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(And if you need a Full Score, the Dover full score is also a very good deal).
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Whereas the above topics have been the subject of a number of previous studies, the novelty of the present approach is in examining them thoroughly in the time domain as well as the frequency domain. The time-domain formulations are derived in two ways: by Fourier transforming the corresponding frequency-domain expressions, and then directly in the time domain from the properties of Green functions. The identity of the results, sometimes after long and difficult mathematical manipulations, helps the reader gain confidence in the final product even if she or he was unable to follow all the details of the derivation. As a mathematician, I was especially impressed by the consistently rigorous level of the treatments. Although mathematical rigor is sometimes dismissed by engineers as largely academic, the authors give ample demonstrations of its practical necessity. For example, the proof in Sections 6.1.1 (or 7.1.3) that the probe output solves the homogeneous Helmholtz equation (or wave equation) outside the region occupied by the sources and the probe is a case study of the need to justify bringing partial differential operators under an integral sign, as a sloppy treatment simply leads to the wrong conclusion that the homogeneous equation is satisfied in all of space!
The book ends with some practical considerations on sampling and numerical applications of the foregoing results.
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In the main body of the book, the critical essay of the same title, Danto's seriousness avoids no questions, but thankfully acknowledges the ultimate futility of asking whether such work is art or pornography. This false disjunction results from the failure to hold together both form and content when looking at art. For Danto, art is the transcendence of form and content; it is both and neither, for it moves beyond both while in some sense preserving them in the work. Although Danto needlessly complicates matters with his use of the terminology of Hegel's dialectic to articulate this transcendence, his discussion is clear enough otherwise. This is best seen in his analysis of the respective testimonies of the legislators and the experts at the Cincinnati trial in which the Contemporary Arts Center and its director, Dennis Barrie, were ultimately acquitted of pandering obscenity and child pornography. Danto shows that while the legislators saw the content and ignored the form, the art experts for the defence saw the form and ignored the content. Though this resulted in the acquittal, Danto rightly emphasizes that for Mapplethorpe, the work was all about making pornography that was art; he "literally became a pornographer with high artistic aims." (78) In Mapplethorpe's words, a work can "be pornography and still have redeeming social value. It can be both, which is my whole point in doing it-to have all the elements of pornography and yet have a structure of lighting that makes it go beyond what it is." (89-90) This attempt to "go beyond what it is" both illustrates Danto's conception of art as transcendence and defines Mapplethorpe's work in particular as a "playing with the edge." (77)
Danto identifies trust as the constant attribute of Mapplethorpe's work which allows the form and content to remain together. "The moral relationship between subject and artist was a condition for the artistic form the images took. The formalism was connected to the content through the mediation of that moral relationship." (79) This trust is attested to by the formal quality of the images, in that they are titled with the subjects' names, posed and lighted in formal abstraction, and clearly constitute something the subjects have allowed, thus presenting the subjects as themselves, but not candidly, rather as they have agreed to be presented. (39) This is why acts of sex are themselves generally not depicted, for here the formalism cannot be maintained. In Mapplethorpe's work, however, there is always the danger of losing this formal control and going "over the edge." (79) It is not just a question of sex and the vulnerability inherent therein, but of danger and violence. For Danto, "a presumption that one's partner could be trusted . . . is the basic connection between sex and love." (41) He ties this trust to "the spontaneous human appetite for feeling danger and being protected at once . . ." (42) The combination of sex, danger, and violence, when contained by formalism through trust, is evident not only in the overtly sexual or violent works. Indeed, Danto is perhaps at his literary best in his discussion of these elements in relation to Mapplethorpe's flowers, fruits, vegetables, and finally the portraits of statues.
Danto's discussion of Mapplethorpe's work is frank, clear, and engaged. In neither oversimplifying the seriousness of the issues nor avoiding the questions raised by the work, he nonetheless leaves open its moral status. This is a great benefit. When it is a matter of "playing with the edge," different people will ultimately experience such an encounter differently. Indeed, this frames what may be the most problematic aspect of looking at Mapplethorpe's work: "It is supposed to be shocking. When morality changes so that it is no longer shocking, Mapplethorpe's intentions will fall away into incomprehensibility." (112) Although his assessment of the historical importance of this work--and that of the seventies in America generally--will surely not persuade everyone, the main achievement here is that Danto gives the reader solid handles by which to grapple with a difficult body of work.
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