Transcendental elements

There are various types of meditation Prayer is probably the best known, but there is also TM (transcendental meditation), mindfulness meditation, and, from the Eastern tradition, Zen meditation, Buddhist meditation, and Taoist meditation. All of these types of meditation focus on quieting the busy mind. The intent is not to remove stimulation but rather to direct the concentration toward one healing element—one... 

From a computational standpoint, the usefulness of the method relies on the simplicity of the calculations needed for the determination of the three equivalent crystals associated with each atom i. This is accomplished by building on the simple concepts of Equivalent Crystal Theory (ECT) [25,26], as will be discussed in detail below. The procedure involves the solution of one simple transcendental equation for the determination of the equilibrium Wigner-Seitz radius i WSE) of ch equivalent crystal. These equations are written in terms of a small number of parameters describing each element in its reference state, and a matrix of perturbative parameters Ay , which describe the changes in the electron density in the vicinity of atom / due to the presence of an atom j (of a different chemical species), in a neighboring site. The determination of parameters for each atom in... 

It would seem necessary at this point to say something about the earher element schemes, especially the nineteenth-century scheme, and how it was that elements were regarded as transcendental and at the same time were characterized by such properties as their atomic weight. This task will be attempted in the following section. 

For Aristotle, the elements themselves are unobservable and transcendental (in Paneth s terminology), although they give rise to all the variety we see before us. The four elements (fire, earth, water, and air) are regarded as property bearers and are responsible for the properties of substance, although they are themselves unobservable. The elements are immaterial qualities impressed on an otherwise undifferentiated primordial matter and are present in all substances. Furthermore, the properties of substances are governed by the proportion of the four elements present within them. 

And, yet, the transcendental aspect of elements was not completely forgotten and continued to serve an explanatory function in nineteenth-century chemistry but not necessarily a microscopic explanation. A chemist could be skeptical of atomistic explanations, as many were in the nineteenth-century, and yet could readily accept a transcendental explanation, for example, for the persistence of the elements in their various compounds. As was alluded to earlier, one of the benefits of regarding the elements as having a transcendental existence is that it provides a way out of the apparent paradox concerning the nature of elements when combined in compounds. Suppose that sodium and chlorine are combined to form sodimn chloride (common salt). In what sense is the poisonous metal sodium present in a sample of white crystalline common salt Similarly, one may ask how it is that the element chlorine, a green and poisonous gas, continues to exist in common salt. Clearly, the elements themselves, in the modern sense of the word, do not appear to survive, or else they would be detectable and one would have a mixture of sodium and chlorine able to show the properties of both these elements. The response available from the nineteenth-century element scheme is that simple substances do not survive in the compound but abstract elements do. ... 

In 1885 the issue was finally conclusively settled in favor of Mendeleev by measurements of the specific heat of beryllium at elevated temperatures. These experiments pointed to an atomic weight of 9.0, in reasonable agreement with Dulong and Petit s law and supported the di-valency of the element (Humpidge, 1885). Above all else, Mendeleev persisted in the belief that beryllium lies in group II because of his faith in the validity of the periodic law, which he believed was essentially a feature of the transcendental elements. All else was rationalized around this central tenet. 

Paneth is clearly not a naive realist because he recognizes two senses of the term element. Indeed, he is the last chemist of any note to have stressed the value in drawing this distinction.In fact, Paneth s element scheme is the one still in use to this day, although most contemporary chemists would probably be loath to recognize a metaphysical or transcendental aspect to the nature of the elements, falsely believing that this might smack of alchemy, which they, of course, take to be a gravely mistaken enterprise. ... 

Kant s notion of element would warrant separate attention. Cf. Carrier (2001), B673-681, (29 161-166, 341-361). Kant followed Stahl in having five elements, which for him were more like regulative ideas of reason and can never be identified empirically. Kant s understanding of these elements changed over time under influence of developments in chemistry. Kant s theory of elements in the KrV is transcendental (not empirical or metaphysical). 

The dimensions of the constants a and /3 are of interest. The constant /3 is an element of the argument of the sine, which is a transcendental function. As such its argument must be dimensionless, and therefore /3 is an inverse time constant. On the other hand, the product of a and qfo must have dimensions of volumetric flow rate and so a must be dimensionless. From basic physics we also know that a is the amplitude of the wave while is the peak-to-peak time or the period of the wave. Now if this is the input to our tank how will the level as a function of time behave ... 

Boyle s statement that nitre consists of volatile nitric acid and a solid residue shows just that oscillation [Schwanken] between the naive-realistic and the transcendental meanings of the terms which we exhibited above as particularly characteristic of the concept of element. (Paneth 2003, 136, emphasis original)... 

Let us return at last to the definition of chemical element, as established by lUPAC. I consider the most intriguing part of Paneth s formulation of this concept of element to be the necessity of schwanken, the oscillation between the abstract transcendental and the concrete naive realist view. In an earlier section of this chapter we noted that this definition suspends the concept of element in a space of speculation between the two poles in much the same way that metaphor suspends judgment between intersecting sets of alternative meanings. Where definitions are intended to attenuate the inherent polysemy of language, metaphor activates multiple sets. The unique feature of the lUPAC definition, seen below, is that it wants it both ways the distinction is spelled out in the second definition but withdrawn by the end ... 

The Mason equivalent circuit may be derived directly from Eq. 19. It is sometimes called a transmission-line circuit model since the transcendental terms in the matrix appear in the same way when modeling power transmission lines. Most importantly, the circuit represents more than one resonance with these transcendental terms. Consider first an element that does not have piezoelectricity, implying the piezoelectric stress coefficient e = 0. The force-velocity relationships in the nonpiezoelectric element would then be... 

Paneth also used the term transcendental elements to denote the elements as basic substances, a term borrowed from the 19 century German philosopher von Hartmann (Paneth 1962). 

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