Mathematical practitioners

Taylor, E.G.R. The mathematical practitioners of Tudor and Stuart England. Cambridge Cambridge Univ P, 1954. 442p. 

Johnston, Mathematical Practitioners , 319. Taylor dismisses Forman s pamphlet as vacuous Mathematical Practitioners, 330. 

DNB Francis R Johnson, Thomas Hood s Inaugural Address as a Mathematical Lecturer of the City of London (1588) , Journal of the History of Ideas, 3 (1942), 94—106 Johnston, Mathematical practitioners Taylor, Mathematieal Praetitioners, 178. 

For the identification of Forman s numerous references to doubting Thomas as attacks on Thomas Hariot, see David B. Quinn and John W. Shirley, A Contemporary List of Hariot References , Renaissance Quarterly, 22 (1969), 9-26, esp. 22. But these also could be read as allusions to Thomas Hood. See also Johnston, Mathematical Practitioners , 335 n. 

The College s dealings with other practitioners, especially the bold ones, informed their perennial encounters with Forman. The case ofThomas Hood, the mathematical practitioner who had dismissed Forman s method for finding the longitude, illustrates the procedure for licensing a university-educated physician. Hood had moved from Cambridge to London in the early 1590s,... 

Ashmole preserved the legacy of Forman s life and work in London, the written terrain that this study has charted. Like these papers, Forman s reputation has outlived him. Fie has featured as a charlatan in histories of astrology, alchemy, and medicine in England, but aside from his involvement (albeit hostile) with the mathematical practitioners, he has had no place in histories of the natural sciences. Fie pursued the occult and wrote in English. Fie was more interested in operative magic, divinatory techniques, and alchemical... 

Johnston, Stephen, Mathematical Practitioners and Instruments in Elizabethan England , Annals of Science, 48 (1991), 319-44. 

Taylor, E. G. R., The Mathematical Practitioners of Tudor and Stuart England (Cambridge, 1967 [1954]). 

The accuracy of absolute risk results depends on (1) whether all the significant contributors to risk have been analyzed, (2) the realism of the mathematical models used to predict failure characteristics and accident phenomena, and (3) the statistical uncertainty associated with the various input data. The achievable accuracy of absolute risk results is very dependent on the type of hazard being analyzed. In studies where the dominant risk contributors can be calibrated with ample historical data (e.g., the risk of an engine failure causing an airplane crash), the uncertainty can be reduced to a few percent. However, many authors of published studies and other expert practitioners have recognized that uncertainties can be greater than 1 to 2 orders of magnitude in studies whose major contributors are rare, catastrophic events. 

Practitioners of SELF explicitly include the dependencies either in the event trees or in the fault trees. Examples of the LESF method that have been examined, treat major dependencies by the definition of degraded states and reevaluate the systems and event trees for the assumed degraded state as well as for the probability of being in that state. Mathematically this is very effective but the dependency coupling is not as pictorial as the SELF method. 

Many analytical practitioners encounter a serious mental block when attempting to deal with factor spaces. The basis of the mental block is twofold. First, all this talk about abstract vector spaces, eigenvectors, regressions on projections of data onto abstract factors, etc., is like a completely alien language. Even worse, the techniques are usually presented as a series of mathematical equations from a statistician s or mathematician s point of view. All of this serves to separate the (un )willing student from a solid relationship with his data a relationship that, usually, is based on visualization. Second, it is often not clear why we would go through all of the trouble in the first place. How can all of these "abstract", nonintuitive manipulations of our data provide any worthwhile benefits ... 

The mathematical methods used for interpolation and extrapolation of the data obtained from accelerated tests, as described in Chapters 8 and 9, include both the mechanistic and the empirical. Arrhenius formula, based on chemical rate kinetics and relating the rate of degradation to temperature, is used very widely. Where there are sufficient data, statistical methods can be applied and probabilities and confidence limits calculated. For many applications a high level of precision is unnecessary. The practitioners of accelerated weathering are only too keen to tell you of its quirks and inaccuracies, but this obscures... 

Lavoisier s dictum that physics should precede chemistry became a logicohistorical interpretation, as he meant it to be, instead of a statement of pedagogical or disciplinary strategy. Paradoxically, the contemporary prestige of physics is associated with this logicohistorical tradition and with the classical and aesthetic appeal of abstract mathematics, rather than with the precision laboratory tradition on which much of modern physics, like chemistry, is based. The founder myth of Lavoisier has been perpetuated in the hagiography of the disciplinary clan of chemistry because of his role not only in the conceptual and linguistic foundations of nineteenth-century chemistry but also in a community of practitioners who refined the social definition of the chemical discipline its formal distinction from "physique" in the Paris Academy, its autonomous status as the subject of the Annales de Chimie, its Janus-faced position astride the abyss that previously divided the philosophical science of the university from the technical practice of the laboratory. 

The disciplinary titles of the practitioners of quantum chemistry and chemical physics varied. Pauling initially wanted his title at Caltech to be professor of theoretical chemistry and mathematical physics, but he accepted CalTech s dropping "mathematical physics" 115 and later preferred to be known as a chemist. 116 Slater always had his principal appointment in a physics department. Mulliken, who had taken his degree at Chicago in chemistry, returned in 1928 as associate professor of physics and retired in 1983 as professor of chemistry and physics. 117... 

Practitioners of quantum chemistry employed both the visual imagery of nineteenth-century theoretical chemists like Kekule and Crum Brown and the abstract symbolism of twentieth-century mathematical physicists like Dirac and Schrodinger. Pauling s Nature of the Chemical Bond abounded in pictures of hexagons, tetrahedrons, spheres, and dumbbells. Mulliken s 1948 memoir on the theory of molecular orbitals included a list of 120 entries for symbols and words having exact definitions and usages in the new mathematical language of quantum chemistry. 

Cass, A. E. G. (Ed.), Biosensors A Practical Approach, Oxford University Press, Oxford, 1990. Although now somewhat dated, many practitioners still regard this as the best book available on the subject. Its style is non-mathematical and almost chatty in parts, thus making it both clear and accessible. 

Our purpose in this chapter is to review the nature of mathematical modeling in the context of modem electrochemistry and to describe how current and emerging trends in computer applications and system development are intended to assist practitioners. One trend is toward the merger of these two disciplines as computer-aided mathematical modeling. 

Calculated descriptors have generally fallen into two broad categories those that seek to model an experimentally determined or physical descriptor (such as ClogP or CpKJ and those that are purely mathematical [such as the Kier and Hall connectivity indices (4)]. Not surprisingly, the latter category has been heavily populated over the years, so much so that QSAR/QSPR practitioners have had to rely on model validation procedures (such as leave-k-out cross-validation) to avoid models built upon chance correlation. Of course, such procedures are far less critical when very few descriptors are used (such as with the Hansch, Leo, and Abraham descriptors) it can even be argued that they are unnecessary. 

A probabilistic risk assessment (PRA) deals with many types of uncertainties. In addition to the uncertainties associated with the model itself and model input, there is also the meta-uncertainty about whether the entire PRA process has been performed properly. Employment of sophisticated mathematical and statistical methods may easily convey the false impression of accuracy, especially when numerical results are presented with a high number of significant figures. But those who produce PR As, and those who evaluate them, should exert caution there are many possible pitfalls, traps, and potential swindles that can arise. Because of the potential for generating seemingly correct results that are far from the intended model of reality, it is imperative that the PRA practitioner carefully evaluates not only model input data but also the assumptions used in the PRA, the model itself, and the calculations inherent within the model. This chapter presents information on performing PRA in a manner that will minimize the introduction of errors associated with the PRA process. 

Since one of the main aims of green chemistry is to reduce the use and/or production of toxic chemicals, it is important for practitioners to be able to make informed decisions about the inherent toxicity of a compound. Where sufficient ecotoxicological data have been generated and risk assessments performed, this can allow for the selection of less toxic options, such as in the case of some surfactants and solvents [94, 95]. When toxicological data are limited, for example, in the development of new pharmaceuticals (see Section 15.4.3) or other consumer products, there are several ways in which information available from other chemicals may be helpful to estimate effect measures for a compound where data are lacking. Of these, the most likely to be used are the structure-activity relationships (SARs, or QSARs when they are quantitative). These relationships are also used to predict chemical properties and behavior (see Chapter 16). There often are similarities in toxicity between chemicals that have related structures and/or functional subunits. Such relationships can be seen in the progressive change in toxicity and are described in QSARs. When several chemicals with similar structures have been tested, the measured effects can be mathematically related to chemical structure [96-98] and QSAR models used to predict the toxicity of substances with similar structure. Any new chemicals that have similar structures can then be assumed to elicit similar responses. 

---