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)

To this day, a hundred and fifty years after Mendeleev's discovery, the overal structure of the periodic system remains unaccounted for in quantum-mechanical terms. Given this dire situation, a handful of scientists in the 1970s embarked on a quest for the symmetries that lie hidden in the periodic table. Their goal was to explain the table's structure in group-theoretical terms. We argue that this symmetry program required an important paradigm shift in the understanding of the nature of (...) chemical elements. The idea, in essence, consisted of treating the chemical elements, not as particles, but as states of a superparticle. We show that the inspiration for this came from elementary particle physics, and in particular from Heisenberg's suggestion to treat the proton and neutron as different states of the nucleon. We provide a careful study of Heisenberg's last paper on the nature of elementary particles, and explain why the Democritean picture of matter no longer applied in modern physics and a Platonic symmetry-based picture was called for instead. We show how Heisenberg's Platonic philosophy came to dominate the field of elementary particle physics, and how it found its culmination point in Gell-Mann's classification of the hadrons in the eightfold way. We argue that it was the success of Heisenberg's approach in elementary particle physics that sparked the group-theoretical approach to the periodic table. We explain how it was applied to the set of chemical elements via a critical examination of the work of the Russian mathematician Abram Ilyich Fet the Turkish-American physicist Asim Orhan Barut, before giving some final reflections. (shrink)

In the last decade, the notion of triad was reintroduced by Eric Scerri, who suggested it as a possible categorical criterion to represent chemical periodicity. In particular, he reformulated the notion of triad in terms of atomic number instead of atomic weights; in this way, the value of the intermediate term of the triad became the exact average of the values of the two extremes. Following the inspiration of Scerri’s work, the main purpose of this article is to obtain a (...) representation where all the relations among the chemical elements that form the groups of the periodic system can be reconstructed on the basis of triads, without using electronic configurations. (shrink)

The exploration of chemical periodicity over the past 250 years led to the development of the Periodic System of Elements and demonstrates the value of vague ideas that ignored early scientific anomalies and instead allowed for extended periods of normal science where new methodologies and concepts are developed. The basic chemical element provides this exploration with direction and explanation and has shown to be a central and historically adaptable concept for a theory of matter far from the reductionist (...) frontier. This is explored in the histories of Prout’s hypothesis, Döbereiner Triads, element inversions necessary when ordering chemical elements by atomic weights, and van den Broeck’s ad-hoc proposal to switch to nuclear charges instead. The development of more accurate methods to determine atomic weights, Rayleigh and Ramsey’s gas separation and analytical techniques, Moseley’s X-ray spectroscopy to identify chemical elements, and more recent accelerator-based cold fusion methods to create new elements at the end of the Periodic Table point to the importance of methodological development complementing conceptual advances. I propose to frame the crossover from physics to chemistry not as a loss of accuracy and precision but as an increased application of vague concepts such as similarity which permit classification. This approach provides epistemic flexibility to adapt to scientific anomalies and the continued growth of chemical compound space and rejects the Procrustean philosophy of reductionist physics. Furthermore, it establishes chemistry with its explanatory and operational autonomy epitomized by the periodic system of elements as a gateway to other experimental sciences. (shrink)

Measurement theory in (Hand in The world through quantification. Oxford University Press, 2004; Suppes and Zinnes in Basic measurement theory. Psychology Series, 1962) is concerned with the assignment of number to objects of phenomena. Representational aspect of measurement is the extent to which the assigned numbers and arithmetics truthfully represent the underlying objects and their relations, and is characteristic to natural sciences; pragmatic aspect is the extent to which the assigned numbers serve purposes other than representing the underlying phenomena, and (...) is characteristic to social sciences (Hand in The world through quantification. Oxford University Press, 2004). Here I criticise this distinction of representational and pragmatic measurements on the basis of the earlier history of the periodic system of chemical elements, viewed in terms of a practice based philosophy of science by Rein Vihalemm. I argue that the periodic system, although a natural scientific system interpretable as a measurement system, has considerable, in Hand’s terms pragmatic, aspects in it. Those aspects include: tampering with the material measurement results for the theoretical ideal of systematicity; adopting metaphysical assumptions that cannot be experimentally proven, like individuality of elements and atomicity; theoretical construction of the abstract entity—element—as the reference of the measurement system amenable to mathematically elegant ordering. Contrary to Suppes and Zinnes (Basic measurement theory. Psychology Series, 1962) I also argue for the dependence of the assigned numerical system on the material-procedural base of the measurement. (shrink)

The spiral form of the Periodic Law is proposed as its fundamental graphic representation. This idea is based on the fact that the spiral is the most appropriate form in description transitions from simple to complicated. The spiral is easily obtained from the linear succession of the elements when they are ranged by growing nuclear charge. The spiral can be simply transformed into many other graphic representations, including tables. This paper suggests the conception of the autonomy of blocks. This (...) autonomy is clearly seen in the variation of the outer electronic shells, in the width and the height of the blocks, as well as the number and properties of elements included therein. The regularities in the changes of element properties are pronounced in certain blocks but actually absent in others. The blocks can be permuted to obtain full-fledged versions of Periodic Table. The new stage of the verification of the blocks autonomy is the use of the total number of the differentiating electrons as an independent variable in describing the properties of the elements and their compounds. Consideration of individual blocks made it possible to deduce the periodic equations valid for all the elements within each block. Formulation of the Periodic Law is advanced: while describing characteristic determining the properties of the elements, the nuclear charge is replaced by the total number of differentiating electrons. Two modifications of the conventional Periodic Table are obtained by minimal changes. The first one shows the secondary and the additional periodicites. Another table shows the total number of differentiating electrons for each element. (shrink)

Between 1869 and 1871, D. I. Mendeleev, a teacher at the University at St Petersburg published a textbook of general chemistry intended for his students. The title, Principles of Chemistry was typical for the time: it meant that chemistry was no longer an inquiry on the ultimate principles of matter but had become a science firmly established on a few principles derived from experiment.

The discovery of the noble gases and their incorporation into the periodic system are examined in this paper. A chronology of experimental reports on argon and helium and the properties relevant to their nature and position in the periodic system is presented. Proposals on the nature of argon and helium that appeared in the aftermath of their discovery are examined in light of the various empirical and theoretical considerations that supported and contradicted them. ``The piece that (...) would not fit'' refers not only to argon, the element that at first seemed not to fit into the periodic system, but also to the piece or pieces of evidence that various researchers and observers were prepared to discard or discount in coming to terms with the newly discovered gases. (shrink)

Dmitrii Mendeleev’s periodic system is known for its predictive accuracy, but talk of its completeness is rarer. This is surprising because completeness was a quality that Mendeleev saw as important for a systematization of the chemical elements. Here, I explain how Mendeleev’s valuing of completeness influenced the development of his periodic system. After introducing five indicators of its completeness, I zoom into one in particular: Mendeleev’s inclusion of a schematic row of oxides. I then show how (...) it guided Mendeleev’s predictions of indium and ekaboron, which suggests that the valuing of completeness was instrumental for making predictions. (shrink)

Attempts to explain the periodic system as a manifestation of regularities in the structure of the atoms of the elements are as old as the system itself. The paper analyses some of the most important of these attempts, in particular such works that are historically connected with the recognition of the electron as a fundamental building block of all matter. The history of the periodic system, the discovery of the electron, and ideas of early atomic (...) structure are closely interwoven and transcend the physics–chemistry boundary. It is pointed out that J. J. Thomson's discovery of the electron in 1897 included a first version of his electron atomic model and that it was used to suggest how the periodic system could be understood microphysically. Thomson's theory did not hold what it promised, but elements of it were included in Niels Bohr's first atomic model. In both cases, Thomson's and Bohr's, the periodic system played an important role, heuristically as well as justificatory. (shrink)

Periodic tables (PTs) are the ‘ultimate paper tools’ of general and inorganic chemistry. There are three fields of open questions concerning the relation between PTs and physics: (i) the relation between the chemical facts and the concept of a periodic system (PS) of chemical elements (CEs) as represented by PTs; (ii) the internal structure of the PS; (iii)␣The relation between the PS and atomistic quantum chemistry. The main open questions refer to (i). The fuzziness of the concepts (...) of chemical properties and of chemical similarities of the CE and their compounds guarantees the autonomy of chemistry. We distinguish between CEs, Elemental Stuffs and Elemental Atoms. We comment on the basic properties of the basic elements. Concerning (ii), two sharp physical numbers (nuclear charge and number of valence electrons) and two coarse fuzzy ranges (ranges of energies and of spatial extensions of the atomic orbitals, AOs) characterize the atoms of the CEs and determine the two-dimensional structure of the PS. Concerning (iii), some relevant ‘facts’ about and from quantum chemistry are reviewed and compared with common ‘textbook facts’. What counts in chemistry is the whole set of nondiffuse orbitals in low-energy average configurations of chemically bonded atoms. Decisive for the periodicity are the energy gaps between the core and valence shells. Diffuse Rydberg orbitals and minute spin–orbit splittings are important in spectroscopy and for philosophers, but less so in chemical science and for the PS. (shrink)

Janet is known almost exclusively for his left-step periodic table (LSPT). A study of his writings shows him to have been a highly creative thinker and a brilliant draftsman. His approach was primarily arithmetic-geometric, but it led him to anticipate the discovery of deuterium, helium-3, transuranian elements, antimatter and energy from nuclear fusion. He recognized the (n + ℓ) rule well before Madelung and correctly placed the actinides. His controversial treatment of helium at the head of the alkaline earth (...) elements might be less provocative if his system were taken in one of its spiral representations. (shrink)

One of the consequences of the renewed interest in philosophical aspects of chemistry has been the corresponding renewed interest in the periodic system of the elements which embodies so much chemical knowledge in an implicit form.We have therefore decided to further promote scholarship on the periodic system by compiling a bibliography of previously published material. As the title of this article implies, we restrict ourselves to secondary sources. Readers interested in primary material can consult a number (...) of useful references for this purpose. These include the classical treatment on the History of the periodic system by van Spronsen as well as Mazurs’s compilation of over 700 forms of the periodic system. Mazurs also includes a detailed bibliography of articles and books in several different languages. Additional sources of primary articles which come to mind include David Knight’s Classics in the History of Chemistry, Carmen Giunta’s web pages for the history of chemistry and entries under individual scientists in the Dictionary of Scientific Biography. Turning to the present compilation we do not claim this to be a comprehensive list, since it partly reflects the interests of the senior author (E.R.S.), namely the relationship between the periodic system and quantum mechanics. For example, in addition to articles specifically on the periodic system we include a number of articles which deal with the related themes of electronic configurations of the elements. This bias also explains the disproportionate number of references to the work of the senior author.We have tried to include as many as possible of the articles on the periodic system which have appeared in the philosophy of science literature. These include Bensaude, Christie, Hettema and Kuipers, Kultgen, Lipton, Maher, Scerri, Shapere and Sundaram, among others. (shrink)

According to scientific procedure, each discipline first describes the phenomena of its research area, then analyzes them, and tinally categorizes them in a system. To date, biology has lacked such a system for its smallest building blocks, the cells. Although the theory of evolution explains certain central evolutionary mechanisms of the cell, there existed no generally accepted theory of the organization of the cell. The endoeytobiotic cell theory is suggested as a possible basis for a satisfying explanation of (...) the structure, function, information, and evolution of the cell. Furthermore, a hypothetical periodic system of the cell is developed. This system consists of eight groups, including the ecological niches fermentation, respiration, photergy, and photosynthesis (each aerobic and anaerobic) and seven periods with increasing numbers of protein biosynthesis machineries (cytoplasma, mitochondria, plastids, endocytobionts). We find furthermore, a division according to typical animal or plant cells and between these two in fungus-like cells. (shrink)

The s, p, d and f blocks of the elements, as delimited by Charles Janet in 1928, can be represented as parallel slices of a regular tetrahedron. They also fit neatly on to the surface of a sphere. The reasons for this are discussed and the possible objections examined. An attempt is made to see whether there are philosophical implications of this unexpected geometrical regularity. A new tetrahedral design in transparent plastic is presented.

A numerical classification was performed on 69 elements with 54 chemicaland physicochemical properties. The elements fell into clusters in closeaccord with the electron shell s-, p- andd-blocks. The f-block elements were not included forlack of sufficiently complete data. The successive periods ofs- and p-block elements appeared in an ovalconfiguration, with d-block elements lying to one side. Morethan three axes were required to give good representation of thevariation, although the interpretation of the higher axes is difficult.Only 15 properties were scorable for (...) the noble gases, but despite thepaucity of properties reflecting chemical reactivity, analysis of the 69elements on these properties still showed the major features seen fromthe full set. (shrink)

In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and (...) stability of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations. (shrink)

The periodic table of the elements is one of the most powerful icons in science: a single document that captures the essence of chemistry in an elegant pattern. Indeed, nothing quite like it exists in biology or physics, or any other branch of science, for that matter. One sees periodic tables everywhere: in industrial labs, workshops, academic labs, and of course, lecture halls. It is sometimes said that chemistry has no deep ideas, unlike physics, which can boast quantum (...) mechanics and relativity, and biology, which has produced the theory of evolution. This view is mistaken, however, since there are in fact two big ideas in chemistry. They are chemical periodicity and chemical bonding, and they are deeply interconnected. The observation that certain elements prefer to combine with specific kinds of elements prompted early chemists to classify the elements in tables of chemical affinity. Later these tables would lead, somewhat indirectly, to the discovery of the periodic system, perhaps the biggest idea in the whole of chemistry. Indeed, periodic tables arose partly through the attempts by Dimitri Mendeleev and numerous others to make sense of the way in which particular elements enter into chemical bonding. (shrink)

This article studies the existence of positive periodic solutions for a class of strongly coupled differential systems. By applying the fixed point theory, several existence results are established. Our main findings generalize and complement those in the literature studies.

A model of dissipative quantum dynamics (with a nonlinear friction term) is applied to systems periodic in time. The model is compared with the standard approaches based on the Floquet theorem. It is shown that for weak frictions the asymptotic states of the dynamics we propose are the periodic steady states which are usually postulated to be the states relevant for the statistical mechanics of time-periodic systems. A solution to the problem of nonuniqueness of the “quasienergies” is (...) proposed. The implication of a nonlinear evolution for Ludwig's axiomatization is briefly outlined. (shrink)

To describe and analyze the unstable periodic orbits of the Rucklidge system, a so-called symbolic encoding method is introduced, which has been proven to be an efficient tool to explore the topological properties concealed in these periodic orbits. In this work, the unstable periodic orbits up to a certain topological length in the Rucklidge system are systematically investigated via a proposed variational method. The dynamics in the Rucklidge system are explored by using phase portrait (...) analysis, Lyapunov exponents, and Poincaré first return maps. Symbolic encodings of the periodic orbits with two and four letters based on the trajectory topology in the phase space are implemented under two sets of parameter values. Meanwhile, the bifurcations of the periodic orbits are explored, significantly improving the understanding of the dynamics of the Rucklidge system. The multiple-letter symbolic encoding method could also be applicable to other nonlinear dynamical systems. (shrink)

The philosopher of chemistry Andrea Woody has recently published a wide-ranging article concerning the turn to practice in the philosophy of science. Her primary example consists of the use of different forms of representations by Lothar Meyer and Mendeleev when they presented their views on chemical periodicity. Woody believes that this distinction can cast light on various issues including why Mendeleev was able to make predictions while Meyer was not. Secondly, she claims that it can clarify the much-debated question concerning (...) the relative values of prediction and accommodation of data in the way that the periodic system was accepted. Thirdly, Woody believes that such differences in the representation of periodicity can be used to argue for the explanatory nature of the periodic table in contrast with the more traditional view that the periodic table is not explanatory. (shrink)

Evolution proceeds in phases, alternatingly convergent and divergent. During the divergent phases, many variants of an evolutionary system arise, and in the convergent phases, these are brought together in a new, higher unity, which in turn varies, and so on. Thus the mechanism of evolution is trialistic, proceeding according to the Hegelian principle (in the widest sense) of thesis, antithesis and synthesis. This mechanism is at the same time mirrored in the structure of the evolving systems, being most clearly (...) expressed in the derivation of periodic systems of the individual levels of evolution. These relationships will be discussed using examples from symbiosis research, population dynamics and biogenesis. (shrink)

This is a translation of another volume of the monumental history of philosophy published in the 1930s by Bréhier. The bibliography is brought up to date by the translator with help from Wesley Piersol. Bréhier writes history of philosophy in the broad sense, showing the social, literary, and political forms taken by philosophical trends of the period. Many of the writings treated in this volume will be unknown to students trained in the Anglo-American tradition. There are only fifteen pages on (...) Scottish realism and British utilitarianism, and a page or so each on Kierkegaard and Emerson. In the substantial chapters on Fichte, Schelling, Hegel, and the trends in German thought following Hegel, one can find summaries of the positions of such philosophers as von Humboldt, Schleiermacher, Herbart, Feuerbach, Stirner, and others. There is a rich section of over a hundred pages on French social philosophy: Fourier, Saint-Simon, Comte, and Proudhon. Early work of Engels and Marx is mentioned, but fuller treatment belongs to the next volume. A chapter on Italian idealism is also included. This period saw the flowering of vast constructive systems. A sense of history and development transformed philosophical problems, and faith in the rational, reflective initiative of human wills was replaced by faith in a mysterious historical force, an immanent law which makes sport of efforts to resist it. The difference in substance is reflected in differences of style. The clarity and naturalness with which eighteenth-century men of action wrote for a general educated public was replaced by constraint, effort, conventionality, and above all, a prophetic and apocalyptic tone in the works of this time.--M. B. M. (shrink)

While symbolic colour use has always played a conspicuous role in science research and education, the use of colour in historic diagrams remains a lacuna in the history of science. Investigating the colour use in diagrams often means uncovering a whole cosmology that is not otherwise explicit in the diagram itself. The periodic table is a salient and iconic example of non-mimetic colour use in science. Andreas von Antropoff's (1924) rectangular table of recurrent rainbow colours is famous, as are (...) Alcindo Flores Cabral's (1949) application of colour in his round snail form, using the RGB scheme, and Mazurs's (1967) pine tree system, consisting of warm and cold colours that he attributed to specific groups of elements—an attribution that we can relate back to humoralism and alchemy. From the first periodic tables in the 19th century, individual researchers have used different colour regimes. While standardization may play an obvious role in chemistry and its diagrams, all the more impressive is the anarchistic use of colour in the various diagrams which continue to be created. This article focuses on periodic tables in chemical journals and text books, and explores and compares the development of colour codes found in the few existing polychrome diagrams from the 1920s to the 1970s. (shrink)

Physical exercise is seen as the main ally for health promotion, preventing and protecting the organism from several diseases. According to WHO, there is a tendency of constant growth in the elderly population in the coming years. The regular practice of exercises by the elderly becomes relevant to minimize the deleterious effects of the aging process and to increase the fitness index. Recently, the world population started a confrontation against Corona Virus Disease (COVID-19), which is the most significant public health (...) challenge globally. Although social isolation is a reasonable measure in an attempt to stop contamination by COVID-19, this measure has limited the ability of individuals to exercise outdoors or in gyms and health clubs, which increased the risk of developing chronic illnesses related to a sedentary lifestyle. The critical point is that the recent recommendations on exercise prescription to combat the potentially harmful effects of COVID-19 failure to adequately address resistance exercise interventions as home-based exercise strategy. Thus, in this paper, we discussed the physical exercise as medicine if the training status is enough to protect the elderly against COVID-19 infection, about the role of physical activity on immunosuppression. Possible risks for COVID-19 infection, and the old training methods, such as no-load resistance training as possible resistance exercise strategies and high-intensity interval training, as new proposals of home-based exercise interventions, could perform during the current COVID-19 pandemic. (shrink)