Primal element

When the author of The Metamorphosis of Metals was seeking for an argument in favour of his view, that water is the source and primal element of all things, he found what he sought in the Biblical text "In the beginning the spirit of God moved upon the face of the waters." Similarly, the author of The Sodic Hydrolith clenches his argument in favour of... 

The alchemists went a step further in their classification of things. They asserted that there is One Thing present in all things that everything is a vehicle for the more or less perfect exhibition of the properties of the One Thing that there is a Primal Element... 

But it is possible that all the chemical elements may be combinations of different quantities of one primal element. Certain facts make this supposition tenable and some chemists expect that the supposition will be proved to be correct. If the hypothetical primal element should be isolated, we should have fulfilled the aim of alchemy, and gained the One Thing but the fulfilment would not be that whereof the alchemists dreamed. 

Akasa, or ether, is assumed not to consist of atoms, but is infinite in extent, continuous and eternal. It cannot be apprehended by the senses, but is the carrier of sound. It is also described by certain authorities as all-pervasive, occupying the same space that is occupied by the various forms of matter, and therefore devoid of the property of impenetrability, characterizing the atoms of other elements. In this respect, it resembles the modern concept of the ether which conveys light. Deussen quotes from the Upanisliad a passage which conveys an idea of akasa as the primal element from which the others were evolved. 

The alchemical process seeks to fan this fire..."carefully, with great judgment and skill." In laboratory alchemy, the Three Essentials of Body, Soul, and Spirit are most important because they provide us a means of manipulating the elements. Many alchemists indicate that the Primal Elements are too subtle even for the most skilled artist and that only Nature can work at that level. The Three Essentials are the fruit of the Elements, which Man can manipulate even at the physical level. 

LIMBOS — The Universal World, the Four Primal Elements of the World, and of all things. Seed and Matter. 

The philosophers of Greece, whose goal was to understand and describe the nature of the universe, made use of the known properties of heat, but they did not separate the concepts of heat and temperature. They knew, for example, that fire—defined as one of the four elements of the universe—would cause the expansion of air, another primal element. In the second or first century B.C., Heron of Alexandria applied this knowledge to invent a steam turbine, but he considered it only a toy. Philon of Alexandria likewise invented several devices that demonstrated the expansion property of heated air (Cohen and Drabkin, 1948 Sarton, 1959). The Greeks went no further in their investigations, although the manuscripts they left inspired the scientific thinkers of the Renaissance (Taylor, 1941). 

It is important to pause here and note what is evolving The identity of the primal substance or substances was debated, but all the debaters seemed comfortable with the assumption that whatever it was, this primal element (or elements) would be found in some portion in all matter. This was the assumption under which chemists would labor for the next 2000 years. One reason for its persistence was the intuitive appeal of arguments offered by philosophers, backed by everyday observation, but another reason was the social upheavals that scattered Greek philosophers throughout the Mediterranean like Anaxagoras seeds. 

A semidefinite program may be written in two complementary formulations, which are known as the primal and dual programs. Eor convenience we define the map M that transforms any vector x) of length n into an h x h matrix M x) by creating each column of the matrix sequentially with the elements of the vector. The primal formulation of the semidefinite program may be expressed in general notation as... 

The first philosopher to theorize about such matters was Thales of Miletus, at the time, the sixth century B.C., the greatest Greek city Asia Minor. According to Thales there was one fundamental element water, the material of which everything was made. To the modern mind, such an idea seems absurd. However, it is much more reasonable than it might appear. Lacking evidence to the contrary, it must have seemed very plausible that everything was made of some primal material. And if it was, water was really not a bad candidate. 

Thales s successor, Anaximander—the exact dates of his birth and death are unknown, but he was said to have been 64 years old in 546 B.C.—agreed that there was one primal material. But he didn t think it was ever encountered on Earth in its pure state. According to Anaximander everything in the world was made of apeiron, a substance that was infinite and eternal, and which could take on numerous forms, including those of all the familiar terrestrial materials. It is neither water nor any of the so-called elements, Anaximander said, but a nature different from them and infinite, from which arise all the heavens and the worlds within them. ... 

Empedocles made no attempt to create a new theory of matter. Instead, he tried to reconcile the thoughts of his various predecessors. He took Thales s theory that everything was made of water and Anaximenes s idea that the primal substance was air, and added two more elements, earth and fire. Empedocles didn t believe that one kind of matter could be transformed into another. Earth couldn t be changed into water, or water into earth, for example. Thus there had to be more than one element. 

Empedocles four elements do not represent a multiplication of the prote hyle, but rather a gloss that conceals its complications. Aristotle agreed that ultimately there was only one primal substance, but it was too remote, too unknowable, to serve as the basis for a philosophy of matter. So he accepted Empedocles elements as a kind of intermediary between this imponderable stuff and the tangible world. This instinct to reduce cosmic questions to manageable ones is one reason why Aristotle was so influential. 

Anaximander appears to have accepted the same fundamental concept of the essential unity of matter, and of its eternal existence, as did Thales, but differs from his elder townsman in his views as to what that simple primal matter may be. Instead of water, he assumes a qualitatively undetermined primal matter, the apeiron. The apeiron is eternal and unlimited in extension. It is not any of the known elements it is possessed of eternal motion, in consequence of which worlds are developed from it in space. As this world has so originated from the apeiron, so in time it will again be absorbed into it. There is something suggestive here of the akasa or ether of certain ancient Hindu concepts.9... 

Ice or snow is converted by the action of heat into water. Therefore it was first water then snow or ice. But all metals can be converted into quicksilver, therefore they were first quicksilver. The method of converting them into quicksilver I shall teach below. But it being granted that a metal can be converted into quicksilver, there is refuted the opinion of those who assert that it is not possible for spirits (spiritus, that is volatile substances) and other materials to be transmuted into the elements and into the nature of metals, unless first reduced to their primal matter. This reduction to their primal matter is easy as I shall show below. Therefore the transmutation of metals is possible and easy. In the same way it can be shown you that the multiplication of metals is possible for everything that is born and grows is multiplied, as is clear with plants and trees. For from one seed a thousand seeds are procreated,... 

Remark 4 The convexity property of v(y) is the fundamental element for the relationship between the primal and dual problems. A number of additional properties of the perturbation function v(y) that follow easily from its convexity are... 

Part 1, comprised of three chapters, focuses on the fundamentals of convex analysis and nonlinear optimization. Chapter 2 discusses the key elements of convex analysis (i.e., convex sets, convex and concave functions, and generalizations of convex and concave functions), which are very important in the study of nonlinear optimization problems. Chapter 3 presents the first and second order optimality conditions for unconstrained and constrained nonlinear optimization. Chapter 4 introduces the basics of duality theory (i.e., the primal problem, the perturbation function, and the dual problem) and presents the weak and strong duality theorem along with the duality gap. Part 1 outlines the basic notions of nonlinear optimization and prepares the reader for Part 2. 

God and Nature, His minister, alone know how to command the primal material elements of bodies. Art could not approach them. But the three, which result from them, become sensible in the resolution of the Mixts. Chemists name them Sulphur, Salt and Mercury36 These are the elements principled. Mercury is formed by the mixture of Water and Earth Sulphur, of Earth and Air Salt, of Air and Water condensed. The Fire of Nature is added to these as a formal principle. Mercury is... 

Boyle was sceptical because he was no longer willing to accept, blindly, the ancient conclusions that had been deduced from first principles. In particular, Boyle was dissatisfied with ancient attempts to identify the elements of the universe by mere reasoning. Instead, he defined elements in a matter-of-fact, practical way. An element, it had been considered ever since Thales time (see page 8), was one of the primal simple substances out of which the universe was composed. Well, then, a suspected element must be tested in order to see if it were really simple. If a substance could be broken into... 

In modern chemistry we credit some one hundred elements—and counting— with being the basic stuff from which all matter is formed, but there was no reason for this to be the first assumption, and it was not. The initial thrust of the philosophical effort was to discover the one basic stuff of nature— the primal substance, the material from which all else is formed. This effort began for the Greeks around 600 bce, on the Aegean shores of Asia Minor, in the Ionian city-state of Miletos, with the first of the Ionian philosophers, Thales. 

Forensic radiochemical assays of a suite of heavy elements (Ra, Ac, Th, Pa, U, Np, Pu, Am, and Cm) were negative, with the exception of Th at trace level. Th-230 is a daughter product of the decay of natural U and was present at a specific activity of (2.21 0.74) dpm/g. As its half-life is not sufficiently long for independent existence derived from primal nucleosynthesis, the presence of Th in the Sc specimen was indicative of a prior association with U (although only 0.15 ppm of residual U remained in the sample). Indeed, the commercial recovery of Sc from U-mining operations is an historic endeavor (Lash and Ross 1961 McGinley and Facer 1976). 

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