Stoicism and Alchemy in Late Antiquity: Zosimus and the Concept of Pneuma

At the beginning of the twentieth century, historians associated the alchemy of the third-century alchemist Zosimus of Panopolis with Platonism and Aristotelianism, explicating his theory of alchemical transmutation under the intellectual umbrella of these philosophical traditions. More recently, scholars of alchemy such as Christina Viano and William Newman have suggested a connection between Zosimean alchemy and Stoicism. Through a close reading of texts in Zosimus’s corpus, this paper posits a Stoic interpretation of several aspects of Zosimean alchemy, focusing on the concepts of pneuma and tension. For Zosimus, I argue, pneuma played a vital role in colouring metals, while tension conferred stability and cohesion upon metallic compounds. This interpretation suggests that Zosimus applied Stoic concepts to describe the alchemical process of tincturing metals.     

Translating Ancient Alchemy: Fragments of Graeco-Egyptian Alchemy in Arabic Compendia

Translation played a vital role in the development and transfer of alchemy in Antiquity and the Early Middle Ages. Since its origins in Graeco-Roman Egypt, alchemy was encapsulated in Greek texts which allegedly relied on Persian or Egyptian sources. Later, a variety of Greek and Byzantine writings were translated into Syriac and Arabic, and these translations were in turn fragmented and disseminated in later Arabic compendia. This paper will first review the main phases of this historical process of transmission of alchemy from one language and culture to another. Second, this process will be examined using two significant case studies: a close analysis of various quotations from Graeco-Egyptian authors (Pseudo-Democritus, Zosimus of Panopolis, and Synesius) as presented in two Arabic dialogues on alchemy, The Tome of Images and The Dialogue between āras and the King Caesar. These sources demonstrate some of the concrete textual realities that underlie general patterns of translation and reception.     

Connections between perturbation theory and the unitary transformation methods of deriving effective Hamiltonians

The connections between open shell Brillouin–Wigner perturbation theory and the Van Vleck unitary transformation formalisms for generating effective Hamiltonians are explored. An explicit expression is obtained relating the generator ? of the unitary transformation e^i? with the amplitudes to be found from perturbation theory. The “renormalization effects” needed to produce the explicit “orthogonal-Hermitian” form of the effective Hamiltonian in perturbation theory are related directly to the generator of the unitary transformation. The conclusions reached previously by Jørgensen and Brandow regarding the identity of the effective Hamiltonians of the formalisms are explicitly verified for the case that the generator ? satisfied the Kemble condition. The procedure suggests how the powerful techniques of perturbation theory can be used within the unitary transformation framework to guarantee properly renormalized wave functions.     

The variation of spectroscopic properties with numbers of electrons

A formalism that describes the variation of the spectroscopic properties, D_e, R_e, and k_e, of homonuclear, diatomic molecules, with the number of molecular electrons has been developed. The theory describes the interrelation of these properties and predicts “critical” behavior in sequences of “isonuclear” and neutral molecules. Detailed calculations are possible with the help of experimental data in lieu of a deeper, dynamical theory of molecular behavior with respect to electron number. The present work points the way toward a first-principle's theory. © 1992 John Wiley & Sons, Inc.     

Hydration of gas-phase gramicidin S (M + 2H)2+ ions formed by electrospray: The transition from solution to gas-phase structure

The hydration of doubly protonated gas-phase ions of gramicidin S formed by electrospray ionization was investigated. Under “gentle” electrospray conditions, a near Gaussian distribution of (M + 2H + nH₂O)²⁺ ions with n up to 50 can be readily formed. These extensively hydrated gas-phase ions should have structures similar to those in solution. For intermediate extents of hydration, the “naked” or unsolvated ion is present in unusually high abundance. This is attributed to a competition between solvation of the charges by water vs intramolecular self-solvation via hydrogen bonding. In addition, “magic” numbers of attached water molecules are observed for n = 8, 11, and 14. These magic numbers are attributed to favorable arrangements of water molecules surrounding the charge and surface of the peptide in the gas phase. These results are indicative of a gentle stepwise transformation from the solution-phase structure of the ion to the preferred gas-phase structure as solvent evaporates from the hydrated ions.     

Discovery by serendipity: a new context for an old riddle

In the last years there has been a great improvement in the development of computational methods for combinatorial chemistry applied to drug discovery. This approach to drug discovery is sometimes called a “rational way” to manage a well known phenomenon in chemistry: serendipity discoveries. Traditionally, serendipity discoveries are understood as accidental findings made when the discoverer is in quest for something else. This ‘traditional’ pattern of serendipity appears to be a good characterization of discoveries where “luck” plays a key role. In this sense, some initial failures in combinatorial chemistry are frequently attributed to a naïf appropriation of a “serendipity model” for discovery (a “serendipity mistake”). In this paper we try to evaluate this statement by criticizing its foundations. It will be suggested that the notion of serendipity has different aspects and that the criticism to the first attempts could be understood as a “serendipity mistake.” We will suggest that “serendipity” strategies, a kind of blind search, can be seen sometimes as a “genuine part” of scientific practice. A discussion will ensue about how this characterization can give us a better understanding of some aspects of serendipity discoveries.     

Humphry Davy: Analogy,Priority, and the “true philosopher”

This essay explores how Davy fashioned himself as, what he called in his poetry, a “true philosopher.” He defined the “true philosopher” as someone who eschewed monetary gain for his scientific work, preferring instead to give knowledge freely for the public good, and as someone working at a higher level than the mere experimentalist. Specifically, Davy presented himself as using the method of analogy to reach his discoveries and emphasised that he understood the “principle” behind his findings. He portrayed himself as one who perceived analogies because he had a wider perspective on the world than many others in his society. The poem in which he describes the “true philosopher” offers us Davy’s private view of this character; the essay then demonstrates how Davy attempted to depict his own character in this way during critical moments in his career.     

On rotations as special cases of unitary transformations with some applications to the theory of spin

Some problems in elementary geometry are approached from the point of view of linear algebra and generalized to the theory of linear spaces of finite or infinite dimensions having a positive definite binary product. The angle ω between two elements of the linear space is defined from the concept of length by means of the cosine-theorem. A rotation is then defined as a special case of a unitary transformation moving all elements the same angle ω, except that under certain circumstances, some elements may stay invariant. In the former case, one speaks of a rotation around an “external axis,” and in the latter case, of a rotation around an “internal axis” defined by the invariant elements. It is shown that the finite rotations U of both types may be expressed in the simple exponential form U = exp(iωm), where the “generator” m in the former case is an operator satisfying the relation m² = 1, and in the latter case, m³ = m. The structure of the group of finite rotations in the former case is clarified in some detail. As an illustration of the theory, some applications to the three- and two-dimensional spaces as well as to the theory of spin are given. The coupling between the ordinary three-dimensional rotations and the spinor transformations is considered in somewhat greater detail.     

Alchemy and Mining: Metallogenesis and Prospecting in Early Mining Books

Abstract

Historians have assumed that alchemy had a close association with mining, but exactly how and why miners were interested in alchemy remains unclear. This paper argues that alchemical theory began to be synthesised with classical and Christian theories of the earth in mining books after 1500, and served an important practical function. The theory of metals that mining officials addressed spoke of mineral vapours (Witterungen) that left visible markings on the earth's surface. The prospector searched for mineral ore in part by studying these indications. Mineral vapours also explained the functioning of the dowsing rod, which prospectors applied to the discovery of ore. Historians of early chemistry and mining have claimed that mining had a modernising influence by stripping alchemy of its theoretical component, but this paper shows something quite to the contrary: mining officials may have been sceptical of the possibility of artificial transmutation, but they were interested in a theory of the earth that could translate into prospecting knowledge.     

Exploiting the analyticity of Schrödinger operators: Theory and the computation of partial cross sections

The idea of dilation, or dilatation, analyticity with respect to complex scaling of the interparticle distances for nonrelativistic atomic or molecular electronic Hamiltonians is now over 20 years old and the first major reviews are just over 10. The method continues to be a fruitful source of new theoretical and computational results. Under the scale transformation r → re^iθ, the usual “spectrum” of bound states is exactly preserved, and scattering continua are “rotated” off the real axis by an angle of −2Re(θ) about their respective thresholds. Useful features of this transformation are (1) that resonances are exposed, and, thus, (complex) resonance eigenvalues are easily calculated as the wave functions are L², and standard results of Kato-type perturbation theory can thus be applied to them; (2) that utilization of this technique to study atoms in ac and dc fields was an early, and still evolving extension of the original theory; and (3) the fact that the “continua” are rotated off the real energy axis allows scattering information to be extracted from computations carried out entirely L² in bases as the usual resolvents of scattering theory are no longer singular on the real axis. After a brief survey of the technique and its applications, these ideas are illustrated by discussion of positive energy-bound states and resonances, the extension of the theory to include the dc Stark effect, and a review of the resolution of the initially perplexing problem of atomic and molecular bound states in continua. These theoretical results are followed by a discussion of some very recent computational results, allowing computation of atomic partial photoionization cross sections with no specific coordinate space enforcement of boundary conditions, a highly advantageous situation for calculation of the partial cross section for three-body breakup, as in the process ℏ ω + He → He²⁺ + e⁻ + e⁻. © 1996 John Wiley & Sons, Inc.     

Experimental determination of Q 0 factors and effective resonance energies with a multi-channel approach: the α-vector method

Some of the Q ₀ and ē _r factors from the 2003 to 2012 recommended k ₀-datasets were adopted from older literature (Lit; before 1984), at the time of the launch of the k ₀-method and have associated uncertainties of 10 %. The ē _r factors on the other hand, were derived analytically in 1979 and 1987 by employing the Breit–Wigner resonance representation, but in 1984 a multi-channel method was proposed for simultaneous Q ₀ and ē _r experimental determination. In this work we assumed the α-dependence of the ē _r parameter proposed later in 1987 for a generalization of this method, which was then employed in the experimental determination of Q ₀ and ē _r factors for 17 (n,γ) target isotopes on up to three channels of the BR1 reactor at the SCK-CEN (Mol, Belgium). Retrospectively, this “α-vector method” can be employed for α-calibration and it provides a practical way of averaging the experimental Q ₀ (and ē _r) results from several laboratories. Our Q ₀ results have 2–3 % uncertainty and are compared with the Lit elsewhere.     

Random-walk theory for localization

A continuous-time random-walk theory has been developed for Anderson localization. On a continuous time scale random walks are performed along extended (i.e., propagating) and localized (i.e., trap) states. Complete information of disorder is contained in a distribution function called “hopping time distribution function” ψ_nm(t), which gives the probability per unit time for transition from state m to state n in time t. The “stay-put” probability ??(t = ∞), which is the probability to rediscover an excitation at a site “0” at time t = ∞ if it was there at t = 0, is obtained in terms of ψ_nm(t). Appropriate forms for ψ_nm(t) are constructed which are in conformity with the photoconductivity experiments on dispersive transport, and ??(∞) are calculated. The results indicate that the entire spectrum consists of three regimes, namely, those of (i) “diffusion,” (ii) “weak diffusion,” and (iii) “no diffusion,” which, respectively, designate the extension, the power-law localization, and the exponential localization of states. The results also shed light on the question of “continuous or discontinuous (?)” transition across the mobility edge.     

A molecular approach to the spurt effect in polymer melt flow

The Doi-Edwards theory of polymer melts, extended to include relaxation processes associated with chain-length equilibration, is used to make quantitative predictions of a discontinuity in the flow curve of a monodisperse melt in a capillary. A fluid interface between regions of high and low deformation rates is found to propagate from the former into the latter. Our results for the “spurt” and its hysteresis compare favorably with experiment using a molecular weight dependence of the ratio of “reptation time” (T_d) to “equilibration time” (T_eq) in agreement with that determined from nonlinear stress relaxation.     

Folded chain crystallization of random terpolymer liquid crystal polymers from the nematic state

The morphology of ca. equimolar random terpolymer liquid crystal polymers of an aliphatic segment of 4–7 carbon atoms, oxybenzoate, and dioxyphenyl crystallized from the nematic state in the form of thin films on glycerine by slow cooling and quenching has been characterized by electron microscopy (TEM) and diffraction (ED). In all cases a folded chain, lamellar structure is found. The ED studies suggest adjacent reentry, and despite a large ΔH, indicate no change in lateral molecular packing at the crystal-“liquid crystal” transition with a transformation to the nematic state at a higher temperature “liquid crystal”-liquid crystal transition. The results are interpreted as suggesting similar folded chain, lamellar morphology in the nematic state. © 1992 John Wiley & Sons, Inc.     

An application of an homogenization method to a model of diffusion in glassy polymers

The sorption of gases in polymers below their glass-transition temperature T_g is known in many cases to be described by the “dual sorption” theory, according to which the gas is held in accordance with both the Langmuir and Henry's laws. Based on this theory, expressions for the “effective diffusion coefficient” in the glassy polymers have been obtained by investigators in the past, notably by Paul and Koros.² The present analysis regards the glassy polymers as inhomogeneous with regions on which the gas sorption follows the Langmuir law. Assuming that the linear dimensions of these regions, which are often referred to as “microvoids” (although they are not space filled by vacuum), are small compared to the macroscopic length of interest but large compared to the mean free path of the penetrant gas molecules, we derive a rigorous relation between the average flux and the concentration gradient in the polymer and show that this relation can be expressed in terms of an “effective diffusion coefficient” D_eff which depends on the details of the microstructure, i.e., the size, shape and spatial distribution of the “microvoids.” This expression for D_eff is shown to reduce to that of Paul and Koros² in two situations: (1) when the “voids” consist of slabs running parallel to the concentration gradient, and (2) when the “voids” are spherical and the temperature of the polymer is not too different from T_g. The results of the present study lead to an alternative procedure for interpreting the experimental data on sorption and permeation which may have some advantages over the procedure currently employed. Finally, the analysis presented here is also applicable to polymers containing adsorptive fillers.     

Application of fourier transform infrared spectroscopy to the study of semicrystalline polymers: Poly(ethylene terephthalate)

An infrared absorbance subtraction technique has been used to “isolate” bands in the composite spectrum of semicrystalline polymers according to their crystalline or amorphous character. Amorphous and crystalline spectra for annealed, melt-quenched, and solution-cast poly(ethylene terephthalate) have been separated. The spectra of the amorphous component show an increased intensity of bands associated with the trans configuration of oxygen about the C? C bond when the polymer is annealed. This increased “trans” band intensity reflects the increased proportion of trans structures as a result of annealing. The amorphous trans bands are shifted approximately 1–3 cm^?1 from their positions in the crystalline “trans” spectrum. The frequency shift of these bands can be attributed to the differences in chain interactions that exist in the amorphous phase and the crystalline lattice. We have also found that under identical anealing conditions the amorphous phase of the melt-quenched polymer contains an increased intensity of conformational trans bands compared to the sample cast from solution.     

Stereocontrolled synthesis of 2,5-linked bistetrahydrofurans via the triepoxide cascade reaction

A complementary set of stereochemically controlled approaches to the preparation of twelve diastereomers of the bistetrahydrofurans 11 is described. The key transformation involves a series of nucleophilic displacement reactions within triepoxides 19-the “end-to-end” triepoxide cascade reaction—which leads, presumably via 22 and 23, after acetylation to bistetrahydrofuran tetraacetates 24. The “inside-out” cyclization of 30 exemplifies a useful variation with significant stereochemical consequences. The role of symmetry in these approaches is discussed. A general mathematical analysis for conceptualizing isomer distribution within multistep sequences is presented.     

Generalized graphs and the Sinanoğlu graphical rules

A comparison of Sinano?lu's VIF (Ref. 1) and generalized graph is presented. Generalized graphs have vertex and edge weights. An abridged history of generalized graphs in theoretical chemistry is given. VIF 's are generalized graphs and therefore have adjacency matrices. The “graphical” rules of Sinano?lu can be represented by congruent transformations on the adjacency matrix. Thus the method of Sinano?lu is incorporated into the broad scheme of graph spectral theory. If the signature of a graph is defined as the collection of the number of positive, zero, and negative eigenvalues of the graph's adjacency matrix, then it is identical to the all-important {n₊, n₀, n_?}, the {number of positive, zero, and negative loops of a reduced graph} or the {number of bonding, nonbonding, and antibonding MO s}. A special case of the Sinano?lu rules is the “multiplication of a vertex” by (?1). In matrix language, this multiplication is an orthogonal transformation of the adjacency matrix. Thus, one can multiply any vertex of a generalized graph by ?1 without changing its eigenvalues.     

Electron microscopic study of dehydration transformations. II. The formation of “superstructures” on the dehydration of goethite and diaspore

It is shown that the satellites observed in the diffraction pattern of the dehydrated single crystal of the mineral goethite, which were previously attributed to a “superstructure,” are better interpreted in terms of small angle scattering by a “texture” of the dehydration product hematite. This texture consists of rows of cavities parallel to the H(003) = G(100) planes with an average distance of 30–50 Å, depending on the stage of the transformation, in a highly twinned hematite matrix. In corundum resulting from the dehydration of diaspore a more isotropic texture is formed and the diffraction pattern exhibits “halos” instead of rows of satellite spots.     

Adiabatic perturbation theory for the degenerate case. I. Perturbation of isolated degenerate or quasidegenerate levels

Adiabatic formulae for secular operators and contracted Hamiltonians in an arbirary combination of degenerate or quasidegenerate subspaces are derived. A detailed consideration of the adiabatic limit in the power series is given, and “stability” of proper linear combinations with respect to a transformation produced by the S_α-matrix is proved.