The Shannon information function (H) has been extensively used in ecology as a statistic of species diversity. Yet, the use of Shannon diversity index has also been criticized, mainly because of its ambiguous ecological interpretation and because of its relatively great sensitivity to the relative abundances of species in the community. In my opinion, the major shortcoming of the traditional perspective (on the possible relation of species diversity with information theory) is that species need for an external receiver (the scientist (...) or ecologist) to exist and transmit information. Because organisms are self-catalized replicating structures that can transmit genotypic information to offspring, it should be evident that any single species has two possible states or alternatives: to be or not to be. In other words, species have no need for an external receiver since they are their own receivers. Therefore, the amount of biological information (at the species scale) in a community with one only species would be species, and not bits as in the traditional perspective. Moreover, species diversity appears to be a monotonic increasing function of (or S) when all species are equally probable (S being species richness), and not a function of as in the traditional perspective. To avoid the noted shortcoming, we could use 2H (instead of H) for calculating species diversity and species evenness (= 2H/S). However, owing to the relatively great sensitivity of H to the relative abundances of species in the community, the value of species dominance (= 1 − 2H/S) is unreasonably high when differences between dominant and subordinate species are considerable, thereby lowering the value of species evenness and diversity. This unsatisfactory behaviour is even more evident for Simpson index and related algorithms. I propose the use of other statistics for a better analysis of community structure, their relationship being: species evenness + species dominance = 1; species diversity × species uniformity = 1; and species diversity = species richness × species evenness. (shrink)

A novel thermodynamic perspective on natural selection is presented. In the case that life continuity is optimized in an ideal system, where relatively constant and homogeneous selective pressures favour a given competing species, natural selection leads that system to a stationary state of maximum genotypic uniformity of life and maximum sustainable consumption of available energy by life (competitive equilibrium). Structurally and functionally, this optimizing tendency towards competitive equilibrium looks similar to the optimizing tendency towards thermodynamic equilibrium of classical thermodynamics (maximum (...) energetic uniformity and maximum degradation of available energy). The principle of competitive exclusion may thus be conceptually viewed as an ecological manifestation of the second law of (classical) thermodynamics. On the other hand, the novel thermodynamic perspective on natural selection is discussed with regard to the open and nonequilibrium system of nature, where selective pressures vary in space and time. In this case, natural selection can induce diversity instead of uniformity, though an optimizing tendendcy towards maximum sustainable consumption of resources (optimization of life continuity) always remains. Overall, it is concluded that the action of natural selection favours the maximization of the sustainable consumption of energy at the level of individual organism. (shrink)

El pensamiento politico medieval concibe a la ley como esencialmente ligada a un concepto de justicia superior y objetivo. El trabajo procura zanjar las divergencias en tomo del concepto ley en Marsilio de Padua. Para ella, se efectua un analisis de la ecuacion entre las facultades cognoscitivas y volitivas que aparecen en el tratamiento del fin de la ley, de las cualidades personales requeridas para el juez, y de la idoneidad dellegislador humano. La ley debe poseer un contenido de justicia (...) que es objeto de una captacion racional y de un recto querer. Sin embargo, ese concepto de justicia adquiere en Marsilio una definicion estrictamente politica: se trata del "equilibria" o la "medida" que deben alcanzar los actos transitivos de los hombres, can el fin de preservar la comunidad politica. (shrink)

This paper explores the ethical dilemma of conflicting loyalties found in whistleblowing. Central to this dilemma is the internal/external disclosure dichotomy; disclosure of organisational wrongdoing to an external recipient is seen as disloyal, whilst disclosure to an internal recipient is seen as loyal. Understanding how the organisation and society have dealt with these problems over the last 30 years is undertaken through an analysis of Vandekerckhove’s project, which seeks to place the normative legitimisations of whistleblowing legislation and organisational whistleblowing policies (...) within a globalisation semantic able to contain this conflict between society and the organisation. This project fails, it is argued, because of Vandekerckhove’s particular understanding of the organisation as an autopoietic system, i.e. an operationally closed system. A case is made to understand organisations as complex systems, i.e. operationally open systems. Critical Complexity theory sees the identities of systems and components as coterminous. In the context of the organisation, this means that the identities of the corporation and its corporate members arise and die together. The whistleblower’s disclosure reconfigures the organisation by forcing the organisation to open up and make its boundaries flexible, making the designation ‘internal’ or ‘external’ to the organisation, and, therefore, who qualifies as a recipient of a disclosure of wrongdoing, flexible. The organisation is restrained from retailing against the whistleblower, because its identities are coterminous. Furthermore, as the disclosure cannot be categorically defined as either internal or external, the question of whether an external disclosure can qualify as an act of organisational loyalty becomes moot. (shrink)

Nos últimos anos, cada vez mais os "ismos" estão sendo deixados de lado. Neste sentido, quando se fala de aristotelismo ou de averroísmo de Marsílio de Pádua, torna-se necessário examinar o que se entende precisamente por tais atributos e, depois, até que ponto, mesmo de forma aproximativa, eles podem ser aplicados a Marsílio.

La doctrtna de Tomás de Aquinorespecto de la delimitación ·entre e! ámbito de lo"natural" - entendiendo por tal la naturaleza"Inferior", esta.. es, e! · ámbito de lo. máterial,corporal y sensible - y el ámbito de lo humanopuede ser reconstruida entres momentos: a) unaintegración inicial dei hombre ai ámbito de lonatural - en particular por la doctrina de launidad esencial de alma y cuerpo; b) una relativaemergencia o trascendencia dei hombre respectodei lo material - en especial por · 1a subsistenciadei alma (...) racional humana y la trascendencia desu fin último; c) una slntesis que marca lacontinuatio entre naturaleza. y hombre, en lamedida en que éste es concebido como "fin detàda la generación". La orientación teleológica dela naturaleza que tiende hacia el hombre, puedeadvertirse en la creciente perfección dei disefiodei orden de las formas naturales, en lascondiciones físicas propias de la corporalidad.humana, y el en proceso generativo dei embriónhumano. En cada caso, ai tender hacia elhombre, la naturaleza busca, en forma mediata,trascenderse a sí misma. (shrink)

El trabajo pone en cuestión la pertinência de la atribución de una concepción contractualista de estilo moderno a Marsilio de Pactua. El análisis de los principales textos del Defensor pacis no muestra la afirmación de un hipotético estado no social dei hombre, ni un fundamento exclusivamente voluntarista o racionalista de la sociedad política, ni una fundamentación de la legitimidad del poder político en la figura de um contrato efectuado por indivíduos autónomos que precedan - temporal o lógicamente - a la (...) constitución de la sociedad política. (shrink)

El trabajo se ocupa de la sección de las Glosas a la Isagogé de Porfirio de Pedro Abelardo dedicada a las tres cuestiones sobre los universales. La parte “destructiva”, en la que Abelardo somete a crítica las doctrinas realistas de Guillermo de Champeaux no tiene un sentido meramente negativo, sino que busca llegar al punto de partida de la propia posición de Abelardo: las cosas no sólo difieren por sus formas (accidentes), sino también por sus materias (esencias). Al hablar de (...) la imagen correspondiente al nombre universal, Abelardo no se detiene a explicar la formación del concepto universal a partir de la cosa, sino que más bien se refiere a la significación intelectual de los términos, en tanto “generan intelecciones”. Esta omisión puede explicarse por el hecho de que, para Abelardo, la inteligencia humana rara vez o nunca llega a captar las esencias de las cosas. (shrink)

My starting point in this article is that investigating the ethics of autonomous vehicles through the lens of the trolley problem is not only limited but also unethical. I construct my case by aligning myself with Niklas Toivakainen, who argues against David Gunkel’s reading of Levinasian ethics as an answer to the “Machine Question”. I adumbrate Toivakainen’s critique that the attempt to give a Levinasian face to the machine is an example of a compensatory logic – a way to avoid (...) a deeper exploration of the moral dynamics from which our technologies emerge. I offer an extended reading of Levinas’s formulation of the face of the other to argue that while the machine cannot signify as a face, the machine can announce or anticipate the signification of the face which the self is infinitely responsible to. I reach this conclusion through focusing on the uncertainty and ambiguity of the signification of the face. I then argue that current approaches to the ethics of autonomous vehicles, based on variations of the trolley problem, fail to locate ethical responsibility to the other, precisely in its attempts to evade uncertainty. I demonstrate how an embrace of uncertainty can make the ethics of autonomous vehicles more ethical through a consideration of the concept of shared space and naked streets in the work of the late Dutch traffic engineer Hans Monderman. (shrink)

El trabajo se ocupa de la concepción acerca de la función y los límites de la enseñanza en el diálogo De magistro de Agustín de Hipona y en la undécima de las Cuestiones disputadas sobre la verdad de Tomás de Aquino. Explorando los límites del lenguaje y de la comunicación, Agustín concluye que el maestro propiamente no enseña, a lo sumo, advierte al discípulo para que pueda reconocer la verdad iluminado por el Maestro Interior. Para Aquino, el maestro propiamente puede (...) enseñar, pero con ello no hace más que asistir al discípulo para que efectúe con su razón el mismo recorrido que hace la razón humana al derivar las conclusiones de la ciencia a partir de los principios del conocimiento humano. A pesar de sus diferencias, ambos coinciden en que la enseñanza es cualquier cosa menos una “transferencia del saber”. (shrink)

O presente artigo trata do caráter contingente ou necessário da relação causal entre a causa primeira e seu efeito, tal como apresentada por Avicena e Tomás de Aquino. Para tanto, aborda o paralelismo no tratamento da inteligência e vontade divinas por parte de ambos os autores. Ambos aceitam que Deus conhece a si mesmo e, conhecendo-se, conhece aquilo que lhe é distinto. Aceitam igualmente que Deus quer ou ama a si mesmo e, querendo a si mesmo, quer acidentalmente o que (...) lhe é distinto. No entanto, discordam com respeito à necessidade ou contingência do mundo. Para Avicena, o mundo é possível em si mesmo, mas “necessário por outro”. Para Tomás, que Deus queira o mundo com necessidade hipotética corresponde mais à necessidade do querer divino, sem que isso determine a contingência ou necessidade do mundo. Com efeito, na visão tomista, é preferível um universo no qual haja mescla de necessidade e contingência, pois isso representa melhor as múltiplas perfeições divinas. (shrink)

The objective of this study was to develop and determine the psychometric properties of an instrument designed to detect traits and behavior that are associated with predatory violent behavior, which is defined as a determined, planned, controlled, and proactive aggression. The sample was comprised of 546 students, mostly in their last year of high school or in their first year of college. The initial instrument had 78 items, ultimately resulting in 15 with good internal consistency (α =.825). Factor analysis showed (...) four factors: anger-in, appeal for weapons, suicidal ideation, and the tendency to take justice into one’s own hands. Said factors showed significant correlations of convergent validity. Data shown here allows inferring that the instrument is a novel and concise tool that evaluates and detects the potential of predatory violent behavior. (shrink)

A la luz de algunas críticas recientes, en el marco de este texto se busca impulsar un debate que tiene lugar en dos frentes: por una parte, la lógica del origen de la lógica y, por otra parte, la relación entre psicoanálisis y marxismo. Para ello se recuperan algunos textos publicados por Alain Badiou hacia finales de la década de 1960, en los que polemiza con Jacques-Alain Miller alrededor de los concepto de "sutura" y "sujeto" (Zizek), para situar tanto las (...) diversas posiciones como las coherentes reconsideraciones a lo largo de su trayectoria intelectual. En efecto, desde "El concepto de modelo" hasta su más reciente trilogía (Teoría del sujeto, El ser y el acontecimiento y Lógica de los Mundos), se propone una perspectiva que lejos de establecer jerarquías y subordinaciones busca promover conexiones a partir de las especificidades y las diferencias a través de esa vía particular que es la filosofía. De este modo resulta posible apreciar que, pese a su crítica respecto de la primacía de la lógica del significante, los conceptos propuestos por Jacques Lacan funcionaron como una notoria fuente de inspiración para Badiou, especialmente en relación con el sujeto del inconsciente. (shrink)

Las miopatías metabólicas son un grupo de trastornos genéticos que disminuyen la capacidad del músculo esquelético para utilizar sustratos energéticos y sintetizar ATP. Estas alteraciones pueden clasificarse en tres tipos fundamentalmente: i) trastornos del metabolismo de los carbohidratos (del glucógeno y de la glucosa), ii) defectos del metabolismo lipídico, y iii) alteraciones de la fosforilación oxidativa –OXPHOS-. Las dos primeras se deben a deficiencias enzimáticas de las rutas metabólicas de degradación y síntesis de glúcidos y lípidos y muestran diversas manifestaciones (...) clínicas, pero una buena parte de ellas cursan con intolerancia al ejercicio. Aunque un buen número de pacientes con estos trastornos musculares presentan síntomas en la infancia, el diagnóstico normalmente se retrasa hasta la segunda y tercera década de la vida. Por tanto, reconocer las características clínicas de estas deficiencias conduce a un diagnóstico precoz y a un mejor tratamiento. Las enfermedades mitocondriales son un grupo de trastornos originados por una deficiencia en la síntesis de ATP a través del sistema de fosforilación oxidativa. Este sistema está formado por proteínas codificadas en los dos genomas de la célula (nuclear y mitocondrial) y, por tanto, pueden presentar un modelo de herencia mendeliano o materno. En esta revisión se describirán las características especiales del sistema genético mitocondrial y las principales mutaciones que causan enfermedades en humanos. (shrink)

Referirse a la multiplicidad es un lugar común cuando se trata de la obra de Alain Badiou, en tanto es una producción de una notoria complejidad y la exploración de sus diversas facetas es adentrarse en un universo de múltiples dimensiones. En este sentido, se propone comparar su producción con un caleidoscopio, un artefacto que revela la multiplicidad como esencia de la unidad y, a su vez, confiere significado a esa diversidad. Esta multiplicidad caleidoscópica no se limita únicamente a la (...) figura del intelectual y sus escritos, sino que se expande hacia otros ámbitos. En efecto, al analizar sus primeras obras y los inicios de su trayectoria intelectual se vuelve evidente la influencia de Sartre, así como sus conexiones posteriores con el estructuralismo francés y, en particular, con la figura de Louis Althusser. Por otra parte, interesa aquí destacar que las producciones de Badiou, lejos de encerrarse en debates del ámbito académico, se entrelazan con tópicos como la cuestión del amor, la cual se conecta de modo directo con el resto de sus reflexiones teóricas y políticas. De este modo, interesa aquí apreciar esta particular intersección que permite una comprensión más profunda de su pensamiento y su preocupación radical por lo social. (shrink)

A INTERFERÊNCIA DO PODER EXECUTIVO NOS ORÇAMENTOS DO PODER JUDICIÁRIO E DO MINISTÉRIO PÚBLICO: SEPARAÇÃO DOS PODERES E IMPACTOS NO EXERCÍCIO DE SUAS FUNÇÕES INSTITUCIONAIS.

We study active set methods for optimization problems in Block Angular Form (BAF). We begin by reviewing some standard basis factorizations, including Saunders' orthogonal factorization and updates for the simplex method that do not impose any restriction on the pivot sequence and maintain the basis factorization structured in BAF throughout the algorithm. We then suggest orthogonal factorization and updating procedures that allow coarse grain parallelization, pivot updates local to the affected blocks, and independent block reinversion. A simple parallel environment appropriate (...) to the description and complexity analysis of test procedures is defined in Section 5. The factorization and updating procedures are presented in Sections 6 and 7. Our update procedure outperforms conventional Updating procedures even in a purely sequential environment. (shrink)

El presente artículo, a partir de la obra del intelectual palestino Edward W. Said, pretende rememorar, tras sesenta años de colonización y ocupación israelí, la Naqbah palestina, es decir, indagar las verdaderas y catastróficas consecuencias de la creación de un «hogar nacional judío» en las tierras de la Palestina histórica. A su vez, se realiza un análisis de la situación de los refugiados palestinos como uno de los más esenciales y trágicos efectos de la creación del Estado de Israel. Así, (...) se perfila la negación sistemática de la ciudadanía para con los refugiados palestinos tanto en el interior de Israel, como en el Líbano, Egipto, o Jordania. (shrink)

ABSTRACT Objective: To contrast relief efforts for the 26 December 2004 tsunami with current global HIV/aids relief efforts and analyse possible reasons for the disparity. Methods: Literature review and ethical analysis. Results: Just over 273,000 people died in the tsunami, resulting in relief efforts of more than US$10 bn, which is sufficient to achieve the United Nation’s long‐term recovery plan for South East Asia. In contrast, 14 times more people died from HIV/aids in 2004, with UNAIDS predicting a US$8 bn (...) funding gap for HIV/aids in developing nations between now and 2007. This disparity raises two important ethical questions. First, what is it that motivates a more empathic response to the victims of the tsunami than to those affected by HIV/AIDS? Second, is there a morally relevant difference between the two tragedies that justifies the difference in the international response? The principle of justice requires that two cases similarly situated be treated similarly. For the difference in the international response to the tsunami and HIV/aids to be justified, the tragedies have to be shown to be dissimilar in some relevant respect. Are the tragedies of the tsunami disaster and the HIV/aids pandemic sufficiently different, in relevant respects, to justify the difference in scope of the response by the international community? Conclusion: We detected no morally relevant distinction between the tsunami and the HIV/aids pandemic that justifies the disparity. Therefore, we must conclude that the international response to HIV/aids violates the fundamental principles of justice and fairness. (shrink)

O texto parte da parábola do bom samaritano para discorrer sobre a contribuição que uma pessoa pode dar para atenuar o sofrimento de uma outra e, em contrapartida, a violência que significa a indiferença ante a dor alheia. Essa parábola ensina que se deve dar especial atenção às pessoas mais frágeis e menos favorecidas da sociedade e que o próximo é a pessoa que está a seu alcance e que esteja padecendo com sua própria miséria, não importando se é um (...) desconhecido ou mesmo um inimigo. Acrescenta que a mobilização para ajudar envolve sacrifício pessoal, mas quando é motivada por amor, não depende nem gera um desejo de retribuição para si. (shrink)

Neste trabalho, investigamos relações que autores psicanalíticos fazem entre histeria e literatura. Fizemos um estudo dos artigos destes autores, e o objetivo foi de expor as temáticas abordadas por eles quando reúnem e interpretam juntas histeria, psicanálise e literatura. Historicamente, tanto a h..

The aim of this paper is to indicate in a contemporary perspective how transhumanism fits into religious discourse as, in seeking to resignify human existence and lead humanity to a posthuman dimension, it finds roots in the ancient gnostic movements, transforming itself into a new Contemporary religion. Given this, we will first try to identify common ground between Gnosticism and Transhumanism, especially the idea linked to the denial of corporeality. In a second moment, we will show the dangers that transhumanism (...) faces when it intends to give man powers to modify its existence, dispensing with the figure of the creator God. (shrink)

: It is often argued that while Kant grounds practical freedom in the idea of transcendental or absolute freedom in the Dialectic of the First Critique, he would have explicitly dissociated these concepts in the Canon. For, in contradiction with the Dialectic, Kant claims in the Canon that through experience we know practical freedom to be one of the natural causes and that the transcendental freedom could be left aside as irrelevant. These claims are usually interpreted in the light of (...) the socalled “patchwork theory” as evidence of an inconsistency between the two sections of the First Critique and of a defense of a mere comparative, compatibilistic or even psychological concept of freedom by Kant in the Canon. In contradistinction to this widespread interpretation, I intend to provide an alternative interpretation of the Canon by showing that the concept of practical freedom contained in it is a genuinely incompatibilistic one and that this section can be reconciled with the Dialectic. Moreover, I intend to show that Henry Allison’s allegedly alternative interpretation is entirely misguided. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

O presente texto se propõe a pensar a problemática afrobrasileira, em especial sua inserção no contexto escolar a partir da Lei 10.639/03, apresentando a capoeira como elo entre educação e cultura afrobrasileira. Esta abordagem será feita a partir de conceitos filosóficos, culturais e educacionais importantes como afroperspectivismo, ancestralidade, cultura oral e popular, assim como a questão da historicidade pensando sua relação com a capoeira.

This article explores the metaphor of Science as provider of sharp images of our environment, using the epistemological framework of Objective Cognitive Constructivism. These sharp images are conveyed by precise scientific hypotheses that, in turn, are encoded by mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leading to the emergence of eigen-solutions characterized by the four essential properties of precision, stability, separability and composability. Finally, this article discusses (...) the role played by ontology and metaphysics in the scientific production process, and in which sense the resulting knowledge can be considered objective. (shrink)

Estudos sobre eficácia escolar, bem como o conceito de capital cultural de Pierre Bourdieu, evidenciam que o contexto socioeconômico e cultural – ou o background – exerce papel fundamental nas notas e resultados obtidos pelos estudantes em exames. Ou seja, segundo esta teoria, alunos com menor background tenderiam a apresentar desempenho inferior em comparação com alunos oriundos de um contexto socioeconômico e cultural mais privilegiado. Nesse sentido, considerando que os bolsistas do Programa Universidade para Todos devem possuir desvantagem de background (...) em relação aos seus colegas pagantes, tendencialmente o seu desempenho deveria ser inferior, afinal o programa, criado em 2004, busca viabilizar o acesso à educação superior por meio da concessão de bolsas de estudos integrais ou parciais de 50%, a estudantes com renda familiar per capita de zero a três salários mínimos que cursaram o ensino médio em escolas públicas ou em escolas privadas na condição de bolsistas. Entretanto, percepções subjetivas de docentes indicam que nem sempre é isso que ocorre, ou seja, bolsistas estariam obtendo, em diversas situações, melhores resultados que os colegas pagantes nas disciplinas que cursam em instituições privadas. Nesse contexto, com o objetivo de refletir sobre aspectos fundamentais da qualidade e da equidade do Prouni, o presente artigo problematiza a suposta superioridade de notas dos bolsistas em disciplinas e no Enade e, ao mesmo tempo, analisa hipóteses que explicariam o desempenho além do esperado desses estudantes provenientes de meios populares. Quanto ao desenvolvimento metodológico da pesquisa, são utilizadas duas fontes de dados. A primeira delas é composta por microdados das avaliações de disciplinas de uma universidade comunitária do Rio Grande do Sul entre os anos de 2009 e 2012. A segunda consiste nos dados do Enade referentes ao ano de 2006. Palavras-chave : Capital cultural. Background. Educação superior. Prouni. (shrink)

This study integrates corpus-assisted text analysis with frame semantics to study a social problem. Taking a cognitive-linguistic approach to critical discourse studies, in this article I examine the linguistic construction of minors in a corpus of 489 articles from the Uruguayan newspaper El País in the context of the so-called ‘Criminal Imputability Referendum’. Throughout, I focus on the construal operation of framing and identify a host of discursive patterns via which minors and adolescents are recurrently placed within the semantic frame (...) CRIME, and within this, they profile the frame elements of perpetrators of violent crimes rather than victims. I argue that, in the context of the referendum, these discursive strategies run the risk of facilitating the consolidation of a strong conceptual link whereby youth become readily associated with criminality, and are subservient to the political views of groups supporting a lower cut-off age for criminal responsibility and more stringent punishments. The observations arrived at in this instance set the foundations for a future experimental study testing whether the discursive patterns unearthed here have an effect on how readers conceptualize minors outside the texts. (shrink)

The purpose of this article consists in offering the reader an initial reflection on five spots to understand identity, thus allowing strong articulating elements —and limitations implied in the category— to be found. A walkaround through the text unveils five authors’ stances with different understanding horizons: Charles Taylor, Ernest Tugendhat, Kwame Appiah, Amartya Sen and Paul Ricoeur. From their statements, some common elements are approached and tentative conclusions are traced, providing closure with further inquiry to the dialogue with university students (...) in the context of Colombia’s Bicentennial Independence Commemoration. (shrink)

Cabrera introduces the reader to philosophy through the analysis of specific moments in various films, which lets him think about the philosophical matters manifested in them. In short, one hundred years of images trying to rethink 2500 years of thinking.

This article discusses the mathematizing of the chemical periodic system as a grid, which leads to a quadratic function or “binódica function” formed by pairs of periods or binodos. We describe the periodic law as an increasing function of the principal quantum number. It works subject to the dialectical laws that generate; first: gradual quantitative changes:, with “duplication” of periods:. Second: radical quantitative changes:, with the emergence of new quantum transitions, growth and a change in the format of the binodos. (...) We use analytical and graphic methods to mathematize Mendeleev’s law, making the size of the binodos and the continuous series depend on the number of the binode, which is the same quantum number. Likewise, we show a graphic representation, in 2D, of a continuous and self-similar spiral function of the elements, in a geometric growth pattern. (shrink)