y Robine: La terapia Gestalt Inspirada por el Pliegue

Este artigo visa aprofundar o conceito de "dobra", mencionado pelo livro "O Self Desdobrado", de Jean-Marie Robine, articulando este conceito às contribuições de Deleuze, através de sua obra intitulada "A Dobra - Leibniz e o Barroco". Para realizar tal articulação, será realizada uma contextualização histórica em relação às críticas leibnizianas ao pensamento cartesiano. Tomando a noção de dobra, segundo a interpretação de Deleuze sobre o trabalho leibniziano, como uma nova fundamentação paradigmática, serão apresentadas algumas possibilidades de utilização na prática clínica da abordagem gestáltica. Serão trazidas novas contribuições de Jean-Marie Robine ao conceito de Self da Gestalt-terapia. Concluindo o artigo, serão apresentadas argumentações tecendo uma plausível analogia entre o pensamento cartesiano tomado como fundamento, e algumas tendências contemporâneas da política brasileira. Reconhecendo como a base de pensamento a partir de um plano cartesiano, pode sugerir uma forma simplificada e reducionista de encarar temas complexos, sistemáticos, e como tal tendência de pensamento é encontrada presentemente em discursos de líderes políticos brasileiros. (AU)

This article aims to deepen the concept of "fold", mentioned in the book "The Unfolded Self", by Jean-Marie Robine, articulating this concept to the contributions of Deleuze, through his work entitled "The Fold - Leibniz and the Baroque". In order to accomplish this articulation, a historical contextualization will be made in relation to the lebnizian critiques of Cartesian thought. Taking the notion of fold, according to Deleuze's interpretation of the leibnizian work, as a new paradigmatic foundation, some possibilities of use in clinical practice of the gestation approach will be presented. New contributions from Jean-Marie Robine will be brought to the concept of Self of Gestalt-therapy. Concluding the article, arguments will be presented that make a plausible analogy between Cartesian thought taken as a foundation, and some contemporary tendencies of Brazilian politics. Recognizing how the basis of thought from a Cartesian plan can suggest a simplified and reductionist way of facing complex and systematic issues, and how such a trend of thought is currently found in speeches of Brazilian political leaders. (AU)

Este artículo pretende profundizar el concepto de "pliegue", mencionado en el libro "El Self Desdoblado", de Jean-Marie Robine, articulando este concepto a las aportaciones de Deleuze, a través de su obra titulada "El pliegue - Leibniz y el Barroco". Para lograr esta articulación, se hará una contextualización histórica en relación con las críticas lebnizianas del pensamiento cartesiano. Tomando la noción de pliegue, según la interpretación de Deleuze de la obra leibniziana, como nuevo fundamento paradigmático, se presentarán algunas posibilidades de uso en la práctica clínica del enfoque gestáltico. Nuevas contribuciones de Jean-Marie Robine serán aportadas al concepto de Self de la terapia Gestalt. Concluyendo el artículo, se presentarán argumentos que hacen una analogía plausible entre el pensamiento cartesiano tomado como base, y algunas tendencias contemporáneas de la política brasileña. Reconocer cómo la base del pensamiento de un plan cartesiano puede sugerir una forma simplificada y reduccionista de enfrentar temas complejos y sistemáticos, y cómo esa tendencia de pensamiento se encuentra actualmente en los discursos de los líderes políticos brasileños. (AU)

Co-fermentation of the main sugar types from a beechwood organosolv hydrolysate by several strains of Bacillus coagulans results in effective lactic acid production.

Bacillus coagulans is an interesting facultative anaerobic microorganism for biotechnological production of lactic acid that arouses interest. To determine the efficiency of biotechnological production of lactic acid from lignocellulosic feedstock hydrolysates, five Bacillus coagulans strains were grown in lignocellulose organosolv hydrolysate from ethanol/water-pulped beechwood. Parameter estimation based on a Monod-type model was used to derive the basic key parameters for a performance evaluation of the batch process. Three of the Bacillus coagulans strains, including DSM No. 2314, were able to produce lactate, primarily via uptake of glucose and xylose. Two other strains were identified as having the ability of utilizing cellobiose to a high degree, but they also had a lower affinity to xylose. The lactate yield concentration varied from 79.4 ±â€¯2.1 g/L to 93.7 ±â€¯1.4 g/L (85.4 ±â€¯4.7 % of consumed carbohydrates) from the diluted organosolv hydrolysate.

Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities.

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens type.

Leibniz on the requisites of an exact arithmetical quadrature.

In this paper we will try to explain how Leibniz justified the idea of an exact arithmetical quadrature. We will do this by comparing Leibniz's exposition with that of John Wallis. In short, we will show that the idea of exactitude in matters of quadratures relies on two fundamental requisites that, according to Leibniz, the infinite series have, namely, that of regularity and that of completeness. In the first part of this paper, we will go deeper into three main features of Leibniz's method, that is: it is an infinitesimal method, it looks for an arithmetical quadrature and it proposes a result that is not approximate, but exact. After that, we will deal with the requisite of the regularity of the series, pointing out that, unlike the inductive method proposed by Wallis, Leibniz propounded some sort of intellectual recognition of what is invariant in the series. Finally, we will consider the requisite of completeness of the series. We will see that, although both Wallis and Leibniz introduced the supposition of completeness, the German thinker went beyond the English mathematician, since he recognized that it is not necessary to look for a number for the quadrature of the circle, given that we have a series that is equal to the area of that curvilinear figure.

Approaching Bilinear Multipliers via a Functional Calculus.

We propose a framework for bilinear multiplier operators defined via the (bivariate) spectral theorem. Under this framework, we prove Coifman-Meyer type multiplier theorems and fractional Leibniz rules. Our theory applies to bilinear multipliers associated with the discrete Laplacian on Z d , general bi-radial bilinear Dunkl multipliers, and to bilinear multipliers associated with the Jacobi expansions.

Who Discovered the Binary System and Arithmetic? Did Leibniz Plagiarize Caramuel?

Gottfried Wilhelm Leibniz (1646-1716) is the self-proclaimed inventor of the binary system and is considered as such by most historians of mathematics and/or mathematicians. Really though, we owe the groundwork of today's computing not to Leibniz but to the Englishman Thomas Harriot and the Spaniard Juan Caramuel de Lobkowitz (1606-1682), whom Leibniz plagiarized. This plagiarism has been identified on the basis of several facts: Caramuel's work on the binary system is earlier than Leibniz's, Leibniz was acquainted-both directly and indirectly-with Caramuel's work and Leibniz had a natural tendency to plagiarize scientific works.

The publication of Newton's Opera Omnia in Geneva and Lausanne (1739-1761): A chapter in the reception of Newtonianism.

During the eighteenth century, several towns located in what is known today as the Suisse romande were extremely receptive toward scientific culture, and most notably Newtonianism. In this paper I deal with a nine-volume publication of Newton's Opera Omnia that was planned in Geneva and Lausanne during the late 1730s and 1740s. This publication has not received the attention it deserves. To the best of my knowledge, even an awareness of its existence is lacking in the literature devoted to the reception of Newtonianism. This paper examines the circumstances of the publication of a complete set of all of Newton's works known at the time, and the motivations of the editors, mathematicians, and publishers who were involved in this editorial enterprise.

Leibniz, the microscope and the concept of preformation.

In recent years a certain emphasis has been put by some scholars on Leibniz's concern about empirical sciences and the relations between such concern and the development of his mature metaphysical system. In this paper I focus on Leibniz's interest for the microscope and the astonishing discoveries that such instrument made possible in the field of the life sciences during the last part of the Seventeenth century. The observation of physical bodies carried out by the "magnifying glasses" revealed a matter swarming everywhere with life and activity, contrary to the cartesian and atomistic view of matter as something sterile and passive. Moreover, the discovery of uncountable complete "animalcula" living in the smallest drop of water provided evidence for the idea of the preformation of every organism. During his lifetime, Leibniz was extremely watchful about the new microscopical discoveries and came into contact with some of the major "observers" of his time, such as Hooke, Leeuwenhoek, Swammerdam and Malpighi. Relying both on some passages in Leibniz's texts and on recent critical studies, I will argue that important aspects of his metaphysics have been strongly affected by the empirical observation of the "invisible world" which the microscope made possible. In the last part of the paper I show how the concept of "preformation", originally drawn from the context of the life sciences, comes to play in Leibniz's philosophy a very general role, going far beyond the scope of biology and shaping important aspects of his overall philosophical system.

Did Samuel Clarke really disavow action at a distance in his correspondence with Leibniz?: Newton, Clarke, and Bentley on gravitation and action at a distance.

In this paper I ague against John Henry's claim that Newton embraced unmediated action at a distance as an explanation of gravity (Henry, 1994, 1999, 2011, 2014). In particular, I take issue with his apparent suggestion that the fact, as he sees it, that two of Newton's prominent followers, namely, Richard Bentley and Samuel Clarke, embraced unmediated action at a distance as an explanation of gravity provides significant supporting evidence that Newton did as well (see Henry, 1994 and 1999). Instead, I argue that while Bentley did ultimately defend the notion of unmediated action at a distance as an explanation of gravity, Newton himself accepted that notion neither in his correspondence with Bentley, as Henry has maintained, nor in any of his later works. I also provide evidence that suggests that Newton did, in fact, accept both the principle of local causation and the passivity of matter. Finally, I argue that whatever the case may be with respect to Newton on the matter, it is clear from his correspondence with Leibniz, as well as from his Boyle lectures, that contrary to what Henry has maintained, Clarke was a stalwart opponent of unmediated action at a distance due to his strong commitment to both the principle of local causation and the passivity of matter.

[Agonism and antagonism]. / Agonisme et antagonisme Agonismo e antagonismo.

This essay considers dissensus as the starting point for the construction of a common epistemic space rather than as the acknowledgement of an irreducible disagreement. In the argumentative confrontation and disagreements, we do not want to identify a process which might lead to agreement through rational debate. The aim of this essay is rather to understand how dissensus leads to the constitution of plural communities. It discusses a certain number of texts of political philosophy (Habermas, Mouffe, etc.), where the notion of agreement is crucial to an analysis of argumentative confrontations. This essay uses the hypothesis to analyse the circulation of Leibniz's dynamics in his correspondence with De Volder. This perspective shows eventually that dissensus is not an obstacle but the basis on which multiple circulations of theories are possible.