Theory free facts

Hull (1999) has performed an important service in his analysis of Popperian ideas and their relationship to biology and especially evolutionary biology. Hull s analysis would have been clearer had he included a discussion of Darwin s five theories and thereby provided a clarification of which parts of evolutionary theory are historical and which are not. Nevertheless, Hull points out (1999 498) that it is ironic that cladists have adopted Popperian ideas because of Popper s absolute stance against induction in scientific testing and against the notion that there are theory-free facts. 

Professor Thomson says of the work that it was undoubtedly the most learned and most luminous treatise on chemistry that the world had yet seen it is nothing less than a complete collection of all the chemical facts and processes which were known in Boerhaave s time. That some of his supposed facts, resting on the authority of many previous writers, were not entirely to be depended upon is not a reproach, for all these facts could not be verified by his own experiments. Yet the work was a conservative summary of chemical facts and theories, free from all mysticism, and presented in orderly, dignified and comprehensive system. 

The use of the conventional spin formulation in conjunction with a spin-free Hamiltonian HSF merely assures symmetry adaptation to a given spin-free permutational symmetry [Asp] without recourse to group theory. In fact, one may symmetry adapt to a given spin-free permutational symmetry without recourse to spin. This is the motivation behind the Spin-Free Quantum Chemistry series.107-116 In this spin-free formulation one uses a spatial electronic ket which is symmetry adapted to a given spin-free permutational symmetry by the application of an appropriate projector. The Pauli-allowed partitions are given by eq. (2-12) and the correspondence with spin by eqs. (2-14) and (2-15). Finally, since in this formulation [Asp] is the only type of permutational symmetry involved, we suppress the superscript SF on [Asp],... 

Some extensions of MEs indentify free space with a medium having o/O [72] in such cases there is a dispersive loss of energy. If one wishes to maintain a relativistic theory, previous fact introduces additional complications. To correct such new difficulties, Lehnert [41,73] postulated additional sources in vacuo (V E 0 when ct 0). 

In Chapter 2, it was mentioned that there is a strong resemblance between bands obtained from nearest-neighbor interactions in the LCAO approximation and the bands obtained from nearly-free-electron theory. In fact, formulae for the interatomic matrix elements based upon that similarity were used to estimate properties of covalent and ionic solids in the chapters that followed, Now that a... 

Neither the principles of thermodynamics nor theories of reaction rates require that there should be such linear relationships. There are, in fact, numerous reaction series that fail to show such correlations. Some insight into the origin of die correlation can be gained by considering the relationship between the correlation equation and the free-energy changes involved in the two processes. The line in Fig 4.2 defines an equation in which m is the slope of the line ... 

Something else should be said about the impact of accommodation- When the (general) theory concerned is strongly supported independently of the fact at issue, the accommodation of some fact, even in this ad hoc way, may well still supply the best explanation that science can currently supply for that fact. So, for example, the best explanation in, say, 1700 for the observation of no stellar parallax was surely the Copemican one—that there must in fact be an apparent parallactic motion but that even the nearest stars are so far away as to make the effect too small to be detected by even the best available telescopes. (Here, as before with Ptolemy and with scientific creationism, we use the phenomenon—no observed parallax—to fix (in this case in a rather loose way) an otherwise free parameter in the theory (distance to the nearest star).)... 

In his original demonstration Gibbs (1874) showed that the surface layer may be considered as a third phase having specific values of density, energy, and entropy, and further that the results of the theory are quite independent of the actual extent of the capillary layer and the way in which it merges into the free fluids on either side. As a matter of fact, the transition... 

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

The first theoretical attempts in the field of time-resolved X-ray diffraction were entirely empirical. More precise theoretical work appeared only in the late 1990s and is due to Wilson et al. [13-16]. However, this theoretical work still remained preliminary. A really satisfactory approach must be statistical. In fact, macroscopic transport coefficients like diffusion constant or chemical rate constant break down at ultrashort time scales. Even the notion of a molecule becomes ambiguous at which interatomic distance can the atoms A and B of a molecule A-B be considered to be free Another element of consideration is that the electric field of the laser pump is strong, and that its interaction with matter is nonlinear. What is needed is thus a statistical theory reminiscent of those from time-resolved optical spectroscopy. A theory of this sort was elaborated by Bratos and co-workers and was published over the last few years [17-19]. 

Gee and Orr have pointed out that the deviations from theory of the heat of dilution and of the entropy of dilution are to some extent mutually compensating. Hence the theoretical expression for the free energy affords a considerably better working approximation than either Eq. (29) for the heat of dilution or Eq. (28) for the configurational entropy of dilution. One must not overlook the fact that, in spite of its shortcomings, the theory as given here is a vast improvement over classical ideal solution theory in applications to polymer solutions. 

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