Historical Dualities

The dualities of supramolecular biomeso-genic organizations [7, 17, 18] reemerge in the process of their scientific discovery. The history of liquid crystals , lovingly retraced by Kelker [13] (Fig. 5), parallels the development of molecular biology [5 - 8]. Liquid crystals are beautiful and mysterious, I am fond of them for both reasons , states de Gennes [19]. And, indeed, how can we not feel attracted to what in the inanimate world seems most closely related to us  

Reinitzer s letter to Lehmann, dated March 14, 1888 [21, 22], which introduces from rather hidden beginnings the history of liquid crystals, is very impressed by their unique appearances. Reinitzer sends two substances with the request to investigate more closely their physical isomerism . He describes previously unnoticed and unknown phenomena Cholesteryl acetate melts to a clear liquid. On cooling the liquid down, a bright color variation moves through the liquid before crystallization. Bright violet, blue, green, yellow and 

Lehmann [14] investigates the preparations with a heated-stage polarization microscope constructed by himself. They remind him of his earlier studies on iodine-silver , and, even more closely, of his endeavors concerning ammonium oleate hydrate . He coins the term liquid crystals . The scientific development of liquid crystals or cystalline liquids (Fig. 6) - terms 

But a generation will pass before liquid crystals will be really wanted. Kelker s MBBA , the first liquid crystal at ambient temperature, will provide the impetus for applicational research in liquid crystals [13]. 

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In this section we state the postulates of quantum mechanics in terms of the properties of linear operators. By way of an introduction to quantum theory, the basic principles have already been presented in Chapters 1 and 2. The purpose of that introduction is to provide a rationale for the quantum concepts by showing how the particle-wave duality leads to the postulate of a wave function based on the properties of a wave packet. Although this approach, based in part on historical development, helps to explain why certain quantum concepts were proposed, the basic principles of quantum mechanics cannot be obtained by any process of deduction. They must be stated as postulates to be accepted because the conclusions drawn from them agree with experiment without exception. 

White Man s Law The Past and Present Status of the American Indian [1971] (Norman University of Oklahoma Press, 1994) Benjamin Ringer, We the People and Others Duality and America s Treatment of Its Racial Minorities (New York Tavistock, 1983) Mary Frances Berry, Black Resistance I White Law A History of Constitutional Racism [1971] (New York Penguin, 1994) Charles Lofgren, The Plessy Case A Legal-Historical Interpretation (New York Oxford, 1987) A. Leon Higginbotham, Jr., In the Matter of Color Race and the American Legal Process The Colonial Period (New York Oxford, 1978). 

Historically, the highest proportion of referrals to social work come from health visitors (Dingwall and Robinson 1993), which indicates both the breadth of their contact with families in the community and their watchfulness over the welfare of the child. The duality of their role as both supportive and monitoring, although not always comfortable, is part of a learned understanding of what it is to be a health visitor ... 

A basic understanding of the quantum theory is essential in many areas of chemistry, especially in connection with spectroscopy and with theories of atomic and molecular structure. The present book gives an introduction to the theory, and its application to elementary atomic structure, but chemical bonding is not discussed. I have tried to put the essential ideas in their historical context, but without retaining the historical introduction which has been traditional with this topic. With the crucial and difficult concepts of wave-particle duality, it seemed to me more important to give modem illustrations to show that they have current applications in chemistry. 

Based on these historical achievements one may ask how far one might be able to extend such quantum experiments and for what kind of objects one might still be able to show the wave-particle duality. Recently, a new set of experiments exceeding the mass and complexity of the previously used objects by about an order of magnitude has been developed in our laboratory. These far-field diffraction experiments with the fullerene molecule Ce0 will be shown in Sec. 1. 

Due to the historical generation of o and a, values from formate and acetate series two inductive parameters exist with different zeros namely methyl and hydrogen respectively. This duality is confusing as both types of inductive parameter are used extensively (the use of most others having died out). The Oj value is the most utilised inductive parameter at present and is the constant of choice when steric effects are absent. The Pavehch-Taft approach is necessary when there are steric effects. The use of a is somewhat confusing as this value can be defined using RCHjCOjEt as the reference [56] under this definition hydrogen is taken as the zero. If [Pg.162]

As for (4.1), the classical abstract method was introduced by Verdier in his treatment of duality for locally compact spaces, then adapted to schemes by Deligne [De ] to show that with j D(.A ) —> Dqc(X) the natural functor, R/ oj has a right adjoint. This suffices only when / is separated, see (3.9.6). The proof given below (for historical reasons, because of the compactness of Deligne s original presentation) is just an elaboration of Deligne s arguments. 

The need for a historical reconstruction of wave-particle duality, the photoelectric effect and quantum theory for students has been recognized in cogent terms by Noyes (1984), a practicing physicist ... 

An historical reconstruction of the events that led to de Broglie s postulation of wave-particle duality and the ensuing controversy within the scientific community. This reconstruction is based on the following aspects ... 

Formulation of six criteria for evaluating general chemistry textbooks based on the historical reconstruction of wave-particle duality (aspects a, b, c, d, and e, in 1 above). 

The presentation by McMurry and Fay (2001) ignores the role played by the experiments conducted by Davisson, Germer, Thomson and Reid. On the other hand, the presentation by Umland and Bellama (1999) ignores the importance of Einstein s contribution which helped de Broglie to postulate wave-particle duality. This clearly shows that a historical reconstruction must emphasize at least the contributions of Einstein, de Broglie, Davisson and Germer. 

Such presentations are surprising (to say the least) as the historical record shows that prominent scientists, such as Planck, Bohr, Sommerfeld and Wien did not accept wave-particle duality until at least 1927, when it was the subject of extensive discussions at the Solvay Conference held in Brussels (cf. Raman and Forman 1969). On the other hand, Einstein and Schrbdinger were the two major supporters of de Broglie s ideas. This clearly shows that novel ideas are difficult to accept and often lead to conflicts and controversies in the scientific community. 

It is plausible to suggest that evaluations of textbooks based on a historical reconstruction, constitute a stepping-stone for further classroom studies to evaluate the effect of including criteria presented here to improve students understanding of wave-particle duality. Besides the criteria, this study provides science teachers with 26 Satisfactory (S) presentations (with extensive excerpts) based on 128 general chemistry textbooks. In their textbook. Physics, the Human Adventure, Holton and Bmsh (2001) have endorsed such strategies in unequivocal terms ... 

It is important to note that wave-particle duality is an important part of our understanding of the modem atomic stmcture based on the wave mechanical model. Historical reconstmction presented in this study shows how scientists themselves had considerable difficulty in understanding and accepting this novel idea. Even leading schools of physicists (Bohr, Planck and Summerheld) were reluctant to incorporate de Broglie s ideas in the corpus of science. This episode shows clearly how (as in so many other episodes in the history of science, cf. Niaz 2009) progress in science is inevitably based on alternative interpretations of experimental data that lead to controversies. Furthermore, it seems that textbooks... 

An important implication of this study (and similar textbook analyses) is that it not only provides a critical appraisal of textbooks based on a historical reconstruction of wave-particle duality but also guidelines for classroom teachers as to how textbook presentations can be complemented and revised. Furthermore, such studies show clearly how history of science forms an integral part of science and thus can play an important role in the science curriculum. It is plausible to suggest that the inclusion of the following activities and discussions in the textbooks can facilitate students understanding and even motivation for exploring other topics of the curriculum ... 

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